Systems and methods for sensor-based prediction of thermal runaway in lithium-ion batteries through strategic sensor array

Abstract

A computer-implemented system predicts occurrence of thermal runaway in a Lithium-ion battery module by modeling thermal, electrochemical, and material degradation under various conditions. The computer-implemented system uses spatiotemporal and thermal data associated with the Lithium-ion battery module to forecast future temperatures along the battery module to identify or predict thermal runaway events.

Description

Atty. Docket No.085067-857987 Client Ref: UA25-090 SYSTEMS AND METHODS FOR SENSOR-BASED PREDICTION OF THERMAL RUNAWAY IN LITHIUM-ION BATTERIES THROUGH STRATEGIC SENSOR ARRAY GOVERNMENT SUPPORT

[0001] This invention was made with government support under DOD #FA9550-24-1-0164. The government has certain rights in the invention. CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This is a PCT application that claims benefit to U.S. provisional application serial number 63 / 703,650 filed on October 4, 2024, which is incorporated by reference in its entirety. FIELD

[0003] The present disclosure generally relates to battery safety, and in particular, to a system and associated method for modeling and predicting thermal runaway in lithium-ion batteries and battery modules. BACKGROUND

[0004] Rechargeable lithium-ion batteries are very common in both industrial and consumer devices. However, lithium-ion batteries also come with safety concerns as they are susceptible to overheating, which can lead to catastrophic and deadly events such as noxious gas leaks, fires, and explosions.

[0005] It is with these observations in mind, among others, that various aspects of the present disclosure were conceived and developed. 1 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG.1A is a schematic illustration of a framework that combines physics-based modeling and machine learning (ML) to predict future battery temperature and detect thermal runaway (TR) in cylindrical Lithium-ion battery (LIB) modules, where the left-hand side shows a multiphysics model used to generate the data set, which is then used in the ML model to predict the occurrence of TR in LIB modules;

[0007] FIG.1B is a simplified block diagram showing an example of a computing device that can be used to implement the framework of FIG.1A;

[0008] FIG.2 is an illustration showing a computational domain for the multiphysics simulation showing a battery module representative unit with a cooling snake assembly and mesh illustration showing all relevant boundary conditions for implementing the framework of FIG.1A;

[0009] FIG.3 is an illustration showing data extraction from COMSOL results to graph-structured temperature data to be used for ML study, where each ^^^^indicates a frame of the current temperature graph for the thermocouple at time step ^^, which is recorded in a graph-structured data matrix;

[0010] FIG.4 is a schematic diagram showing a GNN-LSTM architecture for implementing part of the framework of FIG.1A including processing an input image with a GC layer, reshaping to introduce the information to the LSTM, updating each memory cell with weights from the previous cell, and transforming the data using a flatten layer in an arrangement to be read by a dense (fully connected) layer to give the final output;

[0011] FIGS.5A and 5B are a pair of graphical representations showing multiphysics modeling results that illustrate the variation of general parameters relating to the electrochemical-thermal model with respect to time (where FIG.5A shows charge / discharge curves for one TR hotspot and FIG.5B shows maximum temperatures for the four Li-ion batteries);

[0012] FIGS.6A-6D are a series of graphical representations showing temperature contours for the surface of the batteries for single and two hotspots at 2C charge / discharge rate (where FIG.6A shows a single hotspot at 0.5 hbatt mm, FIG.6B shows a single hotspot at 0.167hbatt mm from the bottom, FIG.6C shows 2 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 two hotspots at 0.5 hbatt mm and 0.83 hbatt mm from the bottom, and FIG.6D shows two hotspots at 0.33 hbatt mm and 0.583hbatt mm from the bottom);

[0013] FIGS.7A and 7B are a pair of graphical representations showing multiphysics modeling results for driving a cycle-informed model, illustrating the variation of general parameters relating to the electrochemical-thermal model with respect to time (where FIG.7A shows charge / discharge curves for one TR hotspot and FIG.7B shows maximum temperatures for the four Li-ion batteries); and

[0014] FIGS.8A-8C are a series of graphical representations showing the temperature prediction of the GNN-LSTM model to forecast battery surface temperature series for the last 350 time steps along with the ground truth values with one hotspot on battery B2 on the test dataset of thermal sensors at 2 points alongthe sensor (where FIG. 8A shows helical type at (0.0143, 0.0071, −0.0022) (left) and(0.0245, 0.0102, −0.0129) (right), FIG. 8B shows helix + straight type at(0.0127, − 0.0053 ,0.0061) (left) and (0.0114, 0, −0.0149) (right), FIG.8C shows Utype at (0.0267, 0.0095, − 0.0003) (left) and (0.0173, 0.0095, − 0.0003) (right); thedimensions are all in meters; due to constraints in ML methodology, surface temperatures are shown as normalized values; and the legend at the bottom shows the corresponding values of the final temperature as shown by the contour of the temperature sensor).

[0015] FIG.9 is a schematic workflow diagram illustrating a physics- informed machine-learning pipeline in which multiphysics simulations generate thermal imagery used to train deep-learning models for thermal-runaway (TR) classification and hotspot detection.

[0016] FIG.10 is a schematic block diagram of a YOLO object-detection network as applied to battery thermal images, showing a convolutional backbone, 1×1 reduction layers, and multiscale detection heads that regress bounding boxes and class probabilities for high-temperature regions.

[0017] FIGS.11A-11C are a series of graphical representations demonstrating multiphysics modeling results, respectively comparing cell voltage versus time during cycling (FIG.11A), solid-electrolyte-interface (SEI) thickness evolution (FIG.11B), and maximum temperature rise (FIG.11C), for batteries with single- versus dual-hotspot scenarios. 3 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0018] FIG.12 is a graphical representation showing total heat-generation rate during cycling for single-hotspot and dual-hotspot cases, highlighting exothermic discharge, endothermic charge behavior, and the exponential increase driven by SEI decomposition.

[0019] FIG.13 is a graphical representation showing capacity-fade and discharge-curve behavior from the multiphysics model, illustrating agreement with representative datasheet performance over repeated cycling.

[0020] FIGS.14A-14D are a series of graphical representations demonstrating representative temperature-contour snapshots from the 3-D multiphysics model for single- and double-hotspot cases at selected axial locations on cylindrical cells in a module, illustrating non-uniform surface-heating patterns.

[0021] FIGS.15A-15E are a series of graphical representations demonstrating confusion matrices for top convolutional-neural-network families (e.g., VGG, ResNet, DenseNet, EfficientNet, MobileNet), summarizing correct classifications and misclassifications for Safe, Critical, and thermal-runaway labels.

[0022] FIG.16 is a graphical representation showing example YOLO detections, including thermal inputs and corresponding outputs with predicted bounding boxes around high-temperature regions for single- and double-hotspot cases.

[0023] FIG.17 is a schematic diagram illustrating a reduced-order electrochemical-thermal (P2D-based) model used to generate temperature fields coupled to SEI-driven heat release and safety cutoff logic.

[0024] FIGS.18A-18D are a series of schematic diagrams depicting hotspot-location configurations on cylindrical cells (single- and two-hotspot placements at different axial and azimuthal positions) used to study how localized heating drives thermal-runaway risk.

[0025] FIG.19 is a graphical representation showing experimental-versus- numerical voltage-capacity curves across multiple C-rates, illustrating validation of the electrochemical model against published data.

[0026] FIGS.20A-20B are a pair of graphical representations demonstrating the FTP-75 driving-cycle inputs used in simulation, with vehicle-speed 4 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 profile versus time (FIG.20A) and the derived battery-current profile versus time (FIG.20B); the cycle is repeated to span the longer simulation duration.

[0027] FIG.21 is a schematic diagram illustrating thermocouple path geometries around cylindrical cell surfaces, including helical, helix-and-straight, and U-type paths, used to collect temperature at distinct spatial coordinates for machine- learning dataset creation.

[0028] FIG.22 is a schematic workflow diagram illustrating dataset preparation, including computation of a distance matrix over sensor coordinates to derive an adjacency matrix for graph construction together with a time-series temperature matrix forming graph-structured inputs.

[0029] FIG.23 is a graphical representation showing training and validation loss versus epochs for a graph-convolution-to-long-short-term-memory forecasting architecture, demonstrating convergence during model training.

[0030] FIG.24 is a graphical representation demonstrating temperature- versus-time traces at two points along each thermal-sensor path (including helical and mixed helix-and-straight cases) for a cell with one hotspot, showing small early- time differences and pronounced divergence during the final discharge cycle as thermal-runaway accelerates.

[0031] Corresponding reference characters indicate corresponding elements among the view of the drawings. The headings used in the figures do not limit the scope of the claims. 5 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 DETAILED DESCRIPTION

[0032] The present disclosure outlines a novel framework combining advanced machine learning (ML) techniques with multiphysics modeling to address safety concerns associated with lithium-ion batteries (LIBs). Herein, the present disclosure reports an ML framework aiming to predict the occurrence of thermal runaway (TR) in the LIB module by employing a multiphysics model that incorporates thermal, electrochemical, and degradation sub-models. The focus of this research lies in understanding the degradation phenomenon associated with the breakdown of the solid electrolyte interface (SEI) on the negative electrode, which can trigger TR. The developed multiphysics model enables the investigation of electrochemical and degradation processes within batteries under various conditions, including constant charge / discharge and driving cycles. To capture the spatio-temporal temperature change, a graph neural network (GNN) for spatial change is coupled with a Long Short-Term Memory (LSTM) network for temporal evolution to form an integrated framework. The results demonstrate the high accuracy of the ML model in predicting battery temperatures in a module based on spatial and temporal temperature data obtained from temperature sensors attached to the batteries, hence, offering a means to detect TR before it occurs by identifying potential thermal hotspots.

[0033] In operation, a processor of a battery management system controlling a battery module accesses a dataset of thermal and electrochemical characteristics of the battery module, the dataset incorporating degradation of a solid electrolyte interface. From this dataset, the processor constructs graph-structured time series data for the battery module, with each node representing a spatial location along the battery module that corresponds to a sensor coordinate along a curved path on a cylindrical cell surface and is associated with temperature values over a plurality of time steps. The processor generates an adjacency matrix from inter-sensor distances between the sensor coordinates and uses the adjacency matrix to compute a spatial dependency representation that encodes spatio-thermal inter-node dependencies. Using these inputs, the system forecasts, for each spatial location, a sequence of future temperatures for a plurality of future time steps by applying an LSTM.

[0034] In some implementations, the LSTM receives a node-embedding sequence derived from the graph-structured time series data and the spatial 6 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 dependency representation, simulates temporal dependence with a long short-term layer, and transforms a hidden state into the sequence of future temperatures for each spatial location along the battery module. The processor can evaluate, based on the sequence of future temperatures, whether a temperature threshold will be exceeded, and the battery management system can initiate a battery-safety response based on the sequence of future temperatures (for example, reducing a charge or discharge current, activating or increasing a cooling system, or issuing a warning). The dataset used for forecasting can include data captured from simulation by simulating operation of a coupled electrochemical-thermal multiphysics model representing the battery module and / or captured empirically as time-dependent temperature data from a plurality of thermocouples positioned along the battery module. The memory can include instructions to train or calibrate the LSTM using the dataset of thermal and electrochemical characteristics, including solid-electrolyte- interface decomposition heat-release events and a driving-cycle current profile. 1. Introduction

[0035] Renowned for their exceptional energy density, extended lifespan, and lightweight design, Lithium-ion batteries (LIBs) are widely used as an energy storage solution. Qiu et al. discussed the impact of electric vehicle development on traditional energy sectors, emphasizing the role of ion batteries in achieving zero emissions. However, safety concerns persist, particularly the risk of thermal runaway (TR) events causing catastrophic failure due to uncontrolled temperature rise from exothermic reactions. TR can occur due to various factors, such as overcharging, over-discharging, high-temperature exposure, manufacturing defects, and internal short circuits. During TR, rapid temperature rise induces stresses, gas generation, and electrolyte decomposition, risking battery failure, fire, or explosion, thus the accurate prediction of TR is essential for LIB safety. Mathematical modeling, is a crucial method for predicting TR in LIBs, offering insights into their thermal behavior, aiding system design, and facilitating effective thermal management strategies.

[0036] In recent years, there has been increasing interest in the use of ML methodologies in battery research, including the prediction of TR events. ML techniques, such as artificial neural networks, support vector machines, and decision trees, can analyze large amounts of data and identify complex patterns and correlations that may not be easily discernible through traditional mathematical 7 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 modeling. The integration of multiphysics simulation and machine learning presents a promising strategy for predicting TR in battery modules. This approach utilizes physics-based models with data-driven algorithms, aiming to achieve heightened accuracy in TR predictions. Several previous publications have reviewed the TR mechanism. The performance of LIBs can also be characterized through temperature curves obtained from Accelerating Rate Calorimeter (ARC) tests. As temperatures rise, a range of degradation processes may take place within the battery, resulting in TR. Three primary degradation mechanisms observed in batteries are solid electrolyte interface (SEI) decomposition, decomposition of cathode, and Li-electrolyte reaction. Such reactions increase the internal temperature, causing the melting of the separator and leading to internal short circuits, which further increase the temperature. Identifying the temperature at which SEI decomposition begins is crucial since it triggers other exothermic reactions, ultimately leading to TR. Therefore, understanding the temperature evolution due to the decomposition of SEI is critical to implement warnings for battery management systems (BMS).

[0037] Several mathematical models have been proposed to describe the thermal behavior of LIBs during TR. These models typically consider various factors, such as heat generation, heat transfer, chemical reactions, and thermal and mechanical stresses, to predict temperature evolution and TR events. For instance, Jindal et al. have proposed a three-mode heat transfer model coupled with electrochemical and abuse-reaction-kinetics models to delineate TR propagation in LIB modules. Validated against literature, their model showcased the effectiveness of active thermal management in preventing damage in an electric vehicle (EV) module (as used in Tesla). Shen et al. have explored nail penetration-induced TR in a large-capacity NCM Li-ion power battery, employing a one-dimensional simulation model in AMEsim software. Mishra et al. advanced TR safety understanding in cylindrical cell modules with a comprehensive numerical model considering vent gas flow, combustion, radiation, and TR phenomena, incorporating non-premixed combustion for practical insights. Xu et al. investigated the effects of design parameters on internal short-circuit behavior in cylindrical lithium-ion batteries, providing crucial insights for battery safety design. Liu et al. employed mechanical indentation techniques to study internal short circuits in lithium-ion batteries, 8 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 mapping their electrochemical safety behavior post-ISC. Jia et al. examined the safety risks of defective lithium-ion batteries caused by external mechanical abuse, proposing methods for early detection and risk evaluation. Liu et al. quantified stress- driven short-circuits in lithium-ion batteries, establishing criteria for short-circuits under mechanical loadings in electric vehicles. Zeng et al. conducted a study on thermal runaway propagation in lithium-ion battery modules, developing a model to predict TRP rates for different battery types. Gao et al. reviewed the thermal safety mechanisms and modeling of lithium-ion batteries, providing comprehensive insights from the material to the module level. Duan et al. investigated stress-driven internal short-circuits in lithium-ion batteries with high SOCs, proposing design modifications to prevent specific ISC modes.

