FRAMEWORK FOR STOCHASTIC

MODELING OF DRAGLINE ENERGY

EFFICIENCY

Maryam Abdi OskoueiDr. Kwame Awuah-offei

1

Introduction

2

Operators’ skills

Operating conditions

Equipment Efficiency

Energy consumption

Objectives:• Study the effects of operators’ practice on

dragline energy efficiency– t-test

• Study the relation between operating parameters and energy efficiency to create a framework for stochastic model of dragline energy efficiency– Correlation analysis

3

Dragline operation

4

Hoist Bucket

Swing out

Dump material

Swing in (Return)

Spot Bucket

Fill Bucket

• A cycle of dragline operation

Ho

ist

Drag

Swing

Data Acquisition

• A coal mine in Powder River basin, Wyoming• Dragline Bucyrus-Erie 1570w – 85 yd3 removes the

blasted overburden5

6- 1300 HP hoist motors4-1300 HP drag motors4- 1045 HP swing motors

Monitoring system• AccuWeigh monitoring system

– Real time monitoring system• Records operating parameters in each cycle

– Adjusted to record energy consumption of three sets of motors

– Records 44 parameters in each cycle stores in database

– 34,327 cycles recorded in 33 days6

Statistical analysis

• Useful parameters # Parameter1 Cycle time2 Swinging out time3 Swing in time4 Bucket loading time5 Dumping time6 Spotting time7 Angle of swinging out8 Bucket loading energy9 Dumping height10 Payload11 Drag energy12 Hoist energy13 Swing energy

Cycle time & cycle time components

Energy consumption

7

Removing the outliers

• Outliers cause inaccurate inferences in the analysis– Number of bucket reloads

Bucket Reload Count Proportion (%)

1 33,493 97.56

2 738 2.15

3 or more 96 0.28

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Boxplot

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Middle quartile/ median

• Boxplot is used to identify the outliers Upper whisker

Upper quartile (q3)

Lower quartile (q1)

Lower whisker

Quartile group 1

Quartile group 2

Quartile group 3

Quartile group 425%

25%

25%

25%

++

+

+outlier

+

• Upper whisker = q3+1.5(q3-q1)

• Lower whisker = q1-1.5(q3-q1)

Removing the outliers

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Operators• 13 operators operated during the 33 days• Working hours more than 32 hours or 2,200 cycles

Operator# of

cyclesTime

(hours)

Material weight

(tonnes)

Energy (kw-h)

Hourly production

(tonnes/hours)

A 3,897 56.9 496,18 44,850 8,719

B 3,611 54.6 450,22 43,894 8,243

C 3,350 49.6 427,23 39,827 8,613

D 3,058 45.6 383,55 36,879 8,404

E 2,211 32.8 277,55 23,395 8,46911

Energy Efficiency• η – energy efficiency• P – payload• E – energy consumption

A B C D E9.5

10

10.5

11

11.5

12

12.5

13

En

erg

y E

ffic

ien

cy

(to

nn

es/K

w-h

)

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𝜂=𝑈𝑠𝑒𝑓𝑢𝑙𝑤𝑜𝑟𝑘𝐼𝑛𝑝𝑢𝑡𝑒𝑛𝑒𝑟𝑔𝑦

≅𝑃𝐸

Normality

• To use the t-test data must follow normal distribution

• Kolmogrov-Smirnov test on energy efficiency of different operators rejects the hypothesis of normality

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Data transformation

• Right skewness• Log transformation

• The assumption of data follows normal distribution is valid:

Histogram plots Central limit theorem

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Results of the t-tests

Operators

Degree of

freedom

Pooled standard deviation

t-statistics CI p-value

D-B 6667 0.1026 2.1065 0.0004 0.0103 0.0352D-E 5267 0.1004 -19.6816 0.0606 -0.0497 <0.001D-A 6953 0.1028 -9.8622 -0.0294 0.0196 <0.001D-C 6406 0.1015 -4.0432 -0.0152 -0.0053 <0.001B-E 5820 0.1000 -22.3968 -0.0657 -0.0552 <0.001B-A 7506 0.1023 -12.6113 -0.0344 -0.0252 <0.001B-C 6959 0.1011 -6.4241 -0.0203 -0.0108 <0.001E-A 6106 0.1003 -11.4764 -0.0359 -0.0254 <0.001E-C 5559 0.0985 -16.6271 -0.0502 -0.0396 <0.001A-C 7245 0.1013 5.9610 0.0096 0.0189 <0.001

at 5% significance level all the t-tests reject the hypothesis of equal mean

15

Pearson correlation

• Evaluate the relation between operating parameters and energy consumptions of swing, drag and hoist motors

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Swing Energy

Parameters PCC p-value

Swing angle 0.86 <0.0001

Cycle time 0.61 <0.0001

Swing out time 0.50 <0.0001

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Swing Energy

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PCC = 0.62 , p-value<0.0001

PCC = 0.57 , p-value<0.0001

PCC = 0.57 , p-value<0.0001

Parameters PCC p-value

Swing angle 0.86 <0.0001

Cycle time 0.61 <0.0001

Swing out time

0.50 <0.0001

• Evaluate the relation between these parameters to avoid confounding and duplicity in the model

Swing Energy

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𝐸𝑆𝑤𝑖𝑛𝑔= 𝑓 𝑠 (𝜔𝑠 ) 𝑡𝑠

Swing power

𝑆𝑤𝑖𝑛𝑔𝑠𝑝𝑒𝑒𝑑(𝜔𝑠)=𝑆𝑤𝑖𝑛𝑔𝑎𝑛𝑔𝑙𝑒𝑆𝑤𝑖𝑛𝑔𝑡𝑖𝑚𝑒

PCC = 0.80, p-value<0.0001

Hoist Energy

Parameters PCC p-value

Dump height 0.84 <0.0001

Dump time 0.36 <0.0001

Payload 0.34 <0.0001

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𝐸𝐻𝑜𝑖𝑠𝑡= 𝑓 h (h𝑑+𝑡𝑑𝑝+𝑃 ) 𝑡h

Hoist power

Drag Energy

Parameters PCC p-value

Bucket loading energy 0.84 <0.0001

Loading time 0.36 <0.0001

21

Drag Energy

Parameters PCC p-value

Bucket loading energy

0.84 <0.0001

Loading time 0.36 <0.0001

22

PCC = 0.82 , p-value<0.0001

𝐸𝐷𝑟𝑎𝑔= 𝑓 𝐷 ( 𝑙𝑡 ) 𝑡𝑑

Drag power

Framework of stochastic model

Drag power Swing powerHoist power

, ,t d t d h d dp h s s sE f l t f h t P t f t

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Drag power Swing powerHoist power

Energy efficiency, , ,t d t d h d dp h s s s

P P

E f l t f h t P t f t

Question?

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