apredictionmodelofforestpreliminaryprecisionfertilization...

Research ArticleA Prediction Model of Forest Preliminary Precision FertilizationBased on Improved GRA-PSO-BP Neural Network

Chen Zuxing12 and Wang Dian 1

1College of Engineering Beijing Forestry University Beijing 100083 China2Liupanshui Normal University Liupanshui 553004 China

Correspondence should be addressed to Wang Dian wangdianbjfueducn

Received 20 March 2020 Revised 20 July 2020 Accepted 7 August 2020 Published 27 August 2020

Academic Editor Pietro Bia

Copyright copy 2020 Chen Zuxing and Wang Dian +is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

+e optimal amount of fertilizer application which was needed by the trees and the factors that influence the fertilization have anintricated nonlinear relationship According to the problems that the traditional fertilization predictionmodel has such as lackingof the scalability and practicality this paper initiates an accurate fertilization prediction model that was based on the GRA-PSO-BP neural network which canmake the accurate fertilization come true and improve the economic benefits of forest industry+ispaper uses the GRA method to determine the input of the neural network as the site index and make the forest age nutrientcontent of the advantage trees biomass of the advantage trees biomass of average trees and target yield as the output numbers ofthe Actual amount of fertilizer applied During the calculation process the global particle swarm optimization algorithm is used tooptimize the initial numbers and threshold numbers of BP neural network which build a phased GRA-PSO-BP accurate fer-tilization model Compared with the prediction algorithm of full input variate that is based on the single BP neural network andthe prediction algorithm of full input variate that is based on PSO-BP Neural Network the GRA method can determine the keyfactors that influence the amount of fertilizer applied in different forest areas and modify the prediction model to improve thescalability and accuracy of the prediction and finally achieve the precision fertilization as the data of different forests updated sowe can see that the prediction result of this paper is more accurate+e result demonstrates that the GRA-PSO-BP neural networkSegment fertilization model is more accurate than the traditional BP neural network and BP Neural Network that was optimizedby the PSO algorithm and specifically the error of the predicted amount of fertilizer application and the actual amount of fertilizerapplication is less than 5 which can effectively guide the fertilization in stages

1 Introduction

In the process of forestry production it is fundamentallyrequired to calculate the amount of fertilizer such as ni-trogen phosphorus and potassium fertilizer for differentforest species and different soil conditions [1] Cunning-hamia lanceolata enjoys the characteristics of fast growthwide application high economic value and easy repro-duction [2] Cunninghamia lanceolata is dependent onfertilizer and humidity In the condition of 25degCndash35degCCunninghamia lanceolata can grow rapidly In this regardfertilization is the key link for high yield of Chinese fir forestFertilization generally applies from young forest to middle-aged forest which plays an important role in forestry

economy Forest fertilization functions as a critical tech-nique to enhance soil fertility improve tree nutrition andfacilitate rapid growth and high yield [3 4] At presentforestry production is increasingly transformed to precisionoperations Cunninghamia lanceolata production is no ex-ception +e premise of precision production of Chinese firforest is precise fertilization since such an agrotechnique canhelp balance the nutrients in soil and increase the nutrientsrequired by trees so as to achieve the target yield In ad-dition the implementation of precision fertilization can savethe fertilizer and phase down environmental pollution

Fertilization prediction model as the key of precisionfertilization in Cunninghoya lanceolata forest has become ahot spot in forestry research In response to this issue under

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 1356096 17 pageshttpsdoiorg10115520201356096

discussion Hu Yueli et al proposed a site-nutrient effectfertilization model [5ndash9] However sometimes this modelcan hardly help to get satisfactory accuracy and stability +etraditional fertilization model can only describe the staticrelationship between the growth of forest and the requiredfertilization nutrients which can hardly reflect the differentgrowth periods of trees In view of the differences in nutrientabsorption capacity and fertilizer application in differentgrowth stages this model cannot be applied to guide thestage fertilization of trees In the past it was difficult tocollect data due to the long growth period of forest+erefore there were few models of forest fertilizationHowever in recent years sensor network can be used tocollect real-time data in forest areas with the burgeoningdevelopment of artificial intelligence It is time to construct apredictive model of accurate fertilization of forest throughthe collected data Similarly as the traditional one the modelcan only exert real-time and accurate small-scale predictionin forest areas considering the complexity of different forestareas and site indices the diversified factors affecting forestfertilization At the same time since there is a high degree ofnonlinearity between site index and dominant wood-relatednutrient content forest age and other influencing factorsthe traditional fertilization model often has inaccurate re-sults due to manifold parameters or low goodness of fittingAs a result the large amount of accumulated data can hardlyserve to guide production practice In the later stage expertexperience is still needed resulting in a waste of manpowermaterial and financial resources

Neural network is considered to be a powerful tool tosolve nonlinear problems [10ndash15] In order to ensure theintegrity of information and improve the precision of fer-tilization prediction the prediction model of multifactorprecision fertilization based on neural network can be usedto solve these problems It can reflect different absorption ofnutrients in different growth periods of young and middleages of trees and apply fertilizer efficiently in the optimalfertilization period of trees +e BP algorithm shows greatpotential to introduce the prediction model of forest fer-tilization With the updating of the data of forest fertilizationexperiment the BP algorithm modifies the existing pre-diction model of fertilization which makes the forecasts ofthe model more precise and get closer to the actual situationHowever the accuracy of predicted results and actual valuesis not fairly reliable on account of some big defects such aslocal optimization slow convergence speed and large de-pendence on training data when a single BP neural networkalgorithm is used to predict the amount of fertilizer appliedto trees In this paper the analyzing method of grey relativity[16ndash19] is introduced to extract the original variable data ofmultiple indexes in advance and the factors with highcorrelation degree are taken as the network input layer andthen the global searching ability of PSO [20ndash25] is used tooptimize the BP neural network which greatly avoids thedefect of the model falling into the local optimum andfurther improves the accuracy Although neural networkprediction has been applied in medical engineering electricpower system and other fields at home and abroad andsome gratifying results have been achieved there are only

few studies on the application of neural network predictionmodel to forest fertilizer application+erefore an improvedGRA-PSO-BP algorithm was used to establish the accuratefertilization model of trees in stages

2 Methodology

21 Test Area Overview and Plot Settings +e experimentaldata are from the state-run forest farm in Renhua CountyGuangdong Province and Liujiashan Forest Farm in ShixingCounty Guangdong Province which is the main productionarea of fir trees with an altitude of less than 500m and thesoil type is the red and yellow soil developed on slates Large-scale fertilization experiments were carried out for youngandmature timber of fir forests and the experimental forestswith different site indexes were classified during the ex-periment according to the utilization of the last round offorest land and the Nanling Mountains fir trees in thedifferent site conditions the experimental forest can bedivided into four types (1) triple-tilled woodlands ofCunninghamia lanceolata with a site index of 5 (2) culti-vated Chinese fir double-tilled woodlands of Cunninghamialanceolata with a site index of 18 (3) first ploughingwoodlands after shrub felling with a site index of 21 and (4)first ploughing woodlands after logged broad-leaf forestswith a site index of 23 Under the condition of the same siteindex the slope direction of the test site is the same theterrain difference is small and the trees are arranged at thesame height +e young forest and the middle-aged foresttest area are respectively set in the forest stands with ap-propriate site index and the area of each test site is 1 hm2+e initial planting density of young trees in the experi-mental forests was 3600 plants1 hm2 In the first 6 to 8years the first thinning was carried out and the forests in themiddle-aged forests were retained at 2700 plantshm2 +esize distribution and density of the forests in each exper-imental area were basically the same +ere are fixed stakesaround each test area and the dominant wood and averagewood in the test area have specific numbers +e growth andnutrient dynamics of dominant wood and average wood inthe test area are measured regularly every year and nitrogenphosphorus and potash fertilizers are applied according tothe fertilization method in the test area

16 plots with age of 5a 19a 22a and 25a were selected inthe above four different site types +e selected average anddominant trees in different areas were logged and thendivided by leaves branches stems barks and roots to weigheach organ of them +e age of leaves and branches wereweighed respectively and the root system was dug to adepth of 60 cm in the range of the canopy Samples of allorgans were evenly sampled and dried at 80degC to determinewater and nutrient content Meanwhile four soil samplingpoints of different stand ages were set up in four different siteindex types 16 soil sampling points in total Take soilsamples in 0sim60 cm soil layer of each soil sampling point+e physicochemical analysis of plant and soil samples wascarried out in accordance with conventional methods andthe determination of the physicochemical properties of thesoil in the experimental forest land is shown in Table 1

