Interval estimator based lithium-ion battery temperature sensor fault detection method

Abstract

The application discloses a lithium ion battery temperature sensor fault detection method based on an interval estimator, relates to the technical field of lithium ion battery temperature sensor fault detection, and comprises the following steps: according to a mathematical model of a lithium ion battery internal temperature system, an interval estimator is used to estimate the lithium ion battery internal temperature in real time, and an estimated error dynamics model of the lithium ion battery internal temperature system is obtained; based on Lyapunov stability theory, the stability of the estimated error dynamics model of the lithium ion battery internal temperature system is analyzed; and based on the interval estimator, a residual generator is designed to determine whether a temperature sensor fault occurs. Compared with the prior art, the application has the beneficial effects that the method can avoid the influence of measurement anomalies on observation performance, improve the adaptability of fault detection on the lithium ion battery temperature system, has good robustness and stability, and can effectively improve the safety and service life of the lithium ion battery.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery temperature sensor fault detection technology, and more specifically, to a lithium-ion battery temperature sensor fault detection method based on an interval estimator. Background Technology

[0002] As a key component of new energy electric vehicles, lithium-ion batteries require extremely precise temperature control. Heat dissipation for drive components is primarily achieved through the cooling circuit and the fan. The fan operates under different conditions based on the temperature of the cooling circuit. If the temperature sensor detecting the cooling circuit temperature malfunctions, its readings will deviate from the actual value. If the measured value is lower than the true value, it may cause the cooling circuit to overheat, affecting normal vehicle operation; if the measured value is higher than the true value, it will cause the fan speed to increase, leading to excessive energy consumption. Therefore, fault detection of lithium-ion battery temperature sensors is essential. Methods for fault detection of lithium-ion battery temperature sensors often require modeling the lithium-ion temperature system. However, due to the long-term operation of lithium-ion batteries, the system is subject to various uncertainties and external disturbances, making fault detection difficult using accurate models.

[0003] For temperature sensor faults, fault detection can typically be achieved by designing an estimator to estimate the model. Fault detection schemes based on interval estimators are not constrained by model uncertainties and measurement noise, improving the adaptability to fault detection in lithium-ion battery temperature systems and possessing significant theoretical and practical value. However, due to the high gain requirements of interval estimators, it is often difficult to obtain estimator gains that meet the requirements. Therefore, most research on interval estimators remains in the theoretical research stage.

[0004] In conclusion, considering the wide application of interval estimators in fault detection, researching fault detection methods based on interval estimators has broad research and application value. Summary of the Invention

[0005] The present invention provides a fault detection method for lithium-ion battery temperature sensors based on an interval estimator, which can solve the above-mentioned problems.

[0006] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0007] This invention provides a fault detection method for lithium-ion battery temperature sensors based on an interval estimator, comprising the following steps:

[0008] Step 1: Based on the mathematical model of the internal temperature system of the lithium-ion battery, establish an interval estimator to estimate the internal temperature of the lithium-ion battery in real time, and obtain the estimation error dynamic model of the internal temperature system of the lithium-ion battery.

[0009] Step 2: Based on Lyapunov stability theory, analyze the stability of the estimation error dynamic model of the internal temperature system of lithium-ion battery;

[0010] Step 3: Based on the stability analysis results of the estimation error dynamic model of the internal temperature system of the lithium-ion battery, use the interval estimator to design a residual generator to determine whether the temperature sensor failure has occurred.

[0011] In a preferred embodiment of the present invention, the mathematical model of the internal temperature system of a lithium-ion battery is as follows:

[0012] T t (x,t)=T xx (x,t)+f(T(x,t),t)+w(x,t)

[0013] The boundary conditions of the mathematical model are T(0,t)=α(t) and T(1,t)=β(t), and the initial condition is T(x,0)=T0(x);

[0014] T(x,t) represents the internal temperature of the lithium-ion battery, t represents time, and x represents the spatial length of the lithium-ion battery. t (x,t) and T xx (x,t) represents the first derivative of the internal temperature T(x,t) of the lithium-ion battery with respect to time and the second derivative with respect to space.

