Simulation of health assessment model for thermal management system of lithium-ion battery based on fuzzy clustering algorithm

Considering the inadequate assessment of the factor decline index in the thermal management system for lithium-ion batteries, which has a negative impact on their efficient utilization, a fuzzy clustering algorithm is suggested to create a simulation model for evaluating the health of the lithium-ion battery thermal management system. In the process of restoring characteristic data by the fuzzy clustering algorithm, according to the characteristic parameters of energy signal and power signal, the decay characteristic results of the lithium-ion battery thermal management system are extracted. Taking the minimum attenuation as a reference, the evaluation function is calculated, the health trend of the lithium-ion battery thermal management system is evaluated, the health grade is established, and the health evaluation model of the lithium-ion battery thermal management system is constructed. The experimental results show that the prediction of the remaining service life of five kinds of lithium-ion batteries by this model is consistent with the actual value, and the average absolute error is always within 0.02, which is superior in health assessment.


Introduction
With the increasing demand for energy in modern society, battery technology has been widely used as an important energy storage device [1].Among these options, lithium-ion batteries have emerged as the preferred choice for energy storage in numerous applications due to their exceptional energy density, extended lifespan, and minimal self-discharge characteristics [2].However, in the practical application process, the condition of lithium-ion batteries is a significant aspect to be considered [3].This is because the chemical processes involved in charging and discharging can lead to lithium-ion batteries often suffering some irreversible damage such as capacity attenuation, internal resistance increase, and polarization [4].
In [5], an environmental test box for battery evaluation is put forward, aiming at testing the health of automobile battery packs, modular batteries, and lithium-ion batteries.Environmental testing of IOP Publishing doi:10.1088/1742-6596/2771/1/012011 2 batteries ranges from small battery cells to large battery packs used in automobiles, telecommunications, and electronic hardware, including rigorous testing of lithium-ion batteries with necessary safety features.In [6], an assessment of the potential risks associated with internal short circuits in lithium-ion batteries is presented, utilizing an active protection approach.An evaluation model is developed, grounded in electrochemical principles, and resolved through the application of the Monte Carlo method.The accuracy of the model is substantiated through empirical data, demonstrating consistency between the simulated outcomes and experimental results obtained from accelerated cycle life tests.
By establishing mathematical models and carrying out simulation analysis, the health status of batteries can be predicted and evaluated.At the same time, thermal management is also an important issue in the field of lithium-ion batteries.A reasonable thermal management strategy can improve the performance, safety, and service life of batteries.Through simulation, the thermal management strategy of the battery can be better optimized, and the performance and safety of the battery can be improved.

Extracting degradation characteristics in the thermal management system of lithium-ion batteries
In the assessment of the health status of a lithium-ion battery's thermal management system, recognizing the declining features of the battery's thermal management system constitutes the preliminary step.The fuzzy clustering algorithm [7] is used to restore more complex characteristic data in the battery, thus reducing the complexity of the remaining life evaluation operation of the battery.Among them, the fuzzy clustering algorithm is a clustering method used to divide data sets into different fuzzy categories [8].This algorithm allows a data point to belong to more than one cluster category, rather than dividing it into unique categories.This is because the fuzzy clustering algorithm takes into account the similarity and uncertainty between data points.The fundamental concept involves ascertaining the degree of affiliation of data points by gauging their proximity to the cluster's centroid.A reduced distance equates to a heightened affiliation of the data point to the cluster.When employing a fuzzy clustering algorithm for the recuperation of characteristic data, the energy signal traits of a lithium-ion battery's thermal management system exhibit the following attributes: In equation ( 1), W Q represents the characteristic parameter of the thermal management system of the lithium-ion battery in the running state; R Q represents the characteristic parameters of the battery thermal management system when it is not running; U Q represents the characteristic parameter of voltage change of the battery thermal management system; I Q represents the characteristic parameter of current change of the battery thermal management system.Leveraging the energy signal characteristics of the lithium-ion battery's thermal management system detailed in [9], the power signal characteristics of the same system can be described as such: In equation ( 2), Q D represents the characteristic parameter of peak power; Q E represents the periodic characteristics during battery charging.According to the characteristic parameters of energy signal and power signal, the decay characteristic results of lithium-ion battery thermal management system are as follows: In equation ( 3), O represents the characteristic parameter of the skewness signal; T represents the standard deviation signal characteristic parameter.When 3 0 Q ˚, the health metric of the thermal management system within lithium-ion batteries is in a perpetual state of decline, providing an understanding of the declining traits of the lithium-ion battery's thermal management system.

