The Investigation Of The Statistic Probability Orthogonality Decomposition Based Fault Isolation Algorithm

As one of the key sectors to the development of the national economy, processindustrynowadaysismoreandmorecomplex. Toguaranteetheprocesssafety,increasethe production efciency, improve the quality of products, and more importantly, toavoid the disastrous accidents, detecting and isolating faults in these processes is ofimportance.Finding the root cause of fault through efective decomposition of the statistic isone of the most active research felds in fault detection and diagnosis. As one decom-position method, MYT decomposition is to decompose the T2in a limited number oforthogonal components which imply the contribution to the statistic. In real process,withalargemountof computation, thismethod cannot be appliedtotheprocesseswithmultiplevariables. Tosolvetheproblem,thisdissertationwhichisbasedonthestatisticprobability orthogonality decomposition proposed the causation MYT decompositionbased fault isolation algorithm that meets the demand of fast fault isolation. Further-more, this algorithm is extended in the aspect of non-Gaussanity and incompletenessof data in real industrial processes.Specifcally, the main contributions of this dissertation are as follows:Based on BN and MYT decomposition method, one causation MYT decompo-sition based fault isolation algorithm was proposed to solve the computation ofMYT decomposition and its decomposition items. Using the conditional depen-dencies between variables, the algorithm proved the equivalence of conditionalprobabilityandcorrespondingMYTdecompositionitemtofaultisolation. From the algorithm, the unique MYT decomposition is obtained and decompositionitems decrease to p, which can quickly isolation the source of the fault.In view of the non-Gaussianity of the real world process data, one gaussian mix-ture model (GMM) based fault isolation algorithm was proposed. The probabil-ity density function of the variables is estimated by the GMM. As the GMM ismixed by many (multivariate) normal distribution, the method described abovecan be used in this algorithm.In view of missing data of the real world process data, a missing data fault iso-lation algorithm was proposed. The algorithm can estimate the distribution ofmissing value(s). To get a more accurate fault detection and fault isolation, thecomputation of expectation of items uses both the mean and variance. Two typeof variable distribution(gaussian and non-gaussian) of missing data is discussedin details.