1

A Machine Learning Approach to Predict Future Power Demand in Real-time for a Battery Operated Car

Somnath Pradhan, Joydeb Roychaudhury Embedded Systems Laboratory

CSIR-Central Mechanical Engineering Research Institute Durgapur, West Bengal, India

som9543@gmail.com, jrc@cmeri.rest.in Abstract—for any battery-employed system, it is essential for the battery management system to correctly predict the present operational condition of the battery. The fail safe operation of a safety critical system like battery operated car or any other lifesaving systems are heavily depend upon earlier prediction of battery life. SOC or State-of-Charge estimation is one of the well-known method to predict the runtime of a battery. Various approaches are adapted by automotive society to correctly predict the runtime or the SOC of a battery like Kalman filter, UKF and many others. This paper proposes a new approach, the method of regression to predict the future power demand of a car while running on the road. The aim is to identify that, the battery will support the run of the car in next 10 seconds or not. The runtime prediction of a battery, not only depends upon the starting SOC but also depends upon other factors like battery health and road profile imposed. To overcome this type of difficulties the self-corrective regression model is proposed and implemented. Experiments performed on different road profiles, validate demanded power by the car in up-coming 10 seconds of its run. The major problem of SoC estimation is to determine initial SoC of a battery. Extensive experiments needed to calculate the initial SoC and which may also vary with the life of the battery. The novelty of this work shows, the method to predict the future power demand by updating its model parameters and without any initial SoC calculation. Model parameters are updated by the introducing new current and voltage sample in the model.

Keywords- Data Driven Prognostic Model; End of Discharge(EoD), State Of Charge (SOC)

I.INTRODUCTION

In the field of prognostic and BHM, data-driven models are very popular due to their intuitive nature and very easy implementation in real-time systems. Regression is one such example of data-driven model. With the development of these new algorithms the field of prognostic under battery management system is growing very rapidly. This paper summarizes the development process of a data-driven approach for a dynamic load discharge scenario, like a battery operated car moving on haphazard road profiles. In our work, Li- Ion battery was used to run the prototype car on road. The development of polynomial

regression model and its outcome to predict the power demand in next 10 seconds are also demonstrated in this paper. The lessons learned from different difficulties we faced to validate the model with real-time data and the pitfalls to develop the model are also discussed in this paper. With the extensive use of Li-Ion batteries in automotive, the development of prognostic health management system for those batteries become new field of research in modern scientific communities. Use of Kalman filters [1], Adaptive Kalman Filter [2],Extended Kalman Filters [3], Artificial Neural Networks [4] are very popular methods in the field of prediction of battery SoC and SoH. These methods provide very accurate prediction but the computational overhead is also very high for a standalone controller to compute. The internal computer system of a car may become unstable due to large calculation overhead in real-time operation. On the other hand Current Integration Methods like Coulomb Counting, Enhanced Coulomb Counting [5] provide very less mathematical computation, however accuracy of prediction is not perfect. In the field of SoC estimation use of lookup tables for open circuit voltage (OCV) to SoC mapping is also very popular [6]. This method needs extensive testing and data collection to make proper data mapping in lookup table. Compared to the above discussed method, data driven and model based approaches [7][8] are more popular in this regard. This paper proposes the implementation of data driven self-corrective and predictive model using polynomial regression method. To estimate the runtime of battery, this model balances the computational overhead and the accuracy. In the initial stage data-driven algorithms like polynomial regression needs large number to training dataset, but allows very fast, easy and computationally inexpensive implementation. This algorithm requires continuous changes of its initial hypothesis with the varying complexity of the problem like dynamic loading discharge profile of a battery in a battery operated car.

The algorithms discussed above provide good result on the similar data set or where the model is trained. The scope of this paper is not only limited to the development of data driven self-corrective and predictive model but it also focuses on development of data acquisition system and implementation of it on a prototype car.

II. DEVELOPMENTOF DATAACQUISITION SYSTEMS Figure – 1, represent the block diagram of the Car control unit. The car is powered with 7.4V, 4.4AH Li-Ion battery. Current Sensor is used to collect the current drawn by the motors and

2014 International Conference on the IMpact of E-Technology on US (IMPETUS)

978-9332-9026-40/14/$31.00 ©2014IEEE 49

2

the battery voltage is continuously sampled by the internal ADC of ATMEGA2560 in every one seconds.

