A Novel Pigeon-Inspired Optimized RBF Model for Parallel Battery Branch Forecasting

CAS Key Laboratory of Human-Machine Intelligence-Synergy Systems, Shenzhen Institutes of Advanced Technology, Shenzhen, China Guangdong Provincial Key Lab of Robotics and Intelligent System, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Beijing, China Ultrasonic Nondestructive Engineering Technology Research Center of Guangdong, Shenzhen 518055, China Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China Department of Electrical Engineering, Shaoxing University, Shaoxing 312000, China University of Chinese Academy of Sciences, Beijing 100000, China 4e Department of Mechanical and Automation Engineering, 4e Chinese University of Hong Kong, Shatin, Hong Kong


Introduction
As an important part of electric vehicles, the life and safety of lithium-ion battery have a profound impact on the service range of electric vehicles. In order to meet the high power and high energy output requirements of these devices, it is usually necessary to perform series and/or parallel topology on battery modules [1,2]. e series connection of batteries can increase the operating voltage, while the parallel connection of batteries can increase the capacity. For seriesconnected battery packs, the battery management system usually provides a balancing module. For parallel battery packs, the single cells will maintain the same terminal voltage and have a certain self-balance. However, the unbalanced current caused by the inconsistency between the single cells will affect the state-of-charge of the battery and the life and safety of the battery pack in the long run [3].
For battery producers, introduction of fully automated production lines does not mean high quality and stable production; in addition to good sources of materials, the management of automated production line is more critical. e inconsistency of the branch batteries in the parallel battery packs will cause current imbalance and reduce battery energy efficiency and even cause some batteries to be overcharged and/or overdischarged.
Battery engineering research mainly focuses on state estimation and how to reduce battery inconsistency for higher energy conversion efficiency and longer battery life, while lacking a comprehensive analysis of the battery inconsistency generation mechanism [4,5]. e battery management system cannot control the current distribution and energy flow between batteries in parallel modules at this stage, which is directly affected by the battery connection topology. erefore, it is difficult to implement the control strategy for the inconsistency of parallel batteries in the vehicle application.
In parallel topology, uneven current exists and degradation rates are different between individual batteries. Previous studies on parallel connection [6] focused on several aspects, including the evolution of current distribution under certain conditions, unbalances on the degradation rate of the battery, design and control of balanced circuits, the effects of connection wires and welding techniques [7][8][9][10], predicting future capacities, and remaining useful life [11,12].
In the field of battery modelling technology, the current distribution is calculated by numerical simulation. e voltage of various batteries can be extracted from the state of charge-voltage curve under the discharge process. is method considers the influence of internal resistance on battery current, without building any model, but it is necessary to repeatedly search for the voltage of various battery under each time step. Brand et al. [13] explore the current distribution within two parallel-connected batteries, and yet how to extend this method to more than two units has not been discussed. Miyatake examines the relationship between discharge capacities of a multicell battery with two different types, but its topology is unraveled [14]. In addition, they derive a mathematical model for discharge characteristics of the multicell battery based on the equivalent circuit model of an individual battery. Bruen and Marco [15] adopt the modelling and experimental method to the evaluation of parallel-connected lithium-ion batteries for an electric vehicle. e rest of this paper is organized as follows. Section 2 introduces the preliminaries of radial basis function neural network and pigeon-inspired optimization. Section 3 presents the pigeon-inspired optimization optimized radial basis function (PIO-RBF) neural network. Section 4 shows the experimental setup. Section 5 analyzes branch current forecasting case study, followed by the main findings and future prospects of this work in Section 6.

