Extremum Response Surface Method Research Articles

Multi-Extremum Adaptive Fuzzy Network Method for Dynamic Reliability Estimation Method of Vectoring Exhaust Nozzle

To enhance the accuracy and efficiency of reliability analysis for an aero-engine vectoring exhaust nozzle (VEN), a multi-extremum adaptive fuzzy network (MEAFN) method is developed by absorbing an adaptive neuro-fuzzy inference system (ANFIS) into the multi-extremum surrogate model (MESM) method. In the proposed method, the MERSM is used to establish the surrogate models of many output responses for the multi-objective integrated reliability analysis of the VEN. The ANFIS method is regarded as the basis function of the MESM method and adopted to improve the modeling precision of the MESM by introducing the membership degree into the input parameters and weights to improve the approximation capability of the neural network model to the high nonlinear reliability analysis of the VEN. The mathematical model of the MEAFN method and reliability analysis thoughts of the VEN is provided in this study. Then, the proposed MEAFN method is applied to conduct the dynamic reliability analysis of the expansion sheet and the triangular connecting rod in the VEN by considering the aerodynamic loads, operation temperature, and material parameters as the random input variables and the stresses and deformations as the output responses, compared with the Monte Carlo method and the extremum response surface method. From the comparison of the methods, it is indicated that the MEAFN method is promising to improve computational efficiency while maintaining accuracy. The efforts of this study provide guidance for the optimization design of the VEN and enrich the reliability theory of the flexible mechanism.

Operational reliability evaluation and analysis framework of civil aircraft complex system based on intelligent extremum machine learning model

To reasonably implement the operational reliability analysis and describe the importance of the influencing parameters for the operation status, a framework for operational reliability evaluation and analysis is proposed. First, an operational reliability evaluation model (OREM) is established based on the data envelopment analysis (DEA) method, which takes quick access recorder (QAR)data as input to comprehensively evaluate the operational characteristics of complex systems to obtain the operational reliability Pr. Then, to enhance the modeling efficiency and simulation performance for the operational reliability analysis of the complex system, we propose an intelligent extremum machine learning model (IEMLM), by integrating extremum response surface method (ERSM), artificial neural network (ANN), improved particle swarm optimization (PSO) algorithm, and Bayesian regularization (BR) algorithm. The operational reliability analysis of a braking system of a civil aircraft is conducted to validate the effectiveness and feasibility of this developed method, by considering the comprehensive influence of system-environment-human. The comparison of IEMLM, RF, and ANN shows that IEMLM improves the analysis accuracy and calculation efficiency. The proposed framework and models can provide useful references for civil aircraft operational reliability analysis, special situation treatment, maintenance, and design.

Intelligent moving extremum weighted surrogate modeling framework for dynamic reliability estimation of complex structures

To improve the dynamic reliability analyses of complex structures, intelligent weighted Kriging-based moving extremum framework (IWKMEF) is developed by absorbing moving least squares (MLS) thought, Gaussian weight, particle swarm optimization (PSO) method and Kriging model into extremum response surface method (ERSM). ERSM method is employed to convert the dynamic output response into extremum values. MLS thought is used to find effective samples. Gaussian weight is to improve modeling precision. PSO method is applied to optimize the local compact support region radius of MLS. The radial deformation of turbine blisk is conducted to verify the effectiveness of IWKMEF method. The results show that the reliability degree of turbine blisk is 0.9984 when the allowable value is 1.9217 × 10−3 m; The developed IWKMEF holds high performance by comparing direct simulation, ERSM and traditional Kriging model. The efforts of this study provide a useful insight for the dynamic reliability analysis of complex structure.

Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

To improve the transient reliability analysis of complex structures, dimensionality reduction (DR)-based extremum surrogate modeling strategy (DRESMS) is developed by absorbing the strengths of DR strategy and extremum response surface method (ERSM). In the proposed method, the DR is applied to find the embedding mapping the input data to high-dimensional space which has the potential to improve the transient reliability model, and the ERSM is used to build the regression relationship between input parameters and output response to establish a reliable surrogate model based on capturing dynamic extreme moments. The transient reliability analysis of turbine blisk is performed to verify the approximate accuracy and simulation performance of the proposed DRESMS with the assist of the comparison of methods. As seen in this study, (i) the reliability degree of turbine blisk fatigue life is 0.9939 when the allowable value of fatigue life is 1.7738×103 cycles (subject to 3 sigma levels), and (ii) the developed DRESMS holds advantages of high-modeling efficiency and low-fitting error, and (iii) the DRESMS holds excellent simulation efficiency and simulation precision. The efforts of this study provide the promising DRESMS to solve the transient probabilistic analysis of complex structures with multi-dimensional input parameters, which is significant in monitoring and maintaining complex structures and mechanical systems with the consideration of large-scale parameters.