The motors are connected with processor via 12V, 16A motor drivers and controlled using PWM. Figure-2, shows the schematic representation of the motor driver connection. Opto-interrupter connected above the motor shafts is used to measure the RPM of motor. Collected voltage and current samples are used to calculate the power delivered by the battery to run the car. Information related to velocity-acceleration is very useful to find out the energy requirement by the car to achieve a final velocity.

A. Calibration Of Current Sensor :- The current sensor is calibrated with standard calibrated multimeter. To calibrate the sensor, data is captured and

compared with the multimeter. Table – 1 shows the comparison between sensor data and the multimeter reading and difference between them. For the next part, regression

method is used to find the relation between error and measured sensor data and experimentally it is found that the relation is linear and can be expressed by linear equation like y mx c= + …………………………… ….. ………(1)

In this equation ‘y’ is the measured error and ‘x’ is the collected current data sample form the sensor.

Algorithm-1, describes the Pseudo Code for

calibration and figure-3, shows the regression curve for sensor calibration.

B. Calculation of Motor Speed :- Motor speed or the RPM of wheel is sampled by opto-interrupted with a slotted disc connected on the motor shaft. In our experiment 60 slotted disc is used. With one full rotation (3600) of motor the connected opto-interrupt generates 60 pulses which is fed in the controller so that in every high rise of the pulse, it can interrupt the controller. One scheduling algorithm was used to monitor the total number of interrupt (Tp).

RPM = (Tp / 60) * 60. =Tp. (2)

From the above equation -2, it can be observed that the RMP is same as the total number of pulse generated in one seconds.

Fig – 3: Plot of Error And Current Sensor Output

Fig – 2: Connection of Motor Driver.

Fig : 1 Bolck Digram ofData Acquisition System

50

3

Algorithm 1: Pseudo Code for Current Sensor Calibration

loop

INITILIZE amp = 0 //reading current sample for i=0 to 100do

amp = amp + readSen();// reading sensor //data and adding with past sample

end for amp = amp / i; // taking average error = 9 * amp - 0.6;// Y = MX+C

// Y is error, values of M = 9and C = -0.6 calculated from experiment amp = amp + error; end loop

Sl. No. M C 1 9 -0.6

The RPM is converted in Radian per seconds (q) and finally liner velocity (Vl) is generating by multiplying it with the radius (r) of the wheel.

(i) ((2* * Rpm(i)) / 60q π= (3)

(i) (i)*rlV q= (4)

2l

1(i) * *V (i)2kE M= (5)

III. PROGNOSTIC FRAMEWORKAND REGRESSION USING CURVE FITTING

In this section the approach to predict the future power demand is presented. Prognosis means something to predict. Regression can be defined as a process which estimates the relation between variables. The experimental results produces set of data points (x1,y1) …..(xN,yN).Where y is the dependent parameter(Response Variable) and x is the independent one (Explanatory Variables). For example temperature is varying with time or in a close circuit one battery power is getting dissipated in a variable load profile scenario. The dependent parameter depends upon the independent parameters with some mathematical function like-

(x)y f= (6)

Curve fitting method is one of the very popular methods to

establish the mathematical relation between the (response and explanatory) variables. To define a best relation, a class of acceptable formulas are chosen and then the best coefficients are calculated so that the error becomes very less. The function depends upon the hidden mathematical model and the model depends upon the collected data or the physical situation. It may be a linear dependency like

y (x) Axf B= = + (7)

Or nonlinear

( ) 2 y f x Ax Bx C= = + + (8)

A successful polynomial interpolation depends upon the accuracy of dataset, up-to a certain digit. Most of the time datasets contains error because of the sensors or data collection

systems. Say, for ‘N’ number of collected data set of xk and yk

the exact value of the function can be realized as

k k(x ) y ekf = + , where ek is measurement error or residuals.

k .k(x ) yke f= − (9)

A best fitting line can be plotted by selecting a proper order of the polynomial, for which sum of square of residuals are minimum. This can be done by an iterative algorithm which plots the curve in different orders and finds the best fit.

Finding Least Error Polynomial And Regression:-

Regression is a statistical method which estimates the relation between response variable (dependent) and input and explanatory variables (Independent) on observational database.

