Lithium-ion battery distributed thermal process sensor fault estimation method

Abstract

The application discloses a kind of lithium ion battery distributed thermal process sensor fault estimation method, comprising: using two-dimensional partial differential equation to describe rectangular lithium ion battery distributed thermodynamic equation;Distributed thermal model of large size lithium ion battery is constructed;Using Chebyshev-Galerkin method, distributed thermodynamic equation and distributed thermal model are decomposed into reduced order model described by standard state space equation in time domain;State variable in reduced order model is constructed using sensor measurement output and a Hurwitz matrix, and enhanced reduced order model is constructed;Enhanced adaptive observer and error state space equation are constructed using enhanced reduced order model;Based on error state space equation, the fault strength of temperature sensor that fails is estimated using fast adaptive algorithm.The application can effectively estimate sensor fault, including time-invariant and time-varying fault, and single sensor and multiple sensor fault.

Description

Technical Field

[0001] This invention relates to the field of sensor fault estimation, and in particular to a method for estimating faults in a distributed thermal process sensor for lithium-ion batteries. Background Technology

[0002] Lithium-ion batteries play a crucial role in the new energy vehicle and energy storage industries due to their advantages such as long cycle life, high charge-discharge rate, and no memory effect. As lithium battery size continues to increase, their energy density further increases. Current technologies employ a number of sensors to monitor distributed thermal processes to achieve uniform temperature control and thermal fault diagnosis. However, if some sensors malfunction, erroneous data acquisition can lead to abnormal thermal modeling, resulting in incorrect responses from the battery thermal management system. Therefore, accurate sensor fault estimation is crucial for maintaining correct distributed thermal modeling and thermal monitoring of large-size lithium-ion batteries.

[0003] Numerous studies have focused on distributed thermal modeling of large-size lithium-ion batteries using multiple sensors. The first category comprises model-based methods, representative of which include the Chebyshev-Gallenkin method, the line method, and the distributed equivalent circuit method, to simulate the two-dimensional / three-dimensional distributed thermal processes of pouch cells. These methods require 9, 3, and 3 thermal sensors, respectively. The second category consists of model-data hybrid methods, including the Karhunen-Loeve (KL), incremental KL, and Gappy KL methods, used for offline, online, and sparse spatiotemporal thermal modeling of pouch cells. These methods utilize 300, 20, and 2 thermocouples, respectively. The third category comprises image-based data-driven methods, which require at least 3 thermocouples for temperature distribution prediction.

[0004] Benefiting from these distributed thermal models, thermal fault diagnosis of large-size lithium-ion batteries based on multiple sensors has recently attracted widespread attention. A multi-filter framework, a multi-scale dynamic analysis method, and a spatiotemporal inference system are proposed, requiring 4, 4, and 9 sensors, respectively.

[0005] The aforementioned multi-sensor-based distributed thermal modeling and fault diagnosis methods have greatly facilitated the safe application of large-size lithium-ion batteries. However, these models assume that the temperature sensors are fault-free. In real-world scenarios, sensors may malfunction due to various complex factors such as shock, vibration, climate, and aging. Sensor faults can be time-invariant or time-varying, including bias, drift, gain, and random faults. Accurate sensor fault estimation is crucial for proper distributed thermal modeling and monitoring.

[0006] Currently, some research has been conducted on sensor fault estimation for lithium-ion batteries in existing technologies. This includes a lumped observer and an extended / adaptive Kalman filter for voltage / current sensor fault estimation in battery packs. These methods do not consider temperature sensor faults. A sliding mode observer and a model-data hybrid fault diagnosis scheme are also included for simultaneously estimating current, voltage, and temperature sensor faults. Both of these methods are implemented on cylindrical batteries, whose thermal processes are described by a lumped equivalent circuit model. These methods cannot be applied to large-size lithium-ion batteries because the thermal processes of large-size lithium-ion batteries are described by two-dimensional / three-dimensional partial differential equations. Furthermore, current research mainly considers bias sensor faults while neglecting time-varying faults. Currently, temperature sensor fault estimation for the distributed thermal processes of large-size lithium batteries has not been explored in depth.

[0007] Therefore, how to provide an effective method for estimating faults of time-invariant and time-varying temperature sensors in distributed thermal processes of lithium-ion batteries is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] This invention addresses the aforementioned research status and existing problems by providing a fault estimation method for distributed thermal process sensors in lithium-ion batteries. Based on spatiotemporal variable separation, the Chebyshev-Gallenkin method is used to decompose distributed thermodynamics into a reduced-order model described by the standard state-space equations. Subsequently, under fault conditions, a fast adaptive observer is designed based on the enhanced reduced-order model to estimate sensor faults. The error convergence is analyzed using the Lyapunov direct method.

