Fault estimation method for distributed thermal process sensor of lithium ion battery

Abstract

The invention discloses a lithium ion battery distributed thermal process sensor fault estimation method. The method comprises the following steps: describing a rectangular lithium ion battery distributed thermodynamic equation by using a two-dimensional partial differential equation; constructing a distributed thermal model of the large-size lithium ion battery; using a Chebyshev-Galerkin method to decompose the distributed thermodynamic equation and the distributed thermal model into reduced-order models described by a standard state space equation in a time domain; a state variable in the reduced-order model is obtained by using sensor measurement output and a Hurvetz matrix construction, and an enhanced reduced-order model is constructed; constructing an enhanced adaptive observer and an error state space equation by using the enhanced reduced-order model; and based on the error state space equation, estimating the fault intensity of the faulted temperature sensor by using a fast adaptive algorithm. The method can effectively estimate sensor faults, including time-invariant and time-varying faults, and single-sensor and multi-sensor faults.

Description

Technical Field

[0001] The present invention relates to the field of sensor fault estimation, and in particular to a method for estimating fault of a distributed thermal process sensor of a lithium-ion battery. Background Art

[0002] Lithium-ion batteries play a vital role in the new energy vehicle and energy storage industries due to their advantages such as long cycle life, high charge and discharge rate, and no memory. As the size of lithium batteries continues to increase, their energy density increases further. In the prior art, a certain number of sensors are arranged to monitor the distributed thermal process in order to achieve uniform temperature control and thermal fault diagnosis. However, once some sensors fail, erroneous collected data will cause thermal modeling anomalies, resulting in erroneous responses from the battery thermal management system. Therefore, accurate sensor fault estimation is crucial to maintaining correct distributed thermal modeling and thermal monitoring of large-size lithium-ion batteries.

[0003] There are many studies on distributed thermal modeling of large-size lithium batteries based on multi-sensors. The first category is model-based methods, and representative methods include the Chebyshev-Galerkin method, the line method, and the distributed equivalent circuit method to simulate the two-dimensional / three-dimensional distributed thermal process of soft-pack batteries. They require 9, 3, and 3 thermal sensors, respectively. The second category is a model-data hybrid method, including the Karhunen-Loeve (KL), incremental KL, and Gappy KL methods, which are used for offline, online, and sparse spatiotemporal thermal modeling of soft-pack batteries. They use 300, 20, and 2 thermocouples, respectively. The third category is an image-based data-driven method, which requires at least 3 thermocouples for temperature distribution prediction.

[0004] Benefiting from these distributed thermal models, multi-sensor based thermal fault diagnosis of large-scale lithium-ion batteries has attracted extensive attention recently. A multi-filter framework, a multi-scale dynamic analysis method, and a spatiotemporal reasoning system are proposed, which require 4, 4, and 9 sensors, respectively.

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

[0006] At present, some research has been conducted on sensor fault estimation of lithium-ion batteries in the prior art. These include a set-valued observer and an extended / adaptive Kalman filter for voltage / current sensor fault estimation of battery packs. These methods do not consider temperature sensor faults. Also included is a sliding mode observer and a model-data hybrid fault diagnosis scheme for simultaneous estimation of current, voltage and temperature sensor faults. Both methods are performed on cylindrical batteries, whose thermal processes are described by lumped equivalent circuit models. These two methods cannot be applied to large-sized lithium-ion batteries because the thermal processes of large-sized lithium-ion batteries are described by two-dimensional / three-dimensional partial differential equations. In addition, current research mainly considers biased sensor faults and ignores time-varying faults. At present, temperature sensor fault estimation for distributed thermal processes of large-sized lithium batteries has not been deeply explored.

[0007] Therefore, how to provide a lithium-ion battery distributed thermal process sensor fault estimation method that can effectively estimate time-invariant and time-varying temperature sensor faults is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the invention

[0008] In view of the above research status and existing problems, the present invention provides a method for fault estimation of distributed thermal process sensors for lithium-ion batteries. Based on the separation of time and space variables, the Chebyshev-Galerkin method is used to decompose the 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 the sensor fault. The error convergence is analyzed using the Lyapunov direct method.