Sl no

Measured Data(mA)

Sensor Data(mA)

Difference(ma)

1 0.7 0.13 0.57 2 0.8 0.14 0.66 3 0.9 0.15 0.75 4 1 0.16 0.84 5 1.1 0.17 0.93 6 1.2 0.18 1.02 7 1.3 0.19 1.11 8 1.4 0.2 1.2 9 1.5 0.21 1.29

10 1.6 0.22 1.38 11 1.7 0.23 1.47 12 1.8 0.24 1.56 13 1.9 0.25 1.65 14 2 0.26 1.74 15 2.1 0.27 1.83 16 2.2 0.28 1.92 17 2.3 0.29 2.01 18 2.4 0.3 2.1 19 2.5 0.31 2.19 20 2.6 0.32 2.28 21 2.7 0.33 2.37 22 2.8 0.34 2.46 23 2.9 0.35 2.55 24 3 0.36 2.64

Table:1 Collected Current Sample for Sensor Calibration

Table:2 coefficients of stright line for current sensor calibration

51

4

The relation is such that, the output can be predicted based on the observed input dataset. Regression analysis helps to understand the behavior of dependent variable when there is some change in one of the independent variable, while other independent variables are fixed.

The method of Polynomial regression provides polynomial to describe the relation between inputs and its corresponding output. It is one of the best methods which balance the accuracy and efficiency. The accuracy increases up-to a certain point, with the increased order of fitted polynomial. But the computational time and memory used also increase. Avery high degree of polynomial may make the Polynomial Regression numerically unstable, whereas very low order of polynomial may not describe the complexities of the function being learned. The main objective of polynomial fitting is to find a best polynomial of allowable degree which interpolates

the dataset of N points, say k k 1{(x , y )}NK =

.Equation-8showsan

example of cubic polynomial. A, B and C are the coefficient of the polynomial. For least-square fitting the optimum values of A, B and C needs to be identified.

Starting with 1st degree polynomial, to find the best fitted equation is given as

20 1 2 ..... n

ny a a x a x a x= + + + + (10)

For the above equation residuals can be calculated as

20

21 2

1

..... )( ( )nii i n i

k

i

a a x a x a xE y=

+ + + += − (11)

The Coefficient of the polynomial can be determined by the solving the matrix given below.

1 01 1

2 12 2

11

1

n

n

nk kk k

y ax xy ax x

y ax x

= (12)

In the matrix notation the above equation is given by

Y XA= (13)

To solve the equation and find the coefficient matrix A both side of equation 17 is multiplied with the transpose of X.

1( ) [9]

T T

T T

X Y X XA

A XX X Y−

==

(14)

The coefficient Matrix is generated by solving equation no 14.

Algorithm2: Pseudo Code for construction of polynomial with fixed degree

Given: XT[n] and YT[n] //Training Dataset

A[], B[] – uses to store temporary calculation values

A[]- coefficient Matrix

Degree<-m//degree of polynomial //Degree of Polynomial will change in auto regression model // Starting win Degree – 1(Linear Plot) If length(XT[n])==length YT[n]do

loop INITILIZE f (x) //fitting algorithm

n = Find The Length of Dataset. F = zeros(n, Degree + 1)

for i=0 to Degree do // fill the columns of F with the power of XT

F[:, i]=XT[i]^(i) // Ref Equation 13 End

FTtans[] = Transpose of F[]

B[]=FTtans[] *F[];

B[] = FTtans[]* Y[];

A[] = B[] / C[];

end loop

end if

A. Updating of Model Parameters with Sensor Data:- Starting with de-noising, final training dataset was

created by removing some incomplete and corrupted runs. This training dataset was collected over time by running the car on different haphazard road profile. The noisy and de- noised training data is shown in figure -8 and 9 respectively.

In the next part of the experiment, our focus is on, learning this dataset based on Polynomial Regression and update the model with new data sample to predict power demand.

The Regression Model takes the pair of inputs Xi

(Time) and Yi (Power demanded by the car) and generates the coefficients for best-fitted polynomial. The operation of developed self-correcting model is explained in figure - 6. The model which automatically changes its parameter to correct its

Figure 6 : Sefl Corrective Model

52

5

output is a self-corrective model.

To generate the best fitted Polynomial, the algorithm starts plotting the curve on the dataset, with 1st degree polynomial. It starts with a linear plot and continuously monitors the residuals converging to a minimum predefined value or not. Next this process repeats itself with an incremented degree and continues till the convergence point reached.