[0009] This invention provides a fault estimation method for distributed thermal process sensors in lithium-ion batteries. Multiple temperature sensors are mounted on the surface of the lithium-ion battery, which is a rectangular lithium-ion battery with dimensions larger than a preset size. The method includes the following steps:

[0010] S1: Considering the heat-affected zones of the positive and negative electrodes of a lithium-ion battery, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of a rectangular lithium-ion battery.

[0011] S2: Based on the temperature field of the temperature sensor and the fault intensity of each temperature sensor, a distributed thermal model of a large-size lithium-ion battery is constructed.

[0012] S3: The Chebyshev-Gallenkin method is used to decompose the distributed thermodynamic equations and distributed thermal models in the time domain into reduced-order models described by the standard state-space equations.

[0013] S4: Using the sensor measurement output and a Hurwitz matrix, the state variables in the reduced-order model are constructed to obtain new state variables, and the enhanced reduced-order model is constructed using the new state variables;

[0014] S5: Construct an enhanced adaptive observer using the enhanced reduced-order model, and the error state-space equation of the enhanced adaptive observer considering the error in the temperature sensor fault intensity estimation.

[0015] S6: Based on the error state-space equation, a fast adaptive algorithm is used to estimate the fault intensity of the temperature sensor that has failed.

[0016] Preferably, in step S1, the distributed thermodynamic equation of the rectangular lithium-ion battery is described using a two-dimensional partial differential equation as follows:

[0017]

[0018] The boundary conditions are:

[0019]

[0020] In the formula, For the Laplace operator; T,T amb , These represent spatiotemporal temperature, ambient temperature, and average temperature, respectively; i∈{x,y} represents spatial coordinates; I, U OCV U and U represent current, open-circuit voltage, and terminal voltage, respectively; ρ is the average density of the lithium battery; C p Specific heat capacity; Q and Q h These are the internal heat generation and lateral heat flux of the battery, respectively; k i h is the thermal conductivity. i =h c / k i , where h c Γ is the thermal convection coefficient; b v is the entropy-heat coefficient; c α1 represents the battery capacity; α2 and α1 are the thermal scaling factors of the battery body and the tabs; S {p,n} A {p,n} and E {p,n} These represent the heat-affected zone, cross-sectional area, and resistance of the positive and negative electrode tabs, respectively; A m Battery area; SOC (State of Charge); C m This refers to the battery capacity.

[0021] Preferably, in step S2, the distributed thermal model for large-size lithium-ion batteries is constructed as follows:

[0022] y m (t)=[T(x1,y1,t),…,T(x N ,y N ,t)] T +Df SF (t);

[0023] In the formula, y m (t) represents the temperature sensor's measurement output at time t; N represents the number of sensors; (x) N ,y N ) represents the spatial coordinates of the Nth sensor; D is the identity matrix; sensor fault f SF(t) It is expressed as follows:

[0024]

[0025] In the formula, sgn(·) is the step function, and t N Let f be the failure time of the Nth sensor. N (t) represents the fault intensity.

[0026] Preferably, in step S3, the reduced-order model described by the standard state-space equations in the time domain is as follows:

[0027]

[0028] in:

[0029]

[0030] u(4,:)=1

[0031]

[0032] In the formula, The time coefficient is M, and the model order is M. For orthogonal basis functions, E(i) m ,j m ) and A(i m ,j m ) are subsets of E and A, respectively; i m and j m ∈[0,(M+1) 2 -1]; N is the number of sensors; Represents the estimators of x and y; It is a synthesized two-dimensional function basis, m∈[0,(M+1)]. 2 -1],α i It is the scaling factor along the i-direction, k i Let i be the thermal conductivity, and i∈{x,y} represent the spatial coordinates. For distributed temperature Auxiliary functions obtained through decoupling.

[0033] Preferably, in step S4, the step of constructing the new state variable includes:

[0034] Use y m (t) and a Herwitz matrix A sTo construct a new state variable x m (t), satisfying the following condition:

[0035]

[0036] Preferably, in step S4, the enhanced reduced-order model is constructed using the new state variables as follows:

[0037]

[0038] In the formula, It is the transformed output, and

[0039]

[0040] In the formula, I p It is an identity matrix.

[0041] Preferably, in step S5, the enhanced adaptive observer is constructed as follows:

[0042]

[0043] In the formula, and They are and f SF The estimated value of (t); It is the observer gain.

