Interval Analysis of Neural Net Adaptive Expert Systems for Diagnosis of Machinery Incipient Failure

Abstract

Abstract Interval calculus is a tool to evaluate a mathematical expression for ranges of values of its parameters. The basic mathematical operations are defined in the interval algebra. Neural networks is an approach leading to engineering expert systems that are capable of learning, self adapting to particular engineering applications and handling fuzzy and interval input information. In traditional machine learning, symbolic representations, such as first order predicate calculus, are used to represent knowledge. The resulting algorithms are specific to the selected representation and presume an ad-hoc knowledge of the system represented. In the neural network representation, knowledge is distributed to a large number of weighted synapses that facilitates learning by experience, realized through modification of the synapses weights according to a chosen learning rule. Traditional classification systems use binary logic. This assumes a clear distinction between two and only two possible states of an event. However, key elements in the human thinking are not numbers but labels of fuzzy sets, that is, classes of objects in which the transition from non-membership to membership is gradual rather than abrupt and ranges of key parameters involved. A heteroassociative neural network is used to map the existing knowledge and acquire new knowledge in learning sessions. The inputs can be binary, fuzzy and interval variables. To process the diagnosis in a back-propagation mode, interval calculus is utilized in algebraic and matrix operations and the diagnosis results in interval output parameters, the identification scores. Interval calculus was programmed in a software package to allow for interval computations. The package includes arithmetic, function and matrix operations. Available experience for failure diagnosis in turbomachinery was utilized to initially teach the system. Additional diagnoses from the author’s experience were taught to the system and additional features and diagnoses defined. Convergence of the procedure depends on the monotonicity of the functions used. For usual networks and threshold functions, convergence is warranted.