Radial Basis Function Neural
Network. RBF neural network is a three-layer feedforward analysis network, which is composed of input layer, hidden layer, and output layer. Figure 1 shows the topology of RBF neural network, in which the function of controlling node transformation in hidden layer is radial basis function.
If the input layer of the RBF neural network has n information source nodes, the input layer can be represented as [x 1 , x 2 , . . ., x n ] T . In the hidden layer, Gaussian function is selected as radial basis function, which is expressed as where ‖ · ‖ is Euclidean norm, c i is the base function center of the i-th node of the hidden layer, c is the width of the basis function of the i-th node in the layer, and σ i is the width of the basis function of the i-th node in the layer. e output layer of the RBF neural network can be obtained by linearly weighting the hidden layer nodes. If the output layer has k output nodes, the j-th output of the RBF neural network can be expressed as In the above formula, w is the connection weight from the i-th hidden layer node to the j-th output layer; Y is the node value of the j-th output layer. e number determining the hidden layer nodes is also the key to realize RBF neural network, in addition to training and optimizing the center C i of hidden layer basis function, the width of hidden layer node σ i , and the weight factor W from hidden layer to output layer. eoretically, with the number of hidden layer nodes increasing, the approximation ability of RBF neural network is stronger and the output is more accurate. However, in practical application, the increase of hidden layer nodes will lead to the increase of training time and learning cost, and the generalization ability of the network will decrease, which will lead to the overlearning and the fault tolerance ability of neural network.
In order to determine the optimal number of hidden layer nodes of RBF neural network, this paper introduces the trial-and-error method. First obtain the initial interval [a, b] of the number of hidden layer nodes of the RBF neural network through the empirical formula, and then calculate and compare the points in the interval one by one to narrow the interval of the number of nodes to determine the optimal number of hidden layer nodes.
where n i , n h , and n 0 are the number of nodes in the input layer, hidden layer, and output layer of the RBF neural network, respectively.

Pigeon-Inspired Optimization.
When the pigeon is far away from the destination, it arrives at the destination with the help of the geomagnetic field and landmark buildings. e key reasons that affect the homing of pigeons can be divided into three categories. e first reason is the sun, the second reason is the Earth's magnetic field, and the third reason is the geomorphic landscape. During the flight of the pigeons, different cruise tools will be used according to situations. In order to idealize some of the homing characteristics of pigeons, two operators are designed by using some rules.

Complexity
(1) Map and Compass Operator. Pigeons can sense the Earth field by using magnetoreception to shape the map in their brains. ey regard the altitude of the sun as compass to adjust the direction. As they fly to their destination, they rely less on sun and magnetic particles. (2) Landmark Operator. When the pigeons fly close to their destination, they will rely on landmarks neighboring them. If they are familiar with the landmarks, they will fly straight to the destination. If they are far from the destination and unfamiliar with the landmarks, they will follow the pigeons who are familiar with the landmarks. e map model is based on the geomagnetic field. x i and v i represent the position and velocity of the i-th pigeon, respectively. With the number of iterations increasing, the pigeon constantly learns from the optimal individual within the interaction range and updates its speed V i and position X i in real time: e speed of the i-th pigeon is determined by the speed of the previous generation and the current best position of the pigeon. R is a map factor, rand is a random number, and t is an algebra; the position of the i-th pigeon is determined by its previous position and current speed. e flight of all pigeons is ensured by the map, and then we can get the best position of the pigeons Xg. Various pigeons will adjust its direction and fly to the pigeon with the best position according to (4), while (5) will adjust its position. e landmark model is built with pigeons using landmarks for navigation. When using landmarks to navigate, the distance from the destination is closer than that from map navigation. If the pigeon is not familiar with the current location landmark, it will fly under the guidance of nearby pigeons; when finding landmark buildings or familiar PIO optimization Environment modelling and parameters initialization Update each pigeon's velocity and position using eqs (4) and eqs (5) Evaluate X i , update X p , X g N c > Nc 1max Update Np, velocity using eqs (6)(7)(8) Evaluate Xi, update X p , X g N c > Nc 2max Nc = Nc

Solar input
Hidden layer Output layer ∑ Forecasting output RBF Figure 1: Procedure of PIO-optimized RBF network. Complexity locations, it will fly freely according to experience. In the landmark model, N p is used to record the number of half pigeons in each generation, and X c (t) is the central position of all pigeons in generation t. If various pigeon can fly a straight distance to the destination, the following formula will be obtained: In the above equation, fitness (X)is the mass of pigeon, equation (9) is for the minimum optimization problem, and equation (10) is for the maximum optimization problem.

Proposed PIO Optimized RBF Neural Network
In this paper, pigeon-inspired optimization is adopted where PIO method is introduced in training the linear and nonlinear parameters given a predetermined RBF network model structure. e detailed implementation procedure of 4 Complexity PIO for current branch path forecasting can be described as follows (as shown in Figure 1) (Algorithm 1).

