Uncertain Noisy Filtering-Based Fault Diagnosis Method for Power Battery Management System

Abstract

The present disclosure discloses an uncertain noisy filtering-based fault diagnosis method for a power battery management system and belongs to the field of power battery fault diagnosis. The method comprises: establishing an electro-thermal coupling model of a power battery system; extending an output vector of the system according to a state constraint of a power battery, and expanding a state vector of the system according to a fault of the power battery system to obtain an augmented system of the power battery system; obtaining an estimation interval of a power battery sensor fault by using a zonotope Kalman filtering method; judging whether the power battery management system has a fault according to upper and lower bounds of fault estimation, and if a fault occurs, determining a fault type and a fault time according to a result. Compared with an existing fault diagnosis method for a system without a state constraint, the present application solves the problem of fault diagnosis of a system with a state constraint by extending the state constraint of the system to the system output vector.

Claims

1. An uncertain noisy filtering-based fault diagnosis method for a power battery management system, wherein the method comprises: step 1: according to the electrochemical mechanism of the power battery discharge process, establishing a second-order Thevenin equivalent circuit model of a power battery; step 2: according to the heat generation mechanism of the power battery, establishing a thermal model of the power battery, and in combination with the second-order Thevenin equivalent circuit model, establishing an electro-thermal coupling model of a power battery system; step 3: acquiring a core temperature and a surface temperature of the power battery in a normal working state, and determining a state constraint of the power battery; step 4: expanding the state constraint of the power battery to a system output vector of the power battery system to obtain a system output variable, and expanding a fault vector of the power battery system to a system state vector to obtain a system state variable; the system output vector being a vector composed of the core temperature and the surface temperature collected by a core temperature sensor and a surface temperature sensor; the fault vector being a vector formed by fault values of the core temperature sensor and the surface temperature sensor; the system state vector referring to a vector composed of an actual core temperature and an actual surface temperature of the power battery; step 5: obtaining a zonotope set according to a system state variable at time k, constructing a zonotope set of a system state variable prediction set at time k+1 according to the corresponding zonotope set of the system state variable at time k, and constructing a strip space at time k+1 according to the system output variable at time k+1; step 6: solving an intersection of the zonotope set of the system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 and the constructed strip space S.sub.k+1 at time k+1, and wrapping with a zonotope of the minimum volume to obtain a zonotope set of a system state variable x.sub.k+1 at time k+1; step 7: acquiring a state estimation interval and a fault estimation interval at time k+1 according to the zonotope set of the system state variable at time k+1, and judging whether the core temperature sensor and the surface temperature sensor in the power battery management system have a fault; wherein the power battery system comprises the power battery and the power battery management system, and the power battery management system comprises the core temperature sensor and the surface temperature sensor for collecting the core temperature and the surface temperature of the power battery.

2. The method according to claim 1, wherein the step 3: acquiring the core temperature and the surface temperature of the power battery in the normal working state, and determining the state constraint of the power battery, comprising: acquiring the core temperature and the surface temperature of the power battery in the normal working state, and determining a state constraint of the system: when the power battery works under a normal working condition, the core temperature T.sub.c satisfies M.sub.1° C.≤T.sub.c≤M.sub.2° C.; there is a difference value between the core temperature and the surface temperature, and the difference value is stabilized within a range of m° C.±ε° C., namely m−ε° C.≤T.sub.c−T.sub.s≤m+ε° C.; determining the state constraint of the system: $\{\begin{array}{c}.Math.T_{c,k}-T_{s,k}-m.Math.\le \epsilon \\ .Math.T_{c,k}-\frac{M_1+M_2}{2}.Math.\le \frac{M_2-M_1}{2}\end{array}$ writing the state constraint of the system into the form of Equation (7):
|y.sub.k−H.sub.kx.sub.k|≤l.sub.k, h(x.sub.k)=γ.sub.k−H.sub.kx.sub.k  (7) where, $l_k=\left[\begin{array}{c}\epsilon \\ \frac{M_2-M_1}{2}\end{array}\right],{\gamma }_k=\left[\begin{array}{c}-m\\ -\frac{M_2-M_1}{2}\end{array}\right],H_k=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right].$

3. The method according to claim 2, wherein, the step 1: according to the electrochemical mechanism of the power battery discharge process, establishing the second-order Thevenin equivalent circuit model of the power battery, comprises: establishing equations as follows according to the electrochemical mechanism of the power battery discharge process: $\begin{array}{cc}U=U_{\mathrm{oc}}-R_{o}i-U_1-U_2& \left(1\right)\end{array}$ $\{\begin{array}{c}{\stackrel{.}{U}}_1=-\frac{1}{R_1{C}_{p1}}{U}_1+\frac{1}{C_{p1}}i\\ {\stackrel{.}{U}}_2=-\frac{1}{R_2{C}_{p2}}{U}_2+\frac{1}{C_{p2}}i\\ \end{array}$ where, U is a voltage at two ends of the battery, U.sub.oc is the internal voltage of the battery, R.sub.1 and C.sub.p1 are respectively electrochemical polarization internal resistance and capacitance, and a voltage at the two ends after R.sub.1 and C.sub.p1 are connected in parallel is U.sub.1; R.sub.2 and C.sub.p2 are respectively concentration polarization resistance and capacitance, and a voltage at the two ends after R.sub.2 and C.sub.p2 are connected in parallel is U.sub.2; i is a discharge current; R.sub.o is the internal resistance of the battery.

