Battery SOH prediction based on adaptive neural network fuzzy inference system

Lead-acid batteries are complex electrochemical systems. Their health status (SOH) is affected by many factors, such as electrolyte ion conductivity, electrolyte concentration, battery internal resistance, self-discharge characteristics, and ambient temperature. The aging failure mechanism is complex, and it is difficult to establish a mathematical model to accurately predict the battery's SOH [1].

Fuzzy neural network technology is an effective method for complex system testing. It can be based on incomplete or incorrect knowledge of the object being tested. A single neural network is just a black box system and cannot provide heuristic knowledge for battery SOH prediction. A single fuzzy prediction can simply implement heuristic knowledge learning, but cannot obtain accurate prediction results. The combination of the two becomes the adaptive neural network fuzzy inference system ANFIS (Adaptive Neural Fuzzy Inference System). Using this system to predict battery SOH can have the advantages of both and achieve accurate prediction [2].

1 Adaptive neural network fuzzy inference system A

simple adaptive fuzzy inference system has 2 inputs and 1 output. For the first-order Sugeno fuzzy model, its general rule consists of the following two if-then judgment branches [3-4]:

Rule 1: If (x is A1) and (y is B1) then (z1=p1x+q1x+r1)
Rule 2: If (x is A2) and (y is B2) then (z2=p2x+q2x+r2)

Where x and y are input values, Ai and Bi are fuzzy sets, and zi is the output value in the domain under the fuzzy rule. The remaining parameters are design parameters determined in the specific model. The system structure of the model is shown in Figure 1.

In the five-layer structure shown in Figure 1, the first layer is all adaptive nodes, and the output of each node is related to the membership function of the input vector. The second layer is a fixed node, which only acts as a multiplier to weightedly multiply the membership function of the input node. The third layer is also a fixed node, which regularizes the output of the previous layer. The fourth layer is an adaptive node, which multiplies the output of the third layer with a first-order polynomial to obtain the output. The fifth layer has only one output node, which is used to weighted average the output of the previous layer to obtain the final prediction result. The relevant weight parameters need to be determined in the second and fourth layers. Once the optimal parameters are determined, the reverse correction stage begins. In this stage, the preset parameter values ​​are dynamically adjusted optimally, and the output value of the neural model system is calculated during the forward propagation process. ANFIS is a universal approximator that can approximate any nonlinear function without limiting the number of fuzzy inferences [5].

2 Battery SOH modeling

2.1 Model input selection

The ANFIS model has the problem of input selection and input space division. The prediction process can be regarded as a mapping from input space to output space. To predict SOH based on discharge characteristics, it is necessary to select sample data that can fully reflect the battery SOH as input and determine the membership function for each input.

For a specific set of batteries, the battery specifications, operating temperature, self-discharge characteristics and electrolyte concentration are roughly constant during a short-term discharge process and can be excluded as input. The internal resistance of the battery is closely related to SOH, but the internal resistance of the battery is not only affected by the degree of degradation, but also by other factors. Therefore, it is not suitable to be selected as an input. The difference between discharge voltages can reflect SOH, but the difference is not a constant and the discharge voltage depends on the discharge current. Therefore, it is not suitable to be used as an input. Summarizing the comparative analysis, the output energy and discharge depth can be selected as the input of the model [6].

2.2 Modeling of battery SOH prediction model

In order to make the output energy of the model not affected by different individuals and models, the output energy is first normalized. Taking the one with the highest output energy as a reference, the ratio of the output energy of each battery to the highest output energy is the normalized data sample. The battery SOH prediction model is modeled to obtain the Sugeno fuzzy inference system model, as shown in Figure 2.

After determining the input variables, the first-order Sugeno fuzzy system model is constructed with the battery SOH as the output, as shown in Figure 2. Four membership functions are used for each input for training, and the data is tested after training to verify the trained model.

3 MATLAB simulation of battery SOH model

3.1 Data selection

Taking the lead-acid battery of an armored vehicle as an example, in the actual test process, due to the limitations of discharge depth and discharge termination voltage, the calculation of the battery SOH generally uses short-term partial discharge data with a discharge depth of 5%~20%.

During the use of the lead-acid battery of an armored vehicle, as the discharge proceeds, the terminal voltage decreases and the density decreases, but in order to prevent the plate from being sulfided and causing damage to the battery, the density cannot be lower than 1.11 g/cm3 for a long time. Therefore, the output energy of the lead-acid battery of an armored vehicle must be guaranteed to be within a certain range. This model uses short-term measurement data with an output energy range of 80%~100% as the input of the ANFIS model.

