Reliability of State-of-Health of the Flexible Li-Ion Batteries Under Various Flexing Conditions and Calendar Aging

The thin Li-ion battery (LIB) is gaining popularity for use in flexible hybrid electronics (FHE), which requires reliability under a variety of flexure circumstances such as folding, bending, and twisting as little state-of-health (SOH) degradations as feasible. There are a variety of power sources available, including superconducting magnetic storage, vanadium redox batteries, lithium-ion batteries, sodium sulfide batteries, zinc bromide batteries, thermal energy storage systems, and nickel-cadmium batteries, all of which have different specific energy, specific power, size, and weight characteristics. Because of its mobility and lightweight, LIB is a power source capable of high specific power (W/Kg), high specific energy (Wh/Kg), and a lower memory effect, making it a good choice for wearable applications. Because thin form factor-based LIBs have a thickness of less than 1 mm, they may have reliability concerns on liquid electrolytes when exposed to the air. Stresses of daily motion, such as folding, bending, and twisting, may cause difficulties on reliability and performance consistency as for such thin power sources. The key challenge is LIB's ability to be working reliably in the situation of stresses such as bending while being exposed to different temperature conditions. The replicating human body motion might be helpful for the development of test methods on the reliability of the battery.

In a prior LIB folding reliability study which has used a carbon nanotube (CNT) current collector and paper separator, LIB was proven to withstand 50 folding cycles with a folding radius of 6 mm in the study [1]. Another research performed a folding test with a 5 mm fold radius [2]. According to the study, 20-fold cycles cause the LIB to lose 1% of its capacity. Another investigation on 180-deg bending was conducted [3]. According to the study, the LIB could withstand 100 bend cycles with just a 12% capacity loss. Another bending test was done on thin LIB with a v-bend shape [4]. They claimed that the bend test might cause capacity degradation. Additional work on v-bend testing for capacity deterioration when discharging at various depths of discharge discovered that after accelerated testing of up to 150 charge–discharge cycles, the bent samples have huge capacity retention than the unbent samples have [5].

In addition to the research, it may be necessary to investigate models for SOH degradation concerning the stresses of everyday human body motions to reduce the several hazards when employing LIB in various wearable applications. Failure analysis may also be required to comprehend the mechanisms of its degradation owing to a variety of factors. Mechanical impacts and chemo-electrical effects are the two major groups that cause LIB degradation. First, mechanical impacts might result from the loss of active material, particle isolation, and decreased electrode which are caused by material expansion and contraction, particle stresses and dislocation defects, and fracture materials caused by deformation, temperature change, and strain. Second, owing to the development of solid electrolyte interphase (SEI), which is induced by lithiation on charge and delithiation on discharge [6] and calendar aging [7], chemo-electrical effects such as loss of Li-ion capacity and impedance increase might occur. Because of the complexity of the impacts, developing a regression model to predict SOH might be difficult. Machine learning based on artificial intelligence (AI) might be useful in the construction of such complicated models. Prior study has performed previous research on an AI-based LI-ion battery regression model [8]. They analyzed several techniques, such as the feed-forward network (FNN), convolutional neural network (CNN), and long short-term memory network (LSTM), by concentrating on model accuracy and time to train the model on the system, to find benefits and downsides.

Twist, fold, and flex-to-install reliability tests were performed in this investigation. The test-stand was created by simulating the daily stresses that the human body faces in a lab setting. A supervised machine learning regression model utilizing the least square and regression tree methods was created to measure acceleration factors and interaction effects among the test conditions and use conditions. Furthermore, an AI-based regression model has been developed to predict the battery life in real-world use scenarios.

The charging and discharging setup and flexing device (dynamic folding, dynamic twisting and static flex-to-install) for the test batteries is presented in Fig. 1. Each dimensional parameters are marked on the Fig. 1, for the replication of the setup and simulation model. To measure current, the current sensor is installed on a positive wire attached to the battery. The charger integrated circuit (IC), electronic load, and DC power supply are used to charge the battery, discharge the battery, and power the IC and relay, respectively. The logic of the battery charge–discharge configuration is controlled by the developed program with LabVIEW™ (2020 SP1) by National Instruments (NI)™. The voltage signal from the load, the IC, and the battery is received by the data acquisition (DAQ) and NI-USB, which is then triggered to the LabVIEW to operate the relay, and then the on-off signal is returned to the load, IC, and battery. Figure 1 displays a variety of flexing test configurations. The fixed and movable fixtures, respectively, are connected to both sides of the battery. The microprocessor controls the moving distance and speed, while the height of the moving fixture controls the folding diameter. Several wires are attached to the traces of the battery to get voltage and current values to validate the SOH degradation of the battery. During the flexing-reliability tests, a total of 60 twisting and folding cycles were performed on each discharge cycle, simulating the demands of daily motion. On a complete depth of charge–discharge, 150 charge–discharge cycles are conducted. Before the start of the testing, each sample was thoroughly discharged as an initial condition. The voltage measured during the test is used to calculate battery degradation.

