Simultaneous parameter and tolerance optimization of structures via probability-interval mixed reliability model

Both structural sizes and dimensional tolerances strongly influence the manufacturing cost and the functional performance of a practical product. This paper presents an optimization method to simultaneously find the optimal combination of structural sizes and dimensional tolerances. Based on a probability-interval mixed reliability model, the imprecision of design parameters is modeled as interval uncertainties fluctuating within allowable tolerance bounds. The optimization model is defined as to minimize the total manufacturing cost under mixed reliability index constraints, which are further transformed into their equivalent formulations by using the performance measure approach. The optimization problem is then solved with the sequential approximate programming. Meanwhile, a numerically stable algorithm based on the trust region method is proposed to efficiently update the target performance points (TPPs) and the worst case points (WCPs), which shows better performance than traditional approaches for highly nonlinear problems. Numerical results reveal that reasonable dimensions and tolerances can be suggested for the minimum manufacturing cost and a desirable structural safety.