Harbitz A (1986) An efficient sampling method for probability of failure calculation. Jensen HA, Mayorga F, Valdebenito MA (2015) Reliability sensitivity estimation of nonlinear structural systems under stochastic excitation: a simulation-based approach. Zhang DQ, Zhang N, Ye N et al (2021) Hybrid learning algorithm of radial basis function networks for reliability analysis. Lu C, Fei CW, Feng YW et al (2021) Probabilistic analysis of structural dynamic response with modified Kriging based on moving extremum framework. The contribution of this paper is helpful for providing a promising inspiration for structural reliability evaluation. The PESVM method is validated to be applicable and efficient for structural reliability analysis. 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. 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. 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. 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. The reading of thesis will elaborate upon the approaches used to achieve these results.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). The research task of the thesis has achieved three types of results: knowledge gained about the challenges in the manufacturing of blisk arising due to innovations in its design that are necessary to achieve the objectives of sustainable aviation, techniques developed for improved planning for manufacturing through the analyze of blisk geometry that determines the total volume of material to be machined and material remaining after roughing and finish machining (before the detailed process planning could start), and design and development of software tools to further automate the process planning for manufacturing blisks. Accordingly, blisk channel and milling process are the two defined boundaries to carry out the research tasks during the thesis. Milling process is most widely used process for manufacturing blisk channel. The analysis of current situation in blisk development also indicates that most cost during production is involved in manufacturing blisk channel. The defined method is specified and evaluated through a graphic model in analogy to blisk channel and afterwards its implementation into a computer solution is used for testing and evaluation of real blisk geometries. The research tasks of this thesis targets this difficult situation by analyzing the current situation in blisk development and defining methods for the evaluation of blisk geometry in order to determine early during blisk design and development, the most suitable process conditions. The requirement to bring innovation approaches into manufacturing planning of blisk has been realized accordingly, in the thesis the methods that handle this complexity in design and provide meaningful data and information to develop an effective process plan are discussed and demonstrated. The need to innovate the system of manufacturing process planning which makes possible to produce large number of blisks in diverse shapes at lower cost is intense. The current practice in process planning will never cope with the increasing number of blisk designs and higher volume for their production. All this complexity of design is a challenge for manufacturers and at the end effect the task to be handled by an expert manufacturing process planner. The objectives of developing light weight aero engines for achieving sustainable and economical aviation are meet by using blisks with smaller diameter, reduced blade pitch and airfoils that have longer profile sections and are more curved, twisted and bowed.
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