基于最小充分统计量模式分析的故障检测方法

统计量模式分析（SPA）最近在故障检测领域取得了广泛应用，其实质是用数据的统计量矩阵来代替原始数据矩阵进行故障检测，然而其统计量的选取存在盲目性且各统计量之间存在复杂的非线性关联关系，难以满足后续应用主成分分析（PCA）完成故障检测所需的基本条件。为了解决这个问题，提出了基于最小充分统计量模式分析的故障检测方法（MSSPA）。该方法首先将原始数据矩阵进行正交变换以消除变量之间的关联性，然后估计出每个变量的概率密度函数或者多个变量的联合概率密度函数，进而求出原始数据的最小充分统计量，并用最小充分统计量来构造统计量矩阵。最小充分统计量的引入还能够有效应对数据的非高斯分布问题。最后，通过在TE过程上的仿真测试验证了该方法用于故障检测的可行性和有效性。

Fault detection method based on minimum sufficient statistics pattern analysis

Recently, the statistic pattern analysis (SPA) has been used with widespread applications in the field of fault detection. Its essence is to use data statistics matrix for process monitoring instead of the original data matrix. However, SPA lacks reasonable method in choosing the statistics variables, also complex nonlinear interactions exist among these statistics variables. As a result, fault detection cannot be processed by using ordinary principal component analysis (PCA) algorithm. In order to solve these problems, a new minimum sufficient statistics pattern analysis (MSSPA) fault detection method is proposed. This method first eliminates the correlations among variables by performing an orthogonal transformation of the raw data matrix, and then estimates the probability density function of the single variables or joint probability density function of multiple variables, so as to acquire the minimum sufficient statistic of original data, and construct the statistic matrix with it. The introduction of minimum sufficient statistics is also beneficial to handle the problem of non-Gaussian distribution of the raw data. Finally, the feasibility and validity of this method for fault detection are verified by testing on the Tennessee Eastmann (TE) process.