[0015] f(T(x,t),t) is a nonlinear function, and its expression is f(T(x,t),t)=k -1 I 2 R s (T(x,t),t), where k represents thermal conductivity, I represents battery output current, and R s (T(x,t),t) represents the battery's internal resistance;

[0016] Battery internal resistance M(t) is a nonlinear function, R s,ref It is a constant, T ref It is a given reference temperature, E a It is the activation energy, and R is the universal gas constant;

[0017] w(x,t) represents the uncertainty within the domain; T(0,t) and T(1,t) represent the values ​​of the internal temperature T(x,t) of the lithium-ion battery at x=0 and x=1, respectively, and their magnitudes are functions of α(t) and β(t); T(x,0) represents the initial internal temperature of the lithium-ion battery, and its magnitude is T0(x).

[0018] In a preferred embodiment of the present invention, the interval estimator is:

[0019]

[0020] in, and T (x,t) represent the upper and lower bound estimates of T(x,t), respectively. and T t (x,t) represent respectively and T The first derivative of (x,t) with respect to time and T xx (x,t) represent respectively and T The second derivative of (x,t) with respect to space; and F i ( T (x,t), Let f(T(x,t),t) represent the upper and lower bound estimates, respectively. and w (x,t) represent the upper and lower bound estimates of w(x,t) respectively; l represents the estimator gain; y(x,t) represents the measurement output obtained from the temperature sensor, and its expression is y(x,t)=cT(x,t)+v(x,t), where c is a positive constant and v(x,t) represents the measurement noise, and satisfies |v(x,t)|<v0, where v0 is a positive constant. and v (x,t) represent the upper and lower bound estimates of v(x,t), respectively.

[0021] In a preferred embodiment of the present invention, the method for constructing an estimation error dynamics model includes:

[0022] 1) Based on the mathematical model and interval estimator of the internal temperature system of a lithium-ion battery, the estimation error dynamic equation is constructed as follows:

[0023]

[0024] e t (x,t)= exx (x,t)-lc e (x,t)+ Y

[0025] in, and They represent and e (x,t) is the first derivative of (x,t) with respect to time; and e xx (x,t) represent respectively and e The second derivative of (x,t) with respect to space;

[0026] The boundary conditions for estimating the error dynamics equation are: and Initial conditions are and e (x,0)= e 0(x);

[0027] and They are The values ​​at x = 0 and x = 1 are of magnitude. and

[0028] e (0,t) and e (1,t) are respectively e The values ​​of (x,t) at x=0 and x=1 are of magnitude . and

[0029] function

[0030] function

[0031] 2) The estimation error dynamic equation is transformed into an estimation error dynamic model based on homogeneous Dirichlet boundary conditions using equivalent substitution:

[0032]

[0033]

[0034] Among them, variables variable i (x,t)= e (x,t)- s (x,t);

[0035] function function

[0036] Boundary conditions are i (0,t)=0 and i (1,t)=0, initial condition is and i (x,0)= i 0(x);

[0037] and They are The values ​​at x = 0 and x = 1; i (0,t) and i (1,t) are respectively i The values ​​of (x,t) at x=0 and x=1;

[0038] function and s t (x,t) represent respectively and s (x,t) is the first derivative with respect to time.

[0039] In a preferred embodiment of the present invention, step 2 specifically includes the following steps:

[0040] Step 2.1: For the estimation error dynamics model, the following Lyapunov function is designed for stability analysis:

[0041]

[0042] Where p is a positive constant and dx represents the differential operator;

[0043] Step 2.2: Differentiate the Lyapunov function with respect to time t and construct the inequality:

[0044]

[0045] in, It is the first derivative of V(t) with respect to time, ρ, γ, and It is a positive number;

[0046] The vector χ(x,t) satisfies The superscript T represents the transpose of the matrix;

[0047] function and F (x,t) satisfies

[0048]

[0049] and F (x,t)=|l|v0-lc s (x,t)- s t (x,t)-lv(x,t)+w(x,t)- w (x,t);

[0050] Matrix Ξ satisfies the following equation:

[0051]

[0052] in, It is a given positive constant;

[0053] Step 2.3: From Ξ < 0, we get Depend on and F Since (x,t) is bounded, we obtain... Where ψ is a positive constant, the sufficient condition for the error kinetic stability of the internal temperature system of a lithium-ion battery is:

[0054] For a lithium-ion battery internal temperature system with uncertainty w(x,t)≥0, given a positive constant c, And γ, if there exist parameters p > 0 and estimator gain l that satisfy the following inequality:

[0055]

[0056] The estimation error of the internal temperature system of a lithium-ion battery is kinetically stable, and the established interval estimator can accurately estimate the internal temperature of the lithium-ion battery.

