## 1 Introduction
[17], the method by which these mechanical loads affect lithium-ion cells was researched, and the results showed that in 18,650 cells stressed in the \(Z\)-direction the mandrel dispatched itself and struck against internal components, which were observed with a micro-computer tomograph, but the electrical performance exhibited no degradation. However, within Ref. [17], the 3 h load profile was carried out ten times with an inspection, so that battery resting time was not enough, resulting in the measurement uncertainty. In addition, each test condition was evaluated only by two single cells, and accidental errors also cannot be neglected, such as a sudden increase in battery resistance for the long-term vibrational test. In summary, while studies above have identified the effects of the vibration on the mechanical structure inside the lithium-ion cells, it is ambiguous whether the vibration had a significant effect on the electrical performance of lithium-ion cells. With regard to the problem of whether the deformation of the mechanical structure inside cells would lead to the degradation of electrical performance, research in Ref. [18] noted that the capacity fading of LiFePO\({}_{4}\) batteries was caused by the formation of cracks inside the electrode material. Therefore, it is reasonable to suspect that the electrical performance of cells would be affected by the structural deformation and cracks inside cells induced by the vibration loading. [PERSON] and [PERSON] from Warwick University, dedicated to studying the vibration durability of lithium-ion batteries, have performed a great deal of related research works and efforts in recent years. In Ref. [19], the authors emphasized that studies on the vibration characteristics of the battery pack should attract more attention; in Ref. [20], the cells natural frequency was proposed by authors for the first time to quantify the mechanical characteristics of cells; in Refs. [21; 22; 23], 18,650 lithium-ion cells of different materials were investigated with different load profiles; and in Ref. [24], the authors defined a process to devise random power spectral density (PSD) profiles utilizing vibration measurements from three contemporary EVs, for undertaking vibration durability evaluations of underfloor mounted rechargeable energy storage systems (RESS). In brief, two scholars have opened up a wide range of the research space for this issue. It is reported that, within Ref. [21], these nickel manganese cobalt oxide (NMC) cells displayed a significant increase in ohmic resistance within the range of 25.82 to 38.09% after vibration testing, and a reduction in the measured 1C energy capacity was observed in some samples, with 12.22% being the greatest reduction observed. Due to the limited sample size employed, therefore, authors performed further research within Ref. [23], and this study identifiedthat both the electrical performance and the mechanical properties of the nickel cobalt aluminum oxide (NCA) lithium-ion cells were relatively unaffected when exposed to the vibration energy that is commensurate with a typical EV life. However, the study also noted that a similar reduction in energy capacity and increase in DC resistance was witnessed within the reference samples, which indicated that the change in these electrical attributes was a function of other environmental conditions. Because the total duration between pre and post-test characterization was 3 months, the effect between the cell ageing and the vibration cannot be fully quantified. The authors also suggested that a further set of repeat tests should be conducted to increase the size of the data set, indicating that a greater sample size is necessary to increase confidence of findings. From the review above, it can be seen that there is a problem when the sample size is too small; results are greatly affected by some accidental errors such as the cell-to-cell variation, the environmental factors and the measurement uncertainty.