[0044] Preferably, in step S5, the error state-space equation of the enhanced adaptive observer is:

[0045]

[0046] In the formula, and

[0047] Preferably, in step S6, the step of estimating the faulty temperature sensor and the fault intensity using a fast adaptive algorithm includes:

[0048]

[0049] In the formula, For learning rate, Let σ be a positive definite symmetric matrix, and let σ be a given scalar.

[0050] The fault estimation method for distributed thermal process sensors in lithium-ion batteries proposed in this invention has the following advantages compared with existing technologies:

[0051] This invention achieves high-precision estimation of sensor faults by establishing a distributed thermal model, deriving a reduced-order model, designing a fast adaptive observer, and conducting convergence analysis. A fast adaptive observer is designed that can effectively estimate sensor faults, including time-invariant and time-varying faults, as well as single-sensor and multi-sensor faults, with a maximum root mean square error of 0.0173.

[0052] Experimental results validated the effectiveness and robustness of the method under different operating conditions and environmental conditions, providing strong technical support for thermal management and fault diagnosis of large-size lithium-ion batteries. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0054] Figure 1 This is a flowchart of the fault estimation method for distributed thermal process sensors in lithium-ion batteries provided in an embodiment of the present invention;

[0055] Figure 2 This is a simulation diagram of a lithium-ion battery temperature sensor failure provided in an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram of sensor layout for reducing model verification provided in an embodiment of the present invention;

[0057] Figure 4 This is a schematic diagram of the temperature of the sensor points provided in an embodiment of the present invention;

[0058] Figure 5 This is a schematic diagram of the experimental platform provided in an embodiment of the present invention;

[0059] Figure 6 This is a diagram showing the current and voltage input signals of the battery testing system under different current modes in the experimental platform provided in this embodiment of the invention;

[0060] Figure 7 This is a schematic diagram of the sensors and fault settings in the experimental platform provided in this embodiment of the invention;

[0061] Figure 8 These are temperature curves and corresponding fault estimation performance diagrams for representative faults F1 and F6 provided in embodiments of the present invention.

[0062] Figure 9These are the temperature curves of representative fault F4 at sensor S3 and representative fault F5 at sensor S4, and the corresponding fault estimation performance diagram provided in the embodiments of the present invention.

[0063] Figure 10 These are temperature curves and corresponding fault estimation performance diagrams for representative faults F7 and F9 provided in embodiments of the present invention.

[0064] Figure 11 These are the temperature curves of representative fault F10 at sensors S1 and S3, the temperature curves of representative fault F11 at sensors S2 and S4, and the corresponding fault estimation performance diagrams provided in this embodiment of the invention. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] like Figure 1 As shown in the figure, this invention provides a method for fault estimation of distributed thermal process sensors in lithium-ion batteries. Multiple temperature sensors are mounted on the surface of the lithium-ion battery, such as... Figure 2 As shown in (a), the lithium-ion battery is a rectangular lithium-ion battery, and its size is larger than the preset size.

[0067] Sensor faults can be either time-invariant or time-varying, including bias, drift, gain, and random faults. For example, ... Figure 2 As shown in (b), four sensors were deployed for distributed thermal monitoring. Figure 2 (c) and (e) show the sampled data and estimated temperature field distribution under normal conditions. Accordingly, Figure 2 (d) and (f) show the sampled data and estimated temperature field distribution when sensor S3 has a bias fault. Figure 2 (f) and Figure 2 (e) By comparison, we can see that the location, value, and distribution profile of the temperature peaks are completely different. This further illustrates that accurate sensor fault estimation is crucial for proper distributed thermal modeling and monitoring.

[0068] Based on the above considerations, a sensor fault estimation framework was developed for the partial differential thermal process of large-size lithium-ion batteries. First, under normal conditions, based on spatiotemporal variable separation, the Chebyshev-Galogenin method is used to decompose the distributed thermodynamics into a reduced-order model described by the standard state-space equations. Then, under fault conditions, a fast adaptive observer is designed based on the reduced-order model to estimate the sensor fault. The error convergence is analyzed using the Lyapunov direct method.

[0069] The specific implementation steps include:

[0070] S1: Considering the heat-affected zones of the positive and negative electrodes of a lithium-ion battery, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of a rectangular lithium-ion battery.

[0071] S2: Based on the temperature field of the temperature sensor and the fault intensity of each temperature sensor, a distributed thermal model of a large-size lithium-ion battery is constructed.

[0072] S3: The Chebyshev-Gallenkin method is used to decompose the distributed thermodynamic equations and distributed thermal models in the time domain into reduced-order models described by the standard state-space equations.