[0009] The present invention provides a method for estimating faults of a distributed thermal process sensor of a lithium-ion battery, wherein a plurality of temperature sensors are installed on the surface of the lithium-ion battery, and the lithium-ion battery is a rectangular lithium-ion battery, and its size is larger than a preset size; the method comprises the following steps:

[0010] S1: Considering the heat affected zone of the positive and negative lugs of lithium-ion batteries, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of rectangular lithium-ion batteries;

[0011] S2: constructing a distributed thermal model of a large-size lithium-ion battery based on the temperature field of the temperature sensor and the fault intensity representation sensor measurement output of each temperature sensor;

[0012] S3: Decomposition of the distributed thermodynamic equations and the distributed thermal model in the time domain into a reduced-order model described by the standard state-space equations using the Chebyshev-Galerkin method;

[0013] S4: constructing a state variable in a reduced-order model using the sensor measurement output and a Hurwitz matrix to obtain a new state variable, and constructing an enhanced reduced-order model using the new state variable;

[0014] S5: constructing an enhanced adaptive observer using the enhanced reduced-order model, and an error state space equation of the enhanced adaptive observer taking into account the error in the estimation of the fault intensity of the temperature sensor;

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

[0016] Preferably, in S1, the two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of the rectangular lithium-ion battery:

[0017]

[0018] The boundary conditions are:

[0019]

[0020] In the formula, is the Laplace operator; T,T amb , are the spatiotemporal temperature, ambient temperature and average temperature respectively; i∈{x,y} represents the spatial coordinate; I, U OCV and U are current, open circuit voltage and terminal voltage respectively; ρ is the average density of lithium battery; C p is the specific heat capacity; Q and Q h are the internal heat generation and lateral heat flux of the battery respectively; k i is the thermal conductivity; h i =h c / k i , where h c is the thermal convection coefficient; Γ b is the entropy thermal coefficient; v c is the battery capacity; α1 and α2 are the thermal scaling coefficients of the battery body and the tab; S {p,n} , A {p,n} and E {p,n} A is the heat affected zone, cross-sectional area and resistance of the positive and negative electrode ears respectively; m is the battery area; SOC is the state of charge; C m is the battery capacity.

[0021] Preferably, in S2, the distributed thermal model of the large-size lithium-ion battery 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) is the measured output of the temperature sensor at time t; N is the number of sensors; (x N ,y N ) is the spatial coordinate of the Nth sensor; D is the unit matrix; sensor fault f SF(t) It is expressed as follows:

[0024]

[0025] Where sgn(·) is the step function, t N is the failure time of the Nth sensor, f N (t) is the fault intensity.

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

[0027]

[0028] in:

[0029]

[0030] u(4,:)=1

[0031]

[0032] In the formula, is the time coefficient, M is the model order; is an orthogonal basis function, E(i m ,j m ) and A(i m ,j m ) are subset elements of E and A respectively; i m and j m ∈[0,(M+1) 2 -1]; N is the number of sensors; represents the estimated value of x and y; is a synthetic two-dimensional function basis, m∈[0,(M+1) 2 -1], α i is the scaling factor along the i direction, k i is the thermal conductivity, i∈{x,y} represents the spatial coordinates, The distribution temperature Decoupled obtained helper functions.

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

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

[0035]

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

[0037]

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

[0039]

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

[0041] Preferably, in S5, constructing an enhanced adaptive observer is:

[0042]

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

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

[0045]

[0046] In the formula, and

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

[0048]

[0049] In the formula, is the learning rate, is a positive definite symmetric matrix and σ is a given scalar.

[0050] The lithium-ion battery distributed thermal process sensor fault estimation method proposed in the present invention has the following beneficial effects compared with the prior art:

[0051] The present invention achieves high-precision estimation of sensor faults by establishing a distributed thermal model, derivation of reduced-order models, design of fast adaptive observers, and 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 estimated root mean square error of 0.0173.