Intelligent Extremum Surrogate Modeling Framework for Dynamic Probabilistic Analysis of Complex Mechanism

The reliability analysis of complex mechanisms involves time-varying, high-nonlinearity, and multiparameters. The traditional way is to employ Monte Carlo (MC) simulation to achieve the reliability level, but this method consumes too much computing resources and is even computationally intractable. To improve the efficiency and accuracy of dynamic probabilistic analysis of complex mechanisms, an intelligent extremum surrogate modeling framework (IESMF, short for) is proposed based on extremum response surface method (ERSM), combined with artificial neural network (ANN) method and an improved optimize particle swarm optimization (PSO) method. Hereinto, the ERSM is used to simplify the dynamic process of output response to the extremum value of transient analysis; ANN is applied to establish a mathematical model between input variables and response, and the improved PSO method is utilized in search of initial weights and thresholds of the model. The effectiveness of the IESMF is demonstrated to perform the Rack-and-pinion steering mechanism (RPSM) reliability analysis. The results show that when the allowable value of gear root stress is equal to 850 MPa, the RPSM has a reliability degree of 0.9971. Through the validation process, it is illustrated that IESMF is accurate and efficient in dynamic probabilistic analysis of complex mechanisms, and its comprehensive performance is better than the MC method and ERSM. The research effort offers new ideas for the reliability estimation of a complex mechanism, thus enriching the method and theory of mechanical reliability design.

Enhanced network learning model with intelligent operator for the motion reliability evaluation of flexible mechanism

The evaluation of flexible mechanism involving multi-body dynamics with high nonlinearity and transients urgently requires an efficient evaluation method to enhance its reliability and safety. In this work, an enhanced network learning method (ENLM) is proposed to improve the modeling precision and simulation efficiency in flexible mechanism reliability evaluation, by introducing generalized regression neural network (GRNN) and multi-population genetic algorithm (MPGA) into extremum response surface method (ERSM). In the ENLM modeling, the ERSM is adopted to reasonably handle transients (time-varying) problem in motion reliability analysis by considering one extreme value in whole response process; the GRNN is applied to address high-nonlinearity in surrogate modeling; the MPGA is utilized to find the optimal model parameters in ENLM modeling. In respect of the developed ENLM, the motion reliability of two-link flexible robot manipulator (TFRM) was evaluated, with regard to the related input random parameters to material density, elastic modulus, section sizes, and deformations of components. In term of this study, it is illustrated that (i) the comprehensive reliability of flexible robot manipulator is 0.951 when the allowable deformation is 1.8×10−2 m; (ii) the maximum deformations of member-1 and member-2 obey normal distributions with the means of 1.45×10−2 m and 1.69×10−2 m as well as the standard variances of 6.77×10−4 m and 4.08×10−4 m, respectively. The comparison of methods demonstrates that the ENLM improves the modeling precision by 3.29% and reduces the simulation efficiency by 1.19 s under 10000 simulations, and the strengths of the ENLM with high modeling precision and high simulation efficiency become more obvious with the increase of simulations. The efforts of this study provide a learning-based reliability analysis way (i.e., ENLM) for the motion reliability design optimization of flexible mechanism and enrich mechanical reliability theory.

Structural dynamic probabilistic evaluation using a surrogate model and genetic algorithm

To improve the computational accuracy and efficiency of dynamic probabilistic analysis of complex structures, an extremum Kriging method (EKM) with multi-population genetic algorithm (MPGA) is proposed fusing extremum response surface method (ERSM), Kriging model and MPGA. Particularly, the EKM is developed by combining the Kriging model and ERSM to handle dynamic processes of related variables and to reduce computational burden by regarding the extreme value of response process in each dynamic analysis within the time domain. The MPGA is used to replace gradient decent to find the hyperparameter θ in the Kriging model by solving the maximum-likelihood equation. The effectiveness of the proposed method was validated by performing the dynamic probabilistic analysis of an aeroengine high-pressure compressor blisk radial running deformation with fluid-thermal-structural interaction. The analytical results illustrate that the reliability degree of the blisk is 0·9956 under the allowable value uallow = 1·75 × 10−3 m, and gas temperature is the leading factor against output response, followed by rotational speed, inlet velocity, material density and outlet pressure. Moreover, the developed MPGA-EKM is superior to other methods in computational accuracy and efficiency. The efforts of this study provide a useful insight to design complex structures and enrich mechanical reliability theory.