[0073] S4: Use sensor measurement output and a Hurwitz matrix to construct the state variables in the reduced-order model, obtain new state variables, and use the new state variables to construct an enhanced reduced-order model;

[0074] S5: Construct an enhanced adaptive observer using an enhanced reduced-order model, and the error state-space equation of the enhanced adaptive observer considering the error in the temperature sensor fault intensity estimation.

[0075] S6: Based on the error state-space equation, a fast adaptive algorithm is used to estimate the fault intensity of the temperature sensor that has failed.

[0076] In one embodiment, since the height and length of a large-size lithium-ion battery are much greater than its thickness, its thermal change along the thickness direction can be ignored. Figure 2 As shown in (a) and (b), the thermal effects of the positive and negative electrode tabs are considered to improve modeling accuracy. Here, it is assumed that the thermally affected area of ​​the tabs is rectangular and embedded within the two-dimensional geometry of the battery body. Therefore, in S1, the distributed thermodynamic equation of the rectangular lithium-ion battery, described using two-dimensional partial differential equations, is:

[0077]

[0078] The boundary conditions are:

[0079]

[0080] In the formula, For the Laplace operator; T,Tamb , These represent spatiotemporal temperature, ambient temperature, and average temperature, respectively; i∈{x,y} represents spatial coordinates; I, U OCV U and U represent current, open-circuit voltage, and terminal voltage, respectively; ρ is the average density of the lithium battery; C p Specific heat capacity; Q and Q h These are the internal heat generation and lateral heat flux of the battery, respectively; k i h is the thermal conductivity. i =h c / k i , where h c Γ is the thermal convection coefficient; b v is the entropy-heat coefficient; c α1 represents the battery capacity; α2 and α1 are the thermal scaling factors of the battery body and the tabs; S {p,n} A {p,n} and R {p,n} These represent the heat-affected zone, cross-sectional area, and resistance of the positive and negative electrode tabs, respectively; A m Battery area; SOC (State of Charge); C m This refers to the battery capacity.

[0081] In this embodiment, the heat-affected zones of the positive and negative electrodes in formula (2) are designed as follows:

[0082] S p (x,y)=[H(x-0.085_-H(x-0.13)]*[H(y-0.199)-H(y-0.2)]

[0083] S n )x,y)=[H(x-0.02)-H(x-0.065)]*[H(y-0.199)-H(y-0.2)]

[0084] In the formula, H(·) is the Herveside function.

[0085] In one embodiment, S2, the distributed thermal model for a large-size lithium-ion battery is constructed as follows:

[0086] y m (t)=[T(x1,y1,t),…,T(x N ,y N ,t)] T +Df SF (t) (6)

[0087] In the formula, y m (t) represents the temperature sensor's measurement output at time t; N represents the number of sensors; (x) N ,y N) represents the spatial coordinates of the Nth sensor; D is the identity matrix; sensor fault f SF(t) It is expressed as follows:

[0088]

[0089] In the formula, sgn(·) is the step function, and t N Let f be the failure time of the Nth sensor. N (t) represents the fault intensity.

[0090] In one embodiment, S3, the time-domain decomposition into a reduced-order model described by the standard state-space equations is as follows:

[0091]

[0092] in:

[0093]

[0094]

[0095] u(4,:)=1

[0096]

[0097] In the formula, The time coefficient is M, and the model order is M. For orthogonal basis functions, E(i) m ,j m ) and A(i m ,j m ) are subsets of E and A, respectively; i m and j m ∈[0,(M+1) 2 -1]; N is the number of sensors; Represents the estimators of x and y; It is a synthesized two-dimensional function basis, m∈[0,(M+1)]. 2 -1],α i It is the scaling factor along the i-direction, k i Let i be the thermal conductivity, and i∈{x,y} represent the spatial coordinates. For distributed temperature Auxiliary functions obtained through decoupling.

[0098] In this embodiment, S3 further includes the following steps:

[0099] S31: Coordinate Transformation: Based on the characteristics of the Chebyshev function, the spatial domain xy coordinates i∈[0,i0] of the two-dimensional distributed lithium battery thermal model are transformed to...

[0100] S32 Boundary Condition Homogenization: The spatiotemporal temperature of the two-dimensional distributed lithium battery thermal model is decoupled to obtain a two-dimensional spatiotemporal thermodynamic expression, which satisfies the homogeneous boundary conditions.

[0101] S33 Reduced-Order Model Construction: The two-dimensional spatiotemporal thermodynamic expression is decomposed into equations represented by two-dimensional orthogonal basis functions along the x-axis and y-axis under the spatiotemporal separation framework; the two-dimensional orthogonal basis functions are used as test functions to multiply the two-dimensional distributed lithium battery thermal model processed by S21-S22, and then integrated over the entire spatial domain to obtain the state-space equation in the time domain, i.e., the reduced-order model.