The preceding study reveals how flexible electronics are deformed in human body motions including bending, folding, and stretching [9]. As shown in the study, they measured the angles of the ankle, hip, knee, elbow, head, neck, shoulder, spine, thorax, and wrist so that offers several scenarios for the use of the applications. In this regard, this study referred to a prior study that created test settings in the lab that mimicked human body movements. The test conditions in this investigation are listed in Table 1.

The test vehicles, LIBs with two kinds of cathode, are shown in Fig. 2. The anode and cathode are the blacktip and silvertip, respectively. A two-sided cathode, two polymers with liquid electrolyte, and two anodes make up the LiNiMnCoO₂ (NMC) battery. Because its cathode is NMC, it is known as the NMC battery. Because this is a thin battery, the same material sequence is symmetrically reproduced twice. The battery capacity might be increased if the cells are stacked more. Due to the electric current flowing through the electrolyte, which is a polymer on a Li-ion polymer battery (LIP), voltage is created on both sides of the anode and cathode. As indicated in Fig. 2, the materials are pouched by an aluminum foil casing. NMC as the cathode has a theoretical potential of 4.3 (V) versus Lithium-ion [10]. The anode potential of graphite is around 0.1 (V). Now that the voltage of the cell is the difference in potential between the cathode and anode, as a result, a normal NMC battery's maximum voltage is 4.2. (V). The voltage of the test vehicle in this investigation is also 4.2 (V).

When it comes to the other test vehicle is LIB with LiCoO₂ (LCO) of the cathode, often referred to as the LCO battery, and its material properties are shown in Table 2. The blacktip and the silver tip are anode and cathode, respectively. The battery consists of a cathode, a polymer, and an anode. The voltage is generated in the same manner as the NMC battery, and the materials are pouched by an aluminum foil case as well. The theoretical potential of the LCO battery is 4.2 (V) as well. In this study, the voltage of the test vehicle is 4.2 (V) as well.

where I is the current, t_measure is the measurement interval, Q_disch is the discharge capacity, Q_disch,o is the initial discharge capacity, Q_rated,disch is the rating discharge capacity. The total product of discharge current for each measurement period is used to compute the battery discharge capacity. The difference between the capacity of the nth cycle and the capacity of the first cycle is used to calculate capacity deterioration. The difference between the discharge capacity in the current cycle and the discharge capacity in the 0th cycle is divided by the rated discharge capacity to determine the SOH of the battery. A normalized SOH value is used to estimate the relative rate of degradation of the battery, which is independent of the variance in the battery's original capacity.

Current versus voltage profiles, and SOH degradation using test factors listed in Table 1 will be shown in this section. Figure 3(a) shows the current with respect to the voltage for different test factors across different numbers of cycles. The NMC battery is charged at 60 mA and 120 mA at 1C and 2C in constant current (CC)-charging and discharged at −60 mA and −120 mA at 1C and 2C in CC-discharging, respectively. The charging current is reduced from the peak current to 4 mA, which is the cutoff current, in constant voltage (CV)-charging. As for the LCO battery, it is charged at 20 mA and 40 mA and discharged at −20 mA and −40 mA, respectively on 1C and 2C. It has the same cutoff current of 4 mA.

Figure 3(b) portrays the voltage versus the percentage of battery capacity for various test factors across various numbers of cycles of NMC batteries. It can be observed that the battery gets charged from 0 percent of state-of-charge (SOC), which is current available capacity, to 80% of SOC via CC-charging while the voltage is increased from 2.7 V to 4.2 V at the same time. In turn, the battery is charged from 80 to 100 percent via 4.2 V CV-charging. The CV-charging process begins at 50% at 2C. During the discharging process, the voltage drops from 4.2 V to 2.7 V, which is the discharge cutoff voltage, and the SOC drops from 100 percent to 0 percent. The properties of the voltage profile remain consistent throughout the charging and discharging process, regardless of the number of charging cycles. It is found that the power and capacity decline in the graph, as shown by the marks in Fig. 3(c). The nominal voltage decreases as twist cycles increase, as indicated in the graph below. Voltage times current times discharge time equals available power capacity. Because the voltage has been reduced, the available power capacity has also been reduced. The power might be reduced due to a loss of rated voltage at constant current caused by an increase in internal resistance caused by active material deformation, current collector damage, and other factors.

