# State-of-Charge Prediction Model for Ni-Cd Batteries Considering Temperature and Noise
## 1 Introduction  
Railway transportation is one of the most critical modes of transportation in China, and high-speed electric multiple units (EMUs) have become a popular choice due to their high carrying efficiency. However, the existing equipment associated with high-speed EMUs in China is not flawless. The Ni-Cd battery management system in the vehicle cannot predict the state of charge (SOC) of the battery [1]. The SOC of the battery can directly reflect its sustainable power supply capacity and is essential for battery energy management [2]. To address this issue and alleviate \"range anxiety\", it is imperative to develop an accurate SOC prediction model [3]. Such a model would aid in formulating an appropriate battery energy management strategy, extending the battery's service life, and ensuring its safe operation [4]. As the SOC of the battery cannot be directly measured, it can only be indirectly estimated by parameters such as the voltage and current [5, 6]. Additionally, the battery SOC is affected by temperature and aging, making precise estimation a challenging task [7, 8]. For Ni-Cd batteries, which have a large capacity and extended discharge cycle [9, 10], establishing an SOC prediction model is even more complex compared to lithium batteries. Establishing an accurate state-of-charge (SOC) prediction model is a research focus worldwide. Several methods have been proposed in the literature to address this issue. For instance, [PERSON] et al. [11] proposed an adaptive adjustment mechanism for an unscented Kalman filter algorithm to predict the SOC based on stochastic difference equations of the battery model. However, since numerical methods were used to solve the system state equation, calculation errors increased over time and failed to respond to abrupt changes in the SOC. [PERSON] et al. [12] used gray theory for parameter analysis and behaviorprediction during battery charging and discharging and proposed a piecewise gray model based on extensive battery aging data to enhance SOC prediction accuracy. [PERSON] et al. [13] developed an extended Kalman filter based on Lebesgue sampling to estimate the SOC, which can reduce computational complexity and cost. [PERSON] et al. [14] used particle swarm optimization to predict the SOC of supercapacitors but the prediction range was limited. Neural networks have been increasingly used due to their strong nonlinear processing and adaptive learning abilities. For example, [PERSON] et al. [15] used multiple linear regression to optimize a long short-term memory (LSTM) network for the dual control of SOC prediction accuracy and range. [PERSON] et al. [16] optimized a backpropagation neural network (BPNN) using a flight strategy and particle swarm optimization to minimize prediction errors. [PERSON] et al. [17] used a recurrent neural network (RNN) as the prediction model and a convolutional neural network (CNN) to extract relevant features from battery data, enhancing the model's generalization ability. The estimation algorithm for the SOC based on recurrent neural networks offers high prediction accuracy. However, it has a complex model structure and long training time, particularly for nickel-cadmium batteries, as in the case of LSTM [18]. A feedforward neural network, known for its simple structure and suitability for online systems due to its limited data requirements, is another option [19]. However, its prediction accuracy is dependent on the initial parameter settings [20; 21], as in the case of a GRNN. It is feasible to optimize its parameters using an optimization algorithm to make the feedforward neural network suitable for adaptive adjustment. Given its simple structure, fewer parameters, strong nonlinear mapping ability, and fast learning speed, a GRNN is ideal for predicting small sample data and can handle unstable data [22; 23]. However, the prediction results obtained using the GRNN model are highly susceptible to the initial parameters.