The actual capacity of the battery can be obtained by the verification discharge test method based on the capacity calculation formula. This paper tests a group of lead-acid batteries of a certain model of armored vehicles, and selects 100 sets of data at discharge depths of 5%, 10%, and 20% to simulate the ANFIS model. The dual inputs of the ANFIS model are x (discharge depth) and y (output energy), and the single output is f (predicted capacity).

3.2 MATLAB simulation of the model

The software used in this experiment is MATLAB 7.8.0 (R2009a), and the simulation environment is the anfisedit tool in toolboxes. The MATLAB simulation steps of the battery SOH are as follows [7]:

(1) Enter the data [xyf] in the main window of the software.

(2) Call the anfisedit tool to load the actual test data [xyf], use 100 sets of data as training data, and use the even-numbered data in the 100 sets of data as test data.

(3) Generate the initial FIS. The structure is shown in Figure 3. The fuzzy system has two input quantities and one output quantity. There are four fuzzy subsets covering each input quantity. Each rule has four outputs, for a total of 16. Finally, all fuzzy subsets are clarified into one output quantity.

(4) Determine the initial membership function of the input. Each input has four membership functions, and the bell-shaped function (GbellMF) [8] is used. First, the parameters of the two initial bell-shaped membership functions are set as R1 [0.025 2 0.05], R2 [0.025 2 0.1], R3 [0.025 2 0.15], R4 [0.025 2 0.2] and E1 [0.04167 2 0.75], E2 [0.0417 2 0.833], E3 [0.0417 2 0.917], E4 [0.04167 2 1], as shown in Figure 4.

(5) Training the initial FIS. The model was trained with training sample data. After 150 trainings, the root mean square error reached 0.032 655, and a good prediction effect was obtained. It can be seen that the ANFIS model has a strong nonlinear mapping ability.

(6) The variation of the input membership function after training. The membership functions of the inputs x and y were improved after training, as shown in Figure 5.

(7) After the system is trained with data, the input and output can be viewed and the battery SOH can be predicted through the fuzzy rule observation window shown in Figure 6.

4 Model verification and data analysis

Using the fuzzy rule observation window shown in Figure 6, the discharge output energy (y) of the battery is measured at different discharge depths (x) of 5%, 10%, and 20%, and the predicted capacity (f) is obtained according to the ANFIS fuzzy rule model obtained by simulation. The actual capacity is obtained by measuring the verification discharge method. The model is verified by comparing the predicted capacity with the measured capacity. The predicted data and measured data of the ANFIS model at 5%, 10%, and 20% discharge depths are shown in Table 1, Table 2, and Table 3, respectively.

Through the degradation degree model prediction in Tables 1 to 3, it is found that at 5% discharge depth, the root mean square error between the predicted value and the measured value is 2.95; at 10% discharge depth, the root mean square error is 2.4; at 20% discharge depth, the root mean square error is 1.614. It can be seen that the accuracy of the model prediction increases with the increase of discharge depth, and it has good applicability for the prediction of SOH of lead-acid batteries for armored vehicles.

In view of the complex causes of battery degradation, an adaptive neural network fuzzy inference system is used to model and predict the battery SOH. The verification of measured data shows that the system has a high accuracy in predicting the battery SOH, and the prediction accuracy gradually improves with the increase of discharge depth.

References
[1] Xue Jianjun. Prediction of Ni-MH battery capacity by the artificial neural network method [J]. Power Sources, 2003, 27 (3): 305-307.
[2] PASSINO KM, YURKOVICH S. Fuzzy Control [M]. Beijing: Tsinghua University Press, 2001: 238-241.
[3] Li Binbin, Chen Tiejun. Inverted pendulum control based on adaptive neural network fuzzy reasoning [J]. Microcomputer Information, 2007, 22 (8): 27-28.
[4] Chen Jiguang, Zhu Lingde, Sun Litang. Deformation data simulation calculation based on adaptive neural network fuzzy reasoning [J]. Computer Engineering and Applications, 2006, 42 (16): 219-221.
[5] Ma Wei. Characteristic modeling and state of charge estimation of lead-acid batteries for electric vehicles [D]. Xi'an: Chang'an University, 2009: 8-10.
[6] Jiang Hai. Research and design of intelligent online monitoring system for batteries [D]. Harbin: Harbin University of Science and Technology, 2007: 22-28.
[7] SINGH P, REISNER D E. Fuzzy logic-based state-of health determination of lead acid batteries [C]. Procs. INTELEC 2002, Montreal, Canada: 583-590.
[8] Wang Jia. Fuzzy estimation of SOC of automotive power battery and its implementation on DSP [D]. Changchun: Jilin University, 2006: 22-23.