2 Mathematical Problems in Engineering

+e discrepancies of site level are due to the differentlocations of the samples which results in different climaticzones slopes slope positions and soil types +e differen-tiated use of forest land at different site levels leads tosignificant differences in the organic matter content nu-trient content and fertilizer utilization rate of the humuslayer in the woodlands Consequently it can be concludedthat the availability of soil nutrients is one of the essentialfactors for different experimental forests

In the selection of the test plots the age of the foreststands has been replaced by space instead of time +eaccuracy of analysis is to some extent affected by thevaried environmental conditions between the dominantwood and the average wood in the same site typeHowever the effects of random errors on the basic trendof tree growth and nutrient absorption changing withforest age were relatively eliminated due to the significantdifference between the growth of dominant and averagestands

22VariationofNutrientContent inOrgansofCunninghamialanceolata Table 2 shows the measured values of nitrogen(N) phosphorus (P) and potassium (K) in different organs

of dominant Chinese fir trees +e nutrient content ofdifferent Chinese firs varies greatly +e order of nutrientcontent in the various parts of the tree is as leaf branch barkroot and stem At the same time it was also shown that thenutrient contents of different organs of Cunninghamialanceolata with different site indexes were different at dif-ferent ages +e content of nitrogen in the leaves increasedwith the increase of the site index and the age of the forestthe content of potassium in the leaves nitrogen phosphoruspotassium in the trunk branches and bark and the contentof the phosphorus and potassium in the roots decreased withthe increase of the age

Table 3 shows the biomass range from average tree todominant tree and the percentage of each organ in Chinesefir forest Based on the data in Tables 2 and 3 the averagenutrient content C of the Chinese fir forest obtained by theweighted average method is calculated asC (1113936 Ciwi)1113936 wi where Ci and wi represent the nutrientcontent and biomass of leaves branches stems bark androots of a single tree respectively Its product sum 1113936 Ciwi isthe total amount of nutrients absorbed by a single tree thetotal organ biomass 1113936 wi is the total biomass of a single treeand the relationship between the total nutrient absorption X

Table 1 Test results of physical and chemical properties of the soil of experimental forest land

Stand age(ta)

Siteindex S Texture Organic matter

(gkgminus1)Total nitrogen

(gkgminus1)Fast-acting

nitrogen (mgkgminus1)Fast-acting

phosphorus (gkgminus1)Fast-acting

potassium (gkgminus1) PH

5a

5 Middlesoil 90 03 16 21 57 46

18 Middlesoil 174 089 277 30 80 49

21 Middlesoil 220 112 32 40 92 50

23 Middlesoil 270 135 48 50 100 52

19a

5 Middlesoil 89 032 164 23 54 45

18 Middlesoil 172 09 28 31 88 48

21 Middlesoil 221 114 32 41 90 51

23 Middlesoil 273 138 476 50 96 53

22a

5 Middlesoil 90 031 161 22 52 44

18 Middlesoil 171 087 281 32 91 47

21 Middlesoil 220 111 32 42 87 54

23 Middlesoil 271 133 481 52 94 51

25a

5 Middlesoil 91 03 162 20 55 48

18 Middlesoil 173 091 282 30 83 49

21 Middlesoil 222 110 32 43 91 53

23 Middlesoil 270 136 479 51 100 51

Mathematical Problems in Engineering 3

per unit area of Chinese fir forest and the average nutrientcontent C is X nwC1000 CW where n is the standdensity w is the average biomass per tree (kgplant) and Wis the biomass per unit area (thm2)

23 Analysis of Influencing Factors +ere are a series ofimportant indexes to calculate the amount of fertilizer appliedto trees such as site index forest age nutrient concentrationof dominant trees dominant wood biomass average wood

Table 2 Nutrient content of dominant Chinese fir of different forest ages under different site conditions gkg

Organ Stand age (ta)Nitrogen Phosphorus Potassium

Site index S Site index S Site index S5 18 21 23 5 18 21 23 5 18 21 23

Leaf

5 68 107 126 138 075 102 109 112 32 47 49 5019 86 121 124 127 084 116 128 106 33 43 47 4922 94 132 135 137 091 112 125 093 34 42 46 4825 101 139 141 142 092 104 107 097 32 41 45 47

Branch

5 39 67 71 73 059 071 074 077 31 40 41 4219 28 45 57 59 049 055 057 059 27 36 37 3922 27 42 55 57 047 052 055 058 26 38 39 3625 25 41 53 56 045 054 056 054 25 37 40 35

Stem

5 11 19 21 23 011 020 023 024 08 17 15 1419 12 14 19 20 008 009 012 014 04 09 11 1322 10 13 16 18 007 008 010 009 05 08 10 1125 09 12 14 13 004 006 008 007 04 07 09 08

Bark

5 28 46 45 47 021 032 034 035 47 36 33 3119 24 19 35 33 010 015 016 018 45 19 18 1722 23 36 34 31 009 011 013 015 41 17 16 1525 22 34 32 29 007 009 011 014 38 15 13 14

Root

5 17 35 38 39 010 027 029 031 34 21 20 1819 14 19 22 25 006 011 014 016 24 16 15 1422 16 17 21 24 005 012 012 017 21 17 16 1525 12 15 20 22 008 010 014 015 20 14 13 12

Table 3 +e biomass range (w) of a single Chinese fir and the percentage of its organs

Standage (ta) Organ

Site index S 5 Site index S 18 Site index S 21 Site index S 23

W (kg) Percentage() W (kg) Percentage

() W (kg) Percentage() W (kg) Percentage

()

5a

Leaf 167plusmn 058 2144 348plusmn 095 2434 398plusmn 104 2204 412plusmn 139 187Branch 125plusmn 044 1605 236plusmn 084 1650 278plusmn 121 154 347plusmn 132 157Stem 260plusmn 08 3340 440plusmn 108 3077 564plusmn 194 3123 637plusmn 251 33Bark 053plusmn 012 6804 096plusmn 033 671 146plusmn 068 808 198plusmn 083 9Root 174plusmn 066 2233 310plusmn 092 2168 420plusmn 146 2325 524plusmn 207 236Tree 779plusmn 26 10000 1430plusmn 412 10000 1806plusmn 633 10000 2204plusmn 812 10000

19a


22a


25a



biomass fertilizer utilization rate and target yield +e siteindex is a natural environmental factor required for forestproduction and is a collection of conditions such as moisturetemperature light intensity and soil fertility In the forest areawith high site index or low site index the fertilization effect isdifficult to show In the forest area with high site index thesoil fertility water temperature light and other conditionsare very good After fertilization the effect on the increase offorest yield is small On the contrary the soil fertility watertemperature light and other conditions are very poor in theforest land with low site index After fertilization due tonatural factors the fertilization effect is also very poor In theeffective site index interval the theoretical limit value of forestproduction is the dominant wood biomass of forest land inpractice so the dominant wood nutrient content is the limitvalue that can be reached by the average wood nutrientcontent after fertilization If the difference between thedominant wood biomass and the average wood biomass isgreater the fertilization effect will be better In addition thetarget yield is also related to the amount of fertilization +etarget yield is determined by the input-output ratio of forestland in previous years and the target yield determines thetarget increase yield that is the amount of fertilization +erelative intensities of the absorbed nutrients of different forestages are different +e best fertilization period the morefertilizer is absorbed At the same time the utilization rate ofthe fertilizer is related to the physical and chemical propertiesof the soil +e physical and chemical properties of the soil indifferent forest land are different so the utilization rate of thefertilizer is also different +e higher the utilization rate thebetter the fertilizer effect Generally three kinds of fixednitrogen phosphorus and potassium fertilizers are applied inforest land +e utilization rate of fertilizer is observedaccording to the different physical and chemical properties ofsoil in different forest land +erefore seven factors includingsite index forest age nutrient concentration of dominanttrees dominant wood biomass average wood biomass fer-tilizer utilization rate and target yield were selected as theinfluencing factors of forest fertilizer application

24 Data Normalization +ree hundred tree growth andnutrient measurement records were obtained +e data ofeach group were X1 site index X2 forest age X3 dominantwood-related nutrient concentration X4 dominant woodbiomass X5 average wood biomass X6 target productionand X7 fixed fertilizer utilization rate Since the input pa-rameters have different dimensions and the orders ofmagnitude of units are also greatly different these will have agreat impact on the training of neural network +ereforethe input parameters need to be normalized In order toimprove the training efficiency an accurate fertilizationmodel is established +e minimum maximum transfor-mation method is used to normalize different data and dealwith the dimensional influence between data +e param-eters are in the range of [minus1 1] and then the parameters ofneural network are trained +e following formula isadopted for normalization

y x minus xmin

xmax minus xmin (1)

