﻿ 融合小波包分解和CSA的电路故障诊断方法

# 融合小波包分解和CSA的电路故障诊断方法A Circuit Fault Diagnosis Method by Fusing Wavelet Packet Decomposition and CSA

Abstract: The basic characteristics of analog circuit make it very difficult to diagnose. A circuit fault diagnosis method by fusing wavelet packet decomposition and CSA is proposed to this problem. Firstly, wavelet packet is introduced to decompose, reconstruct and analyze kinds of fault voltage signals output by analog circuit; the frequency band energy of the corresponding spectrum is obtained as a fault characteristic sample, including training samples and test samples. Then the training samples were studied by using the CSA, and the optimal cluster center was obtained. Finally, the fault is classified according to the Euclidean distance between the test sample and the cluster center, and the fault element localization of the analog circuit is realized. The experimental results show that the method has higher diagnostic accuracy and shorter convergence time.

1. 引言

2. 小波包分析

$\left\{\begin{array}{l}{U}_{j}^{0}={V}_{j}\\ {U}_{j}^{1}={W}_{j}\end{array},\text{\hspace{0.17em}}\text{\hspace{0.17em}}j\in Z$ (1)

${\omega }_{2n}\left(t\right)=\sqrt{2}{\sum }_{k}h\left(k\right){\omega }_{n}\left(2t-k\right)$ (2)

${\omega }_{2n+1}\left(t\right)=\sqrt{2}{\sum }_{k}g\left(k\right){\omega }_{n}\left(2t-k\right)$ (3)

${V}_{i+1}={V}_{j}\oplus {W}_{j}$ (4)

$\left\{\begin{array}{l}{U}_{j+1}^{0}={U}_{j}^{0}\oplus {U}_{j}^{1},\text{\hspace{0.17em}}\text{\hspace{0.17em}}j\in Z\\ {U}_{j+1}^{n}={U}_{j}^{2n}\oplus {U}_{j}^{2n+1},\text{\hspace{0.17em}}\text{\hspace{0.17em}}j\in Z\end{array}$ (5)

$\left\{{d}_{l}^{j+1,n}\right\}$$\left\{{d}_{l}^{j,2n}\right\}$$\left\{{d}_{l}^{j,2n+1}\right\}$ 的公式

${d}_{l}^{j,2n}={\sum }_{k}{h}_{k}-2l{d}_{k}^{j+1,n}$ (6)

${d}_{l}^{j,2n+1}={\sum }_{k}{g}_{k}-2l{d}_{k}^{j+1,n}$ (7)

$\left\{{d}_{l}^{j,2n}\right\}$$\left\{{d}_{l}^{j,2n+1}\right\}$$\left\{{d}_{l}^{j+1,n}\right\}$ 的公式

${d}_{l}^{j+1,n}={\sum }_{k}\left({p}_{l}-2k{d}_{k}^{j,2n}+{q}_{l}-2k{d}_{k}^{i,2n+1}\right)$ (8)

$S=AA{A}_{3}+DA{A}_{3}+AD{A}_{3}+DD{A}_{3}+AA{D}_{3}+DA{D}_{3}+AD{D}_{3}+DD{D}_{3}$

3. 克隆选择算法

1) 高频变异：变异率与亲和力成反比，变异函数定义为：

$MAb11_{V}^{\prime }=MAb11_V+\beta \left(Ao\left(i\right)-MAb11_V\right)×N\left(0,1\right)$ (9)

${f}_{i}=\frac{1}{1+{D}_{i}}$ (10)

${D}_{i}=‖MAb_T\left(i\right)-Ao\left(i\right)‖$ (11)

2) 克隆删除：免疫细胞经过变异后产生的低亲和力的免疫细胞，因得不到与抗原结合的机会而死亡。

3) 克隆增值：根据免疫细胞与抗原的亲和力大小对免疫细胞进行克隆繁殖，亲和力越高，克隆繁殖的机会越大，克隆的数目越多。克隆数目定义为：

Figure 1. Schematic diagram of wavelet packet decomposition structure

${N}_{c}=round\left({f}_{i}×K\right)$ (12)

4. 模拟电路故障诊断

1) 将所获得的故障样本归一化后，一部分作为训练样本 $MAb_X\left(j\right)\left(j=1,2,\cdots ,9\right)$ ，一部分作为测试样本 $MAb_T\left(j\right)\left(j=1,2,\cdots ,9\right)$

2) 删除亲和力最低的10%的免疫细胞，选择亲和力为前90%的免疫细胞进行训练。

3) 根据式(12)确定抗体克隆数目并克隆选择出的免疫细胞，其中K取10。

4) 根据式(9)对克隆的个体进行变异。

5) 在变异后的免疫细胞中选择亲和力前10%的免疫细胞进入记忆细胞中和原来的记忆细胞集组成新的记忆细胞集。

6) 对抗体的聚类中心进行更新。直到满足终止条件，退出并保存抗体的聚类中心，否则转向步骤(2)。

7) 根据式(11)计算抗原与聚类中心的欧氏距离，实现模拟电路故障定位。

5. 诊断实例

Figure 2. Flow chart

Figure 3. Sallen-key band pass filter circuit

Table 1. Sallen-key band pass filter circuit fault mode

Figure 4. The normal state compared with R2 (+50%) and R2 (−50%)

Figure 5. The normal state compared with R3 (+50%) and R3 (−50%)

Figure 6. The normal state compared with C1 (+50%) and C1 (−50%)

Figure 7. The normal state compared with C2 (+50%) and C2 (−50%)

Table 2. Simulation result

Table 3. Comparison of simulation results

6. 结语

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