Research on Sensor Optimal Placement Method Using Quantitative Evaluation of Fault Diagnosability
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摘要: 提出了一种基于故障可诊断性量化评价的传感器优化配置方法.针对可能发生故障的非线性系统，首先，基于K-L散度思想，通过计算故障情形下残差概率密度函数的差异度，得到了系统不同故障下故障可检测性和可分离性的量化指标，由于稀疏内核密度估计和蒙特卡洛算法的引入，克服了K-L散度计算中残差概率密度函数难以估计和非线性结构的K-L散度计算复杂度高的困难；其次，以故障可诊断性的定量评价为基础，借助于动态规划方法给出了系统满足期望故障可诊断性的传感器最优集合；最后，通过数值仿真和实体实验仿真验证了文中方法在故障诊断系统传感器优化配置中的有效性.Abstract: A method of sensor optimal placement using quantitative evaluation of fault diagnosability is proposed. With the idea of K-L divergence, using quantificational indices of fault detectability and isolability under different fault conditions are obtained by calculating the difference degree of residual probability density function. Sparse kernel density estimation and Monte Carlo algorithm are introduced to overcome the difficulty of estimating the residual probability density function of K-L divergence calculation and high complexity of K-L divergence computation of nonlinear structure. Secondly, with the quantitative evaluation of fault diagnosability, the optimal set of sensors satisfying the expected fault diagnosability is given by means of dynamic programming method. Finally, the validity of the proposed method is validated through numerical simulation and physical experiment simulation in a sensor optimal configuration of fault diagnosis system.
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图 1 不同分布集合中概率密度函数的距离示意图
Fig. 1 The distance of probability density function in different distribution sets
表 1 故障可诊断性分析
Table 1 Fault diagnosability analysis
FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ $\times$ 0 0 $\times$ $\times$ $f_{2}$ $\times$ 0 0 $\times$ $\times$ $f_{3}$ $\times$ $\times$ $\times$ 0 $\times$ $f_{4}$ $\times$ $\times$ $\times$ $\times$ 0 
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表 2 故障可诊断性量化评价
Table 2 Quantitative evaluation of fault diagnosability
$\{x_1, x_3\}$ FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ 0.036 0 0 0.058 0.061 $f_{2}$ 0.054 0 0 0.099 0.054 $f_{3}$ 0.008 0.051 0.074 0 0.116 $f_{4}$ 0.093 0.059 0.053 0.129 0
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表 3 故障可诊断性量化评价
Table 3 Quantitative evaluation of fault diagnosability
$\{x_{2}, x_{4} \}$ FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ 0.055 0 0 0.089 0.083 $f_{2}$ 0.086 0 0 0.098 0.063 $f_{3}$ 0.122 0.133 0.126 0 0.285 $f_{4}$ 0.232 0.080 0.059 0.180 0
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表 4 非线性系统故障可诊断性量化评价
Table 4 Quantitative evaluation of fault diagnosability for nonlinear systems
FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ 0.660 0 0 1.412 1.564 $f_{2}$ 0.671 0 0 1.273 2.229 $f_{3}$ 1.532 1.518 1.936 0 0.330 $f_{4}$ 1.510 1.617 2.520 0.202 0
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表 5 非线性系统故障可诊断性量化评价
Table 5 Quantitative evaluation of fault diagnosability for nonlinear systems
{$x_{2}$, $x_{3}$, $x_{4}$} FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ 0.460 0 0 1.142 0.465 $f_{2}$ 0.423 0 0 1.103 1.110 $f_{3}$ 1.067 1.174 1.248 0 0.143 $f_{4}$ 1.028 0.379 1.039 0.156 0
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表 6 车辆电源常见故障描述
Table 6 Common fault description of vehicle power supply
故障 故障描述 $f_{1}$ 发电机失磁 $f_{2}$ 柴油滤清器堵塞 $f_{3}$ 调速器调节失灵 $f_{4}$ 发动机高温 $f_{5}$ 系统超载 $f_{6}$ 励磁模块故障 $f_{7}$ 喷油嘴故障
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表 7 故障可诊断性定性评价
Table 7 Qualitative evaluation of fault diagnosability
$r_{1}$ $r_{2}$ $r_{3}$ $r_{4}$ $r_{5}$ $r_{6}$ $r_{7 }$ $f_{1}$ 0 0 0 1 0 1 0 $f_{2}$ 0 0 0 0 0 1 0 $f_{3}$ 1 0 0 0 1 0 1 $f_{4}$ 0 0 1 0 0 1 0 $f_{5}$ 0 1 1 0 0 0 0 $f_{6}$ 1 1 0 0 0 1 0 $f_{7}$ 0 0 0 0 0 1 0
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表 8 故障可诊断性量化评价
Table 8 Quantitative evaluation of fault diagnosability
FD $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{5}$ $f_{6}$ $f_{7 }$ $f_{1}$ 0.3462 0 0.1298 0.8978 0.1290 0.1432 0.2765 0.0988 $f_{2}$ 0.4387 0.1304 0 0.8070 0.9908 0.1435 0.2787 0 $f_{3}$ 0.2122 0.9029 0.7865 0 0.7434 0.4634 0.4172 0.8432 $f_{4}$ 0.3456 0.1300 0.8990 0.7321 0 0.6432 0.7432 0.8432 $f_{5}$ 0.6783 0.1765 0.1543 0.4764 0.7325 0 0.3434 0.1088 $f_{6}$ 0.5435 0.2910 0.2898 0.4278 0.7000 0.3299 0 0.5898 $f_{7}$ 0.7646 0.0910 0 0.1022 0.7853 0.0987 0.5786 0
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