4. The method according to claim 3, wherein, the step 2: according to the heat generation mechanism of the power battery, establishing the thermal model of the power battery, and in combination with the second-order Thevenin equivalent circuit model of the power battery, establishing the electro-thermal coupling model of the power battery, comprises: 2.1: according to the heat generation mechanism of the power battery, establishing the thermal model of the power battery: $\begin{array}{cc}\{\begin{array}{c}{C}_c{\stackrel{.}{T}}_c=Q_{\mathrm{gen}}+\frac{T_s-T_c}{R_c}\\ C_s{\stackrel{.}{T}}_s=\frac{T_e-T_s}{R_u}-\frac{T_s-T_c}{R_c}\end{array}& \left(2\right)\end{array}$ where T.sub.s and T.sub.c represent the battery surface temperature and the battery core temperature respectively, and T.sub.e represents an ambient temperature; C.sub.s and C.sub.c respectively represent a heat capacity coefficient of a material inside the battery and a heat capacity coefficient of the surface of the battery; R.sub.c represents a thermal resistance between the core and the surface of the battery; R.sub.u represents a convection resistance between the surface of the battery and cooling air; Q.sub.gen represents the heating power of the core of the battery:
Q.sub.gen=i(U.sub.oc−U)=i(R.sub.oi+U.sub.1+U.sub.2)  (3) 2.2: in combination with the second-order Thevenin equivalent circuit model, establishing the electro-thermal coupling model of the power battery system, taking the heating power Q.sub.gen of the core of the battery and the ambient temperature T.sub.e as the input of the electro-thermal coupling model, taking the surface temperature T.sub.s and the core temperature T.sub.c as the state vector of the electro-thermal coupling model, setting a sampling time interval as Δts, discretizing Equation (2), and adding a disturbance noise to obtain the state equation of the electro-thermal coupling model:
x.sub.k+1=Ax.sub.k+Bu.sub.k+D.sub.1w.sub.k  (4) where, x.sub.k∈.sup.n is the system state vector, represents an n-dimensional real number space, x.sub.k=[T.sub.c,k,T.sub.s,k].sup.T, T.sub.c,k an T.sub.s,k respectively represent real values of the core temperature and the surface temperature of the battery at time k; u.sub.k∈.sup.r is a system input matrix at time k; u.sub.k=[Q.sub.gen,kT.sub.e,k].sup.T, w.sub.k∈.sup.w represents an unknown but bounded disturbance noise, {tilde over (w)} is a boundary value; $.Math.w_k.Math.\le \tilde{w};A=\left[\begin{array}{cc}1-\frac{\Delta t}{R_c{C}_c}& \frac{\Delta t}{R_c{C}_c}\\ \frac{\Delta t}{R_c{C}_s}& 1-\frac{\Delta t}{R_c{C}_s}-\frac{\Delta t}{R_u{C}_s}\end{array}\right]$ represents a state space matrix; $B=\left[\begin{array}{cc}\frac{\Delta t}{C_c}& 0\\ 0& \frac{\Delta t}{R_u{C}_s}\end{array}\right]$ represents an input matrix; $D_1=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ represents a disturbance action matrix; taking measured values of the surface temperature T.sub.s and the core temperature T.sub.c as the output of the electro-thermal coupling model, and adding a measurement noise and a sensor fault vector at the same time to obtain the output equation of the electro-thermal coupling model
y.sub.k=Cx.sub.k+D.sub.2v.sub.k+f.sub.k  (5) where, y.sub.k∈.sup.p is the system output vector, .sup.p represents a p-dimensional real number space, y.sub.k=[T.sub.c,k′,T.sub.s,k′].sup.T, T.sub.c,k′ and T.sub.s,k′, respectively represent measured values of the core temperature and the surface temperature of the battery; v.sub.k∈.sup.v represents an unknown but bounded measurement noise, .sup.v represents a v-dimensional real number space, and {tilde over (v)} is a boundary value, $.Math.v_k.Math.\le \tilde{v};C=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ represents an output matrix, and $D_2=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ represents a measurement noise action matrix; f.sub.k=[f.sub.1,k f.sub.2,k].sup.T∈.sup.p represents a sensor fault of the power battery, f.sub.1,k represents a core temperature sensor fault of the power battery, and f.sub.2,k represents a surface temperature sensor fault of the power battery; according to Equation (4) and Equation (5), establishing the electro-thermal coupling model of the power battery system as: $\begin{array}{cc}\{\begin{array}{c}{x}_{k+1}={\mathrm{Ax}}_k+{\mathrm{Bu}}_k+D_1{w}_k\\ y_k={\mathrm{Cx}}_k+D_2{v}_k+f_k\end{array}& \left(6\right)\end{array}$