Health trend assessment based on fuzzy clustering algorithm
In the fitting process [10], on the basis of the above contents, the fuzzy clustering algorithm is introduced to evaluate the health trend in the process of use, and the different health states of the battery are identified by clustering multiple indicators such as battery temperature, current and voltage, with the minimum attenuation as a reference.The evaluation function is as follows: In equation ( 4), K represents the estimated capacity of the battery; D H represents the time breakdown sequence.After completing the above calculation, considering that the capacity attenuation will be directly affected by many factors, an important distribution density parameter is introduced in the processing of the sample.With an increase in the sample count, the weighted representations of random samples progressively approach the actual values, allowing for an evaluation of the lithiumion battery's thermal management system's health progression.The calculation formula is as follows: In equation ( 5), H F represents the weighted value of random samples; J F represents distribution density; K F represents the degree of approximation.Through the above calculation, an assessment of the health trajectory of the thermal management system within lithium-ion batteries is achieved.

Realizing the simulation of the health assessment model
Using the fuzzy clustering algorithm, the fuzzy complementary judgment matrix , it is the fuzzy matrix by default.In order to judge the relative importance of each index, it is necessary to compare any two of them and directly calculate the weight of the fuzzy complementary judgment matrix.The result is as follows: In equation ( 6), M denotes the quantity of elements within the fuzzy matrix.To simplify computations and assess the safety of the lithium-ion battery's thermal management system at various stages, an evaluation score is determined as follows: In equation (7), O H denotes the rated capacity of the battery's thermal management system; Q R denotes the operational input variable of the lithium-ion battery's thermal management system in its functioning state. Assuming

Simulation experiment analysis
To ascertain the practical relevance of the evaluation model proposed in this paper, simulation experiments are carried out to verify it.The model in [5] and the model in [6] are used as comparison models.In comparison to the health assessment model for the lithium-ion battery's thermal management system devised using the fuzzy clustering algorithm presented in this paper, the utilization of the lithium-ion battery's thermal management system encompasses a charging and discharging cycle.Through an examination of the remaining lifespan of the lithium-ion battery and an evaluation of the mean absolute error, it is observed that the battery's capacity experiences a reduction at V1 within the same charging and discharging cycle.The experimental parameters are configured within the aforementioned experimental setting, as specified in Table 1.  1, when the attenuation characteristic parameter is negative, the correlation coefficient is positive, ensuring the overall balance of battery operation.Five different types of lithium-ion batteries are randomly selected as test objects, and the selected experimental objects have health hazards to different degrees.The measured residual service lifespan of the batteries is retrieved from the NASA database.Subsequently, three models are employed to evaluate the remaining lifespan of the five lithium-ion batteries, and the outcomes of these evaluations are presented in Table 2. From Table 2, it is apparent that the model's projection of the remaining service life for the five varieties of lithium-ion batteries concurs fully with the actual measurement, and the prediction accuracy reaches 100%.Therefore, it can be proved that the evaluation results obtained by this model are more accurate in the evaluation process.
Taking the average absolute error as the test index, the evaluation accuracy of this model, the model in [5], and the model in [6] is further tested, and shown in Figure 1.
According to Figure 1, when the proposed model, the model in [5], and the model in [6] are employed to assess the health condition of the lithium-ion battery's thermal management system, the mean absolute error associated with the proposed model, the model in [5] and the model in [6] increases with the increasing number of evaluation samples.The superiority of this model in evaluating the health of the lithium-ion battery's thermal management system has been demonstrated, bolstering the credibility of its practical application, which can evaluate the health state of the battery more accurately, thus elevating the productivity and trustworthiness of the thermal management system and prolonging the battery's service duration.

Conclusion
In this study, a health evaluation model for the thermal management system of lithium-ion batteries, grounded in the fuzzy clustering algorithm, has been devised and executed.Lithium-ion batteries, being a pivotal energy storage technology, their safety, performance, and longevity hold substantial importance in ensuring the stable functioning of power systems and facilitating the transition to clean energy.The integration of the fuzzy clustering algorithm enables a more comprehensive assessment of the health status of lithium-ion batteries, followed by conducting simulation experiments and analyzing the outcomes.The findings reveal that the model's projection of the residual service lifespan for five distinct types of lithium-ion batteries closely aligns with the actual measurements, with the mean absolute error consistently maintaining below 0.02, thus highlighting its exceptionality in health evaluation.However, the accuracy and robustness of the model in this paper need to be further improved, and the scope of application of the model needs more extensive verification and exploration.Future studies can refine the model's algorithm, aiming to enhance the model's precision and dependability; Moreover, the model can be subjected to a wider range of practical applications to substantiate its practicality and viability.

Figure 1 .
Figure 1.Average absolute error results of different models.

Table 1 .
Experimental Parameter Setting Table.

Table 2 .
Evaluation and Comparison Results of Remaining Service Life of Lithium-ion Batteries.