[0057] in,

[0058] In a preferred embodiment of the present invention, step 3 specifically includes the following steps:

[0059] Step 3.1: Under the condition that the estimation error dynamics of the internal temperature system of the lithium-ion battery are stable, construct the following residual generator to determine whether the sensor has failed:

[0060]

[0061] Where h(x,t) represents the residual function. When there is no sensor fault, the measurement output is y(x,t) = cT(x,t) + v(x,t); if a sensor fault occurs, the measurement output is y(x,t) = cT(x,t) + v(x,t) + g(x,t), where g(x,t) represents the sensor fault. It is an estimate of the measured output y(x,t);

[0062] Step 3.2: Based on the interval estimator, the upper and lower bound estimates of the measurement output are as follows:

[0063]

[0064] in, and y (x,t) represent the upper and lower bound estimates of the measured output y(x,t), respectively, and the constant c + The maximum value between c and 0, where c is a constant. - Satisfy c - =c + -c;

[0065] The residual generator in step 3.1 can be further described as follows:

[0066]

[0067] in, and h ( x,t) represent the upper and lower bound estimates of h(x,t), respectively;

[0068] Based on whether 0 belongs to Determine if a sensor malfunction has occurred:

[0069] If the sensor does not malfunction, then Right now

[0070] If the sensor malfunctions, then Right now

[0071] Compared with the prior art, the beneficial effects of the present invention are:

[0072] This invention is the first to apply an interval estimator to fault detection in lithium-ion battery temperature sensors. Compared with existing fault detection methods, this invention can avoid the impact of measurement anomalies on observation performance. The fault detection scheme based on the interval estimator designed in this invention tolerates the effects of model uncertainty, external disturbances, and measurement noise, thus improving the adaptability to fault detection of lithium-ion battery temperature systems. The fault detection method used in this invention has good robustness and stability, and can effectively improve the safety and service life of lithium-ion batteries.

[0073] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0074] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0075] Figure 1 This is a schematic diagram of the design scheme for fault detection of lithium-ion battery temperature sensors;

[0076] Figure 2 This is a simulation diagram of the residual generator;

[0077] Figure 3 The simulation diagrams show the measurement output and residual generator at x = 0.2, x = 0.4, and x = 0.6 in space. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, but not all embodiments.

[0079] Please refer to Figure 1 This invention provides a fault detection method for lithium-ion battery temperature sensors based on an interval estimator, comprising the following steps:

[0080] Step 1: Based on the mathematical model of the internal temperature system of a lithium-ion battery, establish an interval estimator to estimate the internal temperature of the lithium-ion battery in real time. Based on this, obtain the dynamic model of the estimation error of the internal temperature system of the lithium-ion battery. The specific method for this step is as follows:

[0081] 1) The mathematical model for the internal temperature system of a lithium-ion battery is as follows:

[0082] T t (x,t)=T xx (x,t)+f(T(x,t),t)+w(x,t) (1)

[0083] The boundary conditions of the mathematical model for the internal temperature system of a lithium-ion battery are T(0,t)=α(t) and T(1,t)=β(t), and the initial condition is T(x,0)=T0(x).

[0084] T(x,t) represents the internal temperature of the lithium-ion battery, t represents time, and x represents the spatial length of the lithium-ion battery. t (x,t) and T xx (x,t) represents the first derivative of the internal temperature T(x,t) of a lithium-ion battery with respect to time and the second derivative with respect to space.