The operation of the developed recursive algorithm is explained with the flowchart in figure-7 and algorithm -2.

IV. EXPERIMENTAL RESULTS The heart of the entire experiment is to develop a data driven model to predict the power need of a battery operated car in every 10 seconds interval. Precise prediction result depends on the correctness of the collected data to develop the model.

Better the data acquisition system, more robust the model. The training dataset was obtained after running the car on an irregular road profile. Dataset required to validate this model, was collected by running the car on the same and on a different road profile. Raw Training dataset is shown in figure 8. It can be observed from the figure that there is significant noise in data, which makes it difficult to learn the pattern of data.

To overcome this problem, the data was filtered with

the help of a developed 21 point- moving average filter. After filtration, the dynamics of the data pattern can be identified and shown in figure -9.

Next part of the experiment is to fit the data in a

nonlinear regression model based on the developed algorithm. The data was normalized for the training in order to improve the performance of regression. This normalization was done by subtracting the sample mean and dividing it with its standard deviation.

The iterative algorithm tries to fit the data with a polynomial such that the residuals between the actual power demand and the predicted Power demand is very less, to a predefined allowable error. The algorithm starts to fit the data with linear plot and increases the order of fitting till the convergence point reached.

Fig – 10: Figure Shows The Best Fitted Polynomila on The collected Data Sample

Fig – 9: Collected Data Sample filtered with 21 point moving average filter

Fig – 8: Collected Data Sample on road to develop the model

Figure 7 : Flow Chart For Best Polynomial Fitting Algorithm

Fitted Curve

Dataset

53

6

The green curve in figure 10, tracking the training dataset in black dots, is the best fitted polynomial. The convergence of residuals is shown in figure 11 with coefficients of polynomial in table 3.

2 180 1 2 18.....y a a x a x a x= + + + + …………….. (15)

The polynomial is of 18th order and given by equation -18.In this equation ‘y’ is the predicted output and a0 – a18 are coefficients.

In practice 18 degree polynomial is not a good choice, but from table -3 it can be observed that the effects of high order polynomials are very less. The coefficients shows best result up-

to four degree (a0 to a4). Coefficients a5 to a18 are of order of 10-5 to 10-36. So the effect of these coefficients can be neglected. The high order coefficients are generated as the point of convergence was very less below 0.1, shown in figure - 11.Regression method balances the accuracy and efficiency by adjusting the proper order of the polynomial, can be concluded form the observed data. For a real-time operation, the degree of polynomial can be kept low to avoid very high computational overhead which does not affect the accuracy of the model.

After generation of the model, next job is to test its effectiveness by validating it with test dataset. This dataset is collected by running the car on various road profiles.

The old data in the model is replaced by the new data and the parameters of the model are updated accordingly. And the power demand in next 10 second is predicted by the model, after updating its parameters.

Experiments for the validation of the model are done on two types of road profile, one where the car is trained and in untrained surface.

Order

Coeff. Order

Coeff. Order

Coeff.

a18 3.9e-36 a11

-1.071e-16 a4 0.000474

a17 -1.073e-32 a10

1.67e-14 a3 -0.00702

a16 1.337e-29 a9

-1.99e-12 a2 0.05922 a15

-1.016e-26 a8 1.79e-10 a1 0.05922

a14 5.19e-24 a7

-1.19e-08 a0 6.46 a13

-1.91e-21 a6 5.86e-07

a12 5.2e-19 a5

-2.02e-05

Fig – 11: Convergence of residuals for best ffitted curve

Table:3 coefficients of best fitted polynomail

Fig – 13: Updatation Of Model with New Data Sample

Fig – 14: Comparison between actual power demand by car and predected power demand

Fig – 12: Time vs Real Time Sample for validation

Predicted power demand Actual power demand

Fitted Curve

Dataset

54

7

Fig – 17: Fitted Curve On the New Dataset to Track its Dynamics

At the begening of the the experimnent, speed of the car was kept constant. But it is observed that the car was producing dynamic turque and velocity as the road profile was random. Power Consumed by the car, while running on the uneven road surface (shown in figure – 9 ), is dyanamic due this dynamic road profile.

First dataset for model-validation is shown in figure 12.

