Evidence-theory-based uncertain parameter identification method for mechanical systems with imprecise information

In many mechanical engineering practices, the sample information is usually imprecise due to the complex objective environment or various subjective cognitions. In this study, a kind of inverse problem for identifying the uncertain system parameters with imprecise information is investigated by using the evidence theory. First, the uncertain input parameters to be identified are approximately characterized by evidence variables with subinterval-type focal elements. Through the optimization procedure executed in the given computational model, the output response can be expressed as a group of interval numbers with basic probability assignment (BPA). In the subsequent inverse analysis framework, by cumulating the imprecise experimental response measurements with belief degrees to update the response BPAs, the related interval range of unknown evidence variables can be gradually calibrated toward the true value. To improve the optimization efficiency of output response calculation with respect to various focal elements, a relatively simple metamodel is established as an alternative of the original computational model, where the Legendre-type polynomial and Clenshaw–Curtis point are respectively utilized as the basis function and sample construction strategy. Eventually, numerical results in two examples verify that the uncertain parameter identification can be effectively achieved by the presented method.