[0038] In recent years, ML techniques have become increasingly pivotal in battery research, notably for predicting TR events. For instance, Zhu et al. have proposed a multi-ML fusion method utilizing ResNet-CNN pretraining and transfer learning for accurate ISC fault prediction in LIBs. Jia et al. have developed a rapid, accurate machine-learning algorithm to classify battery safety risks based on minimal one-cycle data, blending physics-based modeling with data-driven approaches. Li et al. introduced a data-driven method for detecting battery thermal anomalies by comparing shape similarity in thermal measurements and continuously grouping data into clusters for anomaly detection. These advancements underscore ML’s role in enhancing battery safety through precise fault prediction and risk classification.

[0039] Despite the significant advancements in ML algorithms, there is a limited exploration of data-driven approaches for battery design and TR prediction. A study outlined in Appendix A focused on predicting TR in single cylindrical Li-ion batteries using thermal images and CNNs for classification. Although promising, this approach had some practical limitations, including difficulties in obtaining images within a fully packed battery module with cooling channels and the high cost of such setups. To address these issues, the model is extended to a battery module and collected temperature data using thermal sensors, which are more feasible in practical applications. Focusing on a liquid-cooled module with a generic 2170 cells, a representative unit of four cells is modeled due to computational constraints. The study con-siders SEI decomposition as a major degradation mechanism leading to TR. Additionally, the model incorporates artificially placed hotspots with high 9 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 temperatures in the battery at various locations to trigger TR. The batteries undergo two different load cycles: constant charge / discharge cycles and the Federal Test Procedure 75 (FTP 75) driving cycle to reflect realistic EV behavior. Temperature data is extracted from these thermal sensors at specific coordinates and time steps, creating spatio-temporal data for analysis. Traditional methods like autoregressive integrated moving average (ARIMA), its variants, or simple neural networks (NN) prove inadequate for mid- and long-term temperature prediction. To overcome this, a combined GNN-LSTM network is reported, leveraging temperature history from thermocouples to predict future spatio-temporal temperatures. This analysis aids in determining whether the battery will experience TR. The research contributes to a hybrid methodology, integrating physics-based modeling and data-driven ML for effective TR prediction in battery modules. 2. Methodology

[0040] This section outlines the fused multiphysics and ML strategy for forecasting TR. Initially, a computational method studies battery degradation using an electrochemical-thermal model of a representative LIB battery module unit. Temperature data is extracted from thermocouples attached to the battery surface and preprocessed. Details of the thermocouple orientation are provided in a later section (cf. FIG.21 and Section 6 “Example Implementation Details”). The processed data is then fed into an ML algorithm featuring a GNN-LSTM network, which predicts future battery temperatures based on historical data. FIG.1A illustrates a framework 100 showing a computer-implemented system including an ML process flow. The left-hand part of FIG.1A shows the multiphysics model of a LIB module, generating a dataset of the battery’s thermal and electrochemical characteristics. This dataset is used by the ML algorithm, depicted in the central part of the schematic. The multiphysics model is a 3D representation of cylindrical LIB cells within a module, with a cooling snake between the cells. The central portion of FIG.1A details the ML workflow, starting with thermocouple data (red line around the cylindrical cell). This data is processed through various ML layers, including the graph convolution (GC) layer, which captures spatial characteristics, and the LSTM layer, which identifies temporal patterns. The process concludes with a fully connected neural network layer that integrates the spatial-temporal information to predict TR. 10 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0041] FIG.1B is a schematic block diagram of an example device 200 that may be used with one or more embodiments described herein, e.g., as a component of a system implementing the framework 100 of FIG.1A.

[0042] Device 200 comprises one or more network interfaces 210 (e.g., wired, wireless, PLC, etc.), at least one processor 220, and a memory 240 interconnected by a system bus 250, as well as a power supply 260 (e.g., battery, plug-in, etc.).

[0043] Network interface(s) 210 include the mechanical, electrical, and signaling circuitry for communicating data over the communication links coupled to a communication network. Network interfaces 210 are configured to transmit and / or receive data using a variety of different communication protocols. As illustrated, the box representing network interfaces 210 is shown for simplicity, and it is appreciated that such interfaces may represent different types of network connections such as wireless and wired (physical) connections. Network interfaces 210 are shown separately from power supply 260, however it is appreciated that the interfaces that support PLC protocols may communicate through power supply 260 and / or may be an integral component coupled to power supply 260.

[0044] Memory 240 includes a plurality of storage locations that are addressable by processor 220 and network interfaces 210 for storing software programs and data structures associated with the embodiments described herein. In some embodiments, device 200 may have limited memory or no memory (e.g., no memory for storage other than for programs / processes operating on the device and associated caches). Memory 240 can include instructions executable by the processor 220 that, when executed by the processor 220, cause the processor 220 to implement aspects of the framework 100 of FIG.1A and associated methods outlined herein.

[0045] Processor 220 comprises hardware elements or logic adapted to execute the software programs (e.g., instructions) and manipulate data structures 245. An operating system 242, portions of which are typically resident in memory 240 and executed by the processor, functionally organizes device 200 by, inter alia, invoking operations in support of software processes and / or services executing on the device. These software processes and / or services may include thermal runaway prediction processes / services 290, which can include aspects of the methods and / or 11 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 implementations of various modules described herein. Note that while thermal runaway prediction processes / services 290 is illustrated in centralized memory 240, alternative embodiments provide for the process to be operated within the network interfaces 210, such as a component of a MAC layer, and / or as part of a distributed computing network environment.

[0046] It will be apparent to those skilled in the art that other processor and memory types, including various computer-readable media, may be used to store and execute program instructions pertaining to the techniques described herein. Also, while the description illustrates various processes, it is expressly contemplated that various processes may be embodied as modules or engines configured to operate in accordance with the techniques herein (e.g., according to the functionality of a similar process). In this context, the term module and engine may be interchangeable. In general, the term module or engine refers to model or an organization of interrelated software components / functions. Further, while the thermal runaway prediction processes / services 290 is shown as a standalone process, those skilled in the art will appreciate that this process may be executed as a routine or module within other processes. 2.1. Multiphysics modeling methodology

[0047] The methodology utilized in the multiphysics model and outlined within this section is adapted from a model outlined in Section 5 of the present disclosure (“Development Study: Multiphysics-Driven Learning for Thermal-Runaway Prediction (Illustrative Study)”). Initially, the general electrochemical model is presented, followed by an explanation of the thermal model. Moreover, this section delves into specifics regarding the computational domain and provides a general overview of the model’s implementation. Employing the finite element method (FEM), the multiphysics model aims to replicate the electrochemical-thermal dynamics of a cylindrical battery across diverse scenarios. The electrochemistry is modeled using the pseudo-two-dimensional (P2D) model, and the temperature of the batteries is simulated using a 3D model. The coupling of the two models occurs through the generated heat source from the P2D and the temperature from the 3D model. A detailed description of the theory pertaining to the electrochemical part of the proposed model is outlined in Section 5 of the present disclosure. Initially, under general operation conditions, the cells undergo a continuous charge / discharge load 12 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 (i.e., constant C-rate), leading to heat generation inside the cells due to different electrochemical processes. Subsequently, cells are subjected to the FTP 75 driving cycle load, which simulates authentic vehicular and battery conditions to mirror real- world environmental influences.

[0048] The thermal characteristics, including heat generation during a TR event, are explained through the general equation for the energy conservation solved for essentially three domains, namely battery module representative unit where conduction is the dominant heat transfer mechanism (Eq. (1)), the cooling snake assembly where convection dominates (Eq. (2)) and finally the outer box which is a solid domain composed of the filler material where conduction is the main heat transfer mechanism (Eq. (3)). ^^^^ ^^^^^^^^^^^^ + ∇ ∙ ( (1^^^^−^^^^∇^^^^) = ^̇^g, )

[0049] It should be emphasized that Eq. (2) is solved in conjunction with the Navier-Stokes equations for the incompressible flow inside the cooling snake. Here, ^^^^is the thermal conductivity coefficient of each battery. It takes the form of a symmetric positive-definite tensor (matrix) and is given by: ^^th 0 0^^(4)

[0050] where ^^^^and ^^^^are the average thermal conductivity coefficients of the cooling liquid and the filler material; ^^^^, ^^^^and ^^^^denote the average densities 13 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 of the cells, cooling liquid, and the filler material; ^^^^^^, ^^^^^^and ^^^^^^are the average specific heat capacities of the cells, cooling liquid and the filler material; and ^̇^gis the volumetric heat generation rate for the battery. In some implementations, anisotropic thermal conductivity (in-plane vs through-plane) is reflected in the spatio-thermal couplings among nodes (e.g., via edge weighting and / or learned parameters). The heat generation rate of the cell that is subject to the SEI degradation is given (and further elaborated on in Section 5 of the present disclosure): ^̇^g = ^̇^e + ^̇^SEI, (5)

[0051] where, ^̇^eis calculated as the combined effects from the irreversible heat stemming from Joule heating and activation losses and the reversible heat resulting from electrochemical reactions. Further details about ^̇^eare given in Section 5 of the present disclosure. However, ^̇^SEIis the heat generation rate due to the exothermic SEI decomposition reaction. As stated earlier, the battery undergoes various exothermic reactions during its operation, which can lead to a TR event. During charging and discharging, reversible and irreversible reactions occur within the battery, causing the temperature to increase. Additionally, parasitic reactions take place in the anode of the battery, leading to the formation of SEI. When the SEI grows to a certain extent, it decomposes, releasing heat and causing temperature to rise further. The heat release due to the decomposition of the SEI layer is described by a modified Arrhenius function. According to this function, the rate of the SEI decomposition reaction, and consequently the heat release, increases exponentially with temperature. This behavior is due to the fact that higher temperatures provide more energy to overcome the activation energy barrier for the decomposition reaction. The triggering mechanism for the artificial hotspots is the decomposition of the SEI layer. The SEI decomposition leads to significant heat generation within the battery. The heat generation due to SEI decomposition is given by (6) ^̇^SEI = ^^eℎSEI^^SEI,d ,14 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0052] where, ^^eis the active specific surface area; ℎSEIis the enthalpy of the reaction and ^^SEI,drepresents the reaction kinetics of the SEI decomposition reaction. The exothermic reaction resulting from the decomposition of SEI in batteries significantly elevates the battery’s temperature, giving rise to randomly distributed hotspots within the battery. These high-temperature hotspots are stochastic in nature and can occur spontaneously due to local defects. Standard modeling techniques do not inherently incorporate these hotspots, necessitating their artificial placement in random locations inside the battery during the model creation prior to simulations. These artificially introduced hotspots are specifically associated with the studied degradation mechanism, and their heat release induces self-heating of the battery, consequently triggering TR. The present investigation primarily focuses on the self-heating phenomenon induced by the formation and subsequent decomposition of SEI, which is regarded as the primary degradation process.

[0053] In the multiphysics modeling of a battery module with a cooling serpent, heat dissipation involves both conduction and forced convective heat transfer. The cooling serpent, made of a thermally conductive metal, directly contacts the battery cells, enabling efficient heat conduction to the serpent’s surface. Simultaneously, a liquid coolant circulates within the serpent under forced convection, assuming laminar flow driven by a specified inlet velocity. The coolant actively removes absorbed heat, enhancing the convective heat transfer process. The calculated Reynolds number for the flow is 615, indicating laminar flow, which simplifies the flow simulation and maintains key heat transfer features. This is based on an inlet flow velocity of 0.1 m / s and the cooling serpent’s cross-section. This combined conduction and forced convection model within the multiphysics framework provides valuable insights into the battery module’s thermal behavior. While detailed Navier-Stokes equations are omitted for brevity, this approach effectively captures the heat transfer dynamics. Proper boundary conditions, explained in the following section, are required to solve the problem.

[0054] In EV battery systems, temperature sensors are attached to battery cell surfaces to measure temperature fluctuations during operation. These sensors provide real-time data essential for maintaining optimal performance and safety. During charging and discharging cycles, sensors detect temperature deviations, 15 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 allowing the BMS to adjust parameters like charging rate or activate cooling systems to prevent overheating. Their strategic placement ensures comprehensive coverage, detecting hotspots or uneven temperature distributions that could indicate potential issues. This vigilant monitoring enhances the efficiency, longevity, and reliability of EV battery systems. To mimic temperature measurement and predict TR in a model, artificial curves can be introduced on battery surfaces to represent thermal sensors. The temperature is collected at various time steps and spatial coordinates along these curves. Various orientations are considered for extracting spatio-temporal temperature data for an ML algorithm, including helix, straight line, and combinations,. Details of these orientations are provided in FIG.21 and Section 6 “Example Implementation Details”. In subsequent sections, these curves are referred to as temperature sensors for clarity. 2.1.1. Computational domain

[0055] This subsection is dedicated to the description of the computational domain and the related boundary and initial conditions for the multi-physics model. The multiphysics model includes a P2D model, which solves for the electrochemistry, and a thermal model coupled to it that is responsible for solving the heat transfer. Coupling the P2D model with the 3D thermal model integrates detailed electrochemical processes with spatially resolved thermal dynamics. The P2D model provides heat generation rates for the batteries, which serve as inputs for the 3D thermal model. Conversely, the 3D model provides temperature distributions that influence the reaction kinetics and diffusion processes in the P2D model. Since the P2D model considers only a single temperature value, the average temperature for each battery is used as input. The coupled model is solved iteratively, with data exchanged between the P2D and 3D components at each time step, ensuring accurate capture of both electrochemical and thermal aspects. This iterative process involves solving the P2D model to obtain reaction rates and heat generation, using this data as input for the 3D thermal model to compute temperature distributions, feeding the temperature data back into the P2D model to update reaction kinetics and diffusion coefficients, and repeating until convergence is achieved. A detailed description of the electrochemical model is presented in Section 5, and the computational domain for the P2D model along with the equations, are provided in Section 6 (e.g., FIG.17). The thermal model involves a representative unit of a 16 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 battery module including four cylindrical cells arranged in alternating 2x2 configuration, with an integrated cooling snake assembly. FIG.2 shows the computational domain created in COMSOL Multiphysics, depicting the thermal domain. Further information are provided in the SI. It should be noted that there is a single P2D model for each of the batteries for the electrochemical problem. However, the domains are identical in geometry, hence, only a single figure has been shown for visualization purposes. The 3D domain is discretized using a finite element mesh. Each cylindrical cell is in contact with the cooling assembly, which is designed to dissipate heat away from the cells efficiently. The serpentine cooling configuration is a critical component in the thermal management of the battery module, ensuring uniform temperature distribution and mitigating the risk of TR. The unstructured mesh with quadratic elements is constructed to capture the complex geometry of the cells and the cooling assembly, with a finer resolution at critical areas to ensure accurate simulation results. The mesh density is increased near the interfaces between the cells and the cooling assembly to resolve the thermal gradients and fluid flow characteristics more precisely.