Experimental System.
To explore the current distribution and overall characteristics of parallel battery pack under different discharge processes, an experimental system of LiFePO 4 /graphite battery parallel battery pack was developed. e test bench is composed of battery pack, test system, data acquisition system, and management system machine.
e charging and discharging programming software is built in the management system. In Figure 2, an experimental device for parallel battery test is shown. e data acquisition system (Agilent 34970A, Agilent Limited) can measure voltage with a resolution of 6.5 bits, and the measurement accuracy can reach 0.004%. It is applied to voltage measurement to improve the sample precision of voltages. e measurement system of parallel battery pack is carried out at normal temperature. e charge and discharge management of battery pack is carried out with 17020 programmable measurement system. e abovementioned test system provides independent channels to support the charge and discharge experiment of multiple battery modules.
e Hall current sensor is the key to accurately measure the current distribution in parallel battery packs. Ordinary current shunts are accurate in measuring string current, but in most cases, the increased resistance will seriously affect the current distribution. is is why the contactless current sensor is more suitable for measuring the current distribution of parallel batteries in this work.
In order to measure the current distribution of parallel battery packs, the LHB50A5VY2 Hall-effect current sensor is used in the parallel circuit of the test battery pack. e accuracy of the Hall current sensor is ±0.5%, and the temperature drift coefficient is ±0.5 mv/°C. e Hall current sensor can accurately obtain the current through the wire, and the actual current through the battery is equal to the difference between the values of adjacent Hall current sensors.
e Hall current sensor does not need to be connected to the parallel loop, eliminating the influence of the shunt resistance. In this project, the constant current discharge test was mainly carried out to explore the current distribution condition of the parallel battery branch, and the RBF network optimized by the pigeon group is used to predict the current of the parallel branch.

Branch Current Forecasting Case Study
In this section, the competitive performance of the proposed PIO optimized RBF neural network is adopted in forecasting real world current branches in parallel battery packs scenario. e data is collected from the abovementioned experiment where the batteries are placed under a normal laboratory environment. e data recorded every 1 second ranging from first branch to fifth branch under the 0.3 C discharge rate are adopted in the modelling. In view of the sensors investment, branch current prediction can effectively reduce the number of current sensors in engineering practice. e research on current prediction and prediction accuracy has always been a topic of concern to researchers due to the demand of predicting the branch current distribution characteristics of parallel batteries. In this paper, based on the analysis of the current distribution uncertainty characteristics of parallel battery pack, the pigeon-inspired optimization algorithm is combined with RBF neural network to explore the parallel branch current forecasting. e actual and prediction current scenarios of parallel branch are shown in Figure 3; and the errors of current scenario are shown in Figure 4.
It could be clearly observed in Figure 4 that the PIO achieved a comparatively accurate forecasting curve on training stage possibly due to the parameter training efforts, and yet the error in the prediction stage can be further reduced in the future. e reason for larger error of battery close to load is mainly due to the large change of curve when approaching the battery cutoff voltage.
By comparison of performance of battery module in parallel, the prediction research of parallel branch current    6 Complexity based on PIO optimized RBF was explored, focusing on the maximum error and standard deviation of various parallel branches in the training and prediction stage. It can be clearly found that the standard error and the average error ratio of branch current in the middle position of the parallel battery pack are relatively better than B5 and B1, which may be due to the fact that the current variation of the battery is not very sharp, as shown in Table 1. Moreover, the average error and standard deviation of the battery close to the load end are in the same level as those of the battery far away from the load, but the maximum error ratio of branch current is relatively large in the training stage.

Conclusion and Future Work
A radial basis function (RBF) neural network based on pigeon colony optimization is proposed to predict the current distribution of parallel batteries. e model structure can optimize the parameters of RBF neural network. e competitive performance of the model has been verified in the current branch prediction task of parallel battery pack. e experimental and prediction results are proved to be effective, which provides a new idea for reducing the investment of current detection sensor in parallel battery pack. e future work may be to further optimize the pigeon colony algorithm, further improve the prediction accuracy, and optimize the proposed PIO-RBF model. In addition to its application in the branch current prediction of parallel batteries, the proposed PIO-RBF network has the potential to predict power demand, to forecast wind power generation and many other various random nonlinear power and energy tasks, which offers many possible approaches to shape the future of low-carbon energy.

Data Availability
Research data are mainly from the experiment in this manuscript.

Conflicts of Interest
e authors declare that they have no conflicts of interest.