[0085] f(T(x,t),t) is a nonlinear function, and its expression is f(T(x,t),t)=k -1 I 2 R s (T(x,t),t), where k represents thermal conductivity, with a value of k = 0.61 W / (m·K). I represents the battery output current, with a value of I = 4 A, R s (T(x,t),t) represents the battery's internal resistance, and its expression is: M(t) is a nonlinear function, expressed as M(t) = 90 + sin(t). R s,ref It is a constant with a value of R. s,ref =15mΩ. T ref It is a given reference temperature, the value of which is T. ref =298.15K. E a R and are the activation energy and the universal gas constant, respectively, with a value of E. a =33.8 kJ / mol and R =8.314 J / (mol·K); w(x,t) represents the uncertainty within the domain, and its expression is w(x,t) = sin(πt) / 0.61K; T(0,t) and T(1,t) represent the values ​​of the internal temperature T(x,t) of the lithium-ion battery at x = 0 and x = 1, respectively, and their magnitudes are functions of α(t) and β(t); T(x,0) represents the initial internal temperature of the lithium-ion battery, and its value is T0(x).

[0086] 2) Based on the mathematical model (1) of the internal temperature system of a lithium-ion battery, the following interval estimator is established:

[0087]

[0088] in, and T (x,t) represent the upper and lower bound estimates of T(x,t), respectively. and T t (x,t) represent respectively and T The first derivative of (x,t) with respect to time and T xx (x,t) represent respectively and T The second derivative of (x,t) with respect to space; and F i ( T (x,t), Let f(T(x,t),t) represent the upper and lower bound estimates, respectively. and w (x,t) represent the upper and lower bound estimates of w(x,t), respectively; l represents the estimator gain; y(x,t) represents the measurement output obtained from the temperature sensor, and its expression is y(x,t)=cT(x,t)+v(x,t), where c is a positive constant, v(x,t) represents the measurement noise, and satisfies |v(x,t)|<v0, where v0 is a positive constant. and v (x,t) represent the upper and lower bound estimates of v(x,t), respectively.

[0089] 3) Based on the mathematical model (1) and interval estimator (2) of the internal temperature system of a lithium-ion battery, the following estimation error kinetic equation is obtained:

[0090]

[0091]

[0092] In the formula, e (x,t)=T(x,t)- T (x,t), and e t (x,t) represent respectively and e (x,t) is the first derivative of (x,t) with respect to time; and e xx (x,t) represent respectively and e The second derivative of (x,t) with respect to space; the boundary conditions of (3) and (4) are and Initial conditions are and e (x,0)= e 0(x). and They are The values ​​at x = 0 and x = 1 are of magnitude. and e (0,t) ande (1,t) are respectively e The values ​​of (x,t) at x=0 and x=1 are of magnitude . and

[0093] function

[0094] function

[0095] 4) Using equivalent substitution, the estimation error dynamic equations (3) and (4) are transformed into an estimation error dynamic model based on homogeneous Dirichlet boundary conditions:

[0096]

[0097]

[0098] Among them, variables variable i (x,t)= e (x,t)- s (x,t);

[0099] function

[0100] The boundary conditions for estimating the error dynamics models (5) and (6) are as follows: i (0,t)=0 and i (1,t)=0, initial condition is and i (x,0)= i 0(x).

[0101] and They are The values ​​at x = 0 and x = 1. i (0,t) and i (1,t) are respectively i The values ​​of (x,t) at x=0 and x=1. Function and They represent and s (x,t) is the first derivative with respect to time.

[0102] Step 2: Based on Lyapunov stability theory, analyze the stability of the estimation error dynamic model of the internal temperature system of lithium-ion battery.

[0103] Step 2 is as follows:

[0104] Step 2.1: For the estimation error dynamics models (5) and (6), the following Lyapunov function is designed for stability analysis:

[0105]

[0106] Where p is a positive constant and dx represents the differential operator.

[0107] Step 2.2: Differentiate the Lyapunov function (7) with respect to time t, and obtain the following using inequality techniques:

[0108]

[0109] in, It is the first derivative of V(t) with respect to time, ρ, γ, and It is a positive number;

[0110] The vector χ(x,t) satisfies The superscript T represents the transpose of the matrix.

