A new probabilistic distribution matching PATC formulation using polynomial chaos expansion

In the existing probabilistic hierarchical optimization approaches, such as probabilistic analytical target cascading (PATC), all the stochastic interrelated responses are characterized only by the first two statistical moments. However, due to the high nonlinear relation between the inputs and outputs, the interrelated responses are not necessarily normally distributed. The existing approaches, therefore, may not accurately quantify the probabilistic characteristics of the interrelated responses, and would further prevent achieving the real optimal solution. To overcome this deficiency, a novel PATC approach, named PATC-PCE is developed. By employing the polynomial chaos expansion (PCE) technique, the entire distribution of interrelated response can be characterized by a PCE coefficients vector, and then matched and propagated in the hierarchy. Comparative studies show that PATC-PCE outperforms PATC in terms of yielding more accurate optimal solutions and fewer design cycles when the interrelated response are random non-normal quantities, while at a sacrifice of extra function evaluations.