A strong wind warning method for high speed train using Kalman filter

Li Yuntao, Huang Hong*, Wang Hongye, Yuan Hongyong Institute of Public Safety Research, Department of Engineering Physics

Tsinghua University Beijing, China

liyuntao10@mails.tsinghua.edu.cn

Abstract—In this paper, wind speed and direction along the high speed train railway line was predicted with the help of Kalman filter using simulated data. Results fit well with the true speed and direction. Warning system to adjust train speed was built mainly based on integrated risk coefficient, which was defined as the function of not only wind speed and direction, but also train speed and location.

Keywords- Kalman filter; high speed train; cross wind; monitoring system

I. INTRODUCTION High speed train has become a hot issue in China when the

government announced that miles of railway would reach 13,000 km by the year 2012 [1]. Accident in Wenzhou on July 23rd made the safety of high speed trains more important [2]. Strong wind along the railway threats high speed trains a lot, as the torque generated by both train itself as the result of high velocity and strong wind may cause the train to derail. Several train accidents caused by strong wind have been reported worldwide in recent years [3, 4]. Researchers studied the aerodynamics of high speed train [5, 6], and figured out the correlations among wind direction, wind speed and train speed. Table 1 shows the maximum train speed under different wind conditions, which is used in Beijing-Shanghai high speed railway [7].

To ensure the safety of high speed train, it is necessary to monitor and predict the wind along railway line. There are methods such as Meteorological, Remote Sensing, Computer Calculating and Time Sequences Analytic. Yayoi Misu developed a Time Sequences Analytic Method to predict the maximum wind speed along the railway line using numerical

TABLE 1. MAXIMUM TRAIN SPEED TO DIFFERENT WIND

Wind Speed V(m/s) Train Speed (km/h)

V<15 not limited

15≤V<20 beneath 300

20≤V<25 beneath 200

25≤V<30 beneath 120

30≤V stop

simulation with the data collected by anemometers at one point [8]. Those methods are not easy to use for the models are too complex and require much calculating. Moreover, wind direction hasn’t been taken into consideration in those methods.

In this paper, wind speed and direction along the high speed train railway line was predicted with the help of Kalman filter. And warning system to adjust train speed was built mainly based on integrated risk coefficient, which was defined as the function of not only wind speed and direction, but also train speed and location.

II. METHODS

A. Data Data collected by wind gauge set along the railway line are

recorded every minute. In this paper, only time, instantaneous wind speed and wind direction are needed. Wind direction is accurate into 5 degree, which means 72 kinds of direction will be recorded. Wind speed is set to be the maximum value of every 3 minutes, while wind direction is the average value.

B. Model Wind speed (Yi as the wind speed at time i) is assumed to

be added with definite value (Xi) and random variable (Vi), which obeys the Gauss distribution. Data collected by wind gauge are processed with Least Squares Fitting. Then we use Kalman filter to predict the optimal wind speed recursively in the following steps [9].

1. Basic assumption

Xi/i-1= Xi-1/i-1 （1）

Vi/i-1=Vi-1i-1+0.1 （II）

where Xi/i-1and Vi/i-1 are values at time i calculated based on values at time i-1.

2. Calculating of Kalman filter gain

Ki= Vi/i-1/( Vi/i-1+1) （2）

where Ki is Kalman filter gain.

3. Calculating of definite value

Xi/i=Xi/i-1+(Ki·(Yi-Xi/i-1)) （3） * Corresponding author Tsinghua University Self Research Program 2009THZ06056 Ministry of Science and Technology of the People´s Republic of China

under Grant No. 2011BAK07B02

978-1-4673-0875-5/12/$31.00 ©2012 IEEE

4. Recursion

Vi/i=(1-Ki)·Vi/i-1 （4）

Definite value and random value are predicted with the values of former time step using Kalman filter, and the combination of the two parameters is the predicted wind speed.

C. Revised Model In order to enhance the system reliability, measured data

have to be revised. The error of measurement and its distribution are resulted from the comparison of measured wind speed and predicted value. Error distribution can be used to calculate standard deviation N and the probability P that measured wind speed is larger than prediction. The revised predicted wind speed is as follow:

Vrevised=V+P·N （5）

III. FORCAST AND EARLY WARNING

A. Prediction of Wind Speed The regular measuring range of anemograph is 30 m/s,

which is amount to Forces 11 in Beaufort scale, and is rare on the land. In this paper, wind speed is assumed to be 10 m/s to 12 m/s, in other words, Forces 5 to 6. Wind at this level ranges between Fresh breeze and Strong breeze, which is very common along the railway line, and may threaten the high speed train.

