Reliability- and possibility-based design optimization using inverse analysis methods

Deterministic optimum designs are pushed to design constraint boundaries using multidisciplinary design optimization techniques, leaving little or no room for manufacturing and operating tolerances. Consequently, deterministic optimum designs obtained without considering uncertainties in manufacturing and operating processes could lead to unreliable designs, which necessitate the development and implementation of design optimization methodologies that account input uncertainties.;The design optimization problem that accounts aleatory uncertainty is formulated as Reliability-Based Design Optimization (RBDO). Using the Performance Measure Approach (PMA), the inverse reliability analysis of probabilistic constraints, which can be solved using the Hybrid Mean Value (HMV) method, converts the RBDO problem into a deterministic optimization problem. However, for some highly nonlinear or nonmonotone performance functions, HMV exhibits a slow rate of convergence or even divergence. This study proposes an enriched Hybrid Mean Value (HMV+) method to overcome this disadvantage.;The design optimization problem that accounts epistemic uncertainty is formulated as Possibility-Based Design Optimization (PBDO). Like RBDO, PMA is applicable to PBDO problems, where the inverse possibility analysis of possibilistic constraints, which is the same as the conventional alpha-cut approach, converts the PBDO problem into a deterministic optimization problem. For a numerical method for the inverse possibility analysis, a new Maximal Possibility Search (MPS) method is proposed in this study to overcome the inaccuracy of the vertex method and the computational cost of the multilevel alpha-cut method.;In many industry design problems, we may have to deal with the input statistical random and fuzzy variables simultaneously when there exist both uncertainties with respect to both sufficient and insufficient data. Based on the probability and possibility theories, this study proposes a new Mixed Variable Design Optimization (MVDO) formulation to account both random and fuzzy input variables. To solve the inverse analysis problem of MVDO, this research proposes a new maximal failure search (MFS) method by integrating the enhanced hybrid mean value (HMV+) method and the maximal possibility search (MPS) method. Several mathematical and practical engineering examples are solved to illustrate effectiveness of the proposed PMA-based RBDO, PBDO, and MVDO methods using Hybrid Mean Value (HMV+), NIPS, and MFS algorithms, respectively.