[0111] function and F (x,t) satisfies

[0112]

[0113] and F (x,t)=|l|v0-lc s (x,t)- s t (x,t)-lv(x,t)+w(x,t)- w (x,t).

[0114] Matrix Ξ satisfies the following equation:

[0115]

[0116] in, It is a given positive constant.

[0117] Step 2.3: Derive the sufficient conditions for the stability of the estimation error dynamic model of the internal temperature system of lithium-ion battery.

[0118] Since Ξ < 0, we can obtain because and F If (x,t) is bounded, then we can obtain Where ψ is a positive constant. Therefore, this invention can obtain sufficient conditions for the stability of the dynamic model of the estimation error of the internal temperature system of a lithium-ion battery:

[0119] Theorem 1: For an internal temperature system of a lithium-ion battery with uncertainty w(x,t)≥0, given a positive constant c, And γ, if there exist parameters p > 0 and l that satisfy the following inequality:

[0120]

[0121] The estimation error dynamics of the internal temperature system of the lithium-ion battery are stable, and the established interval estimator can accurately estimate the internal temperature of the lithium-ion battery.

[0122] in,

[0123] Step 3: Based on step 2, design a residual generator based on the interval estimator (2) to determine whether a temperature sensor fault has occurred.

[0124] Step 3 is as follows:

[0125] Step 3.1: Construct the following residual generator to determine whether the sensor has malfunctioned:

[0126]

[0127] Here, h(x,t) represents the residual function. When there is no sensor fault, the measurement output is y(x,t) = cT(x,t) + v(x,t). If a sensor fault occurs, the measurement output is y(x,t) = cT(x,t) + v(x,t) + g(x,t), where g(x,t) represents the sensor fault. It is an estimate of the measured output y(x,t).

[0128] Step 3.2: Based on the interval estimator (2), the upper and lower bound estimates of the measurement output are:

[0129]

[0130] in, and y (x,t) represent the upper and lower bound estimates of the measured output y(x,t), respectively. The constant c + The maximum value between c and 0, where c is a constant. - Satisfy c - =c + -c. Then, the residual generator (10) is further described as follows:

[0131]

[0132] in, and h (x,t) represent the upper and lower bound estimates of h(x,t), respectively. If the sensor does not malfunction, then... Right now

[0133] If the sensor malfunctions, then Right now

[0134] Therefore, the present invention can be based on whether 0 belongs to To determine whether a sensor malfunction has occurred.

[0135] Furthermore, given the constant c = 1, Given γ = 1, and then based on Theorem 1, the parameters p = 1.4 and the estimator gain p = 3.2 can be obtained using MATLAB's LMI toolbox.

[0136] To illustrate the control effect of the present invention in detail, the lithium-ion battery internal temperature estimation method based on the interval estimator described above is simulated in MATLAB.

[0137] First, given the boundary conditions α(t)=298.15+0.1sin(πt) and β(t)=298.15+0.1sin(πt) of the mathematical model (1) of the internal temperature system of the lithium-ion battery, the initial condition T0(x)=298.15, the measurement noise is v(x,t)=0.1sin(t), the maximum noise value is v0=0.1, and the sensor malfunction...

[0138] Then, through MATLAB simulation, the trajectory of the residual generator is as follows: Figure 2 As shown, this indicates that when x∈[0.3,0.5] and t∈[0.3,0.5], That is, the temperature sensor malfunctions at position x∈[0.3,0.5] and time t∈[0.3,0.5] in the lithium-ion battery. Furthermore, to illustrate the variation trajectory of the residual generator in detail, this invention provides... Figure 3 This also indicates that the temperature sensor malfunctions at position x∈[0.3,0.5] and time t∈[0.3,0.5].