Improved Decomposed-Coordinated Kriging Modeling Strategy for Dynamic Probabilistic Analysis of Multicomponent Structures

The probabilistic design of complex structure usually involves the features of numerous components, multiple disciplines, nonlinearity, and transients and, thus, requires lots of simulations as well. To enhance the modeling efficiency and simulation performance for the dynamic probabilistic analysis of the multicomponent structure, we propose an improved decomposed-coordinated Kriging modeling strategy (IDCKMS), by integrating decomposed-coordinated (DC) strategy, extremum response surface method (ERSM), genetic algorithm (GA), and Kriging surrogate model. The GA is used to resolve the maximum-likelihood equation and achieve the optimal values of the Kriging hyperparameter θ . The ERSM is utilized to resolve the response process of outputs in surrogate modeling by extracting the extremum values. The DC strategy is used to coordinate the output responses of analytical objectives. The probabilistic analysis of an aeroengine high-pressure turbine blisk with blade and disk is conducted to validate the effectiveness and feasibility of this developed method, by considering the fluid–thermal–structural interaction. In respect of this investigation, we see that the reliability of turbine blisk is 0.9976 as the allowable value of radial deformation is 2.319 × 10−3 m. In terms of the sensitivity analysis, the highest impact on turbine blisk radial deformation is of gas temperature, followed by angular speed, inlet velocity, material density, outlet pressure, and inlet pressure. By the comparison of methods, including the DC surrogate modeling method (DCSMM) with quadratic polynomial, the DCSMM with Kriging, and the direct simulation with finite-element model, from the model-fitting features and simulation performance perspectives, we discover that the developed IDCKMS is superior to the other three methods in the precision and efficiency of modeling and simulation. The efforts of this article provide a highly efficient and highly accurate technique for the dynamic probabilistic analysis of complex structure and enrich reliability theory.

Probabilistic Fatigue/Creep Optimization of Turbine Bladed Disk with Fuzzy Multi-Extremum Response Surface Method.

To effectively perform the probabilistic fatigue/creep coupling optimization of a turbine bladed disk, this paper develops the fuzzy multi-extremum response surface method (FMERSM) for the comprehensive probabilistic optimization of multi-failure/multi-component structures, which absorbs the ideas of the extremum response surface method, hierarchical strategy, and fuzzy theory. We studied the approaches of FMERSM modeling and fatigue/creep damage evaluation of turbine bladed disks, and gave the procedure for the fuzzy probabilistic fatigue/creep optimization of a multi-component structure with FMERSM. The probabilistic fatigue/creep coupling optimization of turbine bladed disks was implemented by regarding the rotor speed, temperature, and density as optimization parameters; the creep stress, creep strain, fatigue damage, and creep damage as optimization objectives; and the reliability and GH4133B fatigue/creep damages as constraint functions. The results show that gas temperature T and rotor speed ω are the key parameters that should be controlled in bladed disk optimization, and respectively reduce by 85 K and 113 rad/s after optimization, which is promising to extend bladed disk life and decrease failure damages. The simulation results show that this method has a higher modeling accuracy and computational efficiency than the Monte Carlo method (MCM). The efforts of this study provide a new useful method for overall probabilistic multi-failure optimization and enrich mechanical reliability theory.

Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis

The parameters considered in structural dynamic reliability analysis have strong uncertainties during machinery operation, and affect analytical precision and efficiency. To improve structural dynamic fuzzy reliability analysis, we propose the weighted regression-based extremum response surface method (WR-ERSM) based on extremum response surface method (ERSM) and weighted regression (WR), by considering the randomness of design parameters and the fuzziness of the safety criterion. Therein, we utilize the ERSM to process the transient to improve computational efficiency, by transforming the random process of structural output response into a random variable. We employ the WR to find the efficient samples with larger weights to improve the calculative accuracy. The fuzziness of the safety criterion is regarded to improve computational precision in the WR-ERSM. The WR-ERSM is applied to perform the dynamic fuzzy reliability analysis of an aeroengine turbine blisk with the fluid-structure coupling technique, and is verified by the comparison of the Monte Carlo (MC) method, equivalent stochastic transformation method (ESTM) and ERSM, with the emphasis on model-fitting property and simulation performance. As revealed from this investigation, (1) the ERSM has the capacity of processing the transient of the structural dynamic reliability evaluation, and (2) the WR approach is able to improve modeling accuracy, and (3) regarding the fuzzy safety criterion is promising to improve the precision of structural dynamic fuzzy reliability evaluation, and (4) the change rule of turbine blisk structural stress from start to cruise for the aircraft is acquired with the maximum value of structural stress at t = 165 s and the reliability degree (Pr = 0.997) of turbine blisk. The proposed WR-ERSM can improve the efficiency and precision of structural dynamic reliability analysis. Therefore, the efforts of this study provide a promising method for structural dynamic reliability evaluation with respect to working processes.