[0056] Given that the system operates based on electrochemical and thermal principles, it possesses two distinct sets of initial and boundary conditions: one pertaining to the electrochemical model and the other related to thermal aspects and fluid movement. Regarding the electrochemical model, the initial SOC value for the negative electrode is set to be 0.99 and for the positive electrode to be 0.01. In order to balance the electronic current, a potential of 0 V is set on the current collector of the negative electrode. Moreover, the separator boundaries are kept insulated for electric currents. In order to balance the ionic charge in the electrolyte, the current collector boundaries are considered to be insulating. Insulating conditions are also applied to material balances. Additionally, for the diffusion equation in the solid phase, the flux of Li ions is determined by the rate of the local electrochemical reaction at the surface of the particle, and at the center spherical symmetry is present. These are also explained in Section 5. In the thermal model of the coolant through the cooling snake assembly, the batteries are positioned within a casing with filler material. The inlet is designated with a temperature of 298 K, while at the outlet, a zero temperature gradient is set as the boundary condition. The external boundaries at the top and the bottom have been thermally insulated. The battery is 17 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 assumed to have an initial temperature of 298 K. Furthermore, a fully developed flow has been assumed at the inlet and outlet of the cooling compartment. Periodic boundary conditions have been enforced for the side walls of the casing representing repeating units of battery and cooling snake assembly. The walls of the cooling snake are subjected to a no-slip boundary condition. The temperature is continuous across the boundary of the batteries and the cooling snake. The temperature gradient is zero at the outlet of the cooling snake. 2.1.2. Model implementation

[0057] The electrochemical, thermal, and SEI degradation models are implemented in the COMSOL multiphysics software platform. The finite element model employs an unstructured mesh with quadratic elements and utilizes the backward Euler scheme for time discretization. The PARDISO solver from COMSOL 6.1 is used to solve the nonlinear equations system during both the initialization and transient stages. For the simulations presented in this paper, a 3D model incorporating four cylindrical 2170 cells with NMC chemistry is selected. The cooling fluid comprises a 50 % mixture of Ethylene Glycol and water. The negative electrodes include Graphite, while the positive electrode comprises NMC111. The electrolyte is composed of a 3:7 ratio of EC:EMC with a 1 M LiPF6 salt, and the material properties are imported from the COMSOL material library. The model incorporates a user-defined condition, whereby the calculations are halted if the maximum temperature of the battery exceeds 500 K. This condition is crucial since exceeding this threshold can lead to a sudden temperature rise and potential explosion. All the parameters used in the model development of this study are listed in Section 6 (e.g., Table 4) 2.2. Machine learning methodology

[0058] This section is devoted to elucidating the developed ML framework, which is divided into two distinct components. The initial part focuses on the preparation and preprocessing of the dataset, while the subsequent part delineates the implementation of the ML methodology. The ML methodology encompasses the spatio-temporal prediction of temperature, with the major objective of predicting TR in the batteries system. 2.2.1. Dataset preparation and preprocessing 18 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0059] Temperature forecasting constitutes a time-series prediction task, entailing the estimation of future temperature measurements based on historical temperature observations. Since temperature exhibits spatial variation along the temperature sensors, a coordinate network can be established and structured as a graph to represent the structured temperature time series as illustrated in FIG.3. Consequently, any temperature observation at time step ^^ is not independent but rather connected via pairwise connections in the graph. Thus, a data point at time step ^^ can be conceptualized as a graph signal residing on an undirected graph.

[0060] The extraction of relevant parameters for this problem encompasses the spatial coordinates along the sensors and the time-dependent temperature values. LiveLink for MATLAB was used to integrate COMSOL multiphysics with MATLAB, facilitating the expansion of modeling capabilities through programming in the MATLAB environment. This bidirectional interface empowers the utilization of MATLAB as a scripting interface to configure and solve COMSOL multiphysics models. By leveraging this functionality, temperature data along the spatial coordinates were extracted as CSV files for each time step of the battery’s operation. The temperature points in the model were collected at a frequency of 1 s. This frequent data collection is crucial to ensure the accuracy of the ML predictions, as it captures the dynamic thermal behavior of the battery system in detail. However, these files cannot be directly employed for the ML study. Consequently, it is imperative to restructure the data into specific formats suitable for input into the ML study. This process, known as data preparation and preprocessing, constitutes a crucial step in any ML investigation. The collected data was modified and saved into two files. The first file included the distances between the 120 spatial coordinates along the sensors, while the second file contained the temperature measurements collected at those points throughout the entire simulated battery operation. The first file is important for creating the adjacency matrix required to create the graph network for spatial feature identification. An adjacency matrix is an^^ × ^^ matrix filled with either 0 or 1, where ^^ is the total number of nodes.Adjacency matrices are able to represent the existence of edges that connect the node pairs through the value in the matrices. In this work, the coordinates of the thermocouple are assumed to form a graph. The next step was to create the graph adjacency matrix from the distances calculated from the spatial coordinates. 19 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 Subsequently, the dataset necessary for tackling the forecasting problem was generated. The challenge at hand revolves around envisioning forthcoming temperature measurements at various times. To accomplish this, the temperaturestatistics during time intervals ^^ + ^^ + 1, ... , ^^ + ^^ + ℎ was anticipated based onthe prior observations at ^^ + 1, ^^ + 2, ... , ^^ + ^^. Consequently, the model receives ^^arrays comprising ^^ elements, each as inputs for every given time ^^, while h arrays with ^^ elements each serve as the desired outcomes. Here, ^^ symbolizes the count of spatial points in consideration. Next, the temperature array was split into train / - validation / test sets.70% of the dataset was used for training, followed by 10 % for validation and 20 % for the test dataset. Finally, normalization was used for the resulting arrays. 2.2.2. Spatio-temporal prediction of temperature using graph neural network- long short-term memory

[0061] Current battery management systems provide real-time temperature readings; however, they lack the ability to predict future temperature trends. By utilizing the temperature history of batteries during operation and knowing the driving behavior (driving cycle), it is possible to predict future temperature trends, serving as a critical safety criterion for TR prognosis. In this context, data-driven approaches, particularly advanced ML techniques, offer great potential. To address these challenges, this study reports a novel framework that combines a GNN with an LSTM network. This type of network is used for traffic speed forecasting and weather forecasting as well. However, to the best of authors’ knowledge, it has never been utilized in the field of battery research. This integrated GNN-LSTM network takes into account the intricate and variable temperature dependencies present in the historical data. By leveraging the power of GNNs to handle spatial interdependencies and the temporal modeling capabilities of LSTMs, the proposed framework aims to forecast future temperature trends for battery modules accurately. The Convolutional layer in the GNN enables learning and identification of a particular type of feature present at a specific spatial location within the input.

[0062] The GNN is designed to capture spatial relationships between different regions of the battery. The system processes the spatial data represented by the distance matrix to derive an adjacency matrix that defines the graph, with nodes corresponding to sensor coordinates (temperature measurement points) and 20 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 edges representing spatial relationships. The Graph Convolution Layer within the GNN aggregates information from neighboring nodes (temperature measurement points) to compute each node’s representation using the adjacency matrix. In some implementations, anisotropic thermal conductivity (in-plane vs through-plane) is reflected in the spatio-thermal couplings among nodes (e.g., via edge weighting and / or learned parameters). Key operations in this layer include aggregation, where the features of neighboring nodes are summed, averaged, or maximized; combination, where the aggregated features are combined with the node’s original features either through concatenation or addition; and activation, where an activation function (e.g., ReLU) is applied to introduce non-linearity. LSTM, a type of RNN, has been developed specifically for predicting future outputs by leveraging past inputs. LSTM has demonstrated its effectiveness in forecasting based on time-series data. The LSTM component is responsible for capturing the temporal evolution of the thermal and electro-chemical states. It processes sequences of temperature data to predict future temperature trends. The LSTM layer is specifically designed to handle time-series data by capturing long-term dependencies in the sequence of temperature data and maintaining a cell state that is updated at each time step. This layer outputs a sequence of hidden states that summarize the information in the input sequence. The input sequence length parameter defines the number of past time steps (^^) used as input to the model, while the output sequence length parameter defines the number of future time steps (h) that the model predicts.

[0063] Following the LSTM layer, a dense layer is used to produce the final prediction by applying a linear transformation to the LSTM output to match the desired output shape, which is the forecasted temperature values. The combined GNN-LSTM model is constructed by stacking the Graph Convolution Layer and the LSTM layer, followed by the flatten and full connected / dense layer. The model takes sequences of temperature data as input, processes them through the GNN to capture spatial dependencies, and then through the LSTM to capture temporal dependencies, finally outputting the predicted temperature values. FIG.4 shows a general network architecture of the GNN-LSTM network. The architecture includes a series of special layers to better capture the spatial and temporal dependencies of the data. The input layer accepts graph-structured time series data, where each node is associated with features in a series of time steps, and then the GC layer 21 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 applies graph convolution to gather information from neighboring nodes in order to facilitate the capture of spatial dependencies. The subsequent reshaping operation optimizes the output to match the LSTM levels. The LSTM layer formed with a specified number of units efficiently simulates the time dependence of the node embedding sequence. The outputs are reshaped again before feeding them into the flatten layer. Following the flatten layer, fully connected dense layers are used to transform the hidden state of the LSTM into predicted values for each node. This architecture showcases a complex interplay of GC and recurrent neural network components, illustrating a sophisticated approach for learning and forecasting on graph-structured time series data. The workflow involves seamlessly passing information through these layers, collectively enabling the model to learn complex patterns and relationships within the graph.

[0064] The spatial dependency representation may be precomputed and stored (e.g., adjacency matrix from inter-sensor distances) or generated on-the-fly by a spatial encoder (e.g., a graph-convolution block).

[0065] In some embodiments, the battery management system initiates a safety response (e.g., current limiting, enhanced cooling, or a warning) based on predicted future temperatures and an estimated time-to-exceedance of a safety threshold produced by the forecasting network.

[0066] 3. Results and discussion

[0067] This section presents the results pertaining to the multiphysics modeling and the corresponding ML study. The initial phase of the study involves conducting multiphysics modeling under a constant charge / discharge load, followed by automotive simulations that incorporate driving cycles. Subsequently, ML techniques are applied to the data obtained from the multiphysics model, and a comprehensive analysis of the results is conducted. 3.1. Thermo-electrochemical modeling using constant charge / discharge cycles

[0068] Thermal runaway in LIBs is a rapid and explosive event that poses challenges for real-time observation. During battery operation, various side reactions can be triggered, potentially influencing the propagation of TR within the battery and 22 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 leading to localized failure. Due to the complex nature of TR events and limited understanding, accurate modeling of TR remains challenging. In this modeling study, the selection of TR hotspots is performed randomly, considering scenarios with one or two hotspots. A detailed description on the location of the hot-spots is provided in FIG.18A-18B and Section 6 “Example Implementation Details”

[0069] The results focus on constant charge / discharge load conditions, analyzing voltage and temperature profiles for each battery through multiphysics modeling. The influence of the SEI on battery temperature is discussed, and high- temperature hotspots are visualized using temperature contours in a representative battery module unit. Before modeling TR in cylindrical cells, the electrochemical model was validated against experimental data from Waldmann et al. (cf. FIG.19 outlined with respect to Section 6). The model examines the impact of cell degradation on battery temperature and capacity using CCCV charging and constant current discharging for four batteries. Initially, batteries are fully charged and discharged at 1C until reaching a cutoff voltage of 2.7 V, followed by CCCV charging back to 4.2 V. The generated heat is insufficient to trigger SEI decomposition or TR, aligning with the fact that higher C rates increase the risk of TR by generating more heat due to higher current flow. Therefore, cells were operated at a 2C rate. FIGS. 5A and 5B displays charge and discharge profiles for the four batteries, highlighting a hot-spot in battery B2 (FIG.5A) and changes in maximum temperature for each battery (FIG.5B). Ideally, batteries should undergo many charge-discharge cycles to form a substantial SEI, assuming negligible variation from one cycle to another. To illustrate this, the SEI growth rate is accelerated by increasing the pre-exponential factor in the model, enabling expedited TR observation and facilitating efficient analysis of battery behavior. This approach explores SEI growth patterns and potential effects on battery performance and safety under accelerated conditions, providing valuable insights for battery design and thermal management.

[0070] FIGS.5A and 5B show battery B2’s voltage profile, suffering from capacity fade and faster discharge due to SEI degradation. The BMS prevents cells from discharging below their cutoff voltage by adjusting the current based on individual cell states, halting discharge for B2 when it reaches its cutoff voltage. During charging, B2 reaches 4.2 V sooner, prompting the BMS to cut off its current until other cells are fully charged. This rising temperature trend due to cell 23 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 degradation is noted in previous studies. Hotspots cause uneven heat and SEI distribution, but the P2D model assumes uniform SEI growth. Investigating non- uniform SEI formation requires a 3D particle model and a comprehensive battery model, to be explored in future research.