5. The method according to claim 4, wherein, the step 4: expanding the state constraint of the power battery to the system output vector of the power battery system to obtain the system output variable, and expanding the fault vector of the power battery system to the system state vector to obtain the system state variable, comprises: 4.1: expanding the state constraint of the power battery to the system output vector of the power battery system to obtain the system output variable, and according to Equation (6) and Equation (7), obtaining an Equation (8) as follows: $\begin{array}{cc}\{\begin{array}{c}{x}_{k+1}={\mathrm{Ax}}_k+{\mathrm{Bu}}_k+D_1{w}_k\\ {\stackrel{\_}{y}}_k=\stackrel{\_}{C}{x}_k+{\stackrel{\_}{D}}_2{\stackrel{\_}{v}}_k+{\stackrel{\_}{f}}_k\end{array}& \left(8\right)\end{array}$ $\mathrm{where},$ $\stackrel{\_}{C}=\left[\begin{array}{c}C\\ H_k\end{array}\right],{\stackrel{\_}{D}}_2=\left[\begin{array}{cc}{D}_2& 0_{p\times \gamma }\\ 0_{p\times v}& I_{p\times \gamma }\end{array}\right];{\stackrel{\_}{y}}_k=\left[\begin{array}{c}{y}_k\\ {\gamma }_k\end{array}\right],{\stackrel{\_}{v}}_k=\left[\begin{array}{c}{v}_k\\ l_k\end{array}\right],.Math.{\stackrel{\_}{v}}_k.Math.\le \stackrel{\widetilde{\_}}{v},\stackrel{\_}{V}=\mathrm{diag}\left(\stackrel{\widetilde{\_}}{v}\right),{\stackrel{\_}{f}}_k=\left[\begin{array}{c}{f}_k\\ 0_{\gamma }\end{array}\right],{\gamma }_k\in {\gamma }^{};$ I.sub.p+γ is a p+γ-order unit matrix, and .sup.θ represents a γ-dimension real number space; 4.2: expanding the fault vector of the power battery system to the system state vector to obtain the system state variable, and according to Equation (8), obtaining an Equation (9) as follows: $\begin{array}{cc}\{\begin{array}{c}E{\stackrel{\_}{x}}_{k+1}=\stackrel{\_}{A}{\stackrel{\_}{x}}_k+\stackrel{\_}{B}{u}_k+{\stackrel{\_}{D}}_1{w}_k\\ {\stackrel{\_}{y}}_k=C_1{\stackrel{\_}{x}}_k+{\stackrel{\_}{D}}_2{\stackrel{\_}{v}}_k\end{array}& \left(9\right)\end{array}$ $\mathrm{where},$ ${\stackrel{\_}{x}}_k=\left[\frac{x_k}{f_k}\right],E=\left[\begin{array}{cc}I& 0_{n\times \left(p+\gamma \right)}\\ 0_{\left(p+\gamma \right)\times n}& 0_{p+\gamma }\end{array}\right],\stackrel{\_}{A}=\left[\begin{array}{cc}A& 0_{n\times \left(p+\gamma \right)}\\ 0_{\left(p+\gamma \right)\times 2}& 0_{p+\gamma }\end{array}\right],\stackrel{\_}{B}=\left[\begin{array}{c}B\\ 0_{\left(p+\gamma \right)\times r}\end{array}\right],C_1=\begin{array}{cc}[\stackrel{\_}{C}& I],{\stackrel{\_}{D}}_1=\left[\begin{array}{c}{D}_1\\ 0_{\left(p+\gamma \right)\times w}\end{array}\right]\end{array}.$

6. The method according to claim 5, wherein, the step 5: obtaining a corresponding zonotope set according to a system state variable x.sub.k at time k, constructing a zonotope set of a system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 according to the zonotope set of the system state variable x.sub.k at time k, and constructing a strip space S.sub.k+1 at time k+1 according to the system output variable, comprises: 5.1: constructing the zonotope set of a system state variable feasible set {circumflex over (χ)}.sub.k+1 at time k+1; setting a zonotope Z.sub.0=p.sub.0⊕G.sub.0.sup.s, corresponding to an initialization state variable x.sub.k, p.sub.0 representing a central point of the corresponding zonotope at the initial time, G.sub.0 representing a shape matrix of the corresponding zonotope at the initial time, and B.sup.s being a unit box composed of s unit intervals [−1,1]; assuming a zonotope Z.sub.k=p.sub.k⊕G.sub.k.sup.s=p.sub.k,G.sub.k corresponding to the state variable x.sub.k at time k, constructing the zonotope set corresponding to the system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1:
{circumflex over (χ)}.sub.k+1{circumflex over (p)}.sub.k+1,{circumflex over (G)}.sub.k+1  (10)
{circumflex over (p)}.sub.k+1=TĀp.sub.k+TBu.sub.k+Ny.sub.k+1  (11)
{circumflex over (G)}.sub.k+1=[TĀ↓.sub.reG.sub.kTD.sub.1W−ND.sub.2V]  (12)
T=Θ.sup.†α.sub.1+SΨα.sub.1,N=Θ.sup.†α.sub.2+SΨα.sub.2  (13) where, $\Theta =\left[\begin{array}{c}E\\ C_1\end{array}\right],$ Θ.sup.† is the pseudo inverse of Θ; Ψ=I.sub.n+2p+2γ−ΘΘ.sup.†, ${\alpha }_1=\left[\begin{array}{c}{I}_{n+p+\gamma }\\ 0_{\left(p+\gamma \right)\times \left(n+p+\gamma \right)}\end{array}\right],{\alpha }_2=\left[\begin{array}{c}{0}_{\left(n+p+\gamma \right)\times \left(p+\gamma \right)}\\ I_{n+\gamma }\end{array}\right].{\downarrow }_{\mathrm{re}}{\stackrel{\_}{G}}_k\in {n\times q}^{}$ represents a generated matrix after reducing the order of the zonotope of the state at time k, and ↓.sub.re G.sub.k is obtained through Equations (14)-(17): $\begin{array}{cc}Z=.Math.\stackrel{\_}{p},\stackrel{\_}{G}.Math..Math.\stackrel{\_}{p}\oplus \mathrm{rs}\left(\stackrel{\_}{G}\right)n^{}& \left(14\right)\end{array}$ $\begin{array}{cc}\mathrm{rs}\left(\stackrel{\_}{G}\right)=\left[\begin{array}{cccc}\underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{1,j}.Math.& 0& .Math.& 0\\ 0& \underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{2,j}.Math.& .Math.& 0\\ .Math.& .Math.& \ddots & .Math.\\ 0& 0& .Math.& \underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{2,j}.Math.\end{array}\right]& \left(15\right)\end{array}$ $\begin{array}{cc}Z=.Math.\stackrel{\_}{p},\stackrel{\_}{G}.Math..Math..Math.\stackrel{\_}{p},{\downarrow }_{\mathrm{re}}\stackrel{\_}{G}.Math.& \left(16\right)\end{array}$ $\begin{array}{cc}{\downarrow }_{\mathrm{re}}\stackrel{\_}{G}=\{\begin{array}{cc}\stackrel{\_}{G}& s\le q\\ \left[{\stackrel{\_}{G}}_{>}\mathrm{rs}\left({\stackrel{\_}{G}}_{<}\right)\right],& s>q\end{array}& \left(17\right)\end{array}$ 5.2: constructing the strip space S.sub.k+1 at time k+1 according to the system output variable at time k+1:
S.sub.k+1={x.sub.k+1∈R.sup.n+p+γ:|C.sub.1x.sub.k+1−y.sub.k+1|≤D{tilde over (v)}}  (18)

