Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Reliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.     

On efficient computational schemes to calculate structural failure probabilities

Various methods to calculate structural failure probability are compared in the light of their efficiency and accuracy. The investigation is confined to procedures which provide error estimates. Hence it concentrates on approaches based on numerical integration and simulation where particular attention is focused on variance reduction techniques. Importance sampling procedures are recommended as they provide accurate results with acceptable computational efforts. It is shown that the range of simulation can be identified either by utilizing the design point or, even more effectively, adaptive sampling i.e. an Iterative Fast Monte Carlo (IFM) procedure. Finally, the response surface method (RSM) is recommended for larger structures where each calculation of the limit state function requires a complete Finite Element analysis.     

基于非线性本构关系的复合材料风机叶片有限元极限分析与设计

为了研究具有三维复杂构形的复合材料风机叶片的逐次破坏过程和极限承载能力, 将复合材料细观力学非线性本构理论桥联模型与有限元软件ABAQUS通过用户子程序UGENS结合起来对风力发电机叶片结构进行极限强度分析。只需提供纤维和基体的材料性能参数、 纤维体积含量以及蒙皮和增强筋的铺层数据包括铺设角、 层厚和铺层数, 就可预报出复合材料复杂叶片结构的整体承载能力以及叶片破坏所处的位置, 为正确评估和合理设计风机叶片结构提供了一种简便有效的分析方法。以一种20kW风机叶片为例, 用此方法实现了新型复合材料叶片结构的极限分析和合理设计, 提高了叶片的强度和刚度, 有效降低了叶片的重量。本文中的方法同样适用于其它复合材料复杂结构的极限分析与强度设计。      

Sample regeneration algorithm for structural failure probability function estimation

An efficient strategy to approximate the failure probability function in structural reliability problems is proposed. The failure probability function (FPF) is defined as the failure probability of the structure expressed as a function of the design parameters, which in this study are considered to be distribution parameters of random variables representing uncertain model quantities. The task of determining the FPF is commonly numerically demanding since repeated reliability analyses are required. The proposed strategy is based on the concept of augmented reliability analysis, which only requires a single run of a simulation-based reliability method. This paper introduces a new sample regeneration algorithm that allows to generate the required failure samples of design parameters without any additional evaluation of the structural response. In this way, efficiency is further improved while ensuring high accuracy in the estimation of the FPF. To illustrate the efficiency and effectiveness of the method, case studies involving a turbine disk and an aircraft inner flap are included in this study.     

A load space formulation for probabilistic finite element analysis of structural reliability

A load space formulation for calculating the failure probability of complex structures for which the limit state functions are implicit is described in this paper. This formulation is used in conjunction with probabilistic finite element (PEE) analysis and employs a directional simulation to calculate the structural reliability. Apart from the advantage that a lower order space is used, the main advantage of the load space formulation proposed in this paper is that the number of inversions of the structural stiffness matrix and/or its gradients with respect to the material property random variables is reduced dramatically when compared with the usual Monte Carlo simulation (MCS) method. When used in a finite element reliability analysis, this procedure can save significant amounts of CPU time. Numerical examples are presented to show the efficiency and accuracy of the proposed approach.     

随机有限元-最大熵法

本文提出一种用于结构可靠性分析的随机有限元-最大熵法。它是利用随机有限元法计算结构响应量的前几阶矩,然后利用最大熵法拟会响应量的概率分布,据此算出结构的失效概率。此法具有精度较高、计算量较小的优点。     

陶瓷基复合材料涡轮叶盘设计、制备与考核验证

涡轮转子是燃气涡轮发动机的核心部件。针对SiC/SiC涡轮叶盘设计、制备与考核验证开展研究,采用蛛网仿形(SWS)SiC纤维预制体作为涡轮叶盘的增强体,预制体表面分别沉积BN界面相与SiC基体,通“在线加工”方式对SiC/SiC涡轮叶盘分别进行粗加工和精加工,采用大气等离子喷涂方法制备环境障碍涂层,形成满足设计要求的涡轮叶盘。采用CT对SiC/SiC涡轮叶盘进行无损检测,表征叶盘内部缺陷分布。针对制备的SiC/SiC涡轮叶盘开展性能评价、超转试验、台架试验等考核验证,研究表明：SiC/SiC涡轮叶盘最大破坏强度达到300 MPa;在室温超转试验中,当转速达到n=104 166 r/min时,叶片发生断裂,当转速达到n=108 072 r/min时,轮体发生破裂;在发动机台架试验中,累积完成了N=994次最高转速n_max=60 000 r/min的循环载荷及N=100次最高转速n_max=70 000 r/min的循环载荷试车考核。2022年1月1日,SiC/SiC涡轮叶盘在株洲成功完成了首次飞行试验验证,这也是国内陶瓷基复合材料转子首次配装平台...     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