[0102] The specific execution steps are as follows:

[0103] S31: Coordinate Transformation

[0104] Transform the spatial domain i∈[0,i0] into

[0105]

[0106] but:

[0107]

[0108] Where i∈{x,y}, i0∈{x0,y0} are the width and length of the battery, respectively, and α i =2 / i0 is along i

[0109] Scaling factor for direction.

[0110] Substituting equations (9)-(10) into equations (1)-(5), the original two-dimensional thermodynamics of the pouch battery can be expressed as:

[0111]

[0112] Constrained by boundary conditions:

[0113]

[0114] S32: Homogenization of boundary conditions:

[0115] The boundary conditions in formula (12) can be normalized to:

[0116]

[0117] In the formula, β 1i =β 2i =α i ,-γ 1i =γ 2i =h i ,-μ1i =μ 2i =h i T amb .

[0118] Given that the Chebyshev-Galogen method is applicable to uniform boundary conditions, it is necessary to separate non-uniform disturbances in the system. This involves distributing the temperature... Decoupling With auxiliary functions sum:

[0119]

[0120] Then, the two-dimensional thermal process formula (11) can be transformed into:

[0121]

[0122] in

[0123]

[0124] The following homogeneous boundary conditions must be met:

[0125]

[0126] S33: Separation of spatiotemporal variables:

[0127] Then, formulas (15)-(17) can be used in A two-dimensional spatiotemporal thermodynamic model is established. Within the framework of spatiotemporal separation, It can be broken down into:

[0128]

[0129] in and It is along and A basis of orthogonal functions of dimension 1 It is a synthesized two-dimensional function basis. It is the time coefficient, m∈[0,(M+1)] 2 -1], M is the model order.

[0130] along and Orthogonal function basis of directions and Designed as follows:

[0131]

[0132] Where C n It is a Chebyshev polynomial of the first kind, degree n; ξ n and η nThe boundary conditions are satisfied; n∈{j,k}.

[0133] Multiply equation (15) by the test function v, and then integrate over the entire domain:

[0134]

[0135] Where (·,·) represents the inner product operation.

[0136] According to Galerkin's method, let a two-dimensional function basis be established. For the test function v, the original two-dimensional thermal process can be simplified to:

[0137]

[0138] Then, the original two-dimensional thermal process formula (1) and the sensor measurement output formula (6) can be decomposed into a reduced-order model (8) in the time domain.

[0139] The verification process of the order reduction model is given below:

[0140] A total of nine sensors were used to validate the reduced-order thermal model, such as Figure 3 As shown, the pouch battery is divided into 16 equal parts, and 9 sensors (P1-P9) are placed at each node. The ambient temperature is 20℃, and the input current signal is set to the urban road circulation mode UDDS to fully simulate the battery thermal process.

[0141] Figure 4 (a) and (b) show the actual and estimated temperature values ​​at the nine sensors, respectively, with good consistency. Figure 4 (c) To estimate the error fluctuation range, the fluctuation is small, with the peak error not exceeding 0.6℃, meeting the accuracy requirements. The modeling accuracy of the reduced-order model is summarized in Table 1 based on the root mean square error (RMSE). At point P2, the maximum RMSE is 0.2089, while at point P7, the minimum RMSE is 0.0650. The modeling errors of sensors closer to the tabs (P1-P3) are greater than those of sensors farther away (P4-P9). This is because, under normal conditions, the heat generated by the tabs is dominant compared to the heat generated by the battery itself. The overall error is within an acceptable range, demonstrating the effectiveness of the proposed reduced-order model.

[0142] Table 1. Root mean square error of the reduced-order model at 9 validation points.

[0143]

[0144] In one embodiment, the derived reduced-order model (9) can be normalized to the standard state-space equation.

[0145]

[0146] In the formula, x(t) represents the state, u(t) represents the input, and y represents the input. m (t) represents the measured output; A, B, C, D, and E are known constant matrices, for (E -1 A, C) are observables.

[0147] The steps to construct the new state variables include:

[0148] Use y m (t) and a Herwitz matrix A s To construct a new state variable x m (t), satisfying the following condition:

[0149]

[0150] In one embodiment, in S4, combining formulas (22) and (23), the enhanced order reduction model is constructed using the new state variables as follows:

[0151]

[0152] In the formula, It is the transformed output, and

[0153]

[0154] In the formula, I p It is an identity matrix.

[0155] Thus, the sensor fault f in the source system formula (22) SF (t) can be transformed into actuator faults in the enhanced system equation (24). Furthermore, there are no faults in the output equation of equation (24). This is beneficial for the design of subsequent sensor fault estimation algorithms.

