Markov models for assessments and prediction of structural elements

Abstract

Purpose. The purpose of the work is to develop a universal model for assessing the technical condition of the structure in the function of the time of operation. The theoretical basis for the development of a stochastic model for the technical condition of a structure during operation is the Markov theory of random processes. Phenomenological models of cumulative accumulation of damaged due to the natural degradation of elements during the life cycle of operation are considered. The wear of the structure element is described by a Markov discrete process with continuous time. The Markov process, whose evolution over time depends only on a fixed modern state, has found wide application in the system of operation of road bridges. Degradation of elements during operation is considered as a stream of failures that are physically a manifestation of damage to the elements of a structure under the influence of loads and the environment. The degradation of bridge elements is interpreted as a stationary simplest flow of Poissian type. A mathematical model of a random process with continuous time and discrete states is described by the well-known Kolmogorov - Chapman equations. The technique. Theoretical study of the processes of degradation of elements of bridges made in the framework of probability theory and mathematical statistics. Results. The model for assessment and prediction of a technical state of structural elements which is based on the Markov theory of random processes is received.. Markov stochastic models of damage accumulation as a result of natural deterioration, considered herein, are universal. They are well proved theoretically and have a practical orientation. These models may be applied as an effective tool for technical state assessments and prediction of structural residual resource. A key aspect of this approach is the special procedure for evaluating the transition intensity parameter. The main lack of the model is that the basis of the elementary flow with parameter λ = const is accepted. However, the parameter λ is determined for each given element, and every time after a subsequent inspection it can be specified, so the accuracy of the model should increase. Scientific novelty. The study is pioneering. For the first time in the system of operation of structural elements, a stochastic assessment of the technical condition of the structure is proposed. Practical value. The resulting model is a practical tool for managing the reliability and resource of structural elements.