[0071] The TR model aims to derive temperature data from thermocouples attached to batteries, offering insights into TR initiation. Thermocouple orientation details are in Section 6 (cf. FIG.21). This study uses ML on simulation-derived data to predict TR, introducing artificial hotspots within batteries to trigger TR, with their number and locations randomly distributed. Variations in hotspot number and location in battery B2 were used to study cell temperature evolution and its impact on neighboring cells. FIGS.6A-6D show temperature contours for batteries at a constant 2C charge / discharge current. Heat release from SEI decomposition at hotspots in battery B2 raises the module’s temperature, leading to TR. FIGS.6C and 6D depict temperature distributions with two hotspots at different heights in battery B2, where exothermic SEI decomposition reactions increase overall battery temperature, triggering thermal TR. When projecting or mapping a P2D electrochemistry model onto a 3D thermal model, the expectation is for an even distribution of temperature, assuming uniformly distributed heat sources and consistent material properties. However, in real-life scenarios, TR typically initiates at specific points and propagates due to the presence of thermal hotspots. These hotspots are critical indicators of localized heating that could lead to unsafe conditions. The present disclosure emphasizes the importance of these thermal hotspots. They do not naturally emerge in a straightforward projection of the P2D model into a 3D thermal model. To accurately replicate real-life behavior and practical conditions, these hotspots are artificially introduced into the 3D thermal model. This deliberate introduction of hotspots enables us to simulate the initiation and propagation of TR as it would occur in actual battery systems. Consequently, the observed temperature unevenness in the model is a result of these artificially introduced hotspots, ensuring that the model realistically represents the dynamic thermal behavior of the battery under conditions that could lead to TR. 3.2. Thermo-electrochemical modeling using driving cycle

[0072] This subsection transitions from conventional constant charge- discharge cycle modeling to a dynamic real-life scenario. By incorporating real-world 24 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 driving conditions and variations, this approach offers a more accurate representation of the interactions between temperature, electrochemical processes, and the operating environments of LIB modules. Details on the driving cycle data used in this work are provided in Section 6 (cf. FIGS.20A-20B). In this study, a representative unit of 4 batteries is initially fully charged, then subjected to the driving cycle current until they reach the cutoff voltage. After discharge, the batteries are charged at a constant current, simulating a fully discharged EV being recharged. The governing equations and boundary conditions for the batteries remain as explained in previous sections. FIGS.7A and 7B show the discharge / charge characteristics of the batteries in the representative unit and the temperature effect due to SEI degradation. FIG.7A illustrates the discharge / charge characteristics under driving cycle discharge and constant current charge. SEI decomposition is assumed to be the major degradation source in battery B2, which triggers TR at 500 K. FIG.7B shows the temperature evolution of the individual batteries, with battery B2 undergoing SEI decomposition due to assumed internal defects.

[0073] Building upon the outcomes derived from the multiphysics simulation, the subsequent section will be dedicated to applying these findings within the context of the ML investigation. This will be succeeded by a comprehensive analysis of the results obtained. 3.3. Machine learning results

[0074] Numerous ML techniques have demonstrated remarkable potential in examining the characteristics of materials used in LIBs, predicting the battery’s SOC, and identifying instances of battery malfunctions. A relatively novel strategy involves utilizing ML to predict TR occurrences in batteries. The existing literature contains scarce examples of employing data-driven ML concepts for predicting such events. It is believed that there has not been any research that utilizes a spatio- temporal ML technique to predict TR events using data collected from temperature sensors connected to a battery module, which is a unique aspect of this study. The information derived from multiphysics modeling after proper data preprocessing is fed into the ML investigation to predict TR. The model training process involves several steps to ensure effective learning and accurate predictions. First, the preprocessed data is converted into TensorFlow datasets suitable for training. These datasets are created using sequences of input data and corresponding target values, 25 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 which help the model learn the temporal and spatial patterns in the temperature data. Next, the model is compiled with an optimizer (RMSprop) and a loss function (Mean Squared Error). The optimizer adjusts the model parameters to minimize the loss function during training, thereby improving the model’s accuracy. Additionally, the training process includes early stopping based on validation loss to prevent overfitting. This means that training stops if the validation loss does not improve for a certain number of epochs (patience), ensuring that the model generalizes well to new, unseen data. All the networks exhibit satisfactory performance after 100 iterations, with the loss approaching approximately 0.02 %. Similar patterns were observed for the validation set. The details of the learning curve are provided in Section 6 (cf. FIG.23).

[0075] Furthermore, an investigation was conducted to examine the impact of different training batch sizes on the overall model loss. Preference is generally given to larger batch sizes, enabling the model to consider a greater amount of data during each training moment. However, larger batch sizes come with the drawbacks of increased computational memory consumption and prolonged training duration. In this particular analysis, the batch size varied to 32, 64, and 128 while maintaining the same number of training iterations. The comparison of loss between batch sizes 64 and 128 yielded the most favorable outcomes for the proposed network, albeit the latter exhibited slightly higher accuracy at the expense of substantially greater training time and memory usage. Consequently, a batch size of 64 was selected as the optimal choice, and the outcomes were reported accordingly. This study examines the efficiency of the suggested network by utilizing metrics such as the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), which have been considered to state the efficiency of the proposed network. The description and formulas for these metrics are given in the SI. The MAE and RMSE of the proposed model are 0.072 and 0.187, respectively, on the test dataset. The test dataset is not known by the model during training, hence, such a lower value of these metrics indicates the good efficiency of the proposed network. Additionally, the obtained values of the evaluation metrics indicate that this idea can also be well extended to data collected from experimental battery operation in EVs and could significantly help in predicting real-time TR detection in batteries. FIGS. 8A-8C present the ML results for temperature forecasting as a time series curve on 26 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 the test dataset for the proposed network, with a single hotspot on battery B2 for three thermocouple orientations: helix (FIG.8A), helix + straight (FIG.8B), and U type (FIG.8C). The results cover the last 350 time steps, each representing 1 s, corresponding to 30,806 to 31,156 s when TR occurs. While FIGS.5A and 5B show the maximum internal battery temperature, FIGS.8A-8C show temperatures from the sensors. The maximum internal temperature represents hotspot temperatures, which are higher than the local surface temperature. FIGS.8A-8C display ML forecasts for two locations on each thermocouple, highlighting the model’s ability to predict rising temperature trends that lead to TR. Analyzing the ML forecasts (blue) and true values (red) shows the model’s effectiveness in predicting time series temperatures at various thermocouple positions. The dataset was normalized using z-score normalization before training. Thus, the y-axis in FIGS.8A-8C represents normalized surface temperatures, but the final temperature for the entire sensor is also provided in the legends, with the thermal sensor temperature contour shown for the last time step.

[0076] The proposed framework demonstrates remarkable effectiveness in accurately predicting temperature patterns over time, exhibiting minimal deviation from observed values. The test dataset, which included completely unfamiliar samples to the model, ensures the model’s ability to generalize to unseen data. The outstanding performance on this unknown dataset showcases the model’s robustness and adaptability. The results strongly suggest the potential of employing various ML approaches to different configurations of thermocouples on battery cells, enabling reliable predictions of thermal failures. This methodology can be further extended to real-time prediction of thermal failures in EVs, thus enhancing safety measures in EV applications. 4. Summary and conclusions

[0077] A novel framework has been developed to forecast the thermal response of cylindrical LIB modules, integrating multiphysics modeling and ML techniques. The multiphysics model, implemented using COM-SOL software, simulates the electrochemical-thermal characteristics of the cylindrical battery under various conditions. Batteries undergo constant current charge / discharge cycles, followed by a driving cycle during discharge to mimic EV operation. Thermal sensors are strategically positioned to capture surface temperature data, revealing complex 27 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 nonlinear patterns dependent on spatial and temporal variables. To address this complexity, a GNN is combined with an LSTM network, managing spatial and temporal interdependencies effectively.

[0078] Based upon the constant charge / discharge study, initially, the SEI layer grows rapidly during the charge cycles due to being limited by diffusion. Over time, as the layer becomes thicker, its resistance increases, which slows down the growth rate. Consequently, the system transitions from being diffusion-limited to being limited by kinetics. Additionally, the SEI formation led to the reduction of cyclable lithium, and significant capacity fade was observed. Due to this capacity fade the battery B2 reached the cutoff voltage sooner and remained in the rest stage until all the other batteries were discharged to represent appropriate cell balancing. A similar trend was observed when the FTP 75 driving cycle was used. Moreover, the exponential rise in temperature caused by the exothermic heat release due to SEI decomposition in battery B2 was simulated, which has been explained by the Arrhenius equation. The ML results show outstanding performance in predicting the future temperature profiles along the coordinates of the temperature sensors with an MAE of 0.072 and an RMSE of 0.187 on the test dataset.

[0079] While this approach shows promise in enhancing EV safety by predicting battery failures, there are challenges to large-scale implementation. It is crucial to consider various degradation mechanisms and cell designs to build a more comprehensive and reliable dataset. Additionally, diverse driving behaviors impact battery temperature pre-dictions. The model disclosed herein can be retrained with varied driving data, enhancing its predictive capability for better safety outcomes. This adaptability ensures effectiveness across different operational scenarios, contributing to battery safety advancements. Moreover, the multi-physics modeling and ML framework in this study can be adapted to various LIB configurations, including different geometric designs and anode / cathode materials, beyond cylindrical cells.

[0080] The functions performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and operations are provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments. 28 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0081] It should be understood from the foregoing that, while particular embodiments have been illustrated and described, various modifications can be made thereto without departing from the spirit and scope of the invention as will be apparent to those skilled in the art. Such changes and modifications are within the scope and teachings of this invention as defined in the claims appended hereto. 5. Development Study: Multiphysics-Driven Learning for Thermal- Runaway Prediction (Illustrative Study)

[0082] This section outlines a study that relates to the development of the present disclosure. It describes a combined multiphysics modeling and deep- learning workflow used to generate datasets and evaluate model behaviors, including SEI-driven heat-release physics and learning architectures. The study reflects one way to build and analyze training datasets (e.g., by simulating cylindrical cells, introducing hotspot conditions, and deriving temperature time-series), and presents illustrative model choices and metrics. The results are presented to aid understanding and do not limit the systems and methods outlined herein.

[0083] Li-ion batteries (LIBs) are one of the most extensively used energy storage devices and essential pillars in future energy management systems. LIBs offer some of the highest energy and power densities (both volumetric and gravimetric) among many other energy storage technologies. The safety aspects of LIBs have become increasingly crucial for reliable and long-lasting usage. However, recent events of some electric vehicle (EV) explosions show the necessity to reevaluate the safety aspects of LIBs. The major bottleneck with LIBs is the occasional uncontrollable failures in both energetic and non-energetic modes. Both modes may occur due to numerous reasons, such as cell manufacturing flaws, poor (electrical or mechanical) cell design, external (thermal, mechanical, or electrical) abuse of cells, defective protection electronics, and chargers. In this work, the focus is on the most severe energetic failure of the LIBs that occurs due to thermal runaway (TR). In general, TR happens due to a cell’s rapid self-heating sourced from exothermic (electrochemical) reactions, mechanical abuse and / or thermal abuse. During the TR, excessive heat has a detrimental influence on the electrical characteristics and the state-of-charge (SOC) of the LIBs. The extreme heat can cause separator decomposition causing an internal short-circuit, which itself intensifies the heat generation, leading to an accidental explosion of the battery. It is 29 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 quite challenging to directly monitor the events occurring during the TR in practical operating conditions. However, the change in electrical parameters during the TR- like events could potentially indicate the existence of a failure, thus allowing to foresee the LIBs’ malfunction. Predicting such unwanted TR-like events in advance and under real-life conditions is an imperative step in LIBs’ eventual insertion within the next-generation energy storage technologies.

[0084] The mechanism of the TR has been reviewed in many prior publications. The thermal behavior of LIBs can be described by temperature profiles based on the results of accelerating rate calorimeter (ARC) tests. When the temperature increases, multiple degradation mechanisms can occur within the battery that can trigger the TR event. Inside a battery, typically, three major degradation mechanisms are observed, i.e., the SEI decomposition, Li-electrolyte reaction, and a cathode decomposition. These reactions raise the temperature enough to cause the separator to melt down and lead to an internal short circuit in the battery, which further increases the temperature. The decomposition of the solid electrolyte interphase (SEI) is important to identify the temperature at which the cell starts self-heating. When the cell temperature rises to a certain extent, first, the decomposition of the SEI layer takes place and then releases heat. The decomposition of this protective layer can trigger other exothermic reactions and, ultimately, leads to thermal runaway. Therefore, understanding the evolution of the temperature due to the onset of the SEI decomposition is very important for introducing warnings for battery management systems.

[0085] There are serious safety issues for monitoring the TR event experimentally. In this regard, researchers have put forward extensive efforts toward the development of numerical models to predict the TR behavior. Richard and Dahn have utilized ARC to investigate the thermal stability of lithium intercalated mesocarbon microbead (MCMB) electrodes by estimating its self-heating rate. Additionally, Richard and Dahn have presented a mechanism to elucidate the amount of heat that was generated from chemical reactions between the lithiated carbon and the electrolyte. Hatchard et al. drew upon this work and have built a 1D model to estimate the temperature when the TR starts for LCO / graphite cells that are subjected to an oven with a constant temperature. Then, Spotnitz and Franklin have summed up the essential exothermic reactions of the battery components. They 30 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 have developed a 1D model to provide quantitative insights to the contribution of heat generation from separate reactions and used it for various abuse tests. Moreover, Kim et al. have broadened the model proposed by Hatchard et al. to a 3D model where the TR is prompted by thermal abuse (external heating).

[0086] With many of the latest developments in artificial intelligence and data-driven algorithms, it is now possible to significantly advance the state-of-the-art in the study of LIBs and their materials. This allows a significant improvement in the performance of battery technologies to be rapidly achieved. ML has been extensively used in different areas of battery research at different length scales, from fundamental studies of structural properties to end-use applications like EVs. In the studies of structure properties, ML methods have shown to be promising techniques for the investigation of the structure-properties relationships and the understanding of the behavior of the materials employed in LIBs. Another area of research related to LIBs and ML is the battery state-of-charge (SOC) estimation for EVs. This has gained significant recognition in recent times due to the extensive development of EVs. Moreover, there have been significant works on the application of ML to estimate the SOH (State of Health), SOC, and RUL (Remaining Useful Life) using methods such as XGBoost, random forest, and k-nearest neighbor algorithm (KNN). Similarly, ML models are also applied in LIBs prognostics. Additionally, ML methods, namely support vector machine (SVM), relevance vector machine (RVM), and Gaussian process regression (GPR) have been widely used in this area of research. Deep learning (DL) methods like artificial neural networks (ANNs) have been utilized in the area of battery design and health monitoring. Recently, there have been reports of DL / ML models, which include the prediction of simulated / experimental results at reduced computational costs for inspecting and forecasting battery events like the TR. Based on a thorough search, there are only a few papers in the prior literature dedicated to DL / ML usage to predict the TR in LIBs. In this regard, Yamanaka et al. used nail penetration simulations on different input conditions to generate a database and used regression models to inspect the design conditions for better performance of batteries. Naha et al. utilized an ML method known as a random forest classifier to detect internal short circuit (ISC) leading to the TR in batteries from simulated data as input. 31 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0087] Despite ML’s promising capabilities, the existing literature on ML application to battery research is limited to the modeling of materials properties or SOC estimation without relating it to the degradation phenomena. Yet, learning- driven approaches for battery design and thermal runaway prediction are limited to data-driven approaches. Thus, the primary objective of this paper is to develop a combined multiphysics and ML-based approach to predict and prevent the TR in LIBs using thermal images of the battery during operation. The supporting objective is to provide the safety aspects of LIBs operation derived from the multiphysics informed ML techniques. For the multi-physics model, the Panasonic 18650 cylindrical cell has been considered. This cell utilizes Graphite as the negative electrode and NMC as the positive electrode. Since the SEI decomposition sets a pathway for thermal runaway, the SEI decomposition has been considered as the major degradation mechanism in the multiphysics model. Additionally, multiple high- temperature hotspots have been considered at different locations within the battery. From the multiphysics model, thermal images have been generated as sequences of video frames during the battery operation. Next, the extracted images are used for the application of various ML methodologies. In the ML study, a classification technique has been employed using various convolutional neural networks (CNNs) to predict the TR. For this purpose, three labels have been considered, namely, safe, critical, and the TR. The selection of these labels is solely dependent on the maximum surface temperature of the battery and has been explained in detail in the methodology section. Finally, an advanced application of ML has been utilized known as object detection, a technique that has not previously been used in the area of the TR, for the detection of high-temperature hotspots in the battery, which could lead to the TR.

