#### 期刊菜单

Thermal Fault Diagnosis of Li-Ion Battery Actuator Based on Temperature Sampling Data
DOI: 10.12677/JEE.2021.92007, PDF, HTML, XML, 下载: 228  浏览: 464

Abstract: A fault diagnosis method based on set membership filtering is proposed for thermal fault of Li-ion battery. Through constructing electrothermal coupled model, based on the battery temperature sampling data, the Zonotopic Kalman filter algorithm is used to analyze the sampling data to obtain the interval of fault estimation, so as to realize the thermal fault diagnosis of Li-ion battery actuator.

1. 引言

2. 模型建立

Figure 1. Schematic diagram of second-order Thevenin model

$\begin{array}{l}U={U}_{oc}-{R}_{o}I-{U}_{1}-{U}_{2}\hfill \\ \left\{\begin{array}{l}{\stackrel{˙}{U}}_{1}=-\frac{1}{{R}_{1}{C}_{p1}}{U}_{1}+\frac{1}{{C}_{p1}}I\\ {\stackrel{˙}{U}}_{2}=-\frac{1}{{R}_{2}{C}_{p2}}{U}_{2}+\frac{1}{{C}_{p2}}I\end{array}\hfill \end{array}$ (1)

$\left\{\begin{array}{l}{C}_{c}{\stackrel{˙}{T}}_{c}={Q}_{gen}+\frac{{T}_{s}-{T}_{c}}{{R}_{c}}\hfill \\ {C}_{s}{\stackrel{˙}{T}}_{\text{s}}=\frac{{T}_{e}-{T}_{s}}{{R}_{u}}-\frac{{T}_{s}-{T}_{c}}{{R}_{c}}\hfill \end{array}$ (2)

${Q}_{gen}=I\left({U}_{oc}-U\right)=I\left({R}_{o}I+{U}_{1}+{U}_{2}\right)$ (3)

$\left\{\begin{array}{l}{x}_{k+1}=A{x}_{k}+B{u}_{k}+{D}_{1}{w}_{k}\hfill \\ {y}_{k}=C{x}_{k}+{D}_{2}{v}_{k}\hfill \end{array}$ (4)

$A=\left[\begin{array}{cc}1-\frac{\text{Δ}t}{{R}_{c}{C}_{c}}& \frac{\text{Δ}t}{{R}_{c}{C}_{c}}\\ \frac{\text{Δ}t}{{R}_{c}{C}_{s}}& 1-\frac{\text{Δ}t}{{R}_{c}{C}_{s}}-\frac{\text{Δ}t}{{R}_{u}{C}_{s}}\end{array}\right],B=\left[\begin{array}{cc}\frac{\text{Δ}t}{{C}_{c}}& 0\\ 0& \frac{\text{Δ}t}{{R}_{u}{C}_{s}}\end{array}\right],C=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],{D}_{1}={D}_{2}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

3. 集员滤波方法

4. 基于ZKF的锂电池执行器热故障诊断

$\left\{\begin{array}{l}{x}_{k+1}=A{x}_{k}+B{u}_{k}+{f}_{k}+{D}_{1}{w}_{k}\hfill \\ {y}_{k}=C{x}_{k}+{D}_{2}{v}_{k}\hfill \end{array}$ (5)

${\stackrel{¯}{x}}_{k}=\left[\begin{array}{c}{x}_{k}\\ {f}_{k-1}\end{array}\right]$ (6)

$\left\{\begin{array}{l}E{\stackrel{¯}{x}}_{k+1}=\stackrel{¯}{A}{\stackrel{¯}{x}}_{k}+\stackrel{¯}{B}{u}_{k}+{\stackrel{¯}{D}}_{1}{w}_{k}\hfill \\ {y}_{k}=\stackrel{¯}{C}{\stackrel{¯}{x}}_{k}+{D}_{2}{v}_{k}\hfill \end{array}$ (7)

