Fractional-order Optimization Algorithm For Neural Networks And Its Application To Lithium-ion Battery State Of Charge Estimation

To alleviate the worldwide energy crisis and environmental crisis,the electric vehicle industry has been vigorously developed.Lithium-ion batteries are widely used as energy storage batteries for electric vehicles with the advantages of high energy density,low discharge rate,and no memory effect.To ensure the safety of electric vehicles,an advanced battery management system(BMS)is essential.State of charge(SOC)is a critical indicator in the BMS to ensure the safe operation of lithium-ion batteries.However,due to the complexity of the structure of the lithium-ion battery itself,its SOC can not be measured directly by instruments.With the development of fractional order calculus theory,fractional-order calculus has been gradually applied in neural network optimization algorithm,and it is found that the fractional-order optimization algorithm is faster and more accurate.Based on this,this paper mainly studies the accurate estimation of the SOC for lithium-ion batteries under the fractional-order optimization algorithm.Firstly,an improved Hausdorff’s derivative is proposed.The range of the independent variable in the definition of Hausdorff’s derivative is the set of positive real numbers,but in the calculation process,the independent variable will have negative real numbers.Therefore,this paper improves the Hausdorff derivative by introducing symbolic function and absolute value calculation,so that the range of definition of the improved Hausdorff derivative is extended to the negative real set.The improved Hausdorff’s gradient is defined by the improved Hausdorff’s derivative corresponding to the multivariate function.Second,the improved Hausdorff derivative is introduced into the parameter optimization algorithm for both types of neural networks.For Wavelet Neural Network(WNN),the back propagation algorithm is generally used for the training of WNN,and the key of this algorithm is the gradient descent method.Gradient descent is an optimization algorithm that updates the network parameters to find the minimum value of the loss function.However,the traditional gradient descent method suffers from the two problems of easily falling into local extrema and slow convergence.Therefore,in this paper,the integer order gradient is replaced by the modified Hausdorff gradient,and the rules of adaptive change of order in the optimization algorithm are given in the probabilistic form to obtain the optimization algorithm based on fractal derivatives.For Long Short-Term Memory(LSTM)networks,the Adam(Adaptive Moment)algorithm can be updated by computing the gradient of the loss function overall weight and bias parameters in the LSTM network.By replacing the gradient in Adam’s algorithm with the modified Hausdorff gradient,the chain rule consistent with the integer order derivative is obtained by using the local property of the Hausdorff derivative,and the order is introduced as a hyperparameter in the proposed optimization algorithm.Thus,the parameter optimization in the LSTM network is converted into the optimization of order.The method of order rectification is proposed,and the Adam-IH(Adam with the improved Hausdorff derivative)algorithm is designed to dynamically adjust the update rate of parameters.Finally,based on the constructed lithium-ion battery experimental platform,charge and discharge experiments were conducted to obtain the external characteristics of the voltage and current of the lithium-ion battery.The SOC estimation model based on WNN and LSTM network is established,the training and test sets are selected according to the characteristics of the model,and the voltage and current are used as input and SOC as output after normalization.The experimental results show that,compared with the integer-order optimization method,the fractal derivative-based optimization method speeds up the optimization of parameters,improves the accuracy and precision of SOC estimation,and applies to different operating conditions.