[0052] The experimental results verify the effectiveness and robustness of the method under different operating and environmental conditions, providing strong technical support for thermal management and fault diagnosis of large-size lithium-ion batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on the provided drawings without creative work.

[0054] Figure 1 is a flow chart of a method for estimating faults of a distributed thermal process sensor of a lithium-ion battery provided by an embodiment of the present invention;

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

[0056] Figure 3 is a schematic diagram of a sensor layout for reduced-order model verification provided by an embodiment of the present invention;

[0057] Figure 4 is a schematic diagram of the temperature of a sensor point provided by an embodiment of the present invention;

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

[0059] Figure 6 is a diagram of current and voltage input signals of a battery test system under different current modes in an experimental platform provided by an embodiment of the present invention;

[0060] Figure 7 is a schematic diagram of sensor and fault settings in the experimental platform provided by an embodiment of the present invention;

[0061] Figure 8 1 is a schematic diagram of temperature curves of representative faults F1 and F6 and corresponding fault estimation performance provided by an embodiment of the present invention;

[0062] Fig. 91 is a temperature curve of a representative fault F4 at sensor S3, a temperature curve of a representative fault F5 at sensor S4, and a corresponding fault estimation performance schematic diagram provided by an embodiment of the present invention;

[0063] Fig.10 1 is a schematic diagram of temperature curves of representative faults F7 and F9 and corresponding fault estimation performance provided by an embodiment of the present invention;

[0064] Fig.11 1 is a temperature curve of a representative fault F10 at sensors S1 and S3 , a temperature curve of a representative fault F11 at sensors S2 and S4 , and a corresponding fault estimation performance diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] like Figure 1 As shown, an embodiment of the present invention provides a method for estimating faults of a distributed thermal process sensor of a lithium-ion battery. A plurality of temperature sensors are installed 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 both time-invariant and time-varying, including offset, drift, gain, and random faults. Figure 2 As shown in (b), four sensors are deployed for distributed thermal monitoring. Figure 2 (c) and (e) show the sampled data and estimated temperature field distribution under normal conditions. Figure 2 (d) and (f) show the sampled data and estimated temperature field distribution when sensor S3 has a bias fault. Figure 2 (f) Figure 2 By comparing (e), we can see that the temperature peak locations, values, and distribution profiles are completely different. This further illustrates that accurate sensor fault estimation is critical for correct distributed thermal modeling and monitoring.

[0068] Based on the above considerations, a sensor fault estimation framework is developed for the partial differential thermal processes of large-scale lithium-ion batteries. Firstly, under normal conditions, the distributed thermodynamics is decomposed into a reduced-order model described by the standard state-space equations using the Chebyshev-Galerkin method based on the spatiotemporal variable separation. Subsequently, 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 zone of the positive and negative lugs of lithium-ion batteries, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of rectangular lithium-ion batteries;

[0071] S2: Construct a distributed thermal model of large-size lithium-ion batteries based on the temperature field of the temperature sensors and the fault intensity of each temperature sensor to represent the sensor measurement output;

[0072] S3: The distributed thermodynamic equations and the distributed thermal model are decomposed in the time domain into a reduced-order model described by the standard state-space equations using the Chebyshev-Galerkin method;

[0073] S4: Using the 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: Constructing the 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 estimation of the fault intensity of the temperature sensor;

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

[0076] In one embodiment, since the height and length of a large-sized lithium-ion battery are much greater than its thickness, its thermal variation along the thickness direction can be ignored. Figure 2 (a) and (b). In order to improve the modeling accuracy, the thermal effects of the positive and negative pole tabs are considered. It is assumed here that the heat affected zone of the tab is rectangular and embedded in the two-dimensional geometry of the battery body. Therefore, in S1, the distributed thermodynamic equations of rectangular lithium-ion batteries are described using two-dimensional partial differential equations:

[0077]

[0078] The boundary conditions are:

[0079]