7. The method according to claim 6, wherein the step 6: comprises: :
x.sub.k+1∈χ.sub.k+1=p.sub.k+1,G.sub.k+1  (19)
p.sub.k+1={circumflex over (p)}+L.sub.k+1(y.sub.k+1−C.sub.1{circumflex over (p)}.sub.k+1)  (20)
G.sub.k+1=[(I.sub.n+s+γ−L.sub.k+1C.sub.1){circumflex over (G)}.sub.k+1L.sub.k+1D.sub.v]  (21)
L.sub.k+1={circumflex over (G)}.sub.k+1{circumflex over (G)}.sub.k+1.sup.TC.sub.1.sup.T(C.sub.1{circumflex over (G)}.sub.k+1{circumflex over (G)}.sub.k+1.sup.TC.sub.1.sup.T+D.sub.vD.sub.v.sup.T).sup.−1  (22) where, D.sub.v=diag(D.sub.2{tilde over (v)}).

8. The method according to claim 7, wherein, the step 7: acquiring the state estimation interval and the fault estimation interval at time k+1 according to the zonotope set of the system state variable at time k+1, and judging whether the core temperature sensor and the surface temperature sensor in the power battery management system have a fault, comprises: determining the state estimation interval at time k+1 according to Equation (23): $\begin{array}{cc}\{\begin{array}{c}{\stackrel{\_}{x}}_{k+1}^{+}\left(\mu \right)={\stackrel{\_}{p}}_{k+1}\left(\mu \right)+\underset{j=1}{\overset{q}{.Math.}}.Math.{\stackrel{\_}{G}}_{k+1}\left(\mu ,j\right).Math.,\mu =1,.Math.,n+s+\gamma \\ {\stackrel{\_}{x}}_{k+1}^{-}\left(\mu \right)={\stackrel{\_}{p}}_{k+1}\left(\mu \right)-\underset{j=1}{\overset{q}{.Math.}}.Math.{\stackrel{\_}{G}}_{k+1}\left(\mu ,j\right).Math.,\mu =1,.Math.,n+s+\gamma \end{array}& \left(23\right)\end{array}$ where, x.sub.k=1.sup.+(μ), x.sub.k=1.sup.−(μ) respectively represent the minimum upper bound and the maximum lower bound of state estimation at time k+1; determining the fault estimation interval at time k+1 according to Equation (24):
f.sub.k+1.sup.+=[0.sub.p×nI.sub.p0.sub.p×γ]x.sub.k+1.sup.+
f.sub.k+1.sup.−=[0.sub.p×nI.sub.p0.sub.p×γ]x.sub.k+1.sup.−  (24) where, f.sub.k+1.sup.+, f.sub.k+1.sup.− respectively represent the minimum upper bound and the maximum lower bound of the fault estimation at time k+1, and I.sub.p is a p-order unit matrix; if the upper and lower bounds of the fault estimation interval obtained by Equation (24) are on both sides of 0, then a power battery sensor does not have a fault; if the upper and lower bounds of the fault estimation interval obtained by Equation (24) are on one side of 0 at the same time, the power battery sensor has a fault, and a fault value is within a fault estimation range; at the same time, when fault types are different, fault estimation intervals are different, and the fault type of the power battery sensor is judged according to the fault estimation interval.

9. The method according to claim 8, wherein, when the ambient temperature T.sub.e=25° C. and the current is 5 A, the core temperature of the power battery satisfies: 35.8° C.≤T.sub.c≤35.9° C.

10. The method according to claim 9, wherein, the difference value between the core temperature and the surface temperature of the power battery satisfies: 5.77° C.≤T.sub.c−T.sub.s≤5.87° C.

11. The method according to claim 10, wherein, $l_k=\left[\begin{array}{c}0.05\\ 0.05\end{array}\right],{\gamma }_k=\left[\begin{array}{c}-5.82\\ -35.85\end{array}\right],H_k=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right].$

12. A power battery system, wherein, the power battery system comprises a power battery and a power battery management system, the power battery management system comprising a core temperature sensor and a surface temperature sensor for collecting a core temperature and a surface temperature of the power battery, and the power battery system using the method according to claim 1 to perform fault detection on the core temperature sensor and the surface temperature sensor.

13. A power battery management system, comprising a core temperature sensor and a surface temperature sensor for collecting a core temperature and a surface temperature of a power battery, wherein, the power battery management system uses the method according to claim 1 to perform fault detection on the core temperature sensor and the surface temperature sensor.

Description

BRIEF DESCRIPTION OF FIGURES

[0061] In order to more clearly illustrate the technical solutions in the examples of the present disclosure, the accompanying drawings which are required to be used in the description of the examples will be simply introduced. It is obvious that the drawings in the description below are only some examples of the present disclosure, and those skilled in the art can also obtain other drawings according to these drawings without involving any inventive effort.

[0062] FIG. 1 is a flow diagram of uncertain noisy filtering-based fault diagnosis for a power battery management system disclosed in one example of the present disclosure.

[0063] FIG. 2 is an equivalent circuit model diagram of a power battery.

[0064] FIG. 3 is a relation diagram of upper and lower bounds (the upper bound being a dotted line and the lower bound being a dashed line) of fault estimation of the present disclosure and an applied fault value (solid line) when a core temperature sensor fault signal f is applied to a power battery disclosed in one example of the present disclosure.