$\begin{array}{l}E=\left[\begin{array}{cccc}1& 0& -1& 0\\ 0& 1& 0& -1\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],\stackrel{¯}{A}=\left[\begin{array}{cccc}1-\frac{\text{Δ}t}{{R}_{c}{C}_{c}}& \frac{\text{Δ}t}{{R}_{c}{C}_{c}}& 0& 0\\ \frac{\text{Δ}t}{{R}_{c}{C}_{s}}& 1-\frac{\text{Δ}t}{{R}_{c}{C}_{s}}-\frac{\text{Δ}t}{{R}_{u}{C}_{s}}& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],\stackrel{¯}{B}=\left[\begin{array}{cc}\frac{\text{Δ}t}{{C}_{c}}& 0\\ 0& \frac{\text{Δ}t}{{R}_{u}{C}_{s}}\\ 0& 0\\ 0& 0\end{array}\right],\\ {\stackrel{¯}{D}}_{1}=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\\ 0& 0\end{array}\right],\stackrel{¯}{C}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]\end{array}$

$\begin{array}{l}{w}_{k}\in \mathcal{W}=〈0,W〉\\ {v}_{k}\in \mathcal{V}=〈0,V〉\end{array}$ (8)

${\stackrel{^}{\stackrel{¯}{\chi }}}_{k+1}=〈{\stackrel{^}{\stackrel{¯}{p}}}_{k+1},{\stackrel{^}{\stackrel{¯}{G}}}_{k+1}〉$ (9)

${\stackrel{^}{\stackrel{¯}{p}}}_{k+1}=T\stackrel{¯}{A}{\stackrel{¯}{p}}_{k}+T\stackrel{¯}{B}{u}_{k}+N{y}_{k+1}$ (10)

${\stackrel{^}{\stackrel{¯}{G}}}_{k+1}=\left[T\stackrel{¯}{A}{↓}_{re}{\stackrel{¯}{G}}_{k}\text{ }T{\stackrel{¯}{D}}_{1}W\text{}-N{D}_{2}V\right]$ (11)

$T={\text{Θ}}^{†}{\alpha }_{1}+S\text{Ψ}{\alpha }_{1},N={\text{Θ}}^{†}{\alpha }_{2}+S\text{Ψ}{\alpha }_{2}$ (12)

$\mathcal{Z}=〈\stackrel{¯}{p},\stackrel{¯}{G}〉\subseteq \stackrel{¯}{p}\oplus rs\left(\stackrel{¯}{G}\right){B}^{n}$ (13)

$rs\left(\stackrel{¯}{G}\right)=\left[\begin{array}{cccc}\underset{j=1}{\overset{s}{\sum }}|{\stackrel{¯}{G}}_{1,j}|& 0& \cdots & 0\\ 0& \underset{j=1}{\overset{s}{\sum }}|{\stackrel{¯}{G}}_{2,j}|& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \cdots & \underset{j=1}{\overset{s}{\sum }}|{\stackrel{¯}{G}}_{n,j}|\end{array}\right]$ (14)

$\mathcal{Z}=〈\stackrel{¯}{p},\stackrel{¯}{G}〉\subseteq 〈\stackrel{¯}{p},{↓}_{re}\stackrel{¯}{G}〉$ (15)

${↓}_{re}\stackrel{¯}{G}=\left\{\begin{array}{ll}\stackrel{¯}{G},\hfill & \text{}s\le q\hfill \\ \left[\begin{array}{cc}{\stackrel{¯}{G}}_{>}& rs\left({\stackrel{¯}{G}}_{<}\right)\end{array}\right],\hfill & \text{}s>q\hfill \end{array}$ (16)

${\mathcal{S}}_{k+1}=\left\{{\stackrel{¯}{x}}_{k+1}\in {ℝ}^{n+s}:|\stackrel{¯}{C}{\stackrel{¯}{x}}_{k+1}-{y}_{k+1}|\le {D}_{2}\stackrel{˜}{v}\right\}$ (17)

${\stackrel{¯}{x}}_{k+1}\in {\stackrel{¯}{\chi }}_{k+1}=〈{\stackrel{¯}{p}}_{k+1},{\stackrel{¯}{G}}_{k+1}〉$ (18)