Map the data to (minus1 +1) and replace the formula with

y ylowast 2 minus 1 (2)

where y is the normalized value x is the original value of aparameter xmax is the maximum value in the set of valuesand xmin is the minimum value in the set of values

25 Basic BPNN Model +e structure of the basic BPNNconsists of the input layer the hidden layer and the outputlayer as shown in Figure 1 +e BPNN algorithm consists oftwo parts the forward transfer of the input data and the backpropagation of the error between the output data and theexpected data [26 27] One part is the input data through theinput layer to the hidden layer the hidden layer to the outputlayer In the process the calculation will be based on thegiven initial weight and threshold and finally the outputdata will be obtained +e other part is to calculate the errorchange value δj (k) between the actual output and the ex-pected value and then turn to the back propagation and theerror signal δj (k) is propagated back through the originalconnection path through the network to modify the weightof each layer of neurons +e value ωij (jk) and the thresholdθj (k) until the target accuracy are reached

+e hidden layer of BPNN can be one ormore layers It isproved theoretically that the neural network of a singlehidden layer can approximate the nonlinear function witharbitrary precision so that the model can realize the non-linear mapping from input to output With the increase ofthe number of hidden layers the output error of the networkwill decrease [28] +erefore the increase of hidden layerswill improve the accuracy of the network but will make thenetwork structure become complex the running time be-come longer and even lead to the overfitting phenomenon+erefore after the number of neurons in the hidden layer isdetermined by empirical formula the structure of BPNNtree fertilization model is 3-layer structure of 7-12-1

+e BPNN has strong nonlinear mapping ability self-adaptive and good self-learning ability and strong faulttolerance In the absence of a mathematical model thenonlinear mapping between the amount of fertilizer appliedto trees and the factors affecting the effect of fertilization canbe realized By learning and training the relationship be-tween input and output data when the actual output valueand the expected value have a large error the weights andthresholds of each layer of the neural network are constantlyupdated until the accuracy of network error is reached so asto better improve the model

In the figure i j and k are the number of neurons in eachlayer xi is any input signal of each group of data in the input p

in the input layer ωij ωjk and θj θk respectively represent theweight and threshold of each layer φ (middot) and τ (middot) represent thehidden layer and output layer activation functions respectivelyIn the BP neural network algorithm the hidden layer neuronsinput the signal netj when the sample p acts


netj 1113944ωijxi + θj (3)

+e hidden layer neuron node outputs a signal oj whenthe sample p acts

oj φ netj1113872 1113873 φ 1113944ωijxi + θj1113872 1113873 (4)

+e output layer neuron node inputs the signal netkwhen the sample p acts

netk 1113944ωjkOj + θk

1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)

+e output layer neurons output the signal yk when thesample p acts

yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)

In the formula η is the error back propagation learningrate (0lt ηlt 1) δj (k) is the error signal of each layer and theweight and threshold are updated and iterated according to

Δωij(jk) ηδj(k)Oi(j) (7)

Δθj(k) ηδj(k) (8)

+e error variation value of each layer gradually correctsthe fertilization model during the back propagation process

26 Particle Swarm Optimization BPNN Model When asingle BPNNmodel is used to predict the precise fertilizationamount of forest trees the error between the actual outputand the expected value is still large because in the actual usethe convergence speed of the network is relatively slow andit is easy to fall into the local optimization even when thereare few training samples and there may be a fitting problemParticle swarm optimization algorithm has better global

optimization ability +erefore the particle swarm optimi-zation algorithm was proposed to optimize the BPNNmodel +e particle swarm optimization (PSO) algorithm isa swarm intelligence optimization algorithm [29 30] +evelocity characteristics fitness value and position were usedto represent the motion characteristics of the particle Afterinitializing the potential optimal solution particles the speedof the particles determines the search direction and distanceof the particles the fitness value determines the quality of theparticles When the particles move in the preset space theposition is changed according to the individual optimalsolution and the global optimal solution By updating thefitness value of the particle the fitness value is the smallest+e position corresponding to the particle is the optimalsolution as shown in Figure 2 the motion of particles in theparticle swarm leaving its current position in the search areathe velocity vi+1 that this particle is about to update is acombination of various factors It includes vi vp and vGwhich are the current particle speed the past best experienceof individual particles and the best experience of populationparticles

+e weights and thresholds of each layer in the BPNNcan be represented by individual particle swarms +e in-dividual swarms are coded represented by the positionvector of the particle swarm and the optimal populationparticles are output by the iterative algorithm Afterdecoding the BPNN global optimal is obtained Weight andthreshold establish a PSO-BPNN algorithm model Afterdecoding the global optimal weight and threshold of BPNNare obtained and the pso-bpnn algorithm model with 3-layer structure of 7-12-1 is established

27 GRA-PSO-BPNN Model Construction Process +e de-gree of correlation can delicate the correlation in mutualmatters and factors and the Grey correlation degree analysismethod can express the changeable situation in mutualmatters and factors Taking the timeliness and regionality of

Input layer

Site index

Lin Ling

Fixed fertilizerutilization rate

X1

Hidden layer Output layer

Nitrogenapplication

Or phosphorusand potassium

fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)

Figure 1 BP neural network structure


the fertilization model into consideration different forestshave different factors that affect the accuracy of fertilizationresulting that there is no certain model to implement thefertilization model to achieve the accurate prediction so thatthe accurate rate of the prediction is not so well +is re-search adopts the analysis method of Grey Relational degreewhich can analyze the key factors that influence the fertilizerapplication amount in different areas and on the basis of theannual forest data updated by artificial forest which canmake the accurate fertilization come true +e grey relationanalysis method is used to calculate the grey relation be-tween input variables and output results +e specific stepsare as follows

Step 1 Using the formula (9) establish a data matrix xi

xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)

where Xi (1) Xi (2) Xi (3) Xi (300) represents thenumber of sequences Among them i represents siteindex forest age nutrient concentration related todominant wood biomass of dominant wood averagebiomass of wood fixed fertilizer utilization rate andtarget yield which are different factors affecting thefertilization effectStep 2 Establish an initialization changematrix xi

prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889

xiprime(1) xiprime(2) xiprime(3) xi

prime(300)( 1113857

(10)

Step 3 Use formula (11) to calculate the differencesequence where k represents the sequence number

Δoi(k) abs xi(k) minus xiprime1113872 1113873 Δoi(1)Δoi(2) Δoi(300)( 1113857

(11)

Step 4 Calculate the correlation coefficient and the greycorrelation degree by using equations (12) and (13)Step 4 Use formulas (12) and (13) to calculate corre-lation coefficient and grey correlation degree φ is theresolution coefficient 0ltφlt 1 In this study φ 05

ξoi(k) mini minkΔoi(k) + φmaxi maxk Δoi(k)

Δoi(k) + φmini mink Δoi(k) (12)

coi 1300

1113944

300

1ξoi(k) (13)

According to the calculation formula of grey correlationcoefficient the minimum difference mini mink Δoi(k) andthe maximum difference maxi maxk Δoi(k) of N P and Kfertilizers were 8822eminus 06 3483 71719eminus 05 73072388eminus 04 1201 respectively Table 4 shows the greycorrelation coefficient and grey correlation degree betweenthe input variables and the output of the prediction model offorest precise fertilization of nitrogen phosphorus andpotassium

According to the above analysis the grey correlationdegree of X1 site index X2 forest age X3 dominant wood-related nutrient concentration X4 dominant wood biomassX5 average wood biomass and X6 target yield is higher andX7 fixed fertilizer utilization rate is smaller this study usesdata reduction grey correlation analysis to reduce theinfluencing factors of different forest areas for predictingand calculating forest fertilization identifying key factorsaffecting forest fertilization and providing more effectiveinput for the prediction model

Step 1 defines the input and output of the GRA-PSO-BPNN modelCompared with the PSO-BPNN model using the greycorrelation analysis the site index the forest age thedominant wood-related nutrient content the dominantwood biomass the average wood biomass and thetarget yield are used as the network input and theactual fertilization amount is used as the output+erefore there are 300 records 200 for training and100 for validation In the formula the number ofneurons in the input layer x is 6 and the number ofneurons in the output layer y is 1 +e empirical for-mula is used to determine the number m of hiddenneurons

m x + y

radic+ a a isin [1 10] (14)

+e reduction of network error can not only adjust thenumber of hidden layer neurons but also increase thenumber of hidden layer However increasing thenumber of hidden layers will complicate the networkincrease the training time and even overfitting It isbiased towards selecting the single hidden layer BPNN[31] As mentioned above the structure of GRA-PSO-BPNN model is determined to be a 3-layer structure of6-12-1Step 2 Particle Swarm Initialization+e weights and thresholds in the BPNN model are theparameters to be optimized by the PSO algorithm Atthe beginning a certain number of particle swarmindividuals can be randomly generated to represent