Composite Structural Analysis of Flat-Back Shaped Blade for Multi-MW Class Wind Turbine

This paper provides an overview of failure mode estimation based on 3D structural finite element (FE) analysis of the flat-back shaped wind turbine blade. Buckling stability, fiber failure (FF), and inter-fiber failure (IFF) analyses were performed to account for delamination or matrix failure of composite materials and to predict the realistic behavior of the entire blade region. Puck’s fracture criteria were used for IFF evaluation. Blade design loads applicable to multi-megawatt (MW) wind turbine systems were calculated according to the Germanischer Lloyd (GL) guideline and the International Electrotechnical Commission (IEC) 61400-1 standard, under Class IIA wind conditions. After the post-processing of final load results, a number of principal load cases were selected and converted into applied forces at the each section along the blade’s radius of the FE model. Nonlinear static analyses were performed for laminate failure, FF, and IFF check. For buckling stability, linear eigenvalue analysis was performed. As a result, we were able to estimate the failure mode and locate the major weak point.     

Coupling finite element and reliability analysis through proper generalized decomposition model reduction

The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd.     

System reliability analysis of spatial variance frames based on random field and stochastic elastic modulus reduction method

This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames.     

Failure analysis of steam turbine last stage blade tenon and shroud

This paper presents an analysis of the cause of steam turbine blade fractures. Recently, several L-0 blades 28.5 (725 mm) long of a steam turbine fractured 5 in. (125 mm) from the blade root platform, causing the forced outage of the turbine. A finite-element analysis (FEA) of the blade was carried out in the beginning of the last decade to calculate the natural frequencies and de vibratory stresses on the blade. A telemetry test was also conducted. The current investigation analyzed the operational data during the last two years, reviewed the results of previous studies, conducted metallurgical investigations, and identified the mechanical and metallurgical modes of the failure. The results of the investigations showed that improper welding of the shroud to the blade was the principal cause of blade fracture.     

An investigation on the failure of an L-O steam turbine blade

This paper presents an analysis of the cause of steam turbine blade fractures. Recently, several L-0 blades 28.5 in. (725 mm) long of a steam turbine fractured 5 in. (125 mm) from the blade root platform, causing the forced outage of the turbine. A finite-element analysis (FEA) of the blade was carried out in the beginning of the last decade to calculate the natural frequencies and the vibratory stresses on the blade. A telemetry test was also conducted. The current investigation analyzed the operational data during the last two years, reviewed the results of previous studies, conducted metallurgical investigations, and identified the mechanical and metallurgical modes of the failure. The results of the investigations showed that improper welding of the stubs was the principal cause of blade fracture.     

基于自由涡尾迹方法的大型风力机动态响应和尾迹研究

针对大型风力机,在当作柔性和刚性风力机时,可以通过气动和结构耦合动力学用来研究两者尾迹和载荷的区别。在设计和校核阶段,需要考虑风力机结构载荷影响的动态特性和气动性能变化。采用非定常自由涡尾迹方法计算尾迹形状和气动载荷。在考虑气动载荷、惯性载荷和重力载荷影响下,分析了叶片挥舞和摆振动态响应。采用模态法建立起风力机解耦动力学方程,并且进行数值求解该方程。结果表明:风力机考虑柔性变形后,对尾迹形状、动态响应和气动性能产生一定影响。这种柔性和刚体风力机的差异表明气动结构耦合效应对风力机的设计和性能计算具有重要意义。     

An efficient method for estimating failure probability bounds under random-interval mixed uncertainties by combining line sampling with adaptive Kriging

For addressing the low efficiency of structural reliability analysis under the random-interval mixed uncertainties (RIMU), this paper establishes the line sampling method (LS) under the RIMU. The proposed LS divides the reliability analysis under RIMU into two stages. The Markov chain simulation is used to efficiently search the design point under RIMU in the first stage, then the upper and lower bounds of failure probability are estimated by LS in the second stage. To improve the computational efficiency of the proposed LS under RIMU, the Kriging model is employed to reduce the model evaluation numbers in the two stages. For efficiently searching the design point, the Kriging model is constructed and adaptively updated in the first stage to accurately recognize the Markov chain candidate state, and then it is sequentially updated by the improved U learning function in the second stage to accurately estimate the failure probability bounds. The proposed LS under RIMU with Kriging model can not only reduce the model evaluation numbers but also decrease the candidate sample pool size for constructing the Kriging model in two stages. The presented examples demonstrate the superior computational efficiency and accuracy of the proposed method by comparison with some existing methods.     