${\stackrel{¯}{p}}_{k+1}={\stackrel{^}{\stackrel{¯}{p}}}_{k+1}+{L}_{k+1}\left({y}_{k+1}-\stackrel{¯}{C}{\stackrel{^}{\stackrel{¯}{p}}}_{k+1}\right)$ (19)

${\stackrel{¯}{G}}_{k+1}=\left[\left({I}_{n+p}-{L}_{k+1}\stackrel{¯}{C}\right){\stackrel{^}{\stackrel{¯}{G}}}_{k+1}\text{ }{L}_{k+1}{D}_{v}\right]$ (20)

${L}_{k+1}={\stackrel{^}{\stackrel{¯}{G}}}_{k+1}{\stackrel{^}{\stackrel{¯}{G}}}_{k+1}^{\text{T}}{\stackrel{¯}{C}}^{\text{T}}{\left(\stackrel{¯}{C}{\stackrel{^}{\stackrel{¯}{G}}}_{k+1}{\stackrel{^}{\stackrel{¯}{G}}}_{k+1}^{\text{T}}{\stackrel{¯}{C}}^{\text{T}}+{D}_{v}{D}_{v}^{\text{T}}\right)}^{-1}$ (21)

$\left\{\begin{array}{l}{z}^{-}\left(i\right)=p\left(i\right)-\underset{j=1}{\overset{s}{\sum }}|G\left(i,j\right)|\text{ }\text{ },\text{ }i=1,\cdots ,n\\ {z}^{+}\left(i\right)=p\left(i\right)-\underset{j=1}{\overset{s}{\sum }}|G\left(i,j\right)|\text{ }\text{ },\text{ }i=1,\cdots ,n\end{array}$ (22)

$\left\{\begin{array}{l}{\stackrel{¯}{x}}_{k+1}^{+}\left(i\right)={\stackrel{¯}{p}}_{k+1}\left(i\right)+\underset{j=1}{\overset{q}{\sum }}|{\stackrel{¯}{G}}_{k+1}\left(i,j\right)|\text{ }\text{ },\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,\cdots ,n+p\hfill \\ {\stackrel{¯}{x}}_{k+1}^{-}\left(i\right)={\stackrel{¯}{p}}_{k+1}\left(i\right)-\underset{j=1}{\overset{q}{\sum }}|{\stackrel{¯}{G}}_{k+1}\left(i,j\right)|\text{ }\text{ },\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,\cdots ,n+p\hfill \end{array}$ (23)

$\begin{array}{l}{f}_{k}^{+}=\left[\begin{array}{cc}0& {I}_{p}\end{array}\right]{\stackrel{¯}{x}}_{k+1}^{+}\\ {f}_{k}^{-}=\left[\begin{array}{cc}0& {I}_{p}\end{array}\right]{\stackrel{¯}{x}}_{k+1}^{-}\end{array}$ (24)

5. 仿真示例

Table 1. Main parameters of the electrothermal coupling model of lithium battery

${f}_{k}={\left[{f}_{1,k}\text{ }{f}_{2,k}\right]}^{\text{T}}=\left\{\begin{array}{l}{\left[\begin{array}{cc}0& 0\end{array}\right]}^{\text{T}},0\le k<100\hfill \\ {\left[\begin{array}{cc}0.1& 0\end{array}\right]}^{\text{T}},100\le k<300\hfill \\ {\left[\begin{array}{cc}0.2& 0.2\end{array}\right]}^{\text{T}},300\le k<500\hfill \\ {\left[\begin{array}{cc}0.2& 0.4\end{array}\right]}^{\text{T}},k\ge 500\hfill \end{array}$ (25)

Figure 2. Core and surface temperature samples

$S=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\end{array}\right]$ (26)

$T=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ -1& 0& 1& 0\\ 0& -1& 0& 1\end{array}\right],N=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 0\\ 0& 1\end{array}\right]$ (27)

(a) (b)

Figure 3. Lithium battery thermal fault and its estimation intervals

6. 结论

NOTES

*通讯作者。

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