Best previous position

Current position

Best swarm position

νi+1

νi

νGνp

νi+1 = νi + νp + νG

Figure 2 Particle movement in a swarm


and the global optimal position gbest and the individualoptimal position pbest of the particle are initialized+esum of ownership value and threshold value in networkstructure is the dimension d of particle swarm indi-vidual search space that is

d xm + my + m + y (15)

+e d-dimensional vector xti (xt

i1 xti2 xt

id) rep-resents the position vector of the ith particle in the tthgeneration populationStep 3 Particle Velocity Location UpdateAccording to the following formula the particle ve-locity is updated according to the individual optimalsolution and the global optimal solution

v(t + 1) w middot v(t) + c1 middot r1 middot (pbest(t) minus x(t))(

+ c2 middot r2 middot (gbest(t) minus x(t))1113857(16)

Among them pbest (t) and gbest (t) are the individualoptimal solution of the ith particle in the tth generation ofthe d-dimensional space and the global optimal solutionin the tth generation r1 and r2 are in [0 1] c1 c2 arelearning factors w is the inertia weight and the particleposition is updated according to the following formula

x(t + 1) x(t) + v(t + 1) (17)

+e particle group can be evaluated by calculating thefitness value+e smaller the fitness value of the particlegroup is the higher the fitness is +e speed and po-sition of each particle are adjusted based on the fitnessvalue +e particle fitness is calculated according to thefollowing formula Value F is

F 1113944N

i1abs yi minus ti( 1113857 (18)

whereN is the number of samples in the test area abs isthe absolute value function yi is the actual value of thesample i and ti is the predicted value of the sample iStep 4 Optimal Population ParticlesWhen the number of population evolution reaches theupper limit T or the iteration error reaches the setprecision e when the algorithm stops the global op-timal solution can be obtained and mapped to theweight and threshold of the BP network

Step 5 GRA-PSO-BPNN Model TrainingAfter determining the GRA-PSO-BPNN weights andthresholds the training data are input to train the GRA-PSO-BPNN model +e entire model flow is shown inFigure 3

3 Case Study

300 groups of tree growth and nutrient dynamic test datawere measured in the test area and the test data were dividedinto two parts Among them 200 groups of experimentaldata were used as training data to train the stage accuratefertilization model of forest based on neural network and100 groups of experimental data were used as the verificationset of test fertilization model

BPNN models optimized by different algorithms arecompared and verified in the experiment Tansig functionand purelin function are respectively assigned as the ac-tivation functions of hidden layer and output layer In theprocess of adjusting parameters of BPNN model the ac-curacy is found higher when the maximum training times ofBPNN model reaches about 200 times while big error andinconsistencies occur when the training times are more thanor less than 200 times +erefore the max of training timesof the model is set to 200 the target error is 000001 and thelearning rate is 01 Even so the target accuracy is stillunachievable and the training time is about 5sim8 s Based onthe BPNN model the PSO algorithm was used for opti-mization When adjusting the parameters of the PSO-BPNNmodel it is found that accuracy was higher when thepopulation size was about 200 and the training time wasabout 8sim14 s When the population size is significantly lowerthan 200 the accuracy becomes lower when the populationsize is significantly higher than 200 the accuracy remains thesame but the training time becomes longer At the sametime the accuracy is higher when the max of training timesof the PSO-BPNN model is in the range of about 200 timesthe accuracy however becomes lower when it is significantlylower than 200 times When the training times greatly ex-ceed 200 the accuracy remains the same and the trainingtime becomes longer +erefore the maximum trainingtimes of the model is set as 200 +e population size of theparticles in the PSO algorithm is 200 the inertia weight is 1and the learning factor c1 c2 15 +e parameters remainunchanged and the training time is about 4sim10 s when thePSO-BP model is improved to GRA-PSO-BPNN model fortraining With regard to the basic BPNN PSO-BPNN andGRA-PSO-BPNN training models Figures 4ndash6 show the

Table 4 Grey correlation degree and grey correlation coefficient of each influencing factor and output fertilization amount

XNi εoi roi XPi εoi roi XKi εoi roiX1 εo1 (09178 08813) 09105 X1 εo1 (09512 08731) 09334 X1 εo1 (07483 04639) 07512X2 εo2 (09259 08947) 09122 X2 εo2 (09554 08793) 09357 X2 εo2 (07644 04744) 07559X3 εo3 (08972 09323) 09115 X3 εo3 (09372 09191) 09441 X3 εo3 (07312 06561) 07606X4 εo4 (09240 09390) 09232 X4 εo4 (09544 08992) 09398 X4 εo4 (07605 05119) 07715X5 εo5 (09338 09554) 09009 X5 εo5 (09594 09063) 09321 X5 εo5 (07800 05262) 07372X6 εo6 (09194 09516) 09119 X6 εo6 (09520 09046) 09368 X6 εo6 (07514 05229) 07561X7 εo7 (06660 06646) 06142 X7 εo7 (06016 06144) 06736 X7 εo7 (03952 03762) 05868


Start

Grey correlationanalysis

Input data

Data normalization

Adjust network structureparameters

Determining BP neural networktopology

Initialize the particle swarmalgorithm parameter values

Particle velocity and positioninitialization

Calculate the fitness value ofeach particle

If the particleprimes fitness valuexltpbest

Then pbest = x

If the fitness value of the particleis pbestltgbest

Then gbest = pbest

Update particle speed andposition

Meet the terminationconditions

Yes

No

Yes

No

Model accuracy test

Establish PSO-BP neural networkmodel

BP neural network obtains optimal connectionweights and thresholds

Establishing a predictive model of precision fertilizationbased on GRA-PSO-BP forest

Meet the termination conditions

Figure 3 GRA-PSO-BPNN model flow chart

BP network prediction output

10 20 30 40 50 60 70 80 90 1000Sample group

Predictive outputExpected output

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group

BP network prediction error percentage

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )

Figure 4 Prediction results and error analysis of nitrogen phosphorus and potassium fertilizer application rates in BP model

PSO-BP network predictive output

10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group

PSO-BP network prediction error percentage

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued


prediction situation and error percentage of treefertilization

It can be seen from Figures 4ndash6 that the basic BPNNmodel can only predict the change level of forest fertilizationamount and not accurately predict the actual fertilizationamount the accuracy is poor the error range is about 20and the PSO-BPNN model predicts the amount of forestfertilization +e accuracy is obviously improved the errorbetween predicted fertilization amount and actual fertil-ization amount is reduced and the error range is about 10which indicates that the optimization of PSO algorithm has agreat influence on accurately predicting the amount of forestfertilization the main influencing factors of determining theamount of forest fertilization by using grey correlationanalysis method After that the GRA-PSO-BP predictionmodel of this paper further enhances the ability to predictthe amount of forest fertilization +e predicted value of theGRA-PSO-BP neural network model has small fluctuations

near the actual value+emodel has a good prediction effect+e error between the predicted fertilization amount and theactual fertilization amount is within 5 which can reflectthe different forests +e change in nutrient demand duringthe growth phase can well guide the staged precisionfertilization

+e three models were used to predict the nitrogenphosphorus and potassium fertilizer application rates of 8experimental sites and compared with the actual fertilizationuse +e results are shown in Table 5

It can be seen from Table 5 that the error percentagebetween the predicted fertilization amount and the actualfertilization use amount of the GRA-PSO-BP predictionmodel is the smallest and the error is within 5 +e pre-diction accuracy of the GRA-PSO-BP prediction model isbetter than other fertilization models +e prediction ac-curacy is high the error between the predicted fertilizationamount and the actual fertilization usage is small and the


10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )

Figure 5 Prediction results and error analysis of nitrogen phosphorus and potassium fertilizer application rates in the PSO-BP model


0 10 20 30 40 50 60 70 80 90 100Sample group

GRA-PSO-BP network predictive output


014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group

GRA-PSO-BP network prediction error percentage

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )

Figure 6 Prediction results and error analysis of nitrogen phosphorus and potassium fertilizer application rates in GRA-PSO-BP model


generalization performance is good +e model can fullydescribe the mapping relationship between input and out-put According to the target production requirements ofChinese fir forest biomass the practical amount of nitrogenphosphorus and potassium fertilizers can be predictedwhich can guide the staged precision fertilization

On the basis of the above data of actual fertilizer ap-plication of nitrogen phosphorus and potassium andpredicted fertilizer application of nitrogen phosphorus andpotassium the paper calculated the mean square error be-tween fertilization prediction results and expected values ofdifferent neural network algorithms different absolute errorvalues and correlations one by one +e formula for cal-culating the mean square error is shown in (19) Besides thepaper also compared the error and correlation to analyze thetraditional BP Neural Network BP Neural Network that wasoptimized by PSO algorithm and the BP Neural NetworkPrediction Model that was optimized by GRA-PSOalgorithm