[0139] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fault detection method for lithium-ion battery temperature sensors based on interval estimators, characterized in that, Includes the following steps: Step 1: Based on the mathematical model of the internal temperature system of the lithium-ion battery, establish an interval estimator to estimate the internal temperature of the lithium-ion battery in real time, and obtain the estimation error dynamic model of the internal temperature system of the lithium-ion battery. Step 2: Based on Lyapunov stability theory, analyze the stability of the estimation error dynamic model of the internal temperature system of lithium-ion battery; Step 3: Based on the stability analysis results of the estimation error dynamic model of the internal temperature system of the lithium-ion battery, a residual generator is designed using an interval estimator to determine whether a temperature sensor fault has occurred. The judgment logic of the residual generator includes: using the interval estimator to calculate the upper and lower bound estimates of the measurement output to obtain the upper and lower bound estimates of the residual; determining whether 0 belongs to the interval formed by the lower and upper bound estimates of the residual: if 0 belongs to the interval formed, it is determined that the temperature sensor has not failed; if 0 does not belong to the interval formed, it is determined that the temperature sensor has failed.

2. The lithium-ion battery temperature sensor fault detection method based on an interval estimator according to claim 1, characterized in that, The mathematical model of the internal temperature system of a lithium-ion battery is as follows: The boundary conditions of this mathematical model are: and The initial conditions are ; This represents the internal temperature of a lithium-ion battery. Indicates time, This indicates the spatial length of a lithium-ion battery. and Indicates the internal temperature of a lithium-ion battery The first derivative with respect to time and the second derivative with respect to space; It is a nonlinear function, and its expression is: ,in Represents thermal conductivity, Represents the battery output current. This represents the battery's internal resistance; Battery internal resistance , It is a non-linear function. It is a constant. It is a given reference temperature. It is activation energy. It is the universal gas constant; Represents uncertainty within the domain; and These represent the internal temperature of the lithium-ion battery. exist and The value at that location, its size is a function and ; This represents the initial internal temperature of a lithium-ion battery, and its magnitude is... .

3. The lithium-ion battery temperature sensor fault detection method based on an interval estimator according to claim 2, characterized in that, The interval estimator is: in, and Represent The upper and lower bound estimates, and They represent and The first derivative with respect to time and They represent and The second derivative with respect to space; and They represent The upper and lower bound estimates, and They represent The upper and lower bound estimates; Indicates the estimator gain. The measurement output obtained from the temperature sensor is expressed as follows: , It is a positive constant. Indicates the measured noise and satisfies , It is a positive constant; and They represent The upper and lower bound estimates.

4. The lithium-ion battery temperature sensor fault detection method based on an interval estimator according to claim 3, characterized in that, Methods for constructing dynamic models of estimation errors include: 1) Based on the mathematical model and interval estimator of the internal temperature system of a lithium-ion battery, the estimation error dynamic equation is constructed as follows: in, , , and They represent and The first derivative with respect to time; and They represent and The second derivative with respect to space; The boundary conditions for estimating the error dynamics equation are: , , and The initial conditions are and ; and They are exist and The value at that location is [value]. and ; and They are exist and The value at that location is [value]. and ; function ; function ; 2) The estimation error dynamic equation is transformed into an estimation error dynamic model based on homogeneous Dirichlet boundary conditions using equivalent substitution: Among them, variables ,variable ; function ,function ; Boundary conditions are , , and The initial conditions are and ; and They are exist and The value at; and They are exist and The value at; function ,function , and They represent and The first derivative with respect to time.

5. The lithium-ion battery temperature sensor fault detection method based on an interval estimator according to claim 4, characterized in that, Step 2 specifically includes the following steps: Step 2.1: For the estimation error dynamics model, the following Lyapunov function is designed for stability analysis: in, It is a positive constant. Represents the differential operator; Step 2.2: Analyze the Lyapunov function with respect to time. Find the derivative and construct the inequality: in, yes The first derivative with respect to time , and It is a positive number; vector satisfy superscript Represents the transpose of a matrix; function and satisfy and ; matrix Satisfy the following formula: in, , , , , , It is a given positive constant; Step 2.3, from ,get ,Depend on and Bounded, obtained ,in, The sufficient condition for the error kinetic stability of the internal temperature system of a lithium-ion battery, which is a positive constant, is: For those with uncertainty The internal temperature system of a lithium-ion battery, given normal values , , , , and If parameters exist and estimator gain The following inequalities must be satisfied: The estimation error of the internal temperature system of a lithium-ion battery is kinetically stable, and the established interval estimator can accurately estimate the internal temperature of the lithium-ion battery. in, , .

Images