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1. A Safety Factor Method for Reliability-Based Component Design

   https://doi.org/10.1115/1.4049881  

   Yin, Jianhua; Du, Xiaoping (September 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract Reliability-based design (RBD) employs optimization to identify design variables that satisfy the reliability requirement. For many routine component design jobs that do not need optimization, however, RBD may not be applicable, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a modified RBD approach to component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the first-order reliability method (FORM), which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method. 

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2. High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

   https://doi.org/10.1115/1.4051982  

   Yin, Jianhua; Du, Xiaoping (April 2022, Journal of Mechanical Design)

   Abstract Reliability analysis is a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high-dimensional reliability analysis method through a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated after dimension reduction. Dimension reduction is performed with the first iteration of the first-order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 

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3. High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

   https://doi.org/10.1115/DETC2021-70067  

   Yin, Jianhua; Du, Xiaoping (August 2021, Proceedings of the ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference)

   Abstract Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 

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4. A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

   https://doi.org/10.1115/1.4045299  

   Cui, Tonghui; Allison, James T.; Wang, Pingfeng (March 2020, Journal of Mechanical Design)

   While integrated physical and control system co-design has been demonstrated successfully on several engineering system design applications, it has been primarily applied in a deterministic manner without considering uncertainties. An opportunity exists to study non-deterministic co-design strategies, taking into account various uncertainties in an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to ensure an optimized system design being obtained that satisfies all reliability constraints considering particular system uncertainties. While significant advancements have been made in co-design and RBDO separately, little is known about methods where reliability-based dynamic system design and control design optimization are considered jointly. In this article, a comparative study of the formulations and algorithms for reliability-based co-design is conducted, where the co-design problem is integrated with the RBDO framework to yield solutions consisting of an optimal system design and the corresponding control trajectory that satisfy all reliability constraints in the presence of parameter uncertainties. The presented study aims to lay the groundwork for the reliability-based co-design problem by providing a comparison of potential design formulations and problem–solving strategies. Specific problem formulations and probability analysis algorithms are compared using two numerical examples. In addition, the practical efficacy of the reliability-based co-design methodology is demonstrated via a horizontal-axis wind turbine structure and control design problem. 

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5. A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

   https://doi.org/10.1115/DETC2019-98307  

   Cui, Tonghui; Allison, James T.; Wang, Pingfeng (August 2019, American Society of Mechanical Engineers)

   Co-design, or integrated physical and control system design, has been demonstrated successfully for several engineering system design optimization applications, primarily in a deterministic manner. An opportunity exists to study non-deterministic co-design strategies, including incorporation of uncertainty-induced failures, into an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to increase the likelihood of having a feasible design that satisfies all reliability constraints. While significant recent advancements have been made in co-design and RBDO separately, limited work has been done where reliability-based dynamic system design and control design optimization are considered jointly. In this paper, the co-design problem is integrated with the RBDO framework to yield a system-optimal design and the corresponding control trajectory, which satisfy all reliability constraints in the presence of parameter variations. Different problem formulations and RBDO algorithms are compared through numerical examples. The design of a horizontal-axis wind turbine (HAWT) supported by a lattice tower (with parameter uncertainties) is presented to demonstrate the applicability of the proposed method. 

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