σ

ε21 + ε22 + middot middot middot + ε2nn

1113971

(19)

In the formulation n represents the number of calcu-lated mean square error data ε1 ε2 εn indicates thedifference between the actual fertilizer application amount ofnitrogen phosphorus and potassium and the predictedfertilizer application amount of nitrogen phosphorus andpotassium and σ means the square error

Tables 6ndash8 show the prediction models which are thetraditional BP Neural Network BP Neural Network that was

optimized by PSO algorithm and the BP Neural Networkthat was optimized by GRA-PSO algorithm which predictthe correlation and error value between the predicted fer-tilizer application of nitrogen phosphorus and potassiumand the actual fertilizer application rate of nitrogen phos-phorus and potassium

According to the data in above table the mean squareerror of nitrogen phosphorus and potassium fertilizer oftraditional BP neural network are 12797 21253 and 1037In these data the maximum absolute errors are 181 354and 194 +e minimum absolute errors are 107 0097 and0561 +e average absolute errors are 1102 1732 and8243 +e correlation numbers are 09881 09986 and09939 +e mean square error of nitrogen phosphorus andpotassium fertilizer of BP Neural Network that was opti-mized by PSO algorithm are 23151 01590 and 46287 Inthese data the maximum absolute errors are 47 036 and121 +e minimum absolute errors are 014 0023 and0006+e average absolute errors are 1797 0121 and 2481+e correlation numbers are 09997 09999 and 09989 +emean square error of nitrogen phosphorus and potassiumfertilizer of the BP Neural Network that was optimized byGRA-PSO algorithm are 08787 01699 and 12870 In thesedata the maximum absolute errors are 21 03 and 29 +eminimum absolute errors are 001 0002 and 001 +eaverage absolute errors are 0496 0119 and 0794 +ecorrelation numbers are 09999 09999 and 09999

+rough the error value and correlation between thepredicted results of N P and K fertilizer amount and theactual fertilization amount it can be seen that the predictionaccuracy of predication mode of BP neural network

Table 5 Comparison of measured results with predicted results (kghm2)

Number Stand age(ta)

Siteindex S

Actual amount ofnitrogen fertilizer BP Percentage of

error ()PSO-BP

Percentage oferror ()

GRA-PSO-BP


1 5a 5 1738 1631 6551 1767 166 1735 017522 18a 19 8419 9222 8706 8684 3142 8432 01553 21a 22 2181 200 9082 2173 03702 2183 006664 23a 25 2023 219 7628 2033 04784 201 066845 5a 5 1494 1632 8416 1508 09074 1495 005896 18a 19 1199 1305 812 1246 3876 120 006507 21a 22 2165 1993 8605 2146 08908 2164 003678 23a 25 207 2221 679 2099 1402 2091 1021 5a 5 1609 1794 1032 1649 245 1611 012452 18a 19 9811 1085 9558 9659 1552 9818 006373 21a 22 2855 3071 7027 2891 1278 284 07054 23a 25 3958 4312 8206 3975 04255 3988 074715 5a 5 1404 1501 6442 1381 1634 1394 070236 18a 19 1491 1378 8236 1484 05151 1492 003777 21a 22 2494 2745 9125 249 01747 2474 080518 23a 25 3973 4293 7444 3984 02619 3945 069931 5a 5 741 6744 9874 7397 01693 7388 029562 18a 19 111 1041 6643 1106 03362 1102 06643 21a 22 1559 162 5541 1558 007406 1555 032524 23a 25 2379 2538 6257 2416 1557 235 12125 5a 5 8045 7483 7514 8039 007832 8035 013116 18a 19 8788 9375 6267 9121 3791 879 002497 21a 22 1728 1834 5767 1726 008186 173 010178 23a 25 2812 2618 7395 2691 4289 2832 07244


optimized by GRA-PSO algorithm is the best However the8 groups of experimental data are only a small part of the testset And the poor data sampling may achieve the bestpredication accuracy of the BP neural network model op-timized by the GRA-PSO algorithm To assure the bestpredication accuracy of the the BP neural network modeloptimized by the GRA-PSO algorithm under the maximumprobability the probability of significant difference betweenBP neural network model and PSO-BP neural networkmodel and that between the PSO-BP neural network modeland the BP neural network prediction model optimized bythe GRA-BP algorithmmust be calculated DM test providesa calculation method from the perspective of statistics

+e following are the specific methods of DM testBecause three different algorithms predict models in the

span of T 8 the error sequence of predicted and actualvalues of BP network prediction model PSO-BP networkprediction model and GRA-PSO optimized BP networkprediction model are calculated on the span of T 8respectively

Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)

Next calculate the difference sequence Dab [d1ab d2

ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi

bc bi minus ciFinally the mean and standard deviation of Dab and Dab

are calculated and DM statistics are calculated+e formulasare as follows

d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d

i(abbc) minus d(abbc)mean1113872 1113873

2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)

+e DM test theory holds that the distribution of DM isin accordance with the requirements of the standard normaldistribution +erefore by querying the confidence valuescorresponding to DM in the standard normal distributiontable the confidence values of the significant differencesbetween BP network model and PSO-BP network model andbetween PSO-BP network model and BP network predictionmodel optimized by GRA-PSO algorithm can be obtainedwhile the predication of the fertilization amount of nitrogenphosphorus and potassium is advancing It is shown in theresults that when predicting the fertilization amount of

Table 6 Correlation and error value of three models for predicting nitrogen fertilizer

Fertilization model Mean squareerror

Maximum absoluteerror

Minimum absoluteerror

Mean absoluteerror Correlation

Traditional BP neural network 12797 181 107 1102 09881BP neural network optimized by PSOalgorithm 23151 47 014 1797 09997

BP neural network optimized by GRA-PSO algorithm 08787 21 001 0496 09999

Table 7 Correlation and error value of three models for predicting phosphorus fertilizer







Table 8 Correlation and error value of three models for predicting potassium fertilizer








nitrogen phosphorus and potassium the confidence valueswith significant differences between BP network model andPSO-BP network model and between PSO-BP networkmodel and BP network prediction model optimized byGRA-PSO algorithm are 53 68 81 64 61 and 53while due to the smallest prediction errors of BP networkprediction model optimized by the GRA-PSO algorithm itenjoys the highest accuracy and the best effect

+e prediction data of the network training are limitedso the different trained fertilization models are timelinessand regionality while as for this research because it is on thebasis of the annual forest data that was updated by artificialforest and adopted the Analysis method of Grey Relationaldegree to analyze the key factors of fertilizer applicationamount in different areas this can make the precisionfertilization come true After comparing these three pre-diction algorithms the result came out that the square errormaximum absolute error minimum absolute error andaverage absolute error numbers of the BP Neural Networkthat were optimized by GRA-PSO algorithm are small whilethe correlation number of it is large so that the accuracy rateof the BP Neural Network that was optimized by GRA-PSOalgorithm is high and the square error maximum absoluteerror minimum absolute error and average absolute errornumbers of the traditional BP Neural Network and BPNeural Network that were optimized by PSO algorithm arerelatively large but the correlation number is relativelysmall which draws the conclusion that the accuracy rate ofthese two prediction methods is relatively low

4 Conclusions

It is inefficient to determine the amount of fertilization bytraditional experience or basic theoretical model which mayalso cause environmental pollution so it is difficult to adaptto the new situation of precision forestry advocated by thecontemporary world As the current application of sensornetwork is getting more diversified data acquisition in forestarea is easier than before +rough real-time data updatereal-time prediction can be carried out using high-tech tobuild fertilizer model But different fertilization models willhave timeliness and regionality In different forest ecologicalareas it seems to be impossible to accurately make a pre-diction at present using the definite fertilization model withan eye to different factors that affect the precision fertil-ization of trees