Decomposed-Coordinated Framework With Enhanced Extremum Kriging for Multicomponent Dynamic Probabilistic Failure Analyses

For multicomponent structures enduring dynamic workloads coming from multi-physical fields, safety assessment is significant to guarantee the normal operation of entire structure system. In this paper, an enhanced extremum Kriging-based decomposed coordinated framework (E2K-DCF) is proposed to improve the dynamic probabilistic failure analyses of multicomponent structures. In this method, extremum Kriging model (EKM) is developed by introducing Kriging model into extremum response surface method (ERSM) to process the transient response problem and shorten computational burden in dynamic probabilistic failure analyses. Multiple population genetic algorithm (MPGA) is employed to solve maximum likelihood equation (MLE) and find the optimal hyperparameter $\boldsymbol \theta $ in the EKM, which is promising to enhance approximate accuracy; decomposed-coordinated (DC) strategy is used to handle the coordinated relationship of multiple analytical objectives. To validate the proposed E2K-DCF, the probabilistic failure analysis of turbine blisk radial deformation is conducted by comparing with different methods within time domain [0 s, 215 s], considering fluid-thermal-structural interaction. It is revealed that the failure probability of blisk radial deformation is only 0.0022 when the allowable value is $2.5702\times 10^{-3}$ m acquired from real world practice. Compared to the other approaches, this E2K-DCF has obvious advantages in fitting time and accuracy as well as simulation efficiency and accuracy. The results illustrate that the E2K-DCF is effective and applicable in dynamic probabilistic failure analysis. The efforts of this paper provide a novel viewpoint for the transient reliability evaluation of multicomponent structures, which is likely to enrich mechanical reliability theory.

Transient probabilistic design of flexible multibody system using a dynamic fuzzy neural network method with distributed collaborative strategy

To improve the efficiency and accuracy of transient probabilistic analysis of flexible multibody systems, a dynamic fuzzy neural network method-based distributed collaborative strategy is proposed by integrating extremum response surface method and fuzzy neural network. Distributed collaborative dynamic fuzzy neural network method is mathematically modeled and derived by considering the high nonlinearity, strong coupling, and multicomponent characteristics of a flexible multibody system. The proposed method is demonstrated to perform the transient probabilistic analysis of a two-link flexible robot manipulator. We obtain the distributional characteristics, reliability degree, and sensitivity degree of robot manipulator, which are useful for the effective design of robot manipulator. By comparing the full-scale method, extremum response surface method, dynamic fuzzy neural network method, and distributed collaborative dynamic fuzzy neural network method, we find that the distributed collaborative dynamic fuzzy neural network method can be used to perform the transient probabilistic analysis of the robot manipulator and improve the computational efficiency while maintaining a good accuracy. Moreover, this study offers a useful insight for the reliability-based design optimization of flexible multibody systems, and enriches the field of mechanical reliability theory as well.

Dynamic Reliability Design of Multicomponent Structure with Improved Weighted Regression Distributed Collaborative Surrogate Model Method

For dynamic reliability design of complex structures with multiple components, an improved weighted regression distributed collaborative surrogate model method (IWRDCSMM) is developed from the extremum response surface method (ERSM), decomposed-coordinated thought, and improved weighted regression principle. The ERSM is used to address the dynamic reliability and sensitivity analyses of multicomponent structures and enhance the computing efficiency. The decomposed-coordinated thought is applied to handle the relationship among multiple components. The improved weighted regression method is used to find the efficient samples with smaller errors to improve the modeling accuracy. The proposed method is first introduced for dynamic probabilistic analysis (including reliability analysis and sensitivity analysis) of multicomponent structures. The method is then mathematically modeled by adopting the efficient samples selected based on the improved weighted regression method. Finally, the radial deformation dynamic probabilistic analysis of an aeroengine turbine blisk assembled by blade and disk is accomplished, in respect of the IWRDCSMM, fluid-thermal-structure interaction, and the randomness of input parameters within the time domain [0, T]. The results illustrate that the reliability degree of turbine blisk radial deformation is 0.9951 when the allowable value uallow is 2.30 × 10−3 m, and all the input parameters affecting the turbine blisk radial deformation are gas temperature, angular speed, inlet velocity, outlet pressure, material density, and inlet pressure, successively. As revealed by the comparison of different methods, the IWRDCSMM has high fitting speed and simulation efficiency with the guarantee of accuracy. The efforts of this study provide a promising dynamic probabilistic analysis technique for complex structures with multiple components and enrich mechanical reliability theory.