Furthermore, the bottom of Fig. 3(c) illustrates that as the twist cycles increase, the discharge capacity decreases. Owing to the loss of discharge time at constant current resulting from capacity loss due to capacity material degradation, failure, and other factors, available discharge capacity, which is defined as current times discharge time, may be reduced. For example, if the concentration of an electrolyte drops owing to mechanical stress-induced loss of active components, the internal resistance of the battery cell rises, and the chemical reaction slows down. Diffusion, conduction, deformation, and other local physics connected to deterioration in all feasible locations are examples of local physics that are related to each other. For example, diffusivity is changed by mechanical loads, discharging cycles, and calendar aging and is linked to temperature and concentration.

On various test conditions, Fig. 4 displays the SOH versus the number of charging and discharging cycles on the different current rate (C-rate) conditions without flexing. The nonflexing state indicates that the sample is charged and discharged, but not flexed; as a result, the sample exhibits SOH deterioration. It is reasonable to assume that SOH is related to the number of cycles and is influenced by different test circumstances. The SOH deterioration is shown as well in the figure as a function of the number of charge and discharge cycles. The SOH deterioration might be proportional to the number of cycles, allowing us to readily anticipate the battery life. To further understand the impacts of flexural stress on battery life, a comparative study was done. The SOH deterioration on the twist sample is faster than on the nontwist sample, as seen in Fig. 5. When it comes to a 20% deterioration failure threshold, the NMC battery that is twisted by 20 deg failed after 7000 twist cycles at worst, whereas the nontwist sample has not failed. In this case, it is thought that the twisting tension shortens the battery's life. But if the 5 deg case is seen, it seems that SOH degradation is smaller than nonflex case. In these regards, high twist angle could deteriorate the SOH whereas the low twist angle, counterintuitively, is helpful for the SOH of the battery. As for the LCO battery as seen on the Fig. 5, 10 deg twist condition degrade the SOH as compared to the nonflex condition. Figure 6 portrays that folding stress has much more serious consequences, whereas flex-to-install may have only a little impact as shown in Fig. 7. Lastly, Fig. 8 shows the whole comparison between the flexing effects on SOH degradation. As shown in the figure, folding has the largest impact on the SOH degradation while the twisting and flex-to-install have a slight impact on it.

Several experimental findings will be presented, including SOH deterioration with respect to calendar aging variables (temperature and days). Figure 9 displays the SOH versus the number of charge cycles of nonflexing batteries with varying aging temperatures and times. As seen in the graph, the SOH degrades as the number of aging days or the temperature of aging increases. Figure 10 presents the SOH versus the number of charge cycles of flex-to-install batteries aged at various temperatures and times. An effect of the aging days appears to be low on flex-to-install samples. Figure 11 shows the SOH versus the number of charge cycles of twisted batteries with varying aging times at 40 °C. As indicated in Fig. 11, the aging time effect on nonflex situations is large, however, the influence on twisting conditions appears to be insignificant. Figure 12 presents a comparison of SOH versus the number of charge cycles of flexing batteries aged at 40 °C for 25 days. The flex-to-install effect on SOH deterioration is strong in the very early stage of the cycles with the 40 °C and 25 days aged batteries, whereas the twist effect is large at the end. Figure 13 displays a comparison of SOH versus the number of charge cycles of flexing batteries aged at 40 °C for ten days. Figure 12 presents a graph with comparable features to the previous results. Figure 14 depicts the SOH versus the number of charge cycles of twisted batteries aged 65–70 days at various temperatures. As demonstrated in the graph, as the aging temperature rises, the SOH degrades more.

The finite element method (FEM) model was developed to validate the level of strain in a deformed test sample. Ansys Workbench^™ (2021 R2) by Ansys^® was utilized.

To begin, linear regressions using the least square approach and the regression tree method are used to demonstrate variable importance in terms of usage conditions and relationship effects among variables. Second, a regression model based on physical equations will be demonstrated to better comprehend the physical meaning of usage circumstances and acceleration variables that affect SOH deterioration. Finally, AI-powered machine learning will be demonstrated.

The regression tree is a supervised machine learning approach that shows the variable importance of a regression model intuitively and has the benefit of less overfitting difficulties. The tree begins at the root node at the top of the diagram and ends at the terminal node at the bottom. Recursive partitioning is used to divide the nodes to reduce variance, and pruning is used to combine them to reduce the root-mean-squared error (RMSE). The more nodes that are separated, the lower the variance, but too many nodes might raise the RMSE, which is known as overfitting. RMSE is therefore reduced by trimming the nodes.

Figure 16 displays the response plot and residual plot with respect to the expected response, demonstrating the model's reliability. The projected line with 11.81% of RMSE in the first graph appears to be well-matched with the actual response, which represents experimental data. The second graph demonstrates that the residual appears to be well distributed and regular, indicating that the model may be trusted. Figure 17 displays the importance of the variable (also known as a feature).