[0088] In this section, the general workflow of the study that has been carried out is described. First, a computational approach has been developed to investigate battery degradation using an electrochemical-thermal model of LIBs. This is followed by the acquisition of thermal images from the simulations after undergoing further data preprocessing. Then, these images are fed into the DL network for the classification task of predicting three labels related to the TR event. Finally, the detection of high-temperature hotspots in the battery using an object 32 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 detection technique is performed. FIG.9 shows the class of systems modeled in this work (left-hand side) together with the ML workflow (right-hand side). 5.1. Multiphysics modeling methodology

[0089] In this section, the methodology involving the multiphysics model is described. First, the general electrochemical model has been discussed followed by the description of the thermal model. Additionally, the initial and boundary conditions for the model, followed by a general introduction involving the model implementation, have been discussed. The multiphysics model utilizes the finite element method (FEM) to simulate the electrochemical-thermal behavior of a cylindrical battery type at various conditions. The P2D model is used for modeling electrochemistry, and a 3D model has been used to simulate the battery temperature. The two models are then coupled by the generated heat source and the temperature. Highlighting the pivotal role of the P2D model, its reputation is built on a foundation of exceptional accuracy when compared to experimental data. Doyle and Newman’s influential work has unequivocally demonstrated the effectiveness of the P2D model through direct comparisons with experimental results. Notably, the outcomes exhibit commendable alignment with experimental data, particularly in scenarios involving non-uniform SEI growth. This robust validation underscores the reliability and effectiveness of the P2D model in capturing real-world phenomena, further affirming its credibility in our study. A detailed description of the governing equations related to the P2D model and the corresponding boundary conditions has been provided in the supplementary information. In addition to the main graphite-lithium intercalation reaction on the negative electrode, the model considers parasitic SEI formation reaction as well. The kinetic expression for the SEI formation reaction is based on the work of Ekstrom and Linderberg and has been provided in the supplementary information. It is assumed that the SEI formation is limited by a diffusion process through the formed SEI film, with the result that the aging slows down the thickening of the film. In normal operating conditions, the cell is subjected to a continuous charge / discharge load. Consequently, heat generation takes place within the cell due to various electrochemical processes. The thermal characteristics, such as heat generation due to various electrochemical reactions, in the case of the TR event can be described by the general energy conservation equation for both phases (solid and fluid) in the vector form as 33 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 ^^^^ ^^^^p • ∇^^ + ∇ • ^^ = ^^ , (7)^^^^+ ^^^^p^^ genwhere,^^ = ^^∇^^ (8)

[0090] Here, ^^, is the thermal conductivity of the battery. It takes the form of a symmetric positive-definite tensor (matrix) and is given as ^^ 0 0th0 ^^ 0 ^^ = (9) [ ]in

[0091] where, ^^and the through-plane thermal conductivity of the cell. In Eq. (9), ^^ denotes theaverage density of the cell; ^^ is the average specific heat capacity; ^^ is theptemperature; and ^^ is the volumetric heat generation rate (HGR). The HGR of thegencell is given by ^^ = ^^ + ^^ , (10)gen elec SEI

[0092] where, ^^ is the dominant HGR from the fundamentalelecelectrochemical reactions and ^^ is the dominant HGR for the SEI decompositionSEIreaction. The convection term is zero in the solid phase due to the lack of a fluid motion in that phase. The total electrochemical HGR is determined by the sum of irreversible heat from Joule heating and activation losses and reversible heat from electrochemical reaction and is given by ^^^^eq,m ^^ = −(^^ • ∇φ + ^^ • ∇φ ) + ^^ (^^ − ^^ − ^^ )^^ + ^^ , ∑ { }elec ^^ s l l s l m m^^^^^^^^ electrolyte current ^^ electrode potential ^^, electrolyte potential ^^, the equilibriums l s lvoltage for each reaction ^^ , local current due to an electrochemical reaction ^^ ,eq,m mthe active specific surface area ^^ and the change in equilibrium voltage withv,m^^^^eq,mrespect to the temperature for each electrode reaction . It is to be noted that ^^^^the variables ^^ , ^^ , and ^^, ^^ and ^^ are calculated based on the P2D equations. Ass s l l ^^previously mentioned, multiple exothermic reactions can occur inside the battery that may trigger the TR event. When the battery is in operation under charge / discharge 34 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 load, reversible and irreversible reactions take place inside the battery, which releases heat and causes the temperature to rise. Along with these reactions, the SEI-forming parasitic reactions also occur in the anode of the battery. After a certain growth, the SEI undergoes a decomposition reaction, which is exothermic in nature and releases heat. The HGR due to the SEI decomposition reaction is given by ^^SEI = ^^eℎSEI^^SEI,d, (12)

[0094] where, ^^eis the active specific surface area; ℎSEIis the enthalpy of the reaction and ^^SEIrepresents the reaction kinetics of the SEI decomposition reaction. Detailed descriptions of the symbols and additional equations for the reaction kinetics and the corresponding degradation parameters are given elsewhere. It should be noted that the SEI formation has been reported to be a complex mixture of compounds, such as LiF, Li2CO3, lithium ethylene dicarbonate((CH2OCO2Li)2, LEDC) and lithium alkyl carbonates (ROCO2Li). During thedecomposition process, these compounds may have their own series of reactions. However, due to the lack of appropriate kinetic and thermodynamic data associated with all these reactions, it is reasonable to assume one global rate-limiting step for the SEI decomposition process. The intense heat release from the SEI decomposition reaction escalates the temperature of the battery. This creates high- temperature hotspots inside the battery, whose location is completely stochastic. The appearance of such hotspots may occur due to local defects present within the structure of the battery. These local defects can form due to multiple reasons, e.g., deflected current collectors, non-uniform packing, delamination, presence of impurities in the anode / cathode, burrs on the tab. Since modeling does not allow the formation of such hot-spots automatically, these hotspots are introduced artificially within the battery at random locations and simulate the battery operation. These hotspots are directly associated with the degradation mechanism in consideration. The heat release from the degradation of the battery leads to self-heating of the battery in a short period of time and causes a thermal runaway to occur. In this work, the SEI formation / decomposition has been considered as the major degradation phenomenon that leads to the TR. Additionally, the developed model is solved for the continuity and momentum equations, that are given elsewhere. The initial and boundary conditions for the governing equations are provided in the supplementary information. 35 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 5.1.1. Model implementation

[0095] The mathematical model constitutes a multi-scale and multi- domain approach and is implemented in COMSOL Multiphysics. The model uses an unstructured quadratic finite element mesh and the backward Euler scheme for time discretization purposes. The PARDISO (COMSOL, 5.6) solver for a finite element problem to solve the system of linear equations as well as for the initialization and the transient stages is used. For the simulations presented in this paper, a cylindrical 18650 cell with NMC chemistry has been chosen and a 3D model is implemented. A Graphite negative electrode, an NMC811 positive electrode, and an electrolyte 3:7 EC:EMC with a 1 M LiPF6salt from the COMSOL material library have been selected. The model has been simulated with a user-defined condition that when the maximum temperature of the battery exceeds 400 K, the calculations should stop. This has been implemented as the battery will undergo rapid self- heating beyond this point in a short period of time and will eventually explode. 5.2. Deep learning methodology

[0096] The following section is dedicated to the description of the proposed DL framework, and it is structured in two parts: first, the dataset preparation and preprocessing is discussed, followed by the implementation of DL models. The section related to the implementation of the DL model is further divided into two parts. First, the classification technique used to predict the TR from the thermal images obtained from the multi-physics modeling is explained. Next, the development of the object detection technique used to identify the location of high- temperature hotspots has been introduced which eventually leads to thermal runaway. 5.2.1. Dataset preparation and preprocessing

[0097] Initially, simulated thermal images of the battery are collected as sequences of video frames during the battery operation. Such thermal images contain physical features related, for example, to the battery surface temperatures and the cooling airflow. For applying the ML techniques to predict the TR, the temperature is the main subject of discussion. From the simulation results, the thermal images of the battery are saved in a continuous time interval of battery operation, considering a defined time step. To use ML / DL for the task of classification, it is important to divide the images into different labels. As mentioned 36 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 in the introduction, three labels for the classification task have been considered, namely, Safe, Critical, and TR, depending upon the maximum surface temperature of the battery. The extraction and partitioning of these images into various labels are made in such a way that each label contains the same or nearly the same number of images. This is due to the concept of a balanced dataset in ML. In any ML / DL problem, class imbalance is a major problem, as it reduces the accuracy of the model, making the model biased towards the class having higher number of images. Further details on the image collection are provided in the results and discussion section. The next task is to preprocess the extracted data. Image preprocessing involves formatting the images before they can be used for training. This involves certain operations but is not limited to orienting, resizing, and color corrections. For the purpose of data preprocessing, techniques such as image normalization and image augmentation are used. 5.2.2. Thermal runaway classification using convolutional neural network (CNN)

[0098] Image classification involves taking an input (a picture) and predicting a class label or a probability referring to the input is of a particular class. Convolutional neural networks have taken a quantum leap in image recognition. Additional information regarding CNNs has been provided in the SI. In this work, CNNs are used to classify three labels, i.e., safe, critical, and TR, which are directly related to the physical problem.

[0099] Learning takes place through an iterative process known as training. There are two methods by which training can be performed. The first method is learning from scratch. Learning from scratch is building completely a new model or mixing parts of other models and performing the training from the first layer. The second method is transfer learning with fine-tuning. This method includes applying a pre-trained DL model to a dataset of interest. Transfer learning helps users to overcome the need for huge amounts of new data. A model already trained on a particular task will be able to manage a new but similar task with minimal data. Additionally, the process of training can be boosted by utilizing a pre-trained model. This can result in a more effective model. Transfer learning yields the best results when the datasets are similar to the one that the model was already pretrained. For completely different datasets, learning from scratch is preferable. Hence, in this 37 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 study, training from scratch is performed as the dataset is unique compared to other large datasets used to pre-train models.

[0100] The CNN architectures employed in this study, including VGG16, VGG19, ResNet18, ResNet34, ResNet50, ResNet101, DenseNet121, DenseNet201, EfficientNetB6, EfficientNetB7, and MobileNetV3, are pre-established models widely recognized in the field of computer vision. VGG16 and VGG19 are 16- and 19-layer CNN architectures, respectively, widely employed in visual object recognition software research. Both networks process RGB images as input, featuring a sequential stack of convolutional layers with small receptive fields and max-pooling layers. ResNet, or Residual Network, variants used in this study include ResNet18, ResNet34, ResNet50, and ResNet101. These architectures leverage the concept of residual learning, incorporating residual connections to facilitate the training of deeper networks. The increased depth enables superior performance across various classification tasks. DenseNet121 and DenseNet201 are DenseNet architectures, where each layer receives input from all preceding layers. Dense connectivity patterns contribute to efficient parameter usage, addressing vanishing gradient issues and enhancing overall model performance. The EfficientNet family includes EfficientNetB6 and EfficientNetB7, offering efficient scaling of depth, width, and resolution to achieve a balance between model size and accuracy. These networks are particularly well-suited for resource-constrained environments. MobileNetV3 is part of the MobileNet family, designed for efficient deployment on mobile and edge devices. It incorporates inverted residuals and linear bottlenecks for reduced computational cost, making it ideal for real-time applications. These models are well established, and details of their network architecture can be readily found elsewhere. 5.2.3. Object detection using YOLO

[0101] YOLO is an approach in the field of object detection using advanced DL algorithms. Here, object detection is performed as a regression problem, starting from the pixels of the image to the coordinates of the bounding box, to calculate the class probabilities. FIG.10 shows a schematic illustration of YOLO network architecture. In this example, YOLO version 5 has been utilized for the purpose of object detection. The YOLO architecture begins with an input layer that takes battery thermal images as the initial data for the subsequent layers of the 38 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 network. The core of YOLO includes a backbone network comprising twenty-four convolutional layers, which are responsible for extracting hierarchical features from the input image. As these layers progress, they capture increasingly abstract and complex representations, allowing the model to discern intricate patterns in the visual data. Following the convolutional layers, YOLO integrates two fully connected layers that further process the extracted features, enhancing the network’s ability to understand and interpret the visual information. YOLO also incorporates 1x1 reduction layers strategically within the architecture. These layers serve to reduce the dimensionality of the feature maps, optimizing computational efficiency while preserving critical information. Subsequent to the reduction layers, YOLO employs 3x3 convolutional layers. These layers play a crucial role in capturing spatial dependencies within the feature maps, facilitating the model’s understanding of the spatial relationships between different elements in the image. The final stage of theYOLO architecture is the output layer, which produces a 7 × 7 × 30 tensor. Thistensor represents the output of the detection layer of the network, with each cell in a 7x7 grid over the input image producing 30 predictions. Each prediction is a vector that contains the (x, y) coordinates of the center of a bounding box, the width and height of the bounding box, the confidence score (objectness score), and class probabilities for each of the classes the model is trained to recognize. These predictions are encoded in the form of a tensor, and the information can be extracted and used to identify and locate objects within the input image. In essence, the YOLO architecture is carefully designed, progressing through convolutional backbones, fully connected layers, 1x1 reduction layers, and 3x3 convolutionallayers. The final tensor output, structured as 7 × 7 × 30, efficiently encodes richinformation for object localization and class predictions across the image grid. This detailed architecture empowers YOLO to excel in real-time and accurate object detection across a diverse range of datasets and scenarios. 5.3. Results and Discussion

[0102] The primary objective of the present work is to predict thermal runaway in Li-ion batteries using combined multiphysics modeling and advanced ML / DL algorithms. The first part presents and discusses the multiphysics modeling results of Li-ion batteries under a different load. This is followed by the results 39 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 obtained by applying DL techniques to the thermal images obtained from the multiphysics model. 5.4. Thermo-electrochemical model

[0103] It is challenging experimentally to observe the TR events in real time. Moreover, during the battery preparation and its thermal treatment, a variety of side reactions could be triggered. All these features might potentially influence the propagation of the LIB’s TR, causing some parts of the battery to be more susceptible to failures than others. Therefore, the exact modeling of the TR is not straightforward, considering the incomplete state of knowledge about the TR’s associated events. For this reason, in the current modeling work, the locations of the TR hotspots are randomly chosen for cases with one and two hotspots. First, the multiphysics modeling results with one hotspot are presented, followed by the results for two hotspots, with the details of the effect of degradation on battery temperature and the capacity fade.

