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

   https://doi.org/10.1115/DETC2020-22030  

   Yin, Jianhua; Du, Xiaoping (August 2020, doi.org/10.1115/DETC2020-22030)

   null (Ed.)

   Abstract Reliability-based design (RBD) identifies design variables that maintain reliability at a required level. For many routine component design jobs, RBD may not be practical as it requires nonlinear optimization and specific reliability methods, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a practical approach to reliability-based 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, which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to a number of 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 it 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/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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5. Probabilistic Feasibility Design of a Laser Powder Bed Fusion Process Using Integrated First-Order Reliability and Monte Carlo Methods

   https://doi.org/10.1115/1.4050544  

   Meng, Lingbin; Du, Xiaoping; McWilliams, Brandon; Zhang, Jing (September 2021, Journal of Manufacturing Science and Engineering)

   null (Ed.)

   Abstract Quality inconsistency due to uncertainty hinders the extensive applications of a laser powder bed fusion (L-PBF) additive manufacturing process. To address this issue, this study proposes a new and efficient probabilistic method for the reliability analysis and design of the L-PBF process. The method determines a feasible region of the design space for given design requirements at specified reliability levels. If a design point falls into the feasible region, the design requirement will be satisfied with a probability higher or equal to the specified reliability. Since the problem involves the inverse reliability analysis that requires calling the direct reliability analysis repeatedly, directly using Monte Carlo simulation (MCS) is computationally intractable, especially for a high reliability requirement. In this work, a new algorithm is developed to combine MCS and the first-order reliability method (FORM). The algorithm finds the initial feasible region quickly by FORM and then updates it with higher accuracy by MCS. The method is applied to several case studies, where the normalized enthalpy criterion is used as a design requirement. The feasible regions of the normalized enthalpy criterion are obtained as contours with respect to the laser power and laser scan speed at different reliability levels, accounting for uncertainty in seven processing and material parameters. The results show that the proposed method dramatically alleviates the computational cost while maintaining high accuracy. This work provides a guidance for the process design with required reliability. 

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