Improved Kriging with extremum response surface method for structural dynamic reliability and sensitivity analyses

The safety and reliability of any complex mechanical structures are critical to ensure that they can function properly. Therefore, we need to thoroughly evaluate their reliability by performing dynamic probabilistic analyses, including the reliability and sensitivity analyses, which take the variation in the input variables into consideration. The typical approach is by performing the Monte Carlo (MC) simulation, which requires thousands of runs and could be computationally intractable. An efficient and accurate surrogate model can help reduce the computational burden in these analyses. To further reduce the computational complexity, we model only the extremum values, instead of modeling all the output responses within the time domain of interest. The developed surrogate model is called the improved Kriging (IK) algorithm with extremum response surface method (ERSM), or the IK-ERSM model. Compared to the previously developed QP-ERSM, which uses the quadratic polynomial (QP) model, the improved Kriging can better model the nonlinearity within the system. To build the IK model, we employ the genetic algorithm (GA) method to find the Kriging hyperparameters θ, by solving the maximum likelihood equation (MLE). This model shows a good accuracy, with a testing error of less than 1%. The effectiveness of the developed IK-ERSM model is demonstrated to perform the reliability and sensitivity analyses of the compressor blisk radial deformation. For the direct simulation, we consider the fluid–structure coupling of the system, for a more realistic analysis. The results show that the compressor blisk has a reliability degree of 0.9984 when the allowable value of the compressor blisk radial deformation is 1.60×10−3 m. From the sensitivity analysis results, we identify that the angular speed has the highest impact on the output response, followed by the inlet velocity and material density. Through the validation process, we see that the developed IK-ERSM model has a better overall performance than the QP-ERSM and K-ERSM models, in terms of the fitting times and testing errors. With these results, the IK-ERSM is demonstrated to be efficient and accurate in structural dynamic probabilistic analysis. This study provide a useful insight for the dynamic probabilistic design of complex structure and enrich mechanical reliability theory.

Reliability analysis of blade fatigue life based on fuzzy intelligent multiple extremum response surface method

In order to more reasonable analyze the dynamic reliability of aero-engine blade with coupling failure mode. A fuzzy intelligent multiple extremum response surface method (FIMERSM) was proposed. Considering the coupling effect of temperature load and centrifugal load, the maximum stress point, the maximum strain point and the minimum life point on blade were found by deterministic analysis. Then, the density of blade, rotor speed, elastic modulus, blade-tip temperature, blade-root temperature, fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, fatigue ductility exponent, blade width, blade thickness, blade torsion angle, and blade height as input random variables. By using Latin hypercube sampling technique, the sample values of the input random variables were acquired and finite element basic equation was calculated for each samples which obtained the corresponding dynamic output response of their stress, strain, and low cycle fatigue life within the analysis time domain. By taking the entire maximum values of the dynamic output response in the analysis time domain as new output response, the fuzzy intelligent multiple extremum response surface function (FIMERSF) was established. Finally, the dynamic reliability of the blade structure were obtained by using the Monte Carlo method (MCM) large amount linkage sampling of the input random variables and take it into the FIMERSF to calculate the output response. The results imply that the comprehensive reliability of blade is 99.46%. Through the comparison of MCM, Multiple extremum response surface method (MERSM) and FIMERSM, the computational results show that the FIMERSM has high computational precision and computational efficiency.

