## 1 Introduction
These methods have specific advantages  
Figure 1: Ishikawa diagram of the various ageing factors leading to Lithium-ion battery degradation. in SoH estimation. EIS has a shorter measurement time and can be used at particular frequencies for SoC. In contrast, ICA and DVA have the drawback of an extended test duration of approximately 10 h. Furthermore, these methods are not suitable for specific cell states [21]. However, ICA and DVA are superior to EIS in terms of their universal, model-independent applications and low-cost hardware implementations as well as their easy calculation [20]. Nevertheless, LIBs have to be in a steady-state operating condition to apply the previously mentioned diagnostic techniques. Another disadvantage of EIS is that cell processes with a nonlinear current-voltage relation are only slightly excited in EIS due to the low excitation amplitude. Hence, only the linear system behaviour is observed, and relevant nonlinear cell information is not accessible for LIB diagnostics and SoH identification. In general, an efficient BMS benefits from a fast, cheap and accurate on-board SoH diagnosis of the state and the cycle life of LIBs [10; 23]. Recently, a novel dynamic analysis method, the Nonlinear Frequency Response Analysis (NFRA), was established and applied to LIBs to investigate cell behaviour when it is excited with a nonlinear signal [24; 25; 26]. Thus, the effect of ageing mechanisms on the measured cell response is enhanced, and NFRA-based data might be more suitable for reliable SoH identification [24]. The application of NFRA for SoH estimation and RUL prediction is summarised in Figure 2 using a SWOT matrix to assess the NFRA concept as well as its application in LIB diagnostics and SoH identification. The strengths and opportunities of NFRA in LIB diagnostics look promising and motivate our experimental study. The weaknesses and threats seem to be manageable, in particular, as NFRA is a mature tool used in the state diagnosis of non-electrochemical systems. In 1985, NFRA was used for the first time to determine the SoC of lead-acid batteries [27]. In the field of fuel cells, at the stack and cell level, NFRA was successfully applied for system monitoring and analysis [28; 29; 30], but it was also used in more general kinetic studies [31; 32]. Over the last decade, data mining approaches have become popular for diagnosing and predicting the cell state of LIBs in BMSs. There are different approaches to unambiguously identify the complex and multi-scale ageing of LIBs and to predict cell state indicators. Common data-driven diagnostic algorithms use artificial neural networks as well as support vector machines (SVMs). Both methods have already been implemented for state identification and for determining the RUL of LIBs for simple test cases [33; 34; 35]. Since the accuracy of the data-driven processes depends critically on the data basis,  
Figure 2: Strengths-Weakness-Opportunities-Threats (SWOT) analysis of the NFRA for LIB characterisation. one also attempts to increase the information content of the raw data with the help of first-principles models. Hybrid methods ideally combine the benefits of data mining with those of classical modelling principles [36; 37]. Furthermore, they serve as the basis for data mining of electrochemical manipulated variables and measurements, such as current, voltage, internal resistance, maximum usable capacity and impedances [21; 38]. To the authors' knowledge, diagnostic algorithms, which also take NFRA data for LIB diagnosis into account, are currently not available in the literature. In this work, we analyse the applicability of NFRA as a diagnostic tool for LIBs and their SoH. Therefore, an ageing test of LIBs at 25 \({}^{\circ}\)C is presented, and the impact of relevant ageing mechanisms on the nonlinear dynamics of the cells is explained in detail. Following a data mining strategy, an empirical degradation model is derived from informative NFRA data sets.