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Summary This paper investigates a Fletcher‐Reeves conjugate gradient optimized multi‐reservoir echo state network (FRCG‐MESN) to identify battery state of charge (SOC). First, an echo state network with multiple reservoirs is established to estimate battery SOC by using its discharge terminal voltage and current as the inputs, and the FR conjugate gradient algorithm is explored to tune the output weights of the MESN to avoid calculating the inverse matrix. Second, an appropriate amount of Gaussian noise with zero mean is added to the training set to prevent overfitting. Finally, a battery test platform is adopted to sample the discharging data under two working conditions: the Los Angeles 92 and the urban dynamometer driving schedule. The simulation results show that the presented FRCG‐MESN method can accurately identify the battery SOC with different initial SOCs. Applying an appropriate amount of noise to the training set can prevent overfitting efficiently.

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Summary The extreme learning machine (ELM) is a single‐hidden layer feedforword neural network (FNN) without training hidden layer weights/biases. By constructing a recurrent extreme learning machine (Recurrent‐ELM) with time delay lines to model battery dynamic characteristics, a beetle antennae search based recursive least squares (BAS‐RLS) method is explored to online realize the state of charge (SOC) estimation. The contents include: (1) To decrease the computational burden, the ELM model with fixed hidden layer weights is adopted to model battery SOC, and a RLS algorithm is studied to online estimate SOC by using the sampled terminal voltages and currents; (2) To solve the modeling accuracy problem, a Recurrent‐ELM model with past/present voltages and currents, and past SOC as inputs is constructed by adding time delay lines to capture battery dynamic characteristics, so as to promote the battery modeling accuracy; (3) To determine suitable neuron numbers in the hidden layer, the BAS method is introduced to find the optimal neuron number in the hidden layer to promote intelligence of the Recurrent‐ELM based RLS algorithm. Simulation results indicate that the proposed model and method has high precision in SOC estimation compared with traditional method.

Accurate state of health (SOH) estimation plays a significant role in battery management systems (BMS). This paper investigates a Polak-Ribière-Polyak conjugate gradient (PRPCG) algorithm optimized broad learning system (BLS) for lithium-ion battery (LIB) SOH estimation. First, effective health indicators (HIs) are extracted from the voltage curve in the constant current charge process. Second, a hybrid four layers BLS structure with mapped feature nodes and enhancement nodes connecting to the output is established to build both the linear and nonlinear relationships between the HIs and SOH, in which only the output weights require to be trained. Again, the PRPCG algorithm is adopted for searching optimal output weights without matrix inverse calculation during the training process. Furthermore, certain Gaussian noises are added to enhance the training data for solving the locally low accuracy problem. Finally, under the Oxford battery degradation data set, experiments validate the investigated algorithm has high accuracy in SOH estimation with the mean absolute error (MAE) below 1%. The enhanced data can efficiently improve the model generalization ability.