[0156] In one embodiment, in S5, since (E -1 Since A and C are observable, It is also observable. Inspired by adaptive observers, an enhanced adaptive observer is constructed as follows:

[0157]

[0158] In the formula, and They are and f SF The estimated value of (t); It is the observer gain.

[0159] In one embodiment, in S5, combining formulas (24) and (25), the error state space equation of the enhanced adaptive observer is:

[0160]

[0161] In the formula, and

[0162] In one embodiment, in S6, the following fast adaptive algorithm can be used to estimate sensor faults:

[0163]

[0164] The solution is further as follows:

[0165]

[0166] In the formula, For learning rate, Let σ be a positive definite symmetric matrix, and let σ be a given scalar; it includes a proportionality term e. y (t) and an integral term The former helps to improve the estimation speed.

[0167] The following is a convergence analysis of the temperature sensor fault estimation method proposed in the embodiments of the present invention:

[0168] The verification in this embodiment is based on the following assumptions and lemmas:

[0169] Assumption 1: Sensor failure intensity f s The derivative norm of (t) in formula (7) is bounded with respect to time:

[0170]

[0171] In the formula, s∈[1,N], and ∥·∥ represents the Euclidean norm. It is a constant. This assumption is reasonable because the rate of change of sensor fault intensity is bounded in actual processes.

[0172] Assumption 2: It is full column rank, and It is observable. This can be achieved by adjusting the number of sensors and the model order.

[0173] Lemma 1: For a symmetric positive definite matrix For a scalar μ > 0, the following inequalities hold:

[0174]

[0175] Theorem 1: Given scalars μ>0 and σ>0, and satisfying Assumptions 1-2, if there exists a symmetric positive definite matrix... sum matrix The following linear matrix inequalities must be satisfied:

[0176]

[0177] Where * denotes the symmetric element in the symmetric matrix, and:

[0178]

[0179] And it meets the following conditions:

[0180]

[0181] The fast adaptive sensor fault estimation algorithm (28) can achieve e x (t) and e f (t) are uniformly eventually bounded.

[0182] Proof: Choose the following Lyapunov functions.

[0183]

[0184] Combining formulas (17), (28) and (34), Vm ( The derivative of t with respect to time is:

[0185]

[0186] It is easy to prove using formula (32):

[0187]

[0188] Substituting formulas (26) and (36) into formula (35), we get the following formula:

[0189]

[0190] According to Lemma 1, we can obtain:

[0191]

[0192] Substituting (38) into (37), we get:

[0193]

[0194] in,

[0195] When formula (33) holds, i.e. Ξ < 0 and ε = λ is defined. min (-Ξ). Because When the column is full rank, formula (39) is equivalent to Since ε||ζ(t)|| 2 >ξ, then According to Lyapunov's stability theory, state e x (t) and sensor fault estimation error e f (t) will converge to a small set, namely e f (t) and e x (t) is uniformly and ultimately bounded, thus completing the proof.

[0196] Note: Equation (33) can be easily solved separately using the Linear Matrix Inequality Toolbox in Matlab. However, solving both constraint equation (32) and equation (33) simultaneously is difficult. Therefore, it can be transformed into an optimization problem, as shown below.

[0197] minimize Satisfies formulas (33), (31) and:

[0198]

[0199] Among them I E It is an identity matrix.

[0200] The following experimental platform is set up to verify the method of the embodiment of the present invention:

[0201] To facilitate performance evaluation, the root mean square error (RMSE) metric is used to quantify the performance of the proposed sensor fault estimation framework.

[0202]

[0203] Where L m The duration; and f SF (t) represents the estimated sensor fault and the actual sensor fault, respectively.

[0204] Experimental setup

[0205] This study used a soft-pack graphite / lithium iron phosphate battery (3.2V / 20Ah), and the specific parameters of the battery are shown in Table 2. Figure 5 It serves as an experimental platform, consisting of a host computer, a temperature chamber, a battery management system (BMS), and a battery testing system.

[0206] Table 2 Summary of Battery Parameters

[0207]

[0208] The computer manages all equipment; the temperature chamber controls the ambient temperature; the battery management system (BMS) collects temperature, voltage, and current data; and the battery testing system is set to current mode. For example... Figure 6As shown, 1C and 2C constant current, urban road loop mode UDDS, and multi-step loop mode are set as input current signals to fully excite the battery thermal process. The total sampling time is 1000s, and the sampling interval is 1s.