+e traditional methods to determine the amount offertilizer application are empirical method fertilizer effectfunction method and nutrient balance method +e em-pirical method means that forest farmers fertilize trees ontheir willing which is according to their experience andwithout basis +is method is simple and sometimes feasiblebut in most cases it is not accurate enough which oftenresults in insufficient or excessive fertilizer application andmake it not fit the needs of high yield and efficiency offorestry construction +e fertilizer effect function methodneeds a lot of experimental data but the successful rate of thefitting is not high and a lot of data resources are just wastedso that a lot of financial wealth material and human labors

are wasted too +e nutrient balance method often needs tocome up with expert experience because it requires toomany parameters and also there is a relative error in thecalculation of fertilization It is important to find an effectiveand accurate fertilization model Artificial neural networkhas a strong ability to solve nonlinear problems In order tosolve the problem of nonlinear precision fertilization thispaper introduces the neural network modeling method anduses BPNN PSO-BPNN and GRA-PSO-BPNN to constructthree kinds of forest precise fertilization models for com-parative verification and result analysis +rough compar-ison the accuracy of the BPNN model is low and the errorrange is about 20 and it is unstable Although the PSO-BPNN model has high accuracy the error range is about10 considering that the fertilization model mentionedabove is time-sensitive and regional the factors that mayaffect the fertilization are different in different time anddifferent regions In some geographically complex areasmore factors need to be considered to ensure accuratefertilization Since it is difficult for the PSO-BPNN model toidentify the key influencing factors of forest fertilizer ap-plication in different regions the PSO-BPNN model haspoor scalability However the key factors influencing forestfertilizer application in different regions can be determinedby grey relational analysis +e constructed GRA-PSO-BPNN forest tree precision fertilization model not only hashigh accuracy the error range is about 5 and it has a fastercalculation speed but also applicable to the determination offorest fertilizer application in different regions and canconstantly update the forest fertilizer model with goodexpansibility

5 Discussion

With the in-depth development of modern forestry preci-sion forestry is receiving unprecedented attention +eemergence of forest precise fertilization model will greatlypromote the forestry production Forest economy plays animportant role in the society improvement and to improvethe forest economy only the development of artificial fast-growing and high-yielding forest can be depended and theeffective way to improve the productivity of artificial forest isjust precision fertilization +e prediction of precision fer-tilization is a scientific and innovative technology which canachieve five goals ensuring high quality increasing theproduction improving soil quality and ecology and highefficiency taking the factors which affect the amount offertilizer application as the basis and making the fertilizerapplication rate and fertilization target clear before imple-menting it linking the fertilization with economic benefitachieving the quantitative fertilization of forest trees underthe realization of target benefit making a prediction of thebenefit that earned by the fertilization and according to theinvestigation of basic data and soil chemical analysis in forestarea so that the ratio of tree fertilization under the targetbenefit can be calculated making forest fertilization becomean important safeguard measure to improve the quality andyield of commercial forest At the same time as a direction ofprecision forestry technology precision fertilization model


will attract more and more attention of forestry science andtechnology personnel and forestry production managers Inthis paper the GRA-PSO-BPNN prediction model of forestperiodic precise fertilization is of far-reaching significance tosolve the problem of forest fertilization that has beentroubling people for a long time which can be applied byforest-related workers in forestry ecological zones whereconditions are basically the same If the generalization iscarried out in a larger andmore complex area to improve thegeneralization ability of the model it is necessary to considerother factors affecting the amount of forest fertilization suchas soil type organic matter pH and other factors In somecases the GRA-PSO-BPNN precise fertilization model fortrees may need to be updated based on the experience ofexperts which is what needs to be further studied

Data Availability

+e rawprocessed data required to reproduce these findingscannot be shared at this time as the data also forms part of anongoing study

Conflicts of Interest

+e authors declare no conflicts of interest

Authorsrsquo Contributions

Chen Zuxing and Wang Dian contributed analytical toolsand ideas collected and processed the data conductedexperiments and wrote papers and finally finalized the finalversion of the paper

Acknowledgments

+is work was supported by the Central Universityrsquos BasicResearch Project (2016ZCQ08)

References

[1] T Cao L Valsta S Harkonen P Saranpaa and A MakelaldquoEffects of thinning and fertilization on wood properties andeconomic returns for Norway sprucerdquo Forest Ecology andManagement vol 256 no 6 pp 1280ndash1289 2008

[2] T Pukkala ldquoOptimal nitrogen fertilization of boreal coniferforestrdquo Forest Ecosystems vol 4 2017

[3] J Bergh U Nilsson H L Allen U Johansson and N FahlvikldquoLong-term responses of scots pine and Norway spruce standsin Sweden to repeated fertilization and thinningrdquo ForestEcology and Management vol 320 pp 118ndash128 2014

[4] P-O Hedwall P Gong M Ingerslev and J Bergh ldquoFertil-ization in northern forestsmdashbiological economic and envi-ronmental constraints and possibilitiesrdquo ScandinavianJournal of Forest Research vol 29 no 4 pp 301ndash311 2014

[5] W X Hu Yueli Research on Fertilization of Forest TreesmdashIFertilization Geory and Basic Models Zhongnanlin Uni-versity Wuhan China 1994

[6] W X Hu Yueli Study on Dynamic Model of Forest Growthand Nutrient v Nutrient Curve of Chinese fir Forest ZhongnanForestry College Zhongnan China 1999

[7] W XWu Lichao BWang J Wu Z Li andM Lu ldquoResearchprogress in fast-growing and high-yield fertilization

techniques of Paulowniardquo Central South University of Forestryand Technology vol 30 pp 29ndash35 2010

[8] H Y Wu Xiaofu ldquoStudy on fertilization of foresttreesmdashapplication of II fertilization model in Chinese firforestrdquo Zhongnan Forestry College Zhongnan China 1995

[9] H YWu Xiaofu Study on the Growth and Nutrition DynamicModel of Forest TreesmdashFormed Fertilization Model of SiteNutrient Effect Zhongnanlin University Zhongnanlin China2002

[10] L L Bhering C D Cruz L D A Peixoto A M RosadoB G Laviola and M Nascimento ldquoApplication of neuralnetworks to predict volume in eucalyptusrdquo Crop Breeding andApplied Biotechnology vol 15 no 3 pp 125ndash131 2015

[11] S Che X Tan C Xiang et al ldquoStand basal area modelling forChinese fir plantations using an artificial neural networkmodelrdquo Journal of Forestry Research vol 30 no 5pp 1641ndash1649 2019

[12] M J Diamantopoulou and E Milios ldquoModelling total volumeof dominant pine trees in reforestations via multivariateanalysis and artificial neural network modelsrdquo BiosystemsEngineering vol 105 no 3 pp 306ndash315 2010

[13] R Ozccedilelik J R Diamantopoulou and H V Wiant ldquoEsti-mating tree bole volume using artificial neural networkmodels for four species in Turkeyrdquo Journal of EnvironmentalManagement vol 91 no 3 pp 742ndash753 2010

[14] C O Sabatia and H E Burkhart ldquoPredicting site index ofplantation loblolly pine from biophysical variablesrdquo ForestEcology and Management vol 326 pp 142ndash156 2014

[15] A A Vahedi ldquoMonitoring soil carbon pool in the hyrcaniancoastal plain forest of Iran artificial neural network appli-cation in comparison with developing traditional modelsrdquoCatena vol 152 pp 182ndash189 2017

[16] J Xiong T Cui and NMao ldquoGrey correlation analysis on thetotal health expenditure structure and per capita medicalexpenses in Chinardquo Value in Health vol 21 2018

[17] W Xiong L Liu and M Xiong ldquoApplication of gray cor-relation analysis for cleaner productionrdquo Clean Technologiesand Environmental Policy vol 12 no 4 pp 401ndash405 2010

[18] P Zhou Y-J Yao Y-F Ai A-M Liu Z-L Xu and J-C XieldquoGrey correlation analysis of factors influencing maldis-tribution in feeding device of copper flash smeltingrdquo Journalof Central South University vol 19 no 7 pp 1938ndash1945 2012

[19] W Zhang Y Yu X Zhou S Yang and C Li ldquoEvaluatingwater consumption based on water hierarchy structure forsustainable development using grey relational analysis casestudy in Chongqing Chinardquo Sustainability vol 10 no 5p 1538 2018

[20] T Bai H Meng and J Yao ldquoA forecasting method of forestpests based on the rough set and PSO-BP neural networkrdquoNeural Computing and Applications vol 25 no 7-8pp 1699ndash1707 2014

[21] Z Cheng X Li Y Bai and C Li ldquoMulti-scale fuzzy inferencesystem for influent characteristic prediction of wastewatertreatmentrdquo CleanmdashSoil Air Water vol 46 no 7 Article ID1700343 2018

[22] A Ismail D-S Jeng and L L Zhang ldquoAn optimised product-unit neural network with a novel PSO-BP hybrid trainingalgorithm applications to load-deformation analysis of axiallyloaded pilesrdquo Engineering Applications of Artificial Intelli-gence vol 26 no 10 pp 2305ndash2314 2013

[23] X Y Liang Z Yang X S Gu and L C Ling ldquoResearch onactivated carbon supercapacitors electrochemical propertiesbased on improved PSO-BP neural networkrdquo CMC-Com-puters Materials amp Continua vol 13 pp 135ndash151 2009