The dynamics of this dataset is somewhat similar to the dynamics of training dataset, as both the datasets are collected on the similar road profile.

Updated model after fusing all data-set is shown is

figure – 13. This model provides predicted power demanded by the car. Comparison between actual power demand (green line) and predicted power demand (red line) is presented in figure 14.The percentage of average error between actual power demanded by the car while running on the road and predicted power demand varies between 1.5 - 5.5% is shown in figure –15.

The average errors are very high (nearly 50%) when 2nd dataset is used for validation, reflected in figure 20. Pattern of this dataset, updated prediction model and comparison between actual and predicted power demands are presented in figure 16, 17 and 18 respectively.

V. CONCLUSION The algorithm has been found to be working efficiently

if the dynamics of road is known or the model is trained with

Fig – 19: Error Between Actual And Predicted Power Demand

Fig – 18: Comparison Between Actual Data And Predicted Data

Fig – 16: Data with different synamics with training set used to validate the model

Fig – 15: Percentage of Average Error

Predicted power demand Actual power demand

Average Error

Error Fitted Curve

Dataset

Average Error

Error

55

8

very good training dataset. In the figure – 18, maximum error lies in the range of 0-30 percent. But the average error curve increases to 50% due to few data points with very high amplitude.

In the figure -20 the picture of prototype car is shown. This car is used to collect the data on the various road profiles and used for validation.

- As seen in figure 8 and 9, the collected data from real

world are always noisy and without suitable de-noising scheme it is very difficult to learn meaningful relationships from this data. In case of random loading profile like the battery operated car running on haphazard road profiles, the effect of noise may be non-linear which is very difficult to identify and filter-out. A very good filter may also destroy the correct data pattern. In the experiment 21- point moving average filter is used to de- noise the dataset and found to be efficient. Designing of a robust adaptive filter is one of the open challenges for this kind of experiment.

- ARMA model can be used to predict the more accurately as the errors are also consider in this model.

- In future scope more experiments can be done on different terrains and different velocities.

VI. REFERENCES [1] "Probabilistic duration of power estimation for Nickel- metal- hydride

(NiMH) battery under constant load using Kalman filter on chip," in International Conference onAdvances in Engineering, Science and Management (ICAESM), 2012, pp. 641-646, 30-31 March 2012.

[2] Dai Haifeng , Wei Xuezhe, Sun Zechang ,” State and Parameter Estimation of a HEV Li-ion Battery Pack Using Adaptive Kalman Filter with a New SOC-OCV Concept”International Conference onMeasuring Technology and Mechatronics Automation, 2009. ICMTMA '09.

[3] Chen, Xue-Guang; Xia, Fangzhen; Xiang, Jianfeng "Research on SOC hybrid estimation algorithm of power battery based on EKF”, Power and Energy Engineering Conference (APPEEC), 2011 Asia-Pacific,

[4] Cai, Cheng-Hui H. , Du, Dong; Liu, Zhi-Yu; Ge, Jingtian “State-of-charge (SOC) estimation of high power Ni-MH rechargeable battery with artificial neural network”, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02.

[5] Kong Soon Ng, Chin-Sien Moo, Yi-Ping Chen, Yao-Ching Hsieh,“Enhanced coulomb counting method for estimating state-of-chargeand state-of-health of lithium-ion batteries”, Journl of Applied Energy, September 2009.

[6] Lee, S.J. Seoul Nat. Univ., Seoul Kim, J.H.; Lee, J.M.; Cho, B.H. “The State and Parameter Estimation of an Li-Ion Battery Using a New OCV-SOC Concept” Power Electronics Specialists Conference, 2007. PESC 2007.

[7] Wint Thida Zaw, Thinn Thu Naing, “Modeling of Rainfall Prediction over Myanmar Using Polynomial Regression,” 2009 International Conference on Computing Engineering and Technology.

[8] Eugene Kim, Jinkyu Lee, and Kang G. Shin. 2013. Real-time prediction of battery power requirements for electric vehicles. In Proceedings of the ACM/IEEE 4th International Conference on Cyber-Physical Systems (ICCPS '13). ACM, New York, NY, USA, 11-20.

[9] Douglas M. Bates and Donald G. Watts, “Nonlinear Regression Analysis and Its Applic ations”- JOHN WILEY & SONS, INC. Singapore - 2003.

Fig – 20: Prototype Car On Road Profile

56