[0209] Table 2 summarizes the model parameters obtained from the experiments. U in formula (2) OCV It can be represented as:

[0210]

[0211] In formula (2) Γ b It can be represented as:

[0212]

[0213] Under normal conditions, the performance of distributed thermal modeling can be referenced in Appendix B. Taking the urban road circulation pattern UDDS as an example, its maximum prediction error does not exceed 0.6℃. The overall error is acceptable, demonstrating the effectiveness of the reduced-order model derived from the Chebyshev-Gallenkin method.

[0214] In abnormal situations, four sensors are used, each with a pre-set fault, such as... Figure 7 As shown in Table 3, the sensor fault settings are summarized. Four current modes were set (1C, 2C, urban road cycle, and multi-step cycle). The ambient temperature range [10℃, 30℃] was considered. Static and dynamic sensor faults were considered. For example, F1-F2 and F6-F9 are time-invariant bias faults. F3-F5 are time-varying sensor faults, where F3 and F4 are drift faults, and F5 is a gain fault. Since four sensors are used, multiple sensors may fail simultaneously. Therefore, two multi-sensor fault modes, F10 and F11, were set, each containing a bias fault and a time-varying fault occurring at different times and locations.

[0215] Table 3 Sensor Fault Setting Table

[0216]

[0217]

[0218] Where H(·) is the step function. M1 represents multi-sensor fault 1, with a value of 3*H(t-400) occurring at S1, and 20%*H(t-600) occurring at S3. M2 represents multi-sensor fault 2, with a value of -2*H(t-400) occurring at S2, and (-3+3*exp(-0.05(t-600))*

[0219] H(t-600)) occurs at S4.

[0220] Sensor Fault Estimation Verification

[0221] Table 4 summarizes the estimation results for sensor faults F1-F11. At three ambient temperatures (10℃, 20℃, and 30℃), the root mean square errors of bias faults F1, F2, and F6 at sensor S1 are 0.0050, 0.0042, and 0.0033, respectively. The temperature curves for representative faults F1 and F6 are shown below. Figure 8 As shown in (a) and (b). Figure 8 (c) and (d) illustrate the corresponding fault estimation performance, where the estimated fault intensity converges to the true fault value. The root mean square error results and experimental curves verify that the method can accurately estimate time-invariant bias sensor faults and is applicable to a certain range of ambient temperatures.

[0222] Table 4. Root Mean Square Error for Sensor Fault Estimation

[0223] serial number Root mean square error serial number Root mean square error F1 0.0050 F7 0.0040 F2 0.0042 F8 0.0173 F3 0.0050 F9 0.0035 F4 0.0028 F10 0.0042 / 0.0025 F5 0.0024 F11 0.0050 / 0.0028 F6 0.0033 - -

[0224] The root mean square errors of time-varying faults (including drift faults F3-F4 and gain fault F5) are 0.0050, 0.0028 and 0.0024, respectively. Figure 9 (a) and (b) show the temperature curves at F4 and F5 at sensor S3 and sensor S4, respectively. Figure 9 (c) and (d) illustrate the fault estimation performance. Here, the estimated sensor fault curve matches the actual fault curve very well. This indicates that this method also works well in time-varying sensor fault scenarios.

[0225] The root mean square errors of sensors F7, F8, and F9 at sensor S1 in 1C, 2C, and multi-step cyclic modes are 0.0040, 0.0173, and 0.0035, respectively. The temperature curves and estimated performance of faulty sensors F7 and F9 are as follows: Figure 10 As shown, where, Figure 10 (a) shows the F7 temperature curve at sensor S1. Figure 10 (b) shows the temperature curve of F9 at sensor S1. Figure 10 (c) Fault estimation performance of F7 Figure 10 (d) shows the fault estimation performance of F9. Combined with the experimental results of F1-F6 under the urban road loop mode UDDS, it can be concluded that this method is feasible under different current modes.

[0226] F10 and F11 contain a bias fault and a time-varying fault that occurs at different times and locations. Figure 11The temperature curves and estimation performance of F10 and F11 are shown. It can be seen that the method can estimate both faults well at the same time. The root mean square errors of the two faults in F10 are 0.0042 and 0.0025, respectively, and the root mean square errors of the two faults in F11 are 0.0050 and 0.0028, respectively. This proves that the method is applicable to single-sensor and multi-sensor fault environments.

[0227] Furthermore, the sensor fault detection threshold was set to ±0.6℃, the same as the maximum modeling error caused by the reduced-order model based on Chebyshev-Gallenkin. Figure 8-11 As shown, the proposed method can detect sensor faults in real time under all conditions.