[24] C Ren N An J Wang L Li B Hu and D Shang ldquoOptimalparameters selection for BP neural network based on particleswarm optimization a case study of wind speed forecastingrdquoKnowledge-Based Systems vol 56 pp 226ndash239 2014

[25] C Sudheer and S Mathur ldquoParticle swarm optimizationtrained neural network for aquifer parameter estimationrdquoKSCE Journal of Civil Engineering vol 16 pp 298ndash307 2012

[26] T Liu and S Yin ldquoAn improved particle swarm optimizationalgorithm used for BP neural network andmultimedia course-ware evaluationrdquo Multimedia Tools and Applications vol 76no 9 pp 11961ndash11974 2017

[27] I Sutrisno M Abu Jamirsquoin and J Hu ldquoAn improved elmanneural network controller based on quasi-arx neural networkfor nonlinear systemsrdquo IEEJ Transactions on Electrical andElectronic Engineering vol 9 no 5 pp 494ndash501 2014

[28] Y Deng H Xiao J Xu and H Wang ldquoPrediction model ofPSO-BP neural network on coliform amount in special foodrdquoSaudi Journal of Biological Sciences vol 26 no 6 pp 1154ndash1160 2019

[29] X Liu Z Liu Z W Liang S P Zhu J A F O Correia andA M P De Jesus ldquoPSO-BP neural network-based strainprediction of wind turbine bladesrdquo Materials vol 12 no 122019

[30] Y Mei J Q Yang Y Lu et al ldquoBP-ANNmodel coupled withparticle swarm optimization for the efficient prediction of 2-chlorophenol removal in an electro-oxidation systemrdquo In-ternational Journal of Environmental Research and PublicHealth vol 16 2019

[31] S Zhang and J Ou ldquoBP-PSO-based intelligent case retrievalmethod for high-rise structural form selectionrdquo Science ChinaTechnological Sciences vol 56 no 4 pp 940ndash944 2013


discussion Hu Yueli et al proposed a site-nutrient effectfertilization model [5ndash9] However sometimes this modelcan hardly help to get satisfactory accuracy and stability +etraditional fertilization model can only describe the staticrelationship between the growth of forest and the requiredfertilization nutrients which can hardly reflect the differentgrowth periods of trees In view of the differences in nutrientabsorption capacity and fertilizer application in differentgrowth stages this model cannot be applied to guide thestage fertilization of trees In the past it was difficult tocollect data due to the long growth period of forest+erefore there were few models of forest fertilizationHowever in recent years sensor network can be used tocollect real-time data in forest areas with the burgeoningdevelopment of artificial intelligence It is time to construct apredictive model of accurate fertilization of forest throughthe collected data Similarly as the traditional one the modelcan only exert real-time and accurate small-scale predictionin forest areas considering the complexity of different forestareas and site indices the diversified factors affecting forestfertilization At the same time since there is a high degree ofnonlinearity between site index and dominant wood-relatednutrient content forest age and other influencing factorsthe traditional fertilization model often has inaccurate re-sults due to manifold parameters or low goodness of fittingAs a result the large amount of accumulated data can hardlyserve to guide production practice In the later stage expertexperience is still needed resulting in a waste of manpowermaterial and financial resources

Neural network is considered to be a powerful tool tosolve nonlinear problems [10ndash15] In order to ensure theintegrity of information and improve the precision of fer-tilization prediction the prediction model of multifactorprecision fertilization based on neural network can be usedto solve these problems It can reflect different absorption ofnutrients in different growth periods of young and middleages of trees and apply fertilizer efficiently in the optimalfertilization period of trees +e BP algorithm shows greatpotential to introduce the prediction model of forest fer-tilization With the updating of the data of forest fertilizationexperiment the BP algorithm modifies the existing pre-diction model of fertilization which makes the forecasts ofthe model more precise and get closer to the actual situationHowever the accuracy of predicted results and actual valuesis not fairly reliable on account of some big defects such aslocal optimization slow convergence speed and large de-pendence on training data when a single BP neural networkalgorithm is used to predict the amount of fertilizer appliedto trees In this paper the analyzing method of grey relativity[16ndash19] is introduced to extract the original variable data ofmultiple indexes in advance and the factors with highcorrelation degree are taken as the network input layer andthen the global searching ability of PSO [20ndash25] is used tooptimize the BP neural network which greatly avoids thedefect of the model falling into the local optimum andfurther improves the accuracy Although neural networkprediction has been applied in medical engineering electricpower system and other fields at home and abroad andsome gratifying results have been achieved there are only

few studies on the application of neural network predictionmodel to forest fertilizer application+erefore an improvedGRA-PSO-BP algorithm was used to establish the accuratefertilization model of trees in stages

2 Methodology

21 Test Area Overview and Plot Settings +e experimentaldata are from the state-run forest farm in Renhua CountyGuangdong Province and Liujiashan Forest Farm in ShixingCounty Guangdong Province which is the main productionarea of fir trees with an altitude of less than 500m and thesoil type is the red and yellow soil developed on slates Large-scale fertilization experiments were carried out for youngandmature timber of fir forests and the experimental forestswith different site indexes were classified during the ex-periment according to the utilization of the last round offorest land and the Nanling Mountains fir trees in thedifferent site conditions the experimental forest can bedivided into four types (1) triple-tilled woodlands ofCunninghamia lanceolata with a site index of 5 (2) culti-vated Chinese fir double-tilled woodlands of Cunninghamialanceolata with a site index of 18 (3) first ploughingwoodlands after shrub felling with a site index of 21 and (4)first ploughing woodlands after logged broad-leaf forestswith a site index of 23 Under the condition of the same siteindex the slope direction of the test site is the same theterrain difference is small and the trees are arranged at thesame height +e young forest and the middle-aged foresttest area are respectively set in the forest stands with ap-propriate site index and the area of each test site is 1 hm2+e initial planting density of young trees in the experi-mental forests was 3600 plants1 hm2 In the first 6 to 8years the first thinning was carried out and the forests in themiddle-aged forests were retained at 2700 plantshm2 +esize distribution and density of the forests in each exper-imental area were basically the same +ere are fixed stakesaround each test area and the dominant wood and averagewood in the test area have specific numbers +e growth andnutrient dynamics of dominant wood and average wood inthe test area are measured regularly every year and nitrogenphosphorus and potash fertilizers are applied according tothe fertilization method in the test area

16 plots with age of 5a 19a 22a and 25a were selected inthe above four different site types +e selected average anddominant trees in different areas were logged and thendivided by leaves branches stems barks and roots to weigheach organ of them +e age of leaves and branches wereweighed respectively and the root system was dug to adepth of 60 cm in the range of the canopy Samples of allorgans were evenly sampled and dried at 80degC to determinewater and nutrient content Meanwhile four soil samplingpoints of different stand ages were set up in four different siteindex types 16 soil sampling points in total Take soilsamples in 0sim60 cm soil layer of each soil sampling point+e physicochemical analysis of plant and soil samples wascarried out in accordance with conventional methods andthe determination of the physicochemical properties of thesoil in the experimental forest land is shown in Table 1








Stand age(ta)







5a

5 Middlesoil 90 03 16 21 57 46

18 Middlesoil 174 089 277 30 80 49

21 Middlesoil 220 112 32 40 92 50

23 Middlesoil 270 135 48 50 100 52

19a

5 Middlesoil 89 032 164 23 54 45

18 Middlesoil 172 09 28 31 88 48

21 Middlesoil 221 114 32 41 90 51

23 Middlesoil 273 138 476 50 96 53

22a

5 Middlesoil 90 031 161 22 52 44

18 Middlesoil 171 087 281 32 91 47

21 Middlesoil 220 111 32 42 87 54

23 Middlesoil 271 133 481 52 94 51

25a

5 Middlesoil 91 03 162 20 55 48

18 Middlesoil 173 091 282 30 83 49

21 Middlesoil 222 110 32 43 91 53

23 Middlesoil 270 136 479 51 100 51







Leaf

5 68 107 126 138 075 102 109 112 32 47 49 5019 86 121 124 127 084 116 128 106 33 43 47 4922 94 132 135 137 091 112 125 093 34 42 46 4825 101 139 141 142 092 104 107 097 32 41 45 47

Branch

5 39 67 71 73 059 071 074 077 31 40 41 4219 28 45 57 59 049 055 057 059 27 36 37 3922 27 42 55 57 047 052 055 058 26 38 39 3625 25 41 53 56 045 054 056 054 25 37 40 35

Stem

5 11 19 21 23 011 020 023 024 08 17 15 1419 12 14 19 20 008 009 012 014 04 09 11 1322 10 13 16 18 007 008 010 009 05 08 10 1125 09 12 14 13 004 006 008 007 04 07 09 08

