Support vector machines-based pre-calculation error for structural reliability analysis

• Published in: Engineering with computers Vol. 40; no. 1; pp. 477 - 491
• Main Authors: Chen, Jun-Yu, Feng, Yun-Wen, Teng, Da, Lu, Cheng
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2024; Springer Nature B.V
• Subjects: Accuracy; Blisks; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Constraint modelling; Control; Cylinders; Deformation; Efficiency; Error analysis; Lagrange multiplier; Landing gear; Math. Applications in Chemistry; Mathematical and Computational Engineering; Original Article; Reliability analysis; Reliability engineering; Slack variables; Structural reliability; Struts; Support vector machines; Systems Theory; Turbines; Reliability analysis; Support vector machine; Pre-calculation error; Complex structures; Constrains conversion
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-023-01803-0

For enhancing the efficiency and accuracy of structural reliability estimation, a support vector machine-based pre-calculation error (PESVM) is proposed by integrating support vector machine (SVM), constraints conversion, and pre-calculation error (PE). Based on SVM modeling theory, the constraints conversion is applied to transform the original inequality constraints into equality constraints, contributing to the simplification of solving Lagrange multipliers and the improvement of computational efficiency. To eliminate the effects of abnormal values, PE is introduced to act as slack variables that adaptively prescribe the degree of model margin violation, which is workable to improve the calculation precision. Two study cases containing nose landing gear shock strut outer cylinder stress and turbine blisk radial deformation are applied to train the PESVM models and verify their performances compared with other reliability analysis methods. The results show that (i) the PESVM holds highest modeling efficiency and precision among the three methods; (ii) the PESVM shows superior performance than Kriging and SVM in simulation speed and accuracy; (iii) the reliability degrees of two study cases are 0.9973 (shock strut outer cylinder stress) and 0.9975 (turbine blisk radial deformation) when the allowable values 1.4968 × 10 9  Pa and 1.8892 × 10 –3  m subject to 3 σ principle; (iv) the PESVM takes on preferably strong robustness in modeling and simulation. The PESVM method is validated to be applicable and efficient for structural reliability analysis. The contribution of this paper is helpful for providing a promising inspiration for structural reliability evaluation.