Prediction of structural responses with the aid of fuzzy stochastic time series

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Knowledge about the future behaviour of a structure is the basis for far reaching economical and security relevant decisions in our society. Predictions regarding the future occurrence, intensity, and development of environmental influences, such as a moisture penetration and chloride contamination, and of structural damage are indispensable to compute time-dependent safety levels and to estimate the life time of a structure. Sequences of data describing these parameters possess both stochastic uncertainty and informal uncertainty. Therefore, these sequences are considered - as essential extension to the present methods - as realizations of fuzzy stochastic processes. A fuzzy stochastic process is introduced as a stochastic process extended by the dimension fuzziness. Methods for identification and quantification of fuzzy stochastic time series are investigated. For predicting future structural behavior both measurable and non-measurable structural responses are considered. Measurable structural responses and measurable impacts can be predictet directly, whereas nonmeasurable responses can only be predicted indirectly by applying a computational model to time series data for impacts. Suitable prediction models for stationary and nonstationary fuzzy processes, such as a fuzzy ARMA model or fuzzy neural networks, are developed. Both parametric methods in combination with Bayesian theory extended to apply for uncertain data (Fuzzy-Bayes) and nonparametric methods including fuzzy neural network solutions for fuzzy data are taken into consideration.