Modeling Automotive Battery Diagnostics

Mar 1, 2008 12:00 PM
By Neeta Khare and Rekha Govil, Apaji Institute of Mathematics and Applied Computer Technology, Banasthali University

ANN Modeling

The design of an ANN and its training are done using the Neural Network Toolbox of MATLAB version 6.0. The back propagation learning algorithm in a fully connected multilayer architecture of neurons was employed for supervised learning in ANN.^[5] With standard steepest descent, the learning rate was held constant throughout the training.

The performance of the algorithm is very sensitive to the proper setting of the learning rate. If the learning rate is too high, the algorithm will oscillate and become unstable, while if too low, the algorithm takes longer to converge.^[6] The activation functions used are log sigmoid in the hidden layer and purelin at the output layer. A block diagram of the ANN model employed in the present study is shown in Fig. 3.

This work aimed to obtain a generalized ANN model of battery behavior. Therefore, simulation was first performed on training the ANN with separate sets of data for slow discharge and real cranking functions of a car battery of different ages.^[3] (This data appears in a figure in the online version of this article.) Then the same ANN was trained with the combined data of slow discharge and real cranking at all ages at different environmental temperatures.

The loss in accuracy due to generalization was found to be not more than 0.4%. Here we have seen that there is no loss of accuracy when training is done with mixed data of various charged states, but it does take a longer time to learn to converge. The loss of accuracy further increases if training is performed with data on batteries of various ages as shown in Table 1.

After training the ANN with an input-output dataset, it needs to be tested with given data. Fig. 4 shows the results of both training and testing when the data of batteries of different ages, different SoCs and different operating temperatures is employed.

Fuzzy logic was employed for the purpose of transforming the ANN output SG to the target output (i.e., battery SoC).^[7] The complete process is shown in Fig. 5.

In this module all three parameters — input parameters SG and temperature, and output parameter percentage of SoC — are taken to be fuzzy. While the fuzzy membership for the temperature and percentage of SoC parameters are defined with five linguistic variables, the SG parameter is represented by seven fuzzy states. The fuzzy states for each of the three fuzzy variables are given here:

• Temperature (input variable) — very low, low, medium, high and very high

• SG (input variable) — very very low, very low, low, medium, high, very high and very very high

• Percentage of SoC (output variable) — flat, less than half, half, greater than half and full.

For temperature and SG, the membership function is chosen to be Gaussian with extreme states open. For percentage of SoC, the fuzzy membership function is taken to be bell shaped.

If-then rules are defined to specify the relationship between the input and the output. For each input, some rules are fired. For each rule being fired, the degree of membership of the percentage of SoC is implied. Then the membership value of all the outputs is aggregated to produce the final output.

The fuzzy rule base^[8] employed for the case under study is given in Table 2. Implementation of fuzzy logic is done using MATLAB's Fuzzy Logic Toolbox. The inputs and outputs are designated in the Fuzzy Inference System (FIS) editor window in the Fuzzy Logic Toolbox.

The fuzzy rules defined in Table 2 are verified with the observed data. For different sets of data on SG and temperatures, the percentage of SoC is thus computed. A typical result of fuzzy inference is demonstrated in Fig. 6, where temperature equals 45°C (very high), SG equals 1.178 (medium) and the corresponding percentage of SoC is 50% (half charged).