[0065] FIG. 4 is a relation diagram of upper and lower bounds (the upper bound being a dotted line and the lower bound being a dashed line) of fault estimation of the present disclosure and an applied fault value (solid line) when a surface temperature sensor fault signal f.sub.2 is applied to a power battery disclosed in one example of the present disclosure.

DETAILED DESCRIPTION

[0066] In order to make the objects, technical solutions and advantages of the present disclosure clearer, embodiment of the present disclosure will further be described below in detail with reference to the accompanying drawings.

Example 1

[0067] This example provides an uncertain noisy filtering-based fault diagnosis method for a power battery management system, the method is applied in a power battery system, the power battery system includes a power battery and the power battery management system, the power battery management system includes a core temperature sensor and a surface temperature sensor for collecting a core temperature and a surface temperature of the power battery, and the method includes:

[0068] step 1: according to the electrochemical mechanism of the power battery discharge process, establishing a second-order Thevenin equivalent circuit model of a power battery;

[0069] step 2: according to the heat generation mechanism of the power battery, establishing a thermal model of the power battery, and in combination with the second-order Thevenin equivalent circuit model, establishing an electro-thermal coupling model of the power battery system;

[0070] step 3: acquiring a core temperature and a surface temperature of the power battery in a normal working state, and determining a state constraint of the power battery;

[0071] step 4: expanding the state constraint of the power battery to a system output vector of the power battery system to obtain a system output variable, and expanding a fault vector of the power battery system to a system state vector to obtain a system state variable;

[0072] the system output vector being a vector composed of the core temperature and the surface temperature collected by the core temperature sensor and the surface temperature sensor; the fault vector being a vector formed by fault values of the core temperature sensor and the surface temperature sensor; the system state vector referring to a vector composed of an actual core temperature and an actual surface temperature of the power battery;

[0073] step 5: obtaining a corresponding zonotope set according to a system state variable x.sub.k at time k, constructing a zonotope set of a system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 according to the corresponding zonotope set of the system state variable x.sub.k at time k, and constructing a strip space S.sub.k+1 at time k+1 according to the system output variable at time k+1;

[0074] step 6: solving an intersection of the zonotope set of the system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 and the constructed strip space S.sub.k+1 at time k+1, and wrapping with a zonotope of the minimum volume to obtain a zonotope set of a system state variable x.sub.k+1 at time k+1; and

[0075] step 7: acquiring a state estimation interval and a fault estimation interval at time k+1 according to the zonotope set of the system state variable at time k+1, and judging whether the core temperature sensor and the surface temperature sensor in the power battery management system have a fault.

Example 2

[0076] The present disclosure provides an uncertain noisy filtering-based fault diagnosis method for a power battery management system, and referring to FIG. 1, the method includes:

[0077] step 1: according to the electrochemical mechanism of the power battery discharge process, establishing a second-order Thevenin equivalent circuit model of a power battery:

[0078] the second-order Thevenin equivalent circuit diagram of the power battery being as shown in FIG. 2, wherein, U is a voltage at two ends of the battery, U.sub.oc is the internal voltage of the battery, R.sub.1 and C.sub.p1 are respectively electrochemical polarization internal resistance and capacitance, and a voltage at the two ends thereof is U.sub.1. R.sub.2 and C.sub.p2 are respectively concentration polarization resistance and capacitance, and a voltage at the two ends thereof is U.sub.2. i is a discharge current. R.sub.o is the internal resistance of the battery.

[0079] Establishing equations as follows according to the electrochemical mechanism of the power battery discharge process:

[00018]$\begin{array}{cc}U=U_{\propto }-R_{o}i-U_1-U_2& \left(1\right)\end{array}$$\{\begin{array}{c}{\stackrel{.}{U}}_1=-\frac{1}{R_1{C}_{p1}}{U}_1+\frac{1}{C_{p1}}i\\ {\stackrel{.}{U}}_2=-\frac{1}{R_2{C}_{p2}}{U}_2+\frac{1}{C_{p2}}i\end{array}$

[0080] Step 2: according to the heat generation mechanism of the power battery, establishing a thermal model of the power battery, and in combination with the second-order Thevenin equivalent circuit model, establishing an electro-thermal coupling model of the power battery;

[0081] according to the heat generation mechanism of the power battery, establishing the thermal model of the power battery:

[00019]$\begin{array}{cc}\{\begin{array}{c}{C}_c{\dot{T}}_c=Q_{gen}+\frac{T_s-T_c}{R_c}\\ C_s{\dot{T}}_s=\frac{T_e-T_s}{R_u}-\frac{T_s-T_c}{R_c}\end{array}& \left(2\right)\end{array}$

[0082] where T.sub.s and T.sub.c represent the battery surface temperature and the battery core temperature respectively, and T.sub.e represents an ambient temperature. C.sub.s and C.sub.c respectively represent a heat capacity coefficient of a material inside the battery and a heat capacity coefficient of the surface of the battery. R.sub.c represents a thermal resistance between the core and the surface of the battery, and R.sub.u represents a convection resistance between the surface of the battery and cooling air. Q.sub.gen represents the heating power of the core of the battery, and can be obtained through the second-order Thevenin equivalent circuit model of the power battery:

Q.sub.gen=i(U.sub.oc−U)=i(R.sub.oi+U.sub.1+U.sub.2)  (3)

[0083] where, U.sub.1 and U.sub.2 are determined by Equation (1).