[0228] In summary, this invention proposes a fault estimation scheme for large-size lithium-ion battery sensors based on a two-dimensional distributed thermal model. During the normal operation phase, the Chebyshev-Gallenkin method is used to decompose the two-dimensional partial differential equations into a time-domain reduced-order model described by the standard state-space equations. During the fault phase, a fast adaptive observer based on the reduced-order model is designed to estimate sensor faults. It is proven that the estimation error is eventually bounded. Eleven sets of sensor fault experiments were conducted, with a maximum root mean square error of 0.0173. Experimental analysis shows that this method is applicable to different current modes and a certain range of ambient temperatures. It can be used to estimate static and dynamic sensor faults, as well as single and multiple sensor faults occurring at different times and locations.

[0229] The above provides a detailed description of the fault estimation method for distributed thermal process sensors in lithium-ion batteries. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

[0230] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method for fault estimation of distributed thermal process sensors in lithium-ion batteries, characterized in that, Multiple temperature sensors are mounted on the surface of the lithium-ion battery. The lithium-ion battery is a rectangular lithium-ion battery with a size larger than a preset size. The process includes the following steps: S1: Considering the heat-affected zones of the positive and negative electrodes of a lithium-ion battery, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of a rectangular lithium-ion battery. S2: Based on the temperature field of the temperature sensor and the fault intensity representation of each temperature sensor, a distributed thermal model of a large-size lithium-ion battery is constructed as follows: ； In the formula, The temperature sensor's measurement output at time t; Number of sensors; For the first The spatial coordinates of each sensor; Identity matrix; sensor malfunction It is expressed as follows: ； In the formula, It is a step function. For the first The failure time of each sensor, Fault intensity; S3: The Chebyshev-Gallenkin method is used to decompose the distributed thermodynamic equations and distributed thermal models in the time domain into reduced-order models described by the standard state-space equations. S4: Using the sensor measurement output and a Hurwitz matrix, the state variables in the reduced-order model are constructed to obtain new state variables. The enhanced reduced-order model is then constructed using these new state variables. ； In the formula, It is the transformed output, and ； In the formula, It is the identity matrix; , For distributed temperature Auxiliary functions obtained through decoupling; State; For input; The sensor fault is transformed into an actuator fault in the enhanced reduced-order model, and no fault exists in the output equation of the enhanced reduced-order model. S5: Construct an enhanced adaptive observer using the enhanced reduced-order model, and the error state-space equation of the enhanced adaptive observer considering the error in the temperature sensor fault intensity estimation. S6: Based on the error state-space equation, a fast adaptive algorithm is used to estimate the fault intensity of the temperature sensor that has failed.

2. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 1, characterized in that, In S1, the distributed thermodynamic equation of the rectangular lithium-ion battery is described using a two-dimensional partial differential equation as follows: ； ； ； ； The boundary conditions are: ； In the formula, For the Laplace operator; These are spatiotemporal temperature, ambient temperature, and average temperature, respectively. Represents spatial coordinates; , and These are current, open-circuit voltage, and terminal voltage, respectively. This refers to the average density of lithium batteries; Specific heat capacity; and These are the internal heat generation and the lateral heat flux of the battery, respectively. Thermal conductivity; ,in The thermal convection coefficient; It is the entropy heat coefficient; Battery capacity; and For the thermal scaling factor of the battery body and the tabs; , and These are the heat-affected zone, cross-sectional area, and resistance of the positive and negative electrode tabs, respectively. Battery area; In charging state; This refers to the battery capacity.

3. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 1, characterized in that, In S3, the time-domain decomposition into a reduced-order model described by the standard state-space equations is as follows: ； in: ； In the formula, For time coefficient, The model order; These are orthogonal basis functions. and They are respectively and Subset elements; and ; The number of sensors; express The estimate; It is a synthesized two-dimensional function basis. , It is the scaling factor along the i-direction. Thermal conductivity, Representing spatial coordinates For distributed temperature Auxiliary functions obtained through decoupling.

4. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 1, characterized in that, In step S4, the steps for constructing the new state variable include: use and a Herwitz matrix To construct a new state variable It meets the following conditions: 。 5. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 1, characterized in that, In S5, the enhanced adaptive observer is constructed as follows: ； In the formula, , and They are and The estimated value; It is the observer gain.

6. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 5, characterized in that, In step S5, the error state-space equation of the enhanced adaptive observer is: ； In the formula, and .

7. The fault estimation method for distributed thermal process sensors in lithium-ion batteries according to claim 6, characterized in that, In step S6, the step of estimating the faulty temperature sensor and the fault intensity using a fast adaptive algorithm includes: ； In the formula, For learning rate, It is a positive definite symmetric matrix. For a given scalar.

Images