Dynamic neural network method-based improved PSO and BR algorithms for transient probabilistic analysis of flexible mechanism

To improve the computing efficiency and precision of transient probabilistic analysis of flexible mechanism, dynamic neural network method (DNNM)-based improved particle swarm optimization (PSO)/Bayesian regularization (BR) (called as PSO/BR-DNNM) is proposed based on the developed DNNM with the integration of extremum response surface method (ERSM) and artificial neural network (ANN). The mathematical model of DNNM is established based on ANN on the foundation of investigating ERSM. Aiming at the high nonlinearity and strong coupling characteristics of limit state function of flexible mechanism, accurate weights and thresholds of PSO/BR-DNNM function are discussed by searching initial weights and thresholds based on the improved PSO and training final weights and thresholds by the BR-based training performance function. The probabilistic analysis of two-link flexible robot manipulator (TFRM) was investigated with the proposed method. Reliability degree, distribution characteristics and major factors (section sizes of link-2) of TFRM are obtained, which provides a useful reference for a more effective TFRM design. Through the comparison of three methods (Monte Carlo method, DNNM, PSO/BR-DNNM), it is demonstrated that PSO/BR-DNNM reshapes the probability of flexible mechanism probabilistic analysis and improves the computing efficiency while keeping acceptable computational precision. Moreover, the proposed method offers a useful insight for reliability-based design optimization of flexible mechanism and thereby also enriches the theory and method of mechanical reliability design.

Advanced Extremum Response Surface Method for Dynamic Reliability Analysis on Flexible Mechanism

Advanced Extremum Response Surface Method for Dynamic Reliability Analysis on Flexible Mechanism

Application of Probabilistic and Nonprobabilistic Hybrid Reliability Analysis Based on Dynamic Substructural Extremum Response Surface Decoupling Method for a Blisk of the Aeroengine

For the nondeterministic factors of an aeroengine blisk, including both factors with sufficient and insufficient statistical data, based on the dynamic substructural method of determinate analysis, the extremum response surface method of probabilistic analysis, and the interval method of nonprobabilistic analysis, a methodology called the probabilistic and nonprobabilistic hybrid reliability analysis based on dynamic substructural extremum response surface decoupling method (P-NP-HRA-DS-ERSDM) is proposed. The model includes random variables and interval variables to determine the interval failure probability and the interval reliability index. The extremum response surface function and its flow chart of mixed reliability analysis are given. The interval analysis is embedded in the most likely failure point in the iterative process. The probabilistic analysis and nonprobabilistic analysis are investigated alternately. Tuned and mistuned blisks are studied in a complicated environment, and the results are compared with the Monte Carlo method (MCM) and the multilevel nested algorithm (MLNA) to verify that the hybrid model can better handle reliability problems concurrently containing random variables and interval variables; meanwhile, it manifests that the computational efficiency of this method is superior and more reasonable for analysing and designing a mistuned blisk. Therefore, this methodology has very important practical significance.

Reliability-based design optimization for flexible mechanism with particle swarm optimization and advanced extremum response surface method

To improve the computational efficiency of the reliability-based design optimization (RBDO) of flexible mechanism, particle swarm optimization-advanced extremum response surface method (PSO-AERSM) was proposed by integrating particle swarm optimization (PSO) algorithm and advanced extremum response surface method (AERSM). Firstly, the AERSM was developed and its mathematical model was established based on artificial neural network, and the PSO algorithm was investigated. And then the RBDO model of flexible mechanism was presented based on AERSM and PSO. Finally, regarding cross-sectional area as design variable, the reliability optimization of flexible mechanism was implemented subject to reliability degree and uncertainties based on the proposed approach. The optimization results show that the cross-section sizes obviously reduce by 22.96 mm2 while keeping reliability degree. Through the comparison of methods, it is demonstrated that the AERSM holds high computational efficiency while keeping computational precision for the RBDO of flexible mechanism, and PSO algorithm minimizes the response of the objective function. The efforts of this work provide a useful sight for the reliability optimization of flexible mechanism, and enrich and develop the reliability theory as well.

Transient reliability optimization for turbine disk radial deformation

The radial deformation design of turbine disk seriously influences the control of gas turbine high pressure turbine (HPT) blade-tip radial running clearance (BTRRC). To improve the design of BTRRC under continuous operation, the nonlinear dynamic reliability optimization of disk radial deformation was implemented based on extremum response surface method (ERSM), including ERSM-based quadratic function (QF-ERSM) and ERSM-based support vector machine of regression (SR-ERSM). The mathematical models of the two methods were established and the framework of reliability-based dynamic design optimization was developed. The numerical experiments demonstrate that the proposed optimization methods have the promising potential in reducing additional design samples and improving computational efficiency with acceptable precision, in which the SR-ERSM emerges more obviously. Through the case study, we find that disk radial deformation is reduced by about 6.5×10–5 m; δ=1.31×10–3 m is optimal for turbine disk radial deformation design and the proposed methods are verified again. The presented efforts provide an effective optimization method for the nonlinear transient design of motion structures for further research, and enrich mechanical reliability design theory.