[0080] In the formula, is the Laplace operator; T,Tamb , are the spatiotemporal temperature, ambient temperature and average temperature respectively; i∈{x,y} represents the spatial coordinate; I, U OCV and U are current, open circuit voltage and terminal voltage respectively; ρ is the average density of lithium battery; C p is the specific heat capacity; Q and Q h are the internal heat generation and lateral heat flux of the battery respectively; k i is the thermal conductivity; h i =h c / k i , where h c is the thermal convection coefficient; Γ b is the entropy thermal coefficient; v c is the battery capacity; α1 and α2 are the thermal scaling coefficients of the battery body and the tab; S {p,n} , A {p,n} and R {p,n} A is the heat affected zone, cross-sectional area and resistance of the positive and negative electrode ears respectively; m is the battery area; SOC is the state of charge; C m is the battery capacity.

[0081] In this embodiment, the heat affected zones of the positive electrode and the negative electrode 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] Where H(·) is the Heaviside function.

[0085] In one embodiment, in S2, a distributed thermal model of 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) is the measured output of the temperature sensor at time t; N is the number of sensors; (x N ,y N) is the spatial coordinate of the Nth sensor; D is the unit matrix; sensor fault f SF(t) It is expressed as follows:

[0088]

[0089] Where sgn(·) is the step function, t N is the failure time of the Nth sensor, f N (t) is the fault intensity.

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

[0091]

[0092] in:

[0093]

[0094]

[0095] u(4,:)=1

[0096]

[0097] In the formula, is the time coefficient, M is the model order; is an orthogonal basis function, E(i m ,j m ) and A(i m ,j m ) are subset elements of E and A respectively; i m and j m ∈[0,(M+1) 2 -1]; N is the number of sensors; represents the estimated value of x and y; is a synthetic two-dimensional function basis, m∈[0,(M+1) 2 -1], α i is the scaling factor along the i direction, k i is the thermal conductivity, i∈{x,y} represents the spatial coordinates, The distribution temperature Decoupled obtained helper functions.

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

[0099] S31: Coordinate transformation: According to the Chebyshev function characteristics, 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: Decouple the space-time temperature of the two-dimensional distributed lithium battery thermal model to obtain a two-dimensional space-time thermodynamic expression, where the two-dimensional space-time thermodynamic expression satisfies the homogeneous boundary conditions;

[0101] S33 reduced-order model construction: The two-dimensional space-time thermodynamic expression is decomposed into equations represented by two-dimensional orthogonal basis functions along the x-axis and y-axis under the space-time 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 the entire spatial domain is integrated to obtain the state space equation in the time domain, that is, the reduced-order model.

[0102] The specific 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, α i =2 / i0 is along i

[0109] Scaling factor for the direction.

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

[0111]

[0112] Subject to boundary conditions:

[0113]

[0114] S32: Homogenization of boundary conditions:

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

[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] Since the Chebyshev-Galerkin method is applicable to homogeneous boundary conditions, it is necessary to separate the interference of inhomogeneity in the system. Decoupling With helper functions sum:

[0119]

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

[0121]

[0122] in

[0123]

[0124] The following homogeneous boundary conditions are met:

[0125]

[0126] S33: Spatiotemporal Variable Separation:

[0127] Then, we can use formulas (15)-(17) to A two-dimensional space-time thermodynamic model is established on the basis of time and space separation. It can be broken down into:

[0128]

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

[0130] along and Orthogonal function basis of direction and Designed for:

[0131]

[0132] Among them C n is a Chebyshev polynomial of the first kind nth degree; ξ n and η nSatisfy the boundary conditions; n∈{j,k}.

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

[0134]

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

[0136] According to the Galerkin method, let the two-dimensional function basis is the test function v, the original two-dimensional thermal process can be simplified as:

[0137]

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

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

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

[0141] Figure 4 (a) and (b) are the true and estimated values ​​of the temperature at 9 sensors, respectively, with good consistency; Figure 4 (c) is the estimated error fluctuation range, which is small and the peak error does not exceed 0.6℃, meeting the accuracy requirement. From the perspective of the root mean square error, the modeling accuracy of the reduced-order model is summarized in Table 1. At point P2, the root mean square error is maximum 0.2089, while at point P7, the root mean square error is minimum 0.0650. The modeling error of the sensors close to the tabs (P1-P3) is greater than the modeling error of the sensors far away from this position (P4-P9). This is because under normal circumstances, the heat generated by the tabs dominates compared to the heat generated by the battery body. The overall error is within an acceptable range, which illustrates the effectiveness of the proposed reduced-order model.

