# SOH Estimation of Lithium-Ion Battery Pack Based on Integrated State Information from Cells
## 1 Introduction  
As a kind of eco-friendly energy, lithium-ion batteries have been widely used in electronic products, electric vehicles, and various types of aircraft, with advantages, such as stability, high energy density, long lifetimes, environmental protection, and so on. Being part of a power supply device, in practical use, the system performance decline of these battery packs causes accidents without being monitored. Therefore, the accurate assessment of battery health has become a pressing problem of great concern in practical use. The voltage of the lithium-ion battery cell is relatively lower, so batteries must be used in combination. However, most studies about the state of health (SOH) assessment and prediction of lithium-ion batteries are focused on the modeling and methods for objects that we can monitor directly. It means that we can only assess and predict by direct indicators without indirect factors, such as status estimation of cells [1, 2], fault diagnosis tools development [3], remaining useful life (RUL) prediction [4]. For example, in recent studies, the analysis on packs only consider about the indicators captured from the packs, including total current, total voltage. But the problem is that due to the correlation of the electrical connections, the interaction between cells is widespread [5], which means the irregularly degradation process of one cell will cause othercells to deteriorate rapidly [6]. Therefore, the overall performance of a battery pack depends on the comprehensive state of all cells in the structure [7; 8]. Based on this premise, the degradation of a battery pack is essentially the result of the interaction of a large number of cells. Each characteristic of the cells or other items in the pack makes sense for assessment and prediction of the pack, which is always researched as dependency between cells and packs in recent studies. The typical dependency analysis methods that are widely used at present are divided into two classes: the statistical approach represented by Copula [9] and the probability graph model (PGM) [10] represented by a Bayesian network. However, it has been found that there are evident disadvantages for these two classes:  
* The algorithm complexity of a copula is relatively high [11], especially for high-dimension extension problems, such as analysis for battery packs with a great number of cells [12]. Similarly, linear or nonlinear correlation functions that are used to quantize the interaction cannot be extended easily either [13]. * For PGMs, the Bayesian network and the Markov process take advantage of graph structures [14]. Additionally, due to the complication of electrochemical properties, there are many obstacles to establish chemical reaction models for battery packs. Hence, a method that can effectively integrate state information of cells for pack evaluation is needed. Therefore, we aim at expressing the health sate of the whole pack with dependency information from the cells for more practical application. Compared with traditional dependency analysis methods mentioned above, in recent years, data-driven methods shows excellent merits in engineering applications [15]. Modified algorithms based on Kalman filters [16], particle filters, support vector regression [17], neural networks [18], and fuzzy logic also have been applied to the SOH analysis of battery cells. Among these methods, neural networks have been developing the most rapidly in recent years, with strong advantages. For example, [PERSON] et al. established a novel prediction model of lithium-ion battery cycle life using a feed-forward neural network [19]. [PERSON] et al. used a neural network to achieve the short-term power prediction of a battery [20]. Considering about the most critical step for achieving the expression of the interactive degradation within battery packs is how to make use of the multi-degradation information for the system description, the high-dimension data processing is the most significant problem. In this area, deep learning shows strong advantages [21].