[0084] In combination with the second-order Thevenin equivalent circuit model, establishing the electro-thermal coupling model of the power battery system, taking the heating power Q.sub.gen of the core of the battery and the ambient temperature T.sub.e as the input of the electro-thermal coupling model, taking the surface temperature T.sub.s and the core temperature T.sub.c as the state vector of the electro-thermal coupling model, setting a sampling time interval as Δts, discretizing Equation (2), and adding a disturbance noise to obtain the state equation of the electro-thermal coupling model:

X.sub.k+1=AX.sub.k+Bu.sub.k+D.sub.1w.sub.k  (4)

[0085] where, x.sub.k∈.sup.n is the system state vector, .sup.n represents an n-dimensional real number space, x.sub.k=[T.sub.c,k,T.sub.s,k].sup.T, T.sub.c,k and T.sub.s,k respectively represent real values of the core temperature and the surface temperature of the battery at time k, and T represents transposing operation of a matrix; u.sub.k∈.sup.r is a system input matrix at time k, r represents the dimension of u.sub.k, u.sub.k=[(q.sub.gen,k,T.sub.e,k].sup.T; w.sub.k∈.sup.w represents an unknown but bounded disturbance noise, {tilde over (w)} is a boundary value; |w.sub.k|≤{tilde over (w)};

[00020]$A=\left[\begin{array}{cc}1-\frac{\Delta t}{R_c{C}_c}& \frac{\Delta t}{R_c{C}_c}\\ \frac{\Delta t}{R_c{C}_s}& 1-\frac{\Delta t}{R_c{C}_s}-\frac{\Delta t}{R_u{C}_s}\end{array}\right]$

represents a state space matrix;

[00021]$B=\left[\begin{array}{cc}\frac{\Delta t}{C_c}& 0\\ 0& \frac{\Delta t}{R_u{C}_s}\end{array}\right]$

represents an input matrix;

[00022]$D_1=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

represents a disturbance action matrix;

[0086] taking measured values of the surface temperature T.sub.s and the core temperature T.sub.c as the output of the electro-thermal coupling model, and adding a measurement noise and a sensor fault vector at the same time to obtain the output equation of the electro-thermal coupling model:

y.sub.k=Cx.sub.k+D.sub.2v.sub.k+f.sub.k  (5)

[0087] where, y.sub.k∈.sup.p is the system output vector, .sup.p represents a p-dimensional real number space, y.sub.k=[T.sub.c,k′,T.sub.s,k′].sup.T, T.sub.c,k′ and T.sub.s,k′ respectively represent measured values of the core temperature and the surface temperature of the battery; v.sub.k∈.sup.v represents an unknown but bounded measurement noise, i.e.,

[00023]$.Math.v_k.Math.\le \tilde{v};C=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

represents an output matrix, and

[00024]$D_2=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

represents a measurement noise action matrix; f.sub.k∈[f.sub.1,k f.sub.2,k].sup.T∈.sup.p represents a sensor fault of the power battery, f.sub.1,k represents a core temperature sensor fault of the power battery, and f.sub.2,k represents a surface temperature sensor fault of the power battery;

[0088] according to Equation (4) and Equation (5), establishing the electro-thermal coupling model of the power battery system as:

[00025]$\begin{array}{cc}\{\begin{array}{c}{x}_{k+1}=A{x}_k+B{u}_k+D_1{w}_k\\ y_k=C{x}_k+D_2{v}_k+f_k\end{array}& \left(6\right)\end{array}$

[0089] Step 3: acquiring a core temperature and a surface temperature of the power battery in a normal working state, and determining a state constraint of the system:

[0090] when the power battery works under a normal working condition, the core temperature T.sub.c satisfies M.sub.1° C.≤T≤M.sub.2° C.; there is a difference value between the core temperature and the surface temperature, and the difference value is stabilized within a range of m° C.±ε° C., namely m−ε° C.≤T.sub.c−T.sub.s≤m+ε° C.;

[0091] determining the state constraint of the system:

[00026]$\{\begin{array}{c}.Math.T_{c,k}-T_{s,k}-m.Math.\le \epsilon \\ .Math.T_{c,k}-\frac{M_1+M_2}{2}.Math.\le \frac{M_2-M_1}{2}\end{array}$

[0092] writing the state constraint of the system into the form of Equation (7):

|γ.sub.k−H.sub.kx.sub.k|≤l.sub.k, h(x.sub.k)=γ.sub.k−H.sub.kx.sub.k  (7)

[0093] where,

[00027]$l_k=\left[\begin{array}{c}\epsilon \\ \frac{M_2-M_1}{2}\end{array}\right],{\gamma }_k=\left[\begin{array}{c}-m\\ -\frac{M_2-M_1}{2}\end{array}\right],H_k=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right].$

[0094] In actual application, when the current is 5 A and the ambient temperature is 25° C., the power battery works under the normal working condition, the core temperature will be stabilized in the range of [35.8° C.,35.9° C.], namely, 35.8° C.≤T.sub.c≤35.9° C. There is also a difference value between the core temperature and the surface temperature, the difference value will be stabilized in the range of 5.82° C.±0.05° C., namely, 5.77° C.≤T.sub.c−T.sub.s≤5.87° C.

[0095] Therefore,

[00028]$l_k=\left[\begin{array}{c}0.05\\ 0.05\end{array}\right],{\gamma }_k=\left[\begin{array}{c}-5.82\\ -35.85\end{array}\right],H_k=\left[\begin{array}{cc}-1& 1\\ -1& 0\end{array}\right].$

[0096] Step 4: expanding the state constraint of the power battery to a system output vector of the power battery system to obtain a system output variable, and expanding a fault vector of the power battery system to a system state vector to obtain a system state variable;

[0097] expanding the state constraint of the power battery to the system output vector of the power battery system, and according to Equation (6) and Equation (7), obtaining an Equation (8) as follows:

[00029]$\begin{array}{cc}\{\begin{array}{c}{x}_{k+1}=A{x}_k+B{u}_k+D_1{w}_k\\ {\overline{y}}_k=\overline{C}{x}_k+{\overline{D}}_2{\overline{v}}_k+\overline{f_k}\end{array}& \left(8\right)\end{array}$$\mathrm{where},\overline{C}=\left[\begin{array}{c}C\\ H_k\end{array}\right],,{\overline{D}}_2=\left[\begin{array}{cc}{D}_2& 0_{p\times \gamma }\\ 0_{p\times v}& I_{p\times \gamma }\end{array}\right],{\overline{y}}_k=\left[\begin{array}{c}{y}_k\\ {\gamma }_k\end{array}\right],{\overline{v}}_k=\left[\begin{array}{c}{v}_k\\ l_k\end{array}\right],.Math.{\overline{v}}_k.Math.\le \tilde{\overline{v}}-,\overline{V}=\mathrm{diag}\left(\tilde{\overline{v}}\right),\overline{f_k}=\left[\begin{array}{c}{f}_k\\ 0_{\gamma }\end{array}\right],{\gamma }_k\in .$

[0098] Expanding the fault vector of the power battery system to the system state vector to obtain the system state variable, and according to Equation (8), obtaining an Equation (9) as follows:

[00030]$\begin{array}{cc}\{\begin{array}{c}E{\stackrel{\_}{x}}_{k+1}=\overline{A}{\overline{x}}_k+\overline{B}{u}_k+{\overline{D}}_1{w}_k\\ {\overline{y}}_k=C_1{\overline{x}}_k+{\overline{D}}_2{\overline{v}}_k\end{array}& \left(9\right)\end{array}$$\mathrm{where},{\overline{x}}_k=\left[\frac{x_k}{f_k}\right],E=\left[\begin{array}{cc}I& 0_{n\times \left(p+\gamma \right)}\\ 0_{\left(p+\gamma \right)\times n}& 0_{p+\gamma }\end{array}\right],\overline{A}=\left[\begin{array}{cc}A& 0_{n\times \left(p+\gamma \right)}\\ 0_{\left(p+\gamma \right)\times 2}& 0_{p+\gamma }\end{array}\right],\overline{B}=\left[\begin{array}{c}B\\ 0_{\left(p+\gamma \right)\times r}\end{array}\right],C_1=\left[\begin{array}{cc}\overline{C}& I\end{array}\right],{\overline{D}}_1=\left[\begin{array}{c}{D}_1\\ 0_{\left(p+\gamma \right)\times w}\end{array}\right].$

[0099] Step 5: obtaining a corresponding zonotope set according to a system state variable x.sub.k at time k, constructing a zonotope set of a system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 according to the zonotope set of the system state variable x.sub.k at time k, and constructing a strip space S.sub.k+1 at time k+1 according to the system output variable:

[0100] constructing the zonotope set of a system state variable feasible set {circumflex over (χ)}.sub.k+1 at time k+1;

[0101] setting a zonotope Z.sub.0=p.sub.σ⊕G.sub.0.sup.s, corresponding to an initialization state variable x.sub.0, p.sub.0 representing a central point of the corresponding zonotope at the initial time, G.sub.0 representing a shape matrix of the corresponding zonotope at the initial time, and B.sup.s being a unit box composed of s unit intervals [−1,1];

[0102] assuming a zonotope Z.sub.k=p.sub.k⊕G.sub.k.sup.s=p.sub.k,G.sub.k corresponding to the state variable x.sub.k at time k, then constructing the zonotope set corresponding to the system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1

{circumflex over (χ)}.sub.k+1{circumflex over (p)}.sub.k+1,{circumflex over (G)}.sub.k+1  (10)

{circumflex over (p)}.sub.k+1=TĀp.sub.k+TBu.sub.k+Ny.sub.k+1  (11)

{circumflex over (G)}.sub.k+1=[TĀ↓.sub.reG.sub.kTD.sub.1W−ND.sub.2V]  (12)

T=Θ.sup.†α.sub.1+SΨα.sub.1,N=Θ.sup.†α.sub.2+SΨα.sub.2  (13)

[0103] where,

[00031]$\Theta =\left[\begin{array}{c}E\\ C_1\end{array}\right],$

Θ.sup.† is the pseudo inverse of Θ; Ψ=I.sub.n+2p+2γΘΘ.sup.†,

[00032]${\alpha }_1=\left[\begin{array}{c}{I}_{n+p+\gamma }\\ 0_{\left(p+\gamma \right)\times \left(n+p+\gamma \right)}\end{array}\right],{\alpha }_2=\left[\begin{array}{c}{0}_{\left(n+p+\gamma \right)\times \left(p+\gamma \right)}\\ I_{n+\gamma }\end{array}\right].{\downarrow }_{re}{\overline{G}}_k\in {n\times q}^{}$

represents a generated matrix after reducing the order of the zonotope of the state at time k, and ↓.sub.re G.sub.k is obtained through Equations (14)-(17):

[00033]$\begin{array}{cc}Z=.Math.\stackrel{\_}{p},\stackrel{\_}{G}.Math..Math.\stackrel{\_}{p}\oplus \mathrm{rs}\left(\stackrel{\_}{G}\right)n^{}& \left(14\right)\end{array}$$\begin{array}{cc}\mathrm{rs}\left(\stackrel{\_}{G}\right)=\left[\begin{array}{cccc}\underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{1,j}.Math.& 0& .Math.& 0\\ 0& \underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{2,j}.Math.& .Math.& 0\\ .Math.& .Math.& \ddots & .Math.\\ 0& 0& .Math.& \underset{j=1}{\overset{s}{.Math.}}.Math.{\stackrel{\_}{G}}_{n,j}.Math.\end{array}\right]& \left(15\right)\end{array}$$\begin{array}{cc}Z=.Math.\stackrel{\_}{p},\stackrel{\_}{G}.Math..Math..Math.\stackrel{\_}{p},{\downarrow }_{\mathrm{re}}\stackrel{\_}{G}.Math.& \left(16\right)\end{array}$$\begin{array}{cc}{\downarrow }_{\mathrm{re}}\stackrel{\_}{G}=\{\begin{array}{cc}\stackrel{\_}{G},& s\le q\\ [\begin{array}{cc}{\stackrel{\_}{G}}_{>}& \mathrm{rs}\left({\stackrel{\_}{G}}_{<}\right)],\end{array}& s>q\end{array}& \left(17\right)\end{array}$

[0104] where G.sub.> is the first q−n columns of a matrix {tilde over (G)}obtained by arranging the column vector of G in a descending order according to the Euclidean norm, and G.sub.< is the part of {tilde over (G)} with G.sub.> removed.