[0142] Table 1 Root mean square error of the reduced-order model for 9 verification points

[0143]

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

[0145]

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

[0147] The steps to construct a new state variable include:

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

[0149]

[0150] In one embodiment, in S4, formulas (22) and (23) are combined to construct an enhanced reduced-order model using new state variables:

[0151]

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

[0153]

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

[0155] Thus, the sensor fault f of the source system equation (22) SF (t) can be converted into the actuator fault in the enhanced system formula (24). In addition, there is no fault in the output equation of formula (24). This is conducive to the design of subsequent sensor fault estimation algorithm.

[0156] In one embodiment, in S5, due to (E -1 A, C) is observable, so It is also observable. Inspired by the adaptive observer, the enhanced adaptive observer is constructed as:

[0157]

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

[0159] In one embodiment, in S5, combining formula (24) and formula (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 may be used to estimate sensor failure:

[0163]

[0164] Further solution is:

[0165]

[0166] In the formula, is the learning rate, is a positive definite symmetric matrix, σ is a given scalar; it includes a proportional 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 embodiment of the present invention:

[0168] The verification of this example is based on the following assumptions and lemmas:

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

[0170]

[0171] Where s∈[1,N], ∥·∥ represents the Euclidean norm, This assumption is reasonable because the rate of change of sensor fault intensity is bounded in actual process.

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

[0173] Lemma 1: For a symmetric positive definite matrix and scalar μ>0, the following inequality holds:

[0174]

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

[0176]

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

[0178]

[0179] And the following conditions are met:

[0180]

[0181] Then the fast adaptive sensor fault estimation algorithm (28) can be realized x (t) and e f (t) Uniformly eventually bounded.

[0182] Proof: Choose the following Lyapunov function.

[0183]

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

[0185]

[0186] By using formula (32), it is easy to prove that:

[0187]

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

[0189]

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

[0191]

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

[0193]

[0194] in,

[0195] When formula (33) holds, that is, Ξ<0 and ε=λ min (-Ξ). Because The column is full rank, formula (39) is equivalent to Since ε||ζ(t)|| 2 >ξ, then According to Lyapunov stability theory, the 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 eventually bounded, completing the proof.

[0196] Remarks: Equation (33) can be easily solved separately using the Linear Matrix Inequality Toolbox in Matlab. However, it is difficult to solve the constraint equation (32) and Equation (33) simultaneously. 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 is the identity matrix.

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

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

[0202]

[0203] Where L m is the length of time; and f SF (t) are the estimated sensor fault and the actual sensor fault, respectively.

[0204] Experimental Configuration

[0205] This study uses a soft-pack graphite / lithium iron phosphate battery (3.2V / 20Ah). The specific battery parameters are shown in Table 2. Figure 5 It is an experimental platform, which consists of a host, 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 each device, the temperature box controls the ambient temperature, the battery management system BMS collects temperature, voltage, and current data, and the battery test system is set to current mode. Figure 6As shown, 1C, 2C constant current, urban road cycle mode UDDS, and multi-step cycle mode are set as input current signals to fully stimulate 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. OCV It can be expressed as:

[0210]

[0211] Γ in formula (2) b It can be expressed as:

[0212]

[0213] Under normal conditions, the performance of distributed thermal modeling can be referred to Appendix B. Taking the urban road cycle mode UDDS as an example, its maximum prediction error does not exceed 0.6°C. The overall error is acceptable, which illustrates the effectiveness of the reduced-order model derived from the Chebyshev-Galerkin method.