The influence of the discharge cycle is particularly significant for the SOH as a dependent variable, as indicated in the graph. The folding stress is significant among the flex-stresses as well as the C-rate and voltage are significant, while the flex-to-install and twist stress are slightly significant. As previously indicated in Fig. 15, this is due to the low strain level of the twisted sample. The SOH decreases as the number of discharge cycles increases, as indicated in the graphs. The SOH is reduced when the folding distance is raised from 0 to 25 mm, while twisting angle and flex-to-install diameter are unaffected. When the C-rate and voltage are increased, the SOH degradation is worsened.

Although the regression tree can highlight the importance of each feature, it cannot show the impact of the characteristics of interaction among them. Linear interaction regression using the least square approach might be useful in this case. The correlation effects between the features are shown in the following regression model on Eqs. (3)–(5). The model validity might be able to be supported by an R-squared of 93% and RMSE of 2.14%. By deleting nonsignificant variables with high p-values and splitting them into particular use conditions, the equations are able to be abbreviated into several separated equations as follows to illustrate the interaction of the characteristics intuitively. The interaction effect of the twist feature is seen in Eq. (3). The SOH degrades more at 0.6 times twist angle, and the C-rate effect for the NMC battery increases as the twist is increased. As seen in Eq. (3). Additionally, a similar interaction occurs for LCO as shown in Eq. (4). Furthermore, as indicated in Eq. (5), the SOH degradation increases when the folding distance is increased, while its effect decreases as the C-rate is raised.

$Where C1=0.07,C2=0.04,C3=−0.01,C4=4.5×10−8,C5=5.2,C6=0.95,C7=−6.9×10−5,C8=1.2,C9=1.5,C10=0.015,C11=−46,C12=1.5,C13=4.6×10−4,C14=0.5$⁠. Figure 19 shows the forecast of SOH versus discharge cycles at various C-rates. The SOH degrades as the C-rate increases. Figure 20 displays the prediction of SOH versus discharge cycles under various flexing situations. The folding effect has the greatest impact on SOH degradation, while the flex-to-install and twist effects are rather minor. Figure 21 presents the prediction of SOH versus discharge cycles at various aging times at 25 °C. Figure 22 portrays the prediction of SOH versus discharge cycles at various aging times at 40 °C. As seen in Figs. 21 and 22, as the aging time increases, so does the SOH deterioration. Figure 23 shows the prediction of SOH versus discharge cycles at various aging temperatures on 65–70 days. As shown in the graph, as the aging temperature rises, so does the rate of SOH deterioration.

where $l$(k) is the actual SOH (%), $l̂$(k) is the estimated SOH, and K is the number of iteration cycles.

Figure 25 shows the results of fitting the output value and comparing it to the experimental value with R-squared of the training model for model validation with 10, 50, 100, and 300 neurons, respectively. An overview of the comparisons is shown in Fig. 25. The R-squared of training datasets increases from 10-neurons to 50-neurons, and the pace of rising slows. As for cross-validation of the trained model, if the experimental data are used, The R-squared of the test using fitted data slightly decreased from 10 to 50 neurons, then dropped greatly from 50 to 300 neurons. In this case, the optimal number of neurons is thought to be approximately 50, based on the R-squared of the training and fitting tests. Figure 26 presents the MSE with 50 neurons, with the greatest training performance being 0.009 at MSE 454. The least MSE is considered to be in the middle of 1000 epochs, and the findings might support the hypothesis that 50 neurons are the optimal number of neurons.

Figure 27 displays the expected SOH, which was calculated using the created regression model with 50 neurons and the previously described circumstances. The R-squared was 99.9%, as seen in Fig. 27, indicating that the anticipated model is well suited to the experimental data. Figure 28 shows the comprehensive comparative findings between the actual data and predicted data. The predicted SOH of the NMC battery and LCO battery on various use conditions during the charging/discharging cycles in the graphs, is well matched to the experimental value, as seen in the figure. It is expected that a better model could be obtained if the more datasets are utilized to train the regression model.

Twisting, folding, and flex-to-install test protocols were developed for evaluating the reliability of thin flexible Li-ion batteries in this study. The flexing test setups might be able to simulate daily loads caused by human body movements in a lab environment. About 150 charge and discharge cycles are conducted with full depth of charge and discharge and every discharge cycle included 60 dynamic flex cycles so that the total cycles are 9000. The voltage to a state of charge and current to voltage profiles were measured and studied. Furthermore, it was discovered that the test variables might be able to affect the features of the SOH degradation. The data were statistically analyzed using graphs by comparing the findings to other results obtained under various test conditions. The regression model was developed by using supervised machine learning and AI-based machine learning methods to predict SOH and assess the battery life. The models were shown to be able to describe the deterioration of the LIBs in lab testing with tiny errors, which could be avoided by utilizing larger data sets to train the model more precisely.

The work presented in this paper was supported by the members of the CAVE3 Electronics Research Center.