[0104] The developed model is used to investigate the effect of cell degradation on the temperature and battery capacity. For the simulation, a constant current / constant voltage (CCCV) charging is considered. Since, the current at which the voltage was validated is extremely small to initiate significant degradation, the cell is discharged at a 1C rate until it reaches a cut-off voltage of 2.5 V, followed by charging to 4.2 V. However, the heat release during this operation of the battery is observed to be sluggish, and the temperature rise is not sufficient for SEI decomposition to occur. Following this observation, the cell is discharged and charged at a 2C rate. FIGS.11A-11C show the profile for charge and discharge curves pertaining to a single TR hotspot (cf. FIG.11A), the change in the SEI thickness for one (red) and two (blue) TR hotspots, respectively (cf. FIG.11B), and the rise in the maximum cell temperature of the battery for one (red) and two (blue) TR hotspots respectively (cf. FIG.11C). Ideally, any battery needs large number of cycles to show prominent SEI growth, and the differences in the cycle to cycle behavior is usually assumed small. Hence, the SEI growth rate is accelerated by increasing the pre-exponential factor for proof of concept. This is a valid assumption for modeling purposes to observe the TR faster. Additionally, FIG.11B illustrates the effect of the aging process on the growth of SEI formation. It is evident that the aging process slows down the rate of growth of SEI with time. This occurs as we 40 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 have considered the SEI formation to be limited by a diffusion process through the formed SEI film.

[0105] FIGS.11A-11C show the reduction in the SEI thickness during discharge, implying the SEI decomposition reaction. As expected, a comparison between the temporal variations of the temperature in FIG.11C indicates a more rapid temperature rise for the system with two TR hotspots. It should be mentioned that the model terminates after the stop condition is satisfied at 400 K, hence, the SEI does not completely decompose, as illustrated in FIG.11B. SEI decomposition releases heat and increases the temperature of the battery. The exponential trend of the temperature evolution, as seen in FIG.11C is explained by the Arrhenius relation of the SEI decomposition heat release. This trend in the rise of temperature due to the degradation of the battery has been well reported in prior literature. Additionally, it was observed that the electrochemical HGR was significantly lower in comparison to the heat release due to the degradation (SEI decomposition). Hanchard et al. have devised a 1D model to estimate the variation of temperature during the TR event of LCO / graphite cells placed in a constant temperature oven during discharge and report similar temporal temperature profiles as in the results presented in this work. Kim et al. have performed thermal abuse tests based on a 3D lumped model for the TR prompted by heating. The authors have reported the evolution of temperature to follow an exponential trend that is similar to the results shown in FIG. 11C. The introduction of hotpots would induce non-uniform temperature distribution inside the battery and, thus, non-uniform SET generation. However, the SET growth process has been implemented in the P2D model that assumes a uniform SET growth for the negative electrode. The study of non-uniform SET generation requires a 3D particle model in addition to a full-scale battery model and is subject to future work.

[0106] FIG.12 illustrates the total heat generation rate of the battery during operations for single (red) and two (blue) TR hotspots. At the beginning, both curves follow the same trend corresponding to the charge / discharge cycling. During the discharge, exothermic processes dominate, leading to the heat release, while the charging process is endothermic in nature, causing some heat to be absorbed by the battery. The exponential heat generation rate is due to the SET decomposition reaction, which leads the battery to the TR. The model containing a single hotspot 41 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 contains a single Arrhenius function applied at that location, indicating the heat release due to the degradation of the battery, whereas the model with two hotspots contains two Arrhenius functions acting at the locations individually. Due to this reason, the sudden exponential heat release is observed sooner for the model with two hotspots as compared to the one with a single hotspot. A similar trend of heat release leading to the TR has been reported by Feng et al. through experimental and modeling studies.

[0107] The capacity fade can be observed in the discharge curves of graphite / NMC cell through operation for 2C charge / discharge as shown in FIG.13. The first discharge curve obtained from the simulations was directly compared to the datasheet provided by the battery manufacturer. Tt was observed that these results are in good agreement with the experimental test results. Specifically, experimentally the open circuit voltage of 4.2 V, along with the cut-off voltage of 2.5 V agrees well with the modeling results reported in FIG.13. . During the battery operation, the main contribution to the capacity fade is due to the cyclable loss of lithium induced by the SET formation. A shift is observed in the voltage curve at the end of the discharge. Additionally, as the number of cycles increases, the capacity tends to decrease, and the cut-off voltage is reached earlier.

[0108] This SET formation-induced capacity fade has also been observed in experiments. Ramadass et al. and Lin et al. have studied the degradation of different Li-ion cells, and observed a shift in voltage. Additionally, they have reported that an SET layer is formed on the surface of the negative electrode. The passive layer reduces the amount of cyclable lithium that leads to capacity fade with a shift in the potential. Accurate modeling of the TR is a challenging task. The objective during the model construction has been to extract thermal images of the battery, which provide a qualitative aspect of the TR initiation. The goal is to predict TR using ML on the thermal images extracted from simulations. The introduction of hotspots artificially within the battery for the initiation of the TR has already been mentioned. There could be multiple hotspots inside the battery depending upon the degradation mechanisms. The locations of these hotspots are completely random. For this study, the number and locations of the hotspots has been varied within the battery to investigate the evolution of the cell temperature. FIG.14A shows the view of a battery for a constant 2C charge / discharge current with airflow velocity at the 42 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 inlet being 0.1 m s-1. It can be observed that due to the heat release from the SET decomposition at the hotspot location, causes the temperature of the entire battery to rise and eventually lead to the TR. FIGS.14B-14D show the results for the battery temperature with cooling airflow for two high-temperature hotspots at different locations within the battery and the location is given with respect to the height of the battery (ℎ^^^^^^^^) and the radius of the battery (^^^^^^^^^^). Due to the heat release from the SET decomposition reaction, other exothermic reactions are triggered, and this increases the temperature of the entire battery, triggering the TR event. Additionally, we observe distinct thermal behaviors when comparing scenarios with one versus two hotspots. The presence of two hotspots accelerates the thermal gradient development within the cell, underscoring a nonlinear escalation in risk factors leading to TR. This phenomenon is particularly evident in the rate of temperature rise and the spatial temperature distribution. Our analysis provides crucial insights into the interplay of hotspot number and location, offering a comprehensive understanding of their impact on cell safety and performance. 5.5. Deep learning results

[0109] DL enables a significantly broader scope of the study of LIBs. Many ML methods have been shown to be extremely promising in the study of material properties in LIBs and the estimation of the state-of-charge (SOC) of a battery. Due to these efficient applications, DL has received significant attention in recent years. Predicting TR events in batteries using DL is a relatively new approach. There are very few works in the prior literature that use the idea of data- driven DL to forecast such events. Based on a thorough search of relevant literature, there is no work that uses an image-driven DL approach to forecast TR events, which is one of the novel aspects of this work. The multiphysics modeling results are taken as input to different DL techniques to identify and predict the TR. This section is divided into two parts. First, the results for the TR prediction as a classification task based on different DL architectures has been reported. Finally, the object detection technique, based on a regression approach, has been utilized to detect the high-temperature hotspots created within the battery at random locations due to the degradation mechanism. 5.5.1. Thermal runaway classification 43 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0110] The TR classification requires the use of DL algorithms that learns to assign a class label to test data from the problem domain. To perform the task of classification, data preparation, and preprocessing is the most important step. For the data preparation step, images were collected and specified under a particular label based on the maximum temperature of the battery. When the maximum surface temperature is below 340 K, the images belong to the Safe class. The Critical class is defined when the maximum surface temperature is between 340 K and 370 K, also called the transition stage between the Safe and the TR regions. Finally, for temperatures greater than 370 K, the images are considered to belong in the TR class. To ensure an equal number of images for each label, the time at which the images were extracted from the multiphysics model played a vital role. During the simulation, the maximum battery temperature tends to be lower than 340 K for a long period of time due to the normal operation for the initial cycles, hence for this case, the time step is 100 s. For the transition phase between the safe and the TR region, i.e., the critical stage, the time step size is taken to be 10 s due to the process being fast. Finally, for the TR stage, which happens rapidly, the time step size is taken to be 1 s, ensuring an equal number of images extracted for each class of the DL model. This resulted in the collection of 1200 images, with each class having 400 images, respectively. This is the size of the entire dataset. The next step is the data preprocessing, where the images are preprocessed using various techniques that have been discussed in the methodology section. Following this partitioning, the next task involved the splitting of the data into training, validation, and test sets, where the training set is fed as input to the model, and the validation set is used to evaluate the performance of the model during training. The training set contained 80 % of the total number of images in the entire dataset, whereas the validation and the test sets contained 10 %, respectively.

[0111] The performance of the DL model is assessed through the learning curves obtained from the training data. This is provided in the supplementary file. The training is performed over 300 epochs for each of the networks used. Additionally, a study was performed to observe the effect of different hyperparameters on the overall model accuracy using all the networks individually. For this purpose, batch size, optimizer, and the learning rate were chosen to be varied and optimized. Batch size is one of the most important hyperparameters to 44 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 tune in modern DL systems. Larger batch size is mostly preferred as this gives the model the opportunity to look at larger data at any instant of training. The downside of a higher batch size is its high computational memory usage and higher training time. In this study, the batch size is varied as 8, 16, 32, and 64 and training is performed for the same number of epochs. Comparing the accuracies for batch sizes of 32 and 64 gives the best results for all the networks taken into consideration, with the latter giving a slightly higher accuracy at the cost of much higher training time and memory usage. For this reason, a batch size of 32 was chosen. After optimizing batch size, the next important hyperparameter, i.e., the learning rate, was varied. In ML, the learning rate stands as a configurable parameter within optimization algorithms. It plays a pivotal role in dictating the size of each step taken during iterations as the algorithm progresses towards minimizing a loss function. Symbolizing the degree to which recently acquired information supersedes prior knowledge, the learning rate serves as a metaphorical indicator of the swiftness with which an ML model assimilates new insights. Hence, optimizing the learning rate becomes very crucial. For this study, the learning rate was varied across different values of 0.01, 0.001, 0.0001, and 0.00001. The learning rate of 0.00001 yielded a slightly higher accuracy compared to 0.0001 at the cost of significantly longer training times. Therefore, a learning rate of 0.0001 was selected as the final value. Following the optimization of the batch size and the learning rate, the choice of optimizer was varied. Optimizers refer to algorithms or techniques employed to diminish the loss function or enhance production efficiency. These mathematical functions are contingent upon the learnable parameters of a model, namely the weights. Optimizers play a crucial role in determining the adjustments to the weights and learning rate of a neural network, aiding in the reduction of losses. Three popular optimizers – Stochastic Gradient Descent (SGD), Adam, and RMSprop – were considered for the purpose of optimizer tuning. It was revealed that the Adam optimizer delivered the best results, and thus, it was selected as the final optimizer. Following the tuning of hyper-parameters, then the optimized models were trained and tested on the test dataset. Estimation of the essential statistical parameters is necessary for assessing the performance of the model for the classification task. These parameters have already been described in the methodology section. The complete list of values for accuracy, precision, recall, and F1 score is reported in Table 1. Upon analyzing the results presented in Table 1, it becomes evident that 45 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 EfficientNetB7 outperforms its counterparts in terms of accuracy, recall, and F1 score. This finding signifies the superior efficacy of EfficientNetB7 in accurately predicting the class labels of images within the test dataset. Notably, the recall value for EfficientNetB7 stands out as notably higher compared to other networks, a critical aspect given its implication for safety considerations. A high recall value indicates a more precise identification of positive instances, a paramount factor in scenarios where misclassifying images with the TR label could lead to disastrous outcomes. The commendable performance of EfficientNetB7, as indicated by the elevated values of these performance metrics, suggests its potential extension to images derived from experimental data. Moreover, the high values of the performance metrics indicate that this idea can also be well extended to images collected from experimental data and could significantly help in predicting real-time TR detection in batteries.