[0214] In abnormal situations, 4 sensors are used, each with a fault set, such as Figure 7 As shown. Table 3 summarizes the settings of sensor faults. Four current modes (1C, 2C, urban road cycle, and multi-step cycle) are set. The ambient temperature range [10℃, 30℃] is considered. Static and dynamic sensor faults are 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 at the same time. Therefore, two multi-sensor fault modes F10 and F11 are set, both of which contain a bias fault and a time-varying fault that occur at different times and locations.

[0215] Table 3 Sensor fault setting table

[0216]

[0217]

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

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

[0220] Sensor Fault Estimation Validation

[0221] Table 4 summarizes the estimation results of sensor faults F1-F11. Under three ambient temperatures (10℃, 20℃, and 30℃), the RMS errors of bias faults F1, F2, and F6 at sensor S1 are 0.0050, 0.0042, and 0.0033, respectively. The temperature curves of representative faults F1 and F6 are shown in Figure 4. 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 RMS error results and experimental curves verify that the proposed method can well estimate the time-invariant bias sensor fault and is applicable to a certain range of ambient temperatures.

[0222] Table 4 Root mean square error of 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 RMS errors of the time-varying faults (including drift faults F3-F4 and gain fault F5) are 0.0050, 0.0028, and 0.0024, respectively. Fig. 9 (a) and (b) show the temperature profile of F4 at sensor S3 and the temperature profile of F5 at sensor S4. Fig. 9 (c) and (d) illustrate the fault estimation performance. Here, the estimated sensor fault curve can match the actual fault curve very well. This shows that this method can also work well in time-varying sensor fault scenarios.

[0225] The RMS errors of F7, F8, and F9 at sensor S1 in 1C, 2C, and multi-step cycle modes are 0.0040, 0.0173, and 0.0035, respectively. The temperature curves and estimated performance of faults F7 and F9 are shown in Figure 2. Fig.10 As shown, Fig.10 (a) is the F7 temperature curve at sensor S1, Fig.10 (b) is the temperature curve of F9 at sensor S1, Fig.10 (c) is the fault estimation performance of F7, Fig.10 (d) is the fault estimation performance of F9. Combining the experimental results of F1-F6 under the urban road cycle mode UDDS, it can be concluded that this method is feasible under different current modes.

[0226] F10 and F11 consist of a bias fault and a time-varying fault that occur at different times and locations. Fig.11The temperature curves and estimation performance of F10 and F11 are shown. It can be seen that the two faults can be well estimated 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, which proves that the method is suitable for single-sensor and multi-sensor fault environments.

[0227] In addition, the sensor fault detection threshold is set to ±0.6°C, which is the same as the maximum modeling error caused by the reduced-order model based on Chebyshev–Galerkin. Figure 8-11 As shown, the proposed method can detect sensor faults in real time under all conditions.

[0228] In summary, the present invention proposes a fault estimation scheme for large-size lithium-ion battery sensors based on a two-dimensional distributed thermal model. In the normal stage, the Chebyshev-Galerkin method is used to decompose the two-dimensional partial differential equation into a time-domain reduced-order model described by the standard state-space equation. In the fault stage, a fast adaptive observer based on the reduced-order model is designed to estimate the sensor fault. It is proved that the estimation error is ultimately bounded. A total of 11 sets of sensor failure experiments were carried out, and the maximum estimated root mean square error was 0.0173. Experimental analysis shows that the 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 is a detailed introduction to a lithium-ion battery distributed thermal process sensor fault estimation method provided by the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technicians in this field, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0230] In this article, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

