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This paper illustrates two strategies for the detection and classification of abnormal process operating conditions in which multiple process variable trends are available. The first strategy uses a hidden Markov model (HMM) for overall process classification while the second method uses a back-propagation neural network (BPNN) to determine the overall process classification. The methods are compared in terms of their ability to detect and correctly diagnose a variety of abnormal operating conditions for a non-isothermal CSTR simulation. For the case study problem, the BPNN method resulted in better classification accuracy with a moderate increase in training time compared with the HMM approach.

This paper presents a strategy to represent and classify process data for detection of abnormal operating conditions. In representing the data, a wavelet-based smoothing algorithm is used to filter the high frequency noise. A shape analysis technique called triangular episodes then converts the smoothed data into a semi-qualitative form. Two membership functions are implemented to transform the quantitative information in the triangular episodes to a purely symbolic representation. The symbolic data is classified with a set of sequence matching hidden Markov models (HMMs), and the classification is improved by utilizing a time correlated HMM after the sequence matching HMM. The method is tested on simulations with a non-isothermal CSTR and compared with methods that use a back-propagation neural network with and without an ARX model.

This paper presents a strategy to represent and classify process data for detection of abnormal operating conditions. It uses fuzzy triangular episodes for qualitative data representation and a set of hidden Markov models (HMMs) for classification. The method is tested on an industrial vacuum column for detection of column weeping.

Planar polar triangular and quadrilateral stress elements with polar joint freedoms and their element matrices for general forms of shape functions are developed for the stress and deformation analysis of complex planar elastic systems, especially those having contact surfaces between members, rotating machine members and interference fits. Joint freedom irregularities are introduced to permit non-polar sliding joint freedoms on the non-polar contact surfaces, and permit non-polar force applications. Shape functions used permit higher order variations of stresses within the elements as compared to their cartesian counter parts. Three numerical examples (a curved beam, a layered curved vehicle spring and a rotating wheel) illustrate the efficiency and applications of these elements, where some result are compared with those of photoelasticity solutions. Finally article develops method for the stress analysis of complex systems having single or multiple interference fits, where the external loading and the normal interference distributions along the contact surfaces are known, but the contact pressures and the radial displacements of the contact joints on the inner and outer members of the fits are not known. Four additional numerical examples investigate stresses and deformations in elastic systems having single and multiple interference fits, where the results for fits of concentric cylinders are compared with those of exact elasticity solutions. Digital computer programs are made available for the interested reader.