Measured wind speed is simulated with computer in this paper. We assume that wind speed won’t experience a sudden change. The simulated wind speed is divided into three parts, which are called definite value, regularly random value and irregularly random value. Definite value is permanent and won’t change in a long period, and the regularly random value is supposed to accord with Gauss distribution. This assumption makes the wind speed range in specific regulation. The irregularly random value is simulated with the uniform distribution, which can be described as the perturbation of wind. In this part, definite value is set to be 10 m/s, and regular and irregular random value are all set to range from 0 to 1 m/s. The generated wind speed varies with time is shown in Fig.1.

FIGURE 1. SIMULATED WIND SPEED RANGING FROM 10 TO 12 M/S

B. Forcast and Analysis Predicted wind speed calculated only with Kalman filter is

not precise. In this paper, wind speed and wind direction are

simulated using a random function, so revised model can be simplified. Probability P in formula 6 can be replaced with the probability that simulated wind speed exceeds predicted wind speed, and standard deviation N can be substituted with expectation of the exceeded value. The revised wind speed is shown as Fig.2.

The whole system is more reliable after revision, however, in several points, simulated value is still larger than prediction. To ensure the safety of high speed train, we add another 0.3 m/s to the revised result. This can benefit to the train in both safety and efficiency.

FIGURE 2. REVISED WIND SPEED AND PREDICTED VALUE

FIGURE 3. WIND SPEED AND THE CRITICAL ANGLE [10]

FIGURE 4. SIMULATED WIND DIRECTION AND PREDICTED VALUE

C. Prediction of Wind Direction Wind direction is predicted in the same method as wind

speed. In this paper, wind direction is supposed to be divided into two parts. Definite value is set to be 100 degree, which is added to a random value ranges from 0 to 50 degree. All values can be divided by 5 with no remainder. The dangerous intersection angle between train and wind is approximate to 80 degree, as shown in Fig.3.

The correlation of wind speed and critical angle at different train speed, as 70 km/h, 100 km/h and 120 km/h, is presented by Hibino Y [10]. As to high speed train, the average train speed is usually no less than 200 km/h, sometimes even reaches 300 km/h. Correlation of wind speed and critical angle at that speed needs more experiments and aerodynamics analysis, which is not involved in this paper. This correlation function is only assumed to be exist, and the simulation of wind direction is shown in Fig.4.

D. Integrated Risk Coefficient Strong wind warning system is designed to adjust the

velocity of high speed train to ensure both safety and efficiency based on the prediction of wind speed and wind direction along the railway line. When the prediction is completed, the system output three parameters as time, wind speed and wind direction. To decide the optimal train speed, the following questions should be answered. 1) What’s the distance between the high speed train and the location of strong wind? 2) Will the strong wind last for a long time or just an infinitesimal disturbance? 3) How will the strong wind affect the high speed train? 4) Is it safe for the train to pass the location at the present speed or what is the critical safe speed of the train? All those questions are related to several factors, therefore, integrated risk coefficient have to be defined to describe condition of both high speed train and strong wind.

In Fig.3, points above one specific curve mean dangerous, while points beneath the curve are safe. J is a parameter defined as follow.

J=φ0*V0-φ0*f(φ0, U) （7）

where,φ0 is the intersection angle of wind direction and train speed, degree; V0 is the measured wind speed, m/s. The correlation function to describe curve in Fig.3 is defined as V=f(φ, U), whereφ is the intersection angle and U means train speed. V=f(φ, U) is therefore the critical wind speed.

If J is positive, the train is under dangerous condition. And the greater the value J is, the more dangerous the train is. In order to describe the train’s safety condition precisely, we define another parameter D, which is meaningful only when positive.

2

10 0 0 1* * ( , )D V V f U d

φ

φφ φ φ φ= − − ∫ （8）

Because the train needs time to change its velocity, distance between train and dangerous location must be considered.

Integrated risk coefficient is defined to describe the danger per minute.

S=D*Utrain/L*A （9）

where Utrain is the present train speed, km/h; L is the distance, km; and A is a constant, which equals 1/60.

The integrated risk coefficient is a combination of wind speed, wind direction, train speed and distance from wind to train, and warning system to adjust train speed can be built based on this coefficient

IV. CONCLUSION In this paper, wind speed and direction along the high speed

train railway line was predicted with the help of Kalman filter. And warning system to adjust train speed was built mainly based on integrated risk coefficient, which was defined as the function of not only wind speed and direction, but also train speed and location.

The system needs only anemographs along the railway line, and doesn’t need complex models and expensive equipment, therefore it is much easier to apply. The prediction using Kalman filter is accurate and fast, which makes the high speed train more efficient, and much safer.

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