Claims

1. A method for estimating faults of distributed thermal process sensors of lithium-ion batteries, characterized in that: A plurality of temperature sensors are installed on the surface of the lithium-ion battery, and the lithium-ion battery is a rectangular lithium-ion battery, and its size is larger than a preset size; comprising the following steps: S1: Considering the heat affected zone of the positive and negative lugs of lithium-ion batteries, a two-dimensional partial differential equation is used to describe the distributed thermodynamic equation of rectangular lithium-ion batteries; S2: constructing a distributed thermal model of a large-size lithium-ion battery based on the temperature field of the temperature sensor and the fault intensity representation sensor measurement output of each temperature sensor; S3: Decomposition of the distributed thermodynamic equations and the distributed thermal model in the time domain into a reduced-order model described by the standard state-space equations using the Chebyshev-Galerkin method; S4: constructing a state variable in a reduced-order model using the sensor measurement output and a Hurwitz matrix to obtain a new state variable, and constructing an enhanced reduced-order model using the new state variable; S5: constructing an enhanced adaptive observer using the enhanced reduced-order model, and an error state space equation of the enhanced adaptive observer taking into account the error in the estimation of the fault intensity of the temperature sensor; S6: Based on the error state space equation, a fast adaptive algorithm is used to estimate the fault intensity of the faulty temperature sensor.

2. The method for estimating faults of a distributed thermal process sensor for a lithium-ion battery according to claim 1, characterized in that: In S1, the distributed thermodynamic equation of a rectangular lithium-ion battery is described using a two-dimensional partial differential equation: The boundary conditions are: In the formula, is the Laplace operator; T,T amb , are the spatiotemporal temperature, ambient temperature and average temperature respectively; i∈{x,y} represents the spatial coordinate; I, U OCV and U are current, open circuit voltage and terminal voltage respectively; ρ is the average density of lithium battery; C p is the specific heat capacity; Q and Q h are the internal heat generation and lateral heat flux of the battery respectively; k i is the thermal conductivity; h i =h c / k i , where h c is the thermal convection coefficient; Γ b is the entropy thermal coefficient; v c is the battery capacity; α1 and α2 are the thermal scaling coefficients of the battery body and the tab; S {p,n} , A {p,n} and R {p,n} A is the heat affected zone, cross-sectional area and resistance of the positive and negative electrode ears respectively; m is the battery area; SOC is the state of charge; C m is the battery capacity.

3. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 1, characterized in that: In S2, the distributed thermal model of large-size lithium-ion batteries is constructed as follows: y m (t)=[T(x1,y1,t),…,T(x N ,y N ,t)] T +Df SF (t); In the formula, y m (t) is the measured output of the temperature sensor at time t; N is the number of sensors; (x N ,y N ) is the spatial coordinate of the Nth sensor; D is the unit matrix; sensor fault f SF(t) It is expressed as follows: Where sgn(·) is the step function, t N is the failure time of the Nth sensor, f N (t) is the fault intensity.

4. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 1, characterized in that: In S3, the reduced-order model described by the standard state space equation is decomposed in the time domain as follows: in: u(4,:)＝1 In the formula, is the time coefficient, M is the model order; is an orthogonal basis function, E(i m ,j m ) and A(i m ,j m ) are subset elements of E and A respectively; i m and j m ∈[0,(M+1) 2 -1]; N is the number of sensors; represents the estimated value of x and y; is a synthetic two-dimensional function basis, m∈[0,(M+1) 2 -1], α i is the scaling factor along the i direction, k i is the thermal conductivity, i∈{x,y} represents the spatial coordinates, The distribution temperature Decoupled obtained helper functions.

5. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 3, characterized in that: In S4, the step of constructing a new state variable includes: Use y m (t) and a Hurwitz matrix A s To construct a new state variable x m (t), satisfying the following conditions:

6. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 5, characterized in that: In S4, the enhanced reduced-order model is constructed using new state variables: In the formula, is the transformed output, and In the formula, I p is the identity matrix.

7. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 6, characterized in that: In S5, the enhanced adaptive observer is constructed as follows: In the formula, and They are and f SF (t) is an estimated value; is the observer gain.

8. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 7, characterized in that: In S5, the error state space equation of the enhanced adaptive observer is: In the formula, and 9. The method for estimating faults of a distributed thermal process sensor of a lithium-ion battery according to claim 8, characterized in that: In S6, the step of estimating the faulty temperature sensor and the fault intensity by using a fast adaptive algorithm includes: In the formula, is the learning rate, is a positive definite symmetric matrix and σ is a given scalar.

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