Dynamic Reliability Analysis Research Articles

Structural dynamic reliability estimation with advanced extremum Kriging method

To enhance the computational performance of the structural dynamic reliability estimation, advanced extremum Kriging method (AEKM) is proposed fusing Kriging surrogate model, multi-population genetic algorithm and response surface method-based extremum thought (ERSM) in this paper. The applicability of the AEKM is verified via the blisk radial deformation dynamic reliability analysis of an aeroengine high-pressure compressor. The results show that the reliability level of the blisk is 0.9956 as the allowable value of radial running deformation 1.75×10−3 m. Moreover, the developed AEKM is superior to other three surrogate models, including ERSM, K-ERSM and IK-ERSM, in terms of computing precision and analytical efficiency. Besides, the analytical precision of the developed method is basically consistent with the direct simulation, and the analytical time is obviously superior to the direct simulation. Therefore, the AEKM is illustrated to be an effective way for structural dynamic reliability analysis, which enriches complex structural reliability theory.

Dynamic Reliability Analysis of Moment Resisting Concrete Frames

A comprehensive reliability analysis of moment resisting frame is presented in this article in which uncertainties in loadings, material properties, and member cross section properties are included. Performance of designed structures and their reliability in real earthquakes is an important issue these days. In this research study, two moment resisting concrete frame structures, which is the most common type of structures in Iran, are designed based on Section 9 of the Iran National Building Regulations and its analytical model is constructed. Using OpenSEES software, the finite element simulations and reliability analyses are performed with different distribution functions for the mentioned parameters. By using the generated parameters, the ultimate limit functions for structural failure are examined. Results show that incorporating uncertainties in loading, cross section dimension, and material properties could result in a considerable impact on reliability of designed structures.

Dynamic Reliability Analysis of Turbine Blades Under Combined High and Low Cycle Loadings

Turbine blades experience complex loading interactions induced by centrifugal loads, thermal loads, and vibration loads, which lead to the combined high and low cycle fatigue (CCF) failure. Considering the significance in acquiring sufficient data for reliability assessment, it may be imprecise to consider the load and strength as random variables. To deal with the issue, material parameters and working loads involved should be regarded as random variables, like high cycle fatigue stress and low cycle fatigue stress as well as material strength. Hence, the dynamic reliability model with strength degradation is developed based on conventional stress-strength interference theory to investigate the reliability of turbine blades under CCF loading conditions. The validation of the established model is performed by a numerical example, and the results indicate that the proposed model considering strength deterioration is in good coincidence with engineering practice.

Dynamic reliability analysis of a floating offshore wind turbine under wind-wave joint excitations via probability density evolution method

Floating offshore wind turbine (FOWT) towers are dynamically sensitive to wind and wave excitations. Since the wave tends to be harsher with the increase of wind speed, FOWT towers are likely to experience the most severe vibration operating at the cut-out wind speed. In the present study, the short-term dynamic reliability of a spar-type FOWT is evaluated based on the probability density evolution method (PDEM). For this purpose, an integrated coupled dynamics model for the FOWT is firstly established by incorporating the multibody dynamics with the finite element (FE) method. Next, the conditional joint probability distribution of the significant wave height and peak spectral wave period at the cut-out wind speed is constructed based on the copula model. Then, the stochastic dynamic response and reliability of the FOWT can be analyzed via PDEM. The numerical example of reliability analysis of a 5-MW spar-type FOWT operating at the cut-out wind speed is carried out, in which the long-term met-ocean data at a South China Sea site is utilized. Simulation results show that the reliability of the FOWT for normal operation is less than 0.2 when the acceleration at the tower top is adopted as the failure criterion.

Static and Dynamic Reliability Analysis of Laterally Loaded Pile Using Probability Density Function Method

Pile foundation is one of the common foundation forms in marine geotechnical engineering, especially in wind power engineering. Its operation safety is seriously affected by many uncertainties, such as the randomness of ground motion in intensity and frequency. The stochastic reliability analysis method can better characterize these uncertainties in the evaluation of the safety performance of pile foundation. The probability density functions (PDFs) of stochastic systems are important prerequisites for reliability analysis. However, for geotechnical problems, the coupling between parametric and excitation randomness and the nonlinear mechanical properties of rock and soil make it very difficult to obtain the associated PDFs. Instead, the probability density evolution method (PDEM) is introduced and is used to investigate the static and dynamic reliability of laterally loaded piles as an example of a geotechnical problem. Compared with Monte Carlo stochastic simulations, PDEM-based computing is shown to be highly efficient when applied to the seismic design of pile in geotechnical engineering, and its calculation efficiency is 20 times of the former for the seismic dynamic reliability of pile foundation. This study provides a new reference for the efficient design and safety evaluation of offshore pile foundation engineering based on static and dynamic reliability of multiple random factors.

Direct probability integral method for static and dynamic reliability analysis of structures with complicated performance functions

For structural reliability assessment, some performance functions are fairly complicated, which leads to disjoint failure domains, discontinuous structural responses and multiple design points. Thus, such a problem is difficult to be solved by some existing methods, i.e., the design point-based methods and surrogate model-based methods, etc. Although the stochastic sampling-based methods can tackle this issue, much computational effort is needed. In this paper, a novel approach, direct probability integral method (DPIM), is proposed to address static and dynamic reliability assessment for structures with complicated performance functions. The DPIM is established based on the decoupled computation of probability density integral equation and structural physical equation. Firstly, by introducing the point selection technique based on generalized F discrepancy and the smoothing of Dirac delta function, the probability density integral equation is solved directly to calculate the probability density functions (PDFs) of static and dynamic responses of structures with complicated performance functions. Then, the failure probability for static system is acquired by integrating the PDF curve of structural response over failure domain. For stochastic dynamic system, the dynamic reliability assessment is fulfilled efficiently by DPIM combining with extreme value distribution. Finally, six representative examples indicate that DPIM is much more efficient than Monte Carlo simulation to attack the reliability estimation issue of structures containing complicated performance functions.

Transient Reliability Evaluation Approach of Flexible Mechanism with GA-Extremum Neural Network

Efficient analytical model directly enhances the reliability evaluation of flexible mechanism under operation. In this paper, genetic algorithm-based extremum neural network (GA-ENN) is developed as reliability model by introducing the thoughts of extremum and genetic algorithm (GA) into artificial neural network to address the key problems comprising transient response and modeling precision in the dynamic reliability analysis of flexible mechanism in a time domain. The thought of extremum is adopted to simplify transient response process as one extremum value to the difficulty of dynamic reliability analysis induced by transient process response, and the GA is applied to find the optimal model parameters of reliability model. The dynamic reliability analysis of two-link flexible robot manipulator (TFRM) (a typical flexible mechanism) was implemented based on the GA-ENN method, regarding the input random variables of material density, elastic modulus, section sizes of components, and the output response of components’ deformations. From the analysis, the comprehensive reliability of the TFRM is 0.951 when the allowable deformation is 1.8 × 10−2 m. Besides, the maximum deformations of the two components follow the normal distributions with the means of 1.45 × 10−2 m and 1.69 × 10−2 m and the standard variances of 6.77 × 10−4 m and 4.08 × 10−4 m, respectively. Through the comparison of methods, it is illustrated that the developed GA-ENN improves the simulation efficiency and modeling accuracy by overcoming the problems of transient response and model parameter optimization in the dynamic reliability analysis of TFRM.

Dynamic performance reliability analysis of rolling linear guide under parameter uncertainty

This paper presents a dynamic reliability analysis method of rolling linear guide considering the uncertainty of geometric parameters. A three degree of freedom (DOF) dynamic motion model of rolling linear guide that considers the complexity of the actual load is established. In order to improve the accuracy of reliability evaluation, interval model is used to express the uncertainty of geometric parameters. The reliability range of dynamic response is determined according to the accuracy grade of rolling linear guide. The interval reliability calculation method is used to analyze and calculate the horizontal and vertical dynamic reliability of rolling linear guide. Then, the comprehensive dynamic reliability of rolling linear guide is obtained. Finally, the dynamic reliability of the SHS-45R rolling linear guide is analyzed by using the reliability evaluation method described in this paper. And the validity and accuracy of the result is demonstrated by comparing with the Monte Carlo simulation.

Modeling of the rotor-bearing system and dynamic reliability analysis of rotor’s positioning precision

On the basis of the classical two degree of freedom (2-DOF) rotor-bearing system, the stochastic dynamic equations are solved and the dynamic reliability of the rotor’s positioning precision is examined in this paper. Firstly, the stochastic dynamic equations are converted to several deterministic dynamic equations by orthogonal polynomial approximation method. The contact uncertainty coefficient is described by Bernoulli distribution and the instantaneous contact probability of the ball-inner race contact of the rolling bearing is obtained. Then the state function of the system is defined and the statistical fourth moment method is adopted to determine the first four moments of the system response and state function. Edgeworth series technique is used to approach the cumulative distribution function (CDF) of the maximum displacement of the response and the system state function. Different parameters effects on the characteristics of the responses and the reliability of the system are investigated. The comparisons of the results obtained from the Monte Carlo simulation (MCS), the previous study and the present study illustrate the effectiveness of the study.

Active learning and active subspace enhancement for PDEM-based high-dimensional reliability analysis

An efficient reliability method, termed as the AL-AS-GPR-PDEM, is proposed in this study, which effectively combines the probability density evolution method (PDEM) and the Gaussian process regression (GPR) surrogate model enhanced by both the active subspace (AS)-based dimension reduction and the active learning (AL)-based sampling strategy. In this method, the AS-GPR model is developed, where the AS and the GPR are jointly calibrated so as to bypass the tricky prerequisite of gradient information to discover the latent AS of the original parameter space; then, the AL-based sampling strategy is employed to construct a satisfactorily accurate AS-GPR model using as fewer training samples as possible. This treatment allows that the newly-added training sample at each iteration can be simultaneously used to both update the discovered low-dimensional AS and refine the constructed GPR model within the AS. Lastly, the finalized AS-GPR model is employed to predict the equivalent extreme values (EEVs) of structural responses at the representative point set, thereby the PDEM-based reliability analysis can be readily performed based on the estimated EEVs. To testify the effectiveness of the proposed method, four numerical examples are addressed, involving both surrogate modelling of analytical functions with different characteristics and dynamic reliability analysis of linear/nonlinear engineering structures under seismic excitations. It is demonstrated that the proposed method is of satisfactory accuracy and efficiency for structural reliability analysis in high dimensions.

Dynamic reliability and variance-based global sensitivity analysis of pipes conveying fluid with both random