Bark

5 28 46 45 47 021 032 034 035 47 36 33 3119 24 19 35 33 010 015 016 018 45 19 18 1722 23 36 34 31 009 011 013 015 41 17 16 1525 22 34 32 29 007 009 011 014 38 15 13 14

Root

5 17 35 38 39 010 027 029 031 34 21 20 1819 14 19 22 25 006 011 014 016 24 16 15 1422 16 17 21 24 005 012 012 017 21 17 16 1525 12 15 20 22 008 010 014 015 20 14 13 12


Standage (ta) Organ




()

5a


19a


22a


25a





y x minus xmin

xmax minus xmin (1)















1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)


yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)









Input layer

Site index

Lin Ling


X1


Nitrogenapplication


fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)





xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References









































Stand age(ta)







5a

5 Middlesoil 90 03 16 21 57 46

18 Middlesoil 174 089 277 30 80 49

21 Middlesoil 220 112 32 40 92 50

23 Middlesoil 270 135 48 50 100 52

19a

5 Middlesoil 89 032 164 23 54 45

18 Middlesoil 172 09 28 31 88 48

21 Middlesoil 221 114 32 41 90 51

23 Middlesoil 273 138 476 50 96 53

22a

5 Middlesoil 90 031 161 22 52 44

18 Middlesoil 171 087 281 32 91 47

21 Middlesoil 220 111 32 42 87 54

23 Middlesoil 271 133 481 52 94 51

25a

5 Middlesoil 91 03 162 20 55 48

18 Middlesoil 173 091 282 30 83 49

21 Middlesoil 222 110 32 43 91 53

23 Middlesoil 270 136 479 51 100 51







Leaf

5 68 107 126 138 075 102 109 112 32 47 49 5019 86 121 124 127 084 116 128 106 33 43 47 4922 94 132 135 137 091 112 125 093 34 42 46 4825 101 139 141 142 092 104 107 097 32 41 45 47

Branch

5 39 67 71 73 059 071 074 077 31 40 41 4219 28 45 57 59 049 055 057 059 27 36 37 3922 27 42 55 57 047 052 055 058 26 38 39 3625 25 41 53 56 045 054 056 054 25 37 40 35

Stem

5 11 19 21 23 011 020 023 024 08 17 15 1419 12 14 19 20 008 009 012 014 04 09 11 1322 10 13 16 18 007 008 010 009 05 08 10 1125 09 12 14 13 004 006 008 007 04 07 09 08

Bark

5 28 46 45 47 021 032 034 035 47 36 33 3119 24 19 35 33 010 015 016 018 45 19 18 1722 23 36 34 31 009 011 013 015 41 17 16 1525 22 34 32 29 007 009 011 014 38 15 13 14

Root

5 17 35 38 39 010 027 029 031 34 21 20 1819 14 19 22 25 006 011 014 016 24 16 15 1422 16 17 21 24 005 012 012 017 21 17 16 1525 12 15 20 22 008 010 014 015 20 14 13 12


Standage (ta) Organ




()

5a


19a


22a


25a





y x minus xmin

xmax minus xmin (1)















1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)


yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)









Input layer

Site index

Lin Ling


X1


Nitrogenapplication


fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)





xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References








































Leaf

5 68 107 126 138 075 102 109 112 32 47 49 5019 86 121 124 127 084 116 128 106 33 43 47 4922 94 132 135 137 091 112 125 093 34 42 46 4825 101 139 141 142 092 104 107 097 32 41 45 47

Branch

5 39 67 71 73 059 071 074 077 31 40 41 4219 28 45 57 59 049 055 057 059 27 36 37 3922 27 42 55 57 047 052 055 058 26 38 39 3625 25 41 53 56 045 054 056 054 25 37 40 35

Stem

5 11 19 21 23 011 020 023 024 08 17 15 1419 12 14 19 20 008 009 012 014 04 09 11 1322 10 13 16 18 007 008 010 009 05 08 10 1125 09 12 14 13 004 006 008 007 04 07 09 08

Bark

5 28 46 45 47 021 032 034 035 47 36 33 3119 24 19 35 33 010 015 016 018 45 19 18 1722 23 36 34 31 009 011 013 015 41 17 16 1525 22 34 32 29 007 009 011 014 38 15 13 14

Root

5 17 35 38 39 010 027 029 031 34 21 20 1819 14 19 22 25 006 011 014 016 24 16 15 1422 16 17 21 24 005 012 012 017 21 17 16 1525 12 15 20 22 008 010 014 015 20 14 13 12


Standage (ta) Organ




()

5a


19a


22a


25a





y x minus xmin

xmax minus xmin (1)















1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)


yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)









Input layer

Site index

Lin Ling


X1


Nitrogenapplication


fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)





xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References





































y x minus xmin

xmax minus xmin (1)















1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)


yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)









Input layer

Site index

Lin Ling


X1


Nitrogenapplication


fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)





xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References








































1113944 ωjkφ 1113944ωijxi + θj1113872 1113873 + θk1113872 1113873(5)


yk τ netk( 1113857

τ 1113944 ωjkφ 1113944ωjxi + θj1113872 1113873 + θk1113872 11138731113872 1113873(6)









Input layer

Site index

Lin Ling


X1


Nitrogenapplication


fertilizer

X2

X7

φ(middot)

φ(middot)

φ(middot)

θkθj

ωij ωjk

τ(middot)





xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References





































xi xi(1) xi(2) xi(3) xi(300)( 1113857 (9)


prime using

xiprime

xi(1)

xi(1)xi(2)

xi(1)xi(3)

xi(1)

xi(300)

xi(1)1113888 1113889


prime(300)( 1113857

(10)



(11)




coi 1300

1113944

300

1ξoi(k) (13)




m x + y




Current position

Best swarm position

νi+1

νi

νGνp





d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References




































d xm + my + m + y (15)


i1 xti2 xt





x(t + 1) x(t) + v(t + 1) (17)


F 1113944N




3 Case Study






Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References



































Start


Input data

Data normalization







Then pbest = x


Then gbest = pbest



Yes

No

Yes

No

Model accuracy test







10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )

(a)

ndash100 10 20 30 40 50 60 70 80 90 100

Sample group


ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(b)

Figure 4 Continued



10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References




































10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

25

30

Perc

enta

ge er

ror

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash20

ndash15

ndash10

ndash5

0

5

10

15Pe

rcen

tage

erro

r

(f )



10 20 30 40 50 60 70 80 90 1000Sample group

014

016

018

02

022

024

026

028

Pred

icte

d an

d ac

tual

val

ues o

fni

trog

en (t

hm

2 )


(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(b)

Figure 5 Continued








10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References









































10 20 30 40 50 60 70 80 90 1000Sample group


002

0025

003

0035

004

0045

005Pr

edic

ted

and

actu

al v

alue

s of

phos

phor

us (t

hm

2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash15

ndash10

ndash5

0

5

10

Perc

enta

ge o

f err

or

(d)


10 20 30 40 50 60 70 80 90 1000Sample group


014

016

018

02

022

024

026

028

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Perc

enta

ge o

f err

or

(f )



0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References



































0 10 20 30 40 50 60 70 80 90 100Sample group



014

016

018

02

022

024

026

028Pr

edic

ted

and

actu

al v

alue

s of

nitr

ogen

(th

m2 )

(a)

0 10 20 30 40 50 60 70 80 90 100Sample group


ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Perc

enta

ge o

f err

or

(b)


0 10 20 30 40 50 60 70 80 90 100Sample group


002

0025

003

0035

004

0045

005

Pred

icte

d an

d ac

tual

val

ues o

fph

osph

orus

(th

m2 )

(c)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(d)


0 10 20 30 40 50 60 70 80 90 100Sample group


015

02

025

03

Pred

icte

d an

d ac

tual

val

ues o

fpo

tass

ium

(th

m2 )

(e)


0 10 20 30 40 50 60 70 80 90 100Sample group

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Perc

enta

ge o

f err

or

(f )





σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References





































σ


1113971

(19)








Siteindex S


error ()PSO-BP


GRA-PSO-BP







Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References






































Ea a1 a

2 a

T1113960 1113961 (20)

Eb b1 b

2 b

T1113960 1113961 (21)

Ec c1 c

2 c

T1113960 1113961 (22)


ab dT

ab] Dbc [d1bc d2

bc dTbc] where di

ab ai minus bidi



d(abbc)mean 1113936

Ti1 d(abbc)

i

T (23)

d(abbc) std

1113936Ti1 d


2

T minus 1

1113971

(24)

DM d(abbc)mean

d(abbc) std (25)


























4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References





































4 Conclusions




5 Discussion




Data Availability






Acknowledgments


References




































Data Availability






Acknowledgments


References



































apredictionmodelofforestpreliminaryprecisionfertilization...

Documents