Novel interval theory-based parameter identification method for engineering heat transfer systems with epistemic uncertainty

The parameter identification problem with epistemic uncertainty, where only a small amount of experimental information is available, is a challenging issue in engineering. To overcome the drawback of traditional probabilistic methods in dealing with limited data, this paper proposes a novel interval theory-based inverse analysis method. First, the interval variables are introduced to represent the input uncertainties, whose lower and upper bounds are to be identified. Subsequently, an unbiased estimation method is presented to quantify the experimental response interval from limited measurements. Meanwhile, a quantitative metric is defined to characterize the relative errors between computational and experimental response intervals by which the interval parameter identification can be constructed as a nested-loop optimization procedure. To improve the computational efficiency of response prediction with respect to various interval variables, a universal surrogate model is established in the support box via Legendre polynomial chaos expansion, where the expansion coefficients can be evaluated by a collocation method under Clenshaw-Curtis points and Smolyak algorithm. Eventually, a heat conduction example is provided to verify the feasibility of proposed method, especially in the case with noise-contaminated temperature measurements.