Reliability analysis of structures using neural network method

In order to predict the failure probability of a complicated structure, the structural responses usually need to be estimated by a numerical procedure, such as finite element method. To reduce the computational effort required for reliability analysis, response surface method could be used. However the conventional response surface method is still time consuming especially when the number of random variables is large. In this paper, an artificial neural network (ANN)-based response surface method is proposed. In this method, the relation between the random variables (input) and structural responses is established using ANN models. ANN model is then connected to a reliability method, such as first order and second moment (FORM), or Monte Carlo simulation method (MCS), to predict the failure probability. The proposed method is applied to four examples to validate its accuracy and efficiency. The obtained results show that the ANN-based response surface method is more efficient and accurate than the conventional response surface method.     

System reliability analysis and optimization of stiffened panels under compression

A system reliability analysis method and an optimization method of stiffened panels are presented in this paper. The correlations among the system resistances of failure modes are considered to increase computational accuracy. By taking the allowable structural system failure probability as a constraint, the mathematical model of structural optimization is established and the feasible direction method is used to solve it. The effectiveness and efficiency are shown by the illustrative examples.     

A Structural Reliability Analysis Method Based on Radial Basis Function

The first-order reliability method (FORM) is one of the most widely used structural reliability analysis techniques due to its simplicity and efficiency. However, direct using FORM seems disability to work well for complex problems, especially related to high-dimensional variables and computation intensive numerical models. To expand the applicability of the FORM for more practical engineering problems, a response surface (RS) approach based FORM is proposed for structural reliability analysis. The radial basis function (RBF) is employed to approximate the implicit limit-state functions combined with Latin Hypercube Sampling (LHS) strategy. To guarantee the numerical stability, the improved HL-RF (iHL-RF) algorithm is used to assess the reliability index and corresponding probability of failure based on the constructed RS model. The effectiveness of the proposed method is demonstrated through five numerical examples.     

钢筋混凝土框架结构弹塑性数值子结构分析方法

大型复杂土木工程结构在地震作用下失效破坏可能由部分关键构件严重损伤破坏导致,而大部分构件仍处于弹性或小变形状态。该类结构的地震损伤和破坏全过程分析涉及超大规模系统强非线性动力分析,目前尚缺乏能很好兼顾效率和精度的计算理论,基于此,该文提出一种新型高效且实用的弹塑性数值子结构理论和计算方法,将大型复杂结构系统的大规模非线性计算问题转化为整体结构适度规模的线弹性分析和数量与规模均较小的局部隔离子结构非线性分析,其中,线弹性整体结构刚度矩阵的集成及LU三角分解仅需进行一次,大大提高计算效率;少数屈服构件的子结构非线性分析采用精细化有限元模型或不同类型单元模型,精确模拟构件局部损伤破坏机理,有效提高结构整体的计算精度。最后通过对一榀平面钢筋混凝土框架结构进行地震动力弹塑性数值子结构方法分析,验证其高效性与精确性。     

Experimental and numerical studies on the performance and surface streamlines on the blades of a horizontal-axis wind turbine

Investigating laminar separation over the turbine blade of a horizontal-axis wind turbine (HAWT) has been considered an important task to improve the aerodynamic performance of a wind turbine. To better understand the laminar separation phenomena, in this study, the aerodynamic forces of a SD8000 airfoil (representing the sectional blade shape) in the steady-state conditions were first predicted using an incompressible Reynolds-averaged Navier–Stokes solver with the γ–Re _θt and k–k _L–ω transition models. By comparing simulation and experimental results, the k–k _L–ω transition model was chosen to simulate the laminar separation on three-dimensional (3D) turbine blade. Experimentally, a HAWT with three blades was then tested in a close-circuit wind tunnel between the tip speed ratios (TSRs) of 2 and 7 at the wind speed of 10 m/s. In addition, through computational fluid dynamics, the turbine performance and flow characteristics on the blade as blade is rotating were investigated. It is shown that 3D simulations agreed well with the experimental results with regard to the mechanical power of the HAWT at the testing TSRs. Moreover, the separation and reattachment lines on the suction surface of the turbine blade were also observed through the skin friction line, indicating that laminar separation moved toward the trailing edge with the increasing TSR at the blade tip region.