Abstract
For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The mathematical formulae for calculating the feasibility and objective robustness indices and the robustness-based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high-speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.
Highlights
The uncertainties in material properties, geometric dimensions, load conditions and so on are ubiquitous for engineering structures [1]
To avoid the limitations of indirect algorithms for solving interval optimization models, we have proposed a direct interval optimization algorithm for uncertain structures by introducing the concept of the degree of interval constraint violation (DICV) [27] based on Hu’s “center first halfwidth ” interval order relation [28]
It is obvious that both constraints in Eq (13) are fully satisfied at xo and the feasibility robustness is improved after optimization
Summary
The uncertainties in material properties, geometric dimensions, load conditions and so on are ubiquitous for engineering structures [1]. Martínez–Frutos et al [16] proposed a robust shape optimization approach of continuous structures via the level set method, which modeled the uncertainty in loads and material as random variables with different probability distributions as well as random fields It is often difficult or computationally expensive to determine the probabilistic distributions of uncertain factors in many engineering problems [17]. Li et al [24] proposed an actuator placement robust optimization method for active vibration control system with interval parameters Both nominal value and radius of the performance index were considered in the interval optimization model, which was transformed into a deterministic one by weighted processing and solved by GA. The design vectors of an uncertain structure are sorted according to the robustness-based preferential guidelines, which is realized by integrating the Kriging technique and nested GA
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