[0105] Constructing the strip space S.sub.k+1 at time k+1 according to the system output variable at time k+1:

S.sub.k+1={x.sub.k+1∈R.sup.n+p+γ:|C.sub.1x.sub.k+1−y.sub.k+1|≤D{tilde over (v)}}  (18)

[0106] Step 6: solving an intersection of the zonotope set of the system state variable prediction set {circumflex over (χ)}.sub.k+1 at time k+1 and the constructed strip space S.sub.k+1, and wrapping with a zonotope of the minimum volume to obtain a zonotope set of a state variable x.sub.k+1 at time k+1;

[0107] according to the strip space S.sub.k+1 at time k+1 and the zonotope set of the state variable prediction set {circumflex over (χ)}.sub.k+1, in combination with Equations (19)-(22), obtaining the zonotope set of the state variable x.sub.k+1 at time k+1 by calculation.

x.sub.k+1∈χ.sub.k+1=p.sub.k+1,G.sub.k+1  (19)

p.sub.k+1={circumflex over (p)}+L.sub.k+1(y.sub.k+1−C.sub.1{circumflex over (p)}.sub.k+1)  (20)

G.sub.k+1=[(I.sub.n+s+γ−L.sub.k+1C.sub.1){circumflex over (G)}.sub.k+1L.sub.k+1D.sub.v]  (21)

L.sub.k+1={circumflex over (G)}.sub.k+1{circumflex over (G)}.sub.k+1.sup.TC.sub.1.sup.T(C.sub.1{circumflex over (G)}.sub.k+1{circumflex over (G)}.sub.k+1.sup.TC.sub.1.sup.T+D.sub.vD.sub.v.sup.T).sup.−1  (22)

[0108] where, D.sub.v=diag(D.sub.2{tilde over (v)}).

[0109] Step 7: acquiring a state estimation interval and a fault estimation interval at time k+1 according to the zonotope set of the system state variable at time k+1, and judging whether the core temperature sensor and the surface temperature sensor in the power battery management system have a fault:

[0110] determining the state estimation interval at time k+1 according to Equation (23):

[00034]$\begin{array}{cc}\{\begin{array}{c}{\overline{x}}_{k+1}^{+}\left(\mu \right)={\overline{p}}_{k+1}\left(\mu \right)+\stackrel{q}{\underset{j=1}{.Math.}}.Math.{\overline{G}}_{k+1}\left(\mu ,j\right).Math.,\mu =1,.Math.,n+s+\gamma \\ {\overline{x}}_{k+1}^{-}\left(\mu \right)={\overline{p}}_{k+1}\left(\mu \right)-\stackrel{q}{\underset{j=1}{.Math.}}.Math.{\overline{G}}_{k+1}\left(\mu ,j\right).Math.,\mu =1,.Math.,n+s+\gamma \end{array}& \left(23\right)\end{array}$

[0111] where, x.sub.k+1.sup.+(μ), x.sub.+1.sup.−(μ) respectively represent the minimum upper bound and the maximum lower bound of state estimation at time k+1;

[0112] determining the fault estimation interval at time k+1 according to Equation (24):

f.sub.k+1.sup.+=[0.sub.p×nI.sub.p0.sub.p×γ]x.sub.k+1.sup.+

f.sub.k+1.sup.−=[0.sub.p×nI.sub.p0.sub.p×γ]x.sub.k+1.sup.−  (24)

[0113] where, f.sub.k+1.sup.+, f.sub.k+1.sup.− respectively represent the minimum upper bound and the maximum lower bound of the fault estimation at time k+1.

[0114] If the upper and lower bounds of the fault estimation interval obtained by Equation (24) are on both sides of 0, then a power battery sensor does not have a fault. If the upper and lower bounds of the fault estimation interval are on one side of 0 at the same time, it shows that the power battery sensor has a fault, and a fault value is within a fault estimation range; at the same time, when fault types are different, fault estimation intervals are different, and the fault type of the power battery sensor is judged according to the fault estimation interval.

[0115] In order to verify the accuracy and rapidity of the uncertain noisy filtering-based fault diagnosis method for the power battery proposed in the present application, the following simulation experiments are performed: for the power battery system in the normal working state, it is set that two different sensor faults occur during the time period k∈{300, 2000} and k∈{500, 2000}.

[0116] FIG. 3 and FIG. 4 respectively show the changes of the upper and lower bounds of estimation of two types of sensor faults. It can be seen from FIG. 3 that when k∈{0, 300}, the upper and lower bounds of the fault estimation interval are on both sides of 0, and then the system also has no fault signal; when k∈{300, 2000}, the fault estimation interval is on both sides of an applied fault signal, and by this time, a fault signal f.sub.1 is applied to the system. It can be seen from FIG. 4 that when k∈{0, 500}, the upper and lower bounds of the fault estimation interval are on both sides of 0, and then the system also has no fault signal; and when k∈{500, 2000}, the fault estimation interval is on both sides of the applied fault signal, and by this time, a fault signal f.sub.2 is applied to the system. It shows that the fault diagnosis method provided in the present disclosure has the features of high fault detection efficiency and accurate fault diagnosis.

[0117] Some of the steps in the examples of the present disclosure may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as an optical disk or a hard disk.

[0118] The above descriptions are only preferred examples of the present disclosure, and are not intended to limit the present disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection range of the present disclosure.