[0112] FIG.11C show the confusion matrices for the best model for each group of networks considered in this paper. For instance, among the VGG group, the confusion matrix for VGG19 has been reported. Using a similar idea, confusion matrices of ResNet101, DenseNet201, Effi-cientNetB7, and MobileNetV3 are reported. This approach would provide qualitative and quantitative insights about the performance and robustness of different types of network to the given problem rather than just comparing between the same type of networks with different layers. Sincethis is a three-label classification problem, the matrices are 3 × 3 in dimension.Here, the diagonal elements represent the number of images that are rightly classified according to their true labels. The off-diagonal elements represent the number of misclassifications for each label. Considering the first confusion matrix for VGG19, as shown in FIG.15A, there are a total of 5 miss-classifications, all belonging to the same label. Among the 40 images, 35 of them are correctly classified, and among the five misclassifications, one image is misclassified as safe, and the other four images are misclassified as TR. FIG.15B shows the confusion matrix for ResNet101. There are only two misclassifications for this network. Here, one image is misclassified as Critical while being in Safe, and the other one as Safe while being in Critical. FIG.15C shows the confusion matrix for DenseNet201, having 5 misclassifications out of 120 images in total.2 images in the Safe label are misclassified as Critical, and another 2 images in the Critical label are misclassified 46 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 as Safe. Similarly, FIG.15D shows the confusion matrix for EfficientNetB7, having no misclassifications. As the name goes, it is indeed the most efficient model for this problem. Finally, FIG.15E shows the confusion matrix for MobileNetV3, showing the most number of misclassifications among the other models and it is also evident from Table 1 that reports the least accuracy for this model. Additionally, FIGS.15A- 15E show a glimpse of the images for each of the cells in the confusion matrix, which provides a better visual representation and qualitative insight into the results obtained. Overall, it can be concluded that EfficientNetB7 performs the best among all the used DL methodologies. Table 1 Performance of the networks used in this study based on the most important performance metrics. Deep learning architecture Accuracy Precision Recall F1-score VGG16 0.96 0.89 0.88 0.95 VGG19 0.96 0.98 0.87 0.96 ResNet18 0.91 0.88 0.91 0.89 ResNet34 0.95 0.92 0.93 0.95 ResNet50 0.98 0.95 0.95 0.97 ResNet101 0.98 0.96 0.97 0.97 DesneNet121 0.95 0.91 0.93 0.92 DenseNet201 0.96 0.93 0.95 0.96 EfficientNetB6 0.99 0.94 0.96 0.97 EfficientNetB7 0.99 0.97 0.98 0.96 MobileNetV3 0.93 0.90 0.91 0.90

[0113] All three models exhibit good performances in predicting the labels accurately with minimal numbers of miss-classifications, which are acceptable from a statistical point of view. The test set is an unknown set, meaning the model has not previously seen it. A good performance on an unknown set signifies that the model is robust and has a good generalizing ability. The incorporation of scenarios with varying hotspot numbers significantly enhances the predictive robustness of our CNN models. The comparative analysis between single and dual hotspot situations reveals a marked improvement in the model’s ability to discern complex thermal patterns, a key factor in predicting TR. This enhancement is quantified through improved accuracy and recall metrics in our models, indicating their heightened sensitivity to subtle variations in thermal imagery. These findings underscore the 47 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 critical role of diverse training datasets in developing reliable predictive models for battery safety applications. Although the developed ML framework shows outstanding results in predicting thermal failures with great accuracy based on a single thermal image, there are certain challenges to extend it to a real battery module / pack due to its packaging, housing, etc. The results indicate the possibility for the application of various ML techniques to different views of a single cell and accurately predicting thermal failures. This approach can be well extended to the battery pack / module for effective prediction of thermal failures. It should be noted that using CNN with images for this study can sometimes lead to ‘fake warnings’. However, to mitigate this risk, a detailed multiphysics model has been developed in this work, including SEI degradation to initiate TR. This model simulates realistic thermal images of batteries, providing diverse and realistic data for training various CNN architectures. Emphasizing rigorous training on a well-curated dataset, including multiple hotspots, further enhances CNN’s understanding of thermal behavior. Additionally, the methodology incorporates robust data preprocessing, rigorous validation, and hyperparameter tuning during the CNN training process. This multifaceted approach not only improves the CNNs’ predictive capabilities but also ensures their reliability in practical applications. 5.5.2. Object detection

[0114] Object detection is a technique in the field of computer vision that helps to identify and track objects in a video or image. Object detection can be utilized for effectively counting objects in a scene and determining their precise locations, along with accurately labeling them. In this paper, this technique to predict TR events in LIBs is applied. Fig.16 shows some predictions (output of network) of YOLO on different thermal images of batteries obtained from the multiphysics model simulations. In Fig.16, three different images of the battery are shown as the test data for input. These images contain single and double high-temperature hotspots at different locations. The results indicate the high efficiency of YOLO in predicting the regions of TR initiation / hotspots where the temperature is very high compared to the other regions of the battery. This idea can also be extended for real-time TR hotspot detection in experimental battery operation. 48 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 5.6. Study conclusion

[0115] A combined multiphysics model and DL-based framework has been developed for predicting the TR in cylindrical Li-ion batteries. This paper contributes to the prevention of unfortunate events of the explosion of the battery operating devices (e.g., cell phones, EVs) in terms of both practical advances and improved fundamental understanding. The multiphysics model utilizes the COMSOL software to simulate the electrochemical-thermal nature of cylindrical battery type at various conditions. The thermal images of the battery obtained from the simulations are preprocessed for application in DL.

[0116] The ML / DL study is divided into two parts. First, a classification technique is used, which involves using CNNs for real-time prediction of the TR in the battery. Then, the YOLO (an object detection technique) is implemented and applied to the battery thermal images for the detection of the high-temperature hotspot zones. The performances of the DL classification algorithms and the object detection technique show great performance in the classification of the TR and predicting the location of the hotspots in the battery well. In the context of benchmarking thermal runaway classification, this study emphasizes the selection of maximum temperature as a primary criterion, reflecting its direct correlation with critical conditions leading to thermal runaway. The choice is grounded in the practical significance of maximum temperature as a clear and straightforward indicator of peak thermal stress experienced by the battery. This parameter provides a tangible and easily interpretable benchmark for distinguishing safe, critical, and thermal runaway states, aligning with the overarching objective of predicting and preventing thermal runaway in cylindrical Li-ion batteries. While acknowledging the importance of temperature rising rates in understanding thermal dynamics, prioritizing maximum temperature offers a pragmatic and actionable approach for assessing battery safety.

[0117] The developed framework can be extended for real-time TR hotspot detection and for practical battery operation. The main advantage of the proposed DL techniques is that they do not require the physical modeling of the internal battery chemistry, which is cumbersome in the TR scenario, rather, they rely only on the experimental / modeling data and the collected thermal images. 49 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0118] There are certain practical challenges associated with acquiring thermal images in real-world scenarios. However, the decision to incorporate thermal images as inputs for the ML modeling is based on their unique advantages, providing a comprehensive representation of spatial and temporal temperature variations within the battery. This approach enables early detection of potential issues and seamless integration with the multiphysics modeling methodology. While recognizing concerns about data storage, we argue that the benefits in predictive accuracy and safety outcomes justify the use of thermal images. With advancing technology facilitating the handling of large datasets, including thermal imaging data, making it increasingly practical to handle large datasets. Although this method of predicting battery failures seems a viable option towards ensuring the safety of electric vehicles, there are a few potential limitations in its practical implementation on a large scale. Firstly, the initial cost to setup might be significantly high. Secondly, the various types of degradation that are possible, along with more cell designs, should be considered as well. This would help in creating a larger dataset that would be more reliable than the present one. It must be noted that the developed multiphysics modeling and ML framework is generic and may be well extended to various Lithium-ion batteries with various geometric configurations and contrasting anode / cathode materials in addition to cylindrical cells. 6. Example Implementation Details (COMSOL simulation modeling methodology)

[0119] This section provides example implementation details and additional results for representative embodiments, including modeling geometry and boundary conditions, dataset preparation, sensor-path configurations on cylindrical cells (e.g., helical, helix-plus-straight, and U-type paths), and representative driving- cycle inputs. 6.1. Model geometry

[0120] The battery module’s geometry is meticulously defined in SolidWorks and has been imported into COMSOL Multiphysics. This includes:

[0121] Individual cells: Each cell’s dimensions and spatial arrangement within the module.

[0122] Cooling channels: The pathways designed for thermal management within the module. 50 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0123] Filler material: The material to fill the void spaces of the battery module representative unit. The geometry (cf. FIG.17) is designed to accurately reflect the physical layout of the battery module (3D model) and the 1D layout representing the P2D model, ensuring that all components are represented with high fidelity. 6.2. Material properties

[0124] Relevant material properties are assigned to different components of the battery module and the P2D model to ensure realistic simulation results. The cooling fluid comprises a 50% mixture of Ethylene Glycol and water. The negative electrodes include Graphite, while the positive electrode includes NMC111. The electrolyte is composed of a 3:7 ratio of EC:EMC with a 1M LiPF6 salt, and the material properties are imported from the COMSOL material library and relevant literature. 6.3. Governing equations

[0125] The simulation employs the electrochemical equations for the cell model, the continuity equation, momentum equations for the fluid flow, and the energy equation for the thermal model of the battery module representative unit.

[0126] Electrochemical model (P2D model):

[0127] The pseudo-2-dimensional (P2D) model has been proposed by Doyle et al. This model includes three regions, i.e., the “negative electrode- separator-positive electrode”. Below are some of the main features of the P2D model: 1. The P2D model represents a 1D continuum description of the battery and assumes porous electrode as spheres, and uses the 1D cross-section of the cell to simulate the flow of ions during the charge and discharge of the battery. 2. The Butler-Volmer equation (cf. Eq. (23)) is used to model the electrochemical charge transfer reaction at the interface of the electrodes and the electrolytes. 3. Equations for binary electrolytes are utilized to model material balance and ionic charge balances in the electrolyte. 4. Transport properties in the electrode are modeled using a homogenization approach (the Bruggeman relation).

[0128] The general schematic of the model is shown in FIG.17.

[0129] The governing equations are solved for four dependent variables: 51 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0130] ^^s, the electrode potential (solid phase potential),

[0131] ^^l, the electrolyte potential (electrolyte phase potential),

[0132] ^^s, the concentration of lithium ions in the solid phase,

[0133] ^^l, the concentration of lithium ions in the electrolyte phase. 6.3.1. Mass conservation in the solid phase

[0134] The transport equation for the solid phase is given by Fick’s second law of diffusion as ^^^^s (13)^^^^= −∇ ∙ (−^^s∇^^s)

[0135] Boundary^^^^ −^^ss^^^^|^^=0 = 0, −^^^^^^^^s^^^^|^^=^^p = −^^θ, (14)

[0136] surface, caused by the electrochemical insertion reactions. 6.3.2. Charge conservation in solid phase

[0137] The charge conservation in the solid phase is given by combining the generalized Ohm’s law and the Faraday law as ∇∙ (−^^s,eff∇^^s) = −^^v,total + ^^s. (15)

[0138] Note:case.

[0139] Boundary conditions are given by ^^ −^^ =app, = ∇^^ = 0. (16)6.3.3. Mass conservation in the electrolyte phase

[0140] The mass conservation equation in the electrolyte phase is given by ^^^^ ^ ^^l + ∇ ∙ +^^l^^+^^ =−^^ Li+,m^v,m^^where,52 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 ^^2^^ ^^^^ ^^^^^^^^ l= −^^ ∇^^ + ( l,effl,eff l^^)(1 +^^^^^^^^) (1 − ^^+)∇^^^^^^l. (18)l

[0141] −^^ ∇^^| = −^^ ∇^^| . (19)l,eff 1 ^^=0 l,eff l ^^=^^6.3.4. Charge conservation in the electrolyte phase

[0142] The charge conservation equation in the electrolyte phase ∇∙ ^^ = ^^ + ^^, (20)l v,total lwhere, 2^^ ^^^^ ^^^^^^^^l,eff ( ) (21) ^^ = −^^ ∇^^ + ( )(1 + ) 1 − ^^ ∇^^^^^^.l l,eff l + l^^ ^^^^^^^^l

[0144] Boundary conditions are given as −^^ ∇^^| = −^^ ∇^^| . (22)s,eff s ^^=0 s,eff s ^^=^^6.3.5. Kinetics of electrochemical reaction

[0145] The kinetics of the electrochemical reaction can be given by the Butler-Volmer equation as 1− ^^ ^^ ( )^^ ^^⁄ ⁄n p n p^^ ^^ − − ^^6.3.6. Kinetics of the parasitic SEI formation reaction

[0146] Ekström and Lindberg formulated the kinetic expression for the SEI formation. The authors have reported the fitting of model parameters, using a lumped 0D model, to the experimental data during cycling for various states-of- charge. Additionally, only the Graphite aging effects were considered in this work. The kinetics of the parasitic reaction is given by the following kinetic expression for the local current density, ^^ in the negative graphite electrode^^^^^^,^^^^^^^^^^loc,ref ^^ = − 1 + ^^^^53 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090

[0147] Detailed definitions of symbols and further model descriptions are given elsewhere.

[0148] Additionally, Tables 2 and 3 contain the subscripts and parameter descriptions for the P2D model. Table 2 List of subscripts used in P2D equations. Name Description s Solid phase l Electrolyte phase n Negative electrode sep Separator p Positive electrode app Applied m Reactions under the porous electrode node Table 3 List of parameters for the P2D equations. Parameters Description ^^sDiffusivity of Li-ions in solid phase ^^pDistance of the surface of the particle to the center(radius) ^^seffEffective conductivity in solid phase ^^leffEffective conductivity in the electrolyte phaseApplied current ^^lPorosity (electrolyte phase volume fraction) ^^l,effEffective diffusion coefficient of Li-ion in the electrolyte phase ^^ Electrode plate area^^ Length of the cell^^+Transference number of Li-ion (depends on the material of electrolyte) ^^LiKinetic current from charge- transfer reaction (Butler-Volmer kinetics) ^^n⁄ pCharge transfer coefficient for NE / PE 54 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 Parameters Description ^^ Overpotential^^0Exchange current density ^^nLength of the negative electrode ^^sepLength of the separator ^^pLength of the positive electrode 6.4. Thermal Model

[0149] The thermal characteristics, including heat generation during a TR event, are explained through the general equation for the energy conservation solved for essentially three domains, namely battery module representative unit where conduction is the dominant heat transfer mechanism (Eq.1), the cooling snake assembly where convection dominates (Eq.2) and finally the outer box which is a solid domain composed of the filler material where conduction is the main heat transfer mechanism (Eq.3) ^^^^ ^^^^^^^^pb + ^^ ∙ ( (25^^^^−^^^^^^^^^^) = ^̇^g, )

[0150] Navier-Stokes equations for the incompressible flow inside the cooling snake. Here, ^^^^is the thermal conductivity coefficient of each battery. It takes the form of a symmetric positive-definite tensor (matrix) and is given by, ^^^^ℎ 0 0

[0151] where ^^^^of the cooling liquid and the filler material; ^^^^, ^^^^and ^^^^denote the average densities of the cells, cooling liquid, and the filler material; ^^pb, ^^pland ^^poare the average specific heat capacities of the cells, cooling liquid and the filler material, and ^̇^gis the volumetric heat generation rate for the battery. The heat generation rate of the cell that is subject to the SEI degradation is given by, 55 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 ^̇^g = ^̇^e + ^̇^SEI, (29)

[0152] where, ^̇^eis calculated as the combined effects from the irreversible heat stemming from Joule heating and activation losses and the reversible heat resulting from electrochemical reactions. Further details about ^̇^egiven in our previous work. However, ^̇^SEIis the heat generation rate due to the exothermic SEI decomposition reaction. 6.5. Boundary and Initial Conditions

[0153] Appropriate boundary and initial conditions are set to accurately represent the operational environment.

[0154] Electrochemical boundary conditions: Since the model is electro-thermal, there are two sets of initial conditions, i.e., electrochemical and thermal with the flow. For the electrochemical part, the initial SOC values for the negative electrode is set to be 0.99 and for the positive electrode to be 0.01. Since the battery starts with a discharge cycle followed by a charge cycle, the negative electrode should have the highest concentration of Li-ions and the positive should have the lowest. Following this assumption, the initial Li-ion concentration in thenegative electrode is assumed to be 0.99 × ^^s,neg_max, where ^^s,neg_max is themaximum Li-ion concentration for the negative electrode. Additionally, the initial Li-ion concentration in the positive electrode is assumed to be 0.01 × ^^s,pos_max, where^^s,pos_maxis the maximum Li-ion concentration for the positive electrode. In order to balance the electronic current, we have set a potential of 0 V on the current collector of the negative electrode. The value of the current is specified at the positive electrode current collector. In this model, the current density is cycled through a discharge stage, followed by the charging stage. Moreover, the separator boundaries are kept insulated for electric currents. In order to balance the ionic charge in the electrolyte, we have considered the current collector boundaries to be insulating. Insulating conditions are also applied to material balances. Additionally, the material flux is determined by the rate of the local electrochemical reaction at the surface of the particle.

[0155] Thermal boundary conditions: In the thermal model of the coolant through the cooling snake assembly, the batteries are positioned within a casing with filler material. The inlet is designated with a temperature of 298 K, while 56 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 at the outlet, a zero temperature gradient is set as the boundary condition. The external boundaries at the top and the bottom have been thermally insulated. The battery is assumed to have an initial temperature of 298 K. Furthermore, a fully developed flow has been assumed at the inlet and outlet of the cooling compartment. Periodic boundary conditions have been enforced for the side walls of the casing representing repeating units of battery and cooling snake assembly. The walls of the cooling snake are subjected to a no-slip boundary condition. The temperature is continuous across the boundary of the batteries and the cooling snake. The temperature gradient is zero at the outlet of the cooling snake. 6.6. Meshing

[0156] The geometry is discretized using a finite element mesh, crucial for the accuracy of the simulation. The meshing involves:

[0157] Mesh density adjustment: Critical regions, such as those near cooling channels and potential hotspots, are meshed more finely to capture detailed thermal and electrochemical phenomena.

[0158] Element type and Size: Selection of appropriate element types and sizes to balance accuracy and computational efficiency. The final mesh was selected based on the grid independence test. 6.7. Coupling of multiphysics

[0159] The thermal and electrochemical models are coupled to simulate the interactions between heat generation and electrochemical reactions. This involves:

[0160] Multiphysics integration: Using COMSOL’s multiphysics capabilities, the heat transfer and electrochemical equations are solved simultaneously.

[0161] Data exchange: Heat generation rates from the electrochemical reactions are fed into the thermal model, and temperature distributions from the thermal model affect the electrochemical reaction kinetics. 6.8. Simulation

[0162] The problem is solved in three steps. In the first step, the steady state flow at the reference temperature is solved. The second step solves for thepotentials in the battery model at t = 0. The third step is a time-dependent study of57 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 the full problem, where the steady-state solution from the first two steps are used to set the initial values for the potentials. The velocity and pressure of the cooling fluid are assumed to be almost unaffected by the heat transfer from the battery. 6.9. Post-processing

[0163] After the simulation runs, the results are analyzed using COMSOL’s post-processing tools:

[0164] Temperature distribution: Visualization of temperature profiles within the battery module.

[0165] Heat generation rates: Analysis of heat generation rates and identification of hotspots.

[0166] State of charge: Examination of the state of charge distribution across the battery cells.

[0167] Voltage distribution: Analysis of the voltage distribution within the battery cells, providing insights into the electrical performance and capacity fade. 6.10. List of Parameters

[0168] Table 4 lists all the parameters used in the multiphysics calculations. Table 4 Model parameters for the multiphysics calculations. Parameter Value General System size 0.08x0.06x0.08 m Initial temperature 298 K Inlet flow velocity 0.1 m s‒1Cylindrical LIB related Form factor 2170 Dimensions Diameter 21 mmHeight 70 mm58 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 Parameter Value Thermal conductivity In-plane 30 W m‒1 K‒1Through-plane 1.29 W m‒1 K‒1Negative electrode: Thickness 40 µmParticle radius 26.2 µmSolid phase volume fraction 0.58Charge transfer coefficient 0.5Separator: Thickness 20 µmPositive electrode: Thickness 35 µmParticle radius 10.7 µmSolid phase volume fraction 0.5Charge transfer coefficient 0.5Electrolyte phase volume fraction 0.37Maximum voltage 4.2 V Cut-off voltage 2.5 V Capacity (typ.) 4800 mAh

[0169] It is to be noted that all parameters used in the simulations, apart from the ones listed in Table 4 are taken from the COMSOL Material Database. 6.11. Computational Domain

[0170] The thermal domain involves a representative unit of a battery module including four cylindrical cells arranged in alternating 2x2 configuration, with an integrated cooling snake assembly. The 3D domain is discretized using a finite element mesh. Each cylindrical cell, labeled B1 through B4, is in contact with the cooling assembly, indicated by the red zigzag lines, which is designed to dissipate 59 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 heat away from the cells efficiently. The serpentine cooling configuration is a critical component in the thermal management of the battery module, ensuring uniform temperature distribution and mitigating the risk of TR. The unstructured mesh with quadratic elements is constructed to capture the complex geometry of the cells and the cooling assembly, with a finer resolution at critical areas to ensure accurate simulation results. The mesh density is increased near the interfaces between the cells and the cooling assembly to resolve the thermal gradients and fluid flow characteristics more precisely. Additionally, the figure shows the boundary conditions, which are further described below. 6.12. Location of Hotspots

[0171] FIGS.18A-18D show a general schematic on the location of the hotspots in battery B2 considered in this study. Specifically, for FIG.18A, the hotspot is located at coordinates (0.015,0,0). In FIG.18B, the corresponding hotspot can be found at coordinates (0.015,0,‒0.023). For FIG.18C, there are two hotspots situated at (0.015,0,0.023) and (0.015,0,0), and finally FIG.18D, which displays the two hotspots at (0.015,0,0.006) and (0.015,0,‒0.012). Each coordinate set represents the precise location of hotspots, underscoring the variability observed across the evaluated cases. 6.13. Experimental Validation

[0172] Here, we provide the validation of our developed electrochemical P2D model. The validation includes the comparison between the discharge voltage characteristics obtained by the P2D model and the experimental data reported by Waldmann et al. For this purpose, the discharge curves were compared directly against the experimental data at various discharge rates (FIG.19). The model’s prediction is in good agreement with the experimental data during the initial discharge cycle, demonstrating the accuracy of the model. 6.14. Driving Cycle Information

[0173] FIGS.20A-20B show all the important results pertaining to driving cycle load. FIG.20A shows the typical FTP75 driving cycle obtained from EPA. This driving cycle shows the variation of the speed of a car (mph) with time (s). The EPA driving cycle is provided for up to 1874 seconds. However, the batteries do not completely discharge in that short time frame. Hence, the EPA driving cycles are repeated after every 1877 seconds until the battery discharges to its lower cutoff 60 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 voltage of 2.5 V. FIG.20B illustrates the corresponding current applied obtained from the driving cycle. The current profile is dictated by the acceleration, which depends exclusively on the profile of the applied driving cycle.

[0174] The FTP 75 cycle includes three distinct phases: the Cold Start Phase (Bag 1), Transient Phase (Bag 2), and Hot Start Phase (Bag 3). The Cold Start Phase, lasting 505 seconds, represents the start of a journey with the engine cold and includes multiple accelerations and decelerations, mimicking stop-and-go traffic conditions. The Transient Phase follows, simulating more consistent driving with a mix of urban and highway conditions, moderate accelerations, decelerations, and steady cruising speeds, lasting 867 seconds. The Hot Start Phase, also 505 seconds long, occurs after a brief stop, representing a restart with the engine already warm, replicating similar driving conditions to the cold start phase but with the engine in a warmed-up state. 6.15. Since the FTP 75 driving cycle is only provided for a total duration of 1877 seconds, we looped the cycle to match the longer duration of our simulation. This is a valid assumption for modeling purposes, ensuring that the battery cells are subjected to a continuous dynamic load that accurately represents extended real-world driving conditions. In our study, a representative unit of four batteries was initially fully charged and then subjected to the FTP 75 driving cycle current until they reached the cutoff voltage. This discharge process under the driving cycle simulates the real-world operating conditions of an EV, capturing the thermal and electrochemical behavior of the battery system under varying load conditions. After completing the discharge phase, the batteries were recharged at a constant current, simulating the recharging process of a fully discharged EV. This approach ensures that the study comprehensively represents both the discharge and recharge cycles of EV operation. Thermocouple orientation

[0175] FIG.21 shows the orientation of the thermocouples around a single battery. It should be mentioned that each battery is equipped with the same type of orientation. However, for illustration purposes, we show a single battery. These various orientations of the thermocouples were used to collect the temperature of the 61 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 battery at different spatial coordinates and at different time steps. This data was then used to prepare the dataset for the machine learning study. 6.16. TensorFlow dataset creation for ML study

[0176] Temperature points in the model were collected at a frequency of 1 second, a crucial step to ensure the accuracy of the machine ML predictions as it captures the dynamic thermal behavior of the battery system in detail. However, these raw files could not be directly employed for the ML study. Consequently, it was imperative to restructure the data into specific formats suitable for ML input. This process, known as data preparation and preprocessing, constitutes a crucial step in any ML investigation.

[0177] The collected data was modified and saved into two distinct files. The first file contained the distances between the 120 spatial coordinates along the sensors, while the second file contained the temperature measurements collected at those points throughout the entire simulated battery operation. This restructuring is illustrated in FIG.22, which shows a schematic workflow for the preparation of the data matrices used for the ML study.

[0178] The first file, the distance matrix, is essential for creating the adjacency matrix required to construct the graph network for spatial featureidentification. An adjacency matrix is an ^^ ^^ ^^ matrix, where ^^ is the total number ofnodes. Adjacency matrices represent the existence of edges that connect the node pairs through the values in the matrices. In this work, the coordinates of the thermocouples are assumed to form a graph. The second file, the temperature matrix, contains time-series data of temperature readings at each spatial coordinate, capturing the thermal behavior over time. 6.17. Training Curve

[0179] During the so-called training, the model undergoes training on a specific dataset and then undergoes evaluation on a separate validation dataset after each training iteration. The resulting performance measurements for both datasets across all epochs are shown in FIG.23. Learning curves aid in addressing issues such as underfitting or overfitting, as well as assessing the representativeness of the training and validation datasets. By examining the results presented in FIG.23, it can be observed that all the networks exhibit satisfactory 62 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 performance after 100 iterations, with the loss approaching approximately 0.02%. Similar patterns can be observed for the validation set. 6.18. Evaluation Metrics

[0180] Evaluation of the crucial statistical factors is vital in evaluating the model’s effectiveness in predicting future outcomes. This study examines the efficiency of the network by utilizing metrics such as the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The concept of absolute deviation pertains to the size of the contrast between the projected outcome of an observation and the authentic value of that observation. MAE calculates the mean value of absolute deviations for a set of projections and observations, serving as an assessment of the overall magnitude of discrepancies within the entire set. MAE is given as ^^^^^^ =^^ Σ^^^^=1 | (30)^^^^^^ − ^̂^^^|

[0181] where ^^ isis the predicted value

[0182] RMSE represents one of the primary performance evaluators for a regression model, quantifying the average variation between predicted values and actual values. It offers an approximation of the model’s effectiveness in predicting the desired outcome. It measures the square root of the average of the squared differences between the predicted and actual values and is given as ^^^^^^^^^^^^ 2 )6.19.

[0183] FIG.24 shows the temperature evolution over time at two points along each thermal sensor. In the upper panel of FIG.24, the temperature is collected at coordinates (0.0143, 0.0071, -0.0022) and (0.0245, 0.0102, -0.0129) for the helical type sensor. Since the first point is closer to the hotspot, it exhibits a higher final temperature compared to the latter point. In the lower panel of FIG.24, the temperature is collected at coordinates (0.0127, -0.0053, 0.0061) and (0.0114, 0, -0.0149) for the mixed helical and straight type sensor. A similar temperature trend can be observed here. It should be noted that since TR is a rapid phenomenon occurring in the last discharge cycle, the battery temperature at initial time steps 63 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 remains almost similar along the shown coordinates. However, a significant temperature difference becomes evident only during the last cycle due to the rapid progression of TR, which sharply increases the hotspot temperature. 64 106209412.1

Claims

Atty. Docket No.085067-857987 Client Ref: UA25-090 CLAIMS What is claimed is:

1. A system, comprising: a processor in communication with a memory of a battery management system controlling a battery module, the memory including instructions executable by the processor to: access a dataset of thermal and electrochemical characteristics of the battery module, the dataset incorporating degradation of a solid electrolyte interface; construct graph-structured time series data for the battery module from the dataset, each node of the graph-structured time series data representing a spatial location along the battery module corresponding to a sensor coordinate along a curved path on a cylindrical cell surface of the battery module and being associated with temperature values over a plurality of time steps; forecast, for each spatial location and using a long short-term memory network, a sequence of future temperatures for a plurality of future time steps based on the graph-structured time series data and on a spatial dependency representation encoding spatio-thermal inter-node dependencies; and initiate, based on the sequence of future temperatures, a battery- safety response by the battery management system.

2. The system of claim 1, the memory including instructions executable by the processor to: generate an adjacency matrix from inter-sensor distances between sensor coordinates, and the spatial dependency representation using the adjacency matrix.

3. The system of claim 1, the memory including instructions executable by the processor to: 65 106209412.1Atty. Docket No.085067-857987 Client Ref: UA25-090 simulate operation of a coupled electrochemical-thermal multiphysics model representing the battery module; and capture, based on the simulation, at least a portion of the dataset of thermal and electrochemical characteristics.

4. The system of claim 1, the memory including instructions executable by the processor to: capture empirical time-dependent temperature data from a plurality of thermocouples positioned along the battery module.

5. The system of claim 1, the long short-term memory network including a long short-term layer that simulates a time dependence of a node embedding sequence present within the graph-structured time series data and the spatial dependency representation.

6. The system of claim 1, the memory further including instructions executable by the processor to: transform a hidden state of the long short-term memory network into the sequence of future temperatures for each spatial location along the battery module.

7. The system of claim 1, the memory including instructions executable by the processor to: train or calibrate the long short-term memory network using the dataset of thermal and electrochemical characteristics, the dataset including solid- electrolyte-interface decomposition heat-release events and a driving- cycle current profile.

8. The system of claim 1, the memory including instructions executable by the processor to: evaluate, based on the sequence of future temperatures, whether a temperature threshold will be exceeded. 66 106209412.1

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