发动机亚定故障方程组整体优化解分布函数模型

A Distribution Function Model of Integrated Optimization Algorithm for Resolving Underdetermined Jet Engine Fault Equation

提出了求解发动机亚定故障方程组整体优化解的分布函数模型.该模型利用一种可以控制自变量数值在整体解中分布的分布函数与亚定故障方程组的残差平方和构成复合目标函数,同时以物理合理性准则作为约束条件,构成一个非线性规划问题.分布函数模型可以在小于、等于特别是大于故障方程个数的各种复杂情况下给出全面的故障诊断信息,从而为目前迫切需要解决的发动机性能监控与故障诊断中在测量参数不足的情况下,对发动机进行全面性能诊断的技术难题提供出一种切实可行而又十分有效的数学模型.首次提出了作为评价发动机全面性能诊断算法有效性指标的相似度的概念,并且以JT9D发动机全面性能诊断问题为例,利用Monte Carlo随机模拟方法确定了分布函数模型可以达到的相似度值.研究结果表明,分布函数模型的相似度可达0.9以上.还利用JT9D发动机的实际故障样本对分布函数模型进行了检验.

Abstrac: A distribution function model (DFM) of integrated optimization algorithm for resolving underdetermined jet engine fault equation is presented in the paper. The DFM is a non-linear mathematical programming problem which is formed by the objective function (the weighted square sum of the so-called distribution function able to control the variable value distribution in integrated solution and the residual square sum of the fault equation) and the constrained condition determined by the criterion of reasonableness in physics.The DFM can give overall fault diagnosis information in the case of the fault number (the number of fault patterns happening simultaneously) being less, equal or even greater than the number of fault equations, thus providing a practical method for resolving the difficult technical problem of the overall engine performance diagnosis with inadequate measurements. In addition, a concept of similarity degree to estimate the efficiency of overall engine performance diagnosis is presented for the first time and, taking the JT9D engine overall performance diagnosis as an example,the similarity degree value of the DFM is determined by making use of Monte Carlo random simulation. As shown by the result of the study, the similarity degree can reach an encouraging value of greater than 0.90. A test of the DFM is also ma.de in the paper by making use of a JT9D fault sample.