一种新的研究区间不确定性传播方法

摘要

不确定性及其传播问题存在于许多实际问题中，但传统的优化方法在准确性和效率方面具有一定的局限性。据此，提出一种新的研究区间不确定性传播机制的方法。利用 D-S(dempster-shafer)证据理论研究认知不确定性的表达方式，应用混沌多项式展开技术量化随机变量函数响应的不确定性，再将混沌多项式转换为 Bernstein 形式，从而利用 Bernstein 多项式系数找到响应的取值范围。实例研究了闭区间上 D-S 结构通过非线性函数的传播问题，通过与传统优化方法的对比分析，展示了新方法在研究区间不确定性传播问题上的优势，验证了该方法的有效性。%Uncertainty and its propagation issues exist in many practical problems.However, traditional optimization methods have the limitation on accuracy and efficiency.A new method is proposed for the study of interval uncertainty propagation mechanism:D-S evidence theory is used to research the expression of epistemic uncertainty,polynomial chaos expansion technique to quantify the uncertainty in the response of random variables,and the polynomial is converted to Bernstein form.Finally,the range of response by using the Bernstein polynomial coefficients is identified.A study of closed D-S structure on the interval propagation thought a nonlinear function shows the advantage on the interval uncertainty propagation compared with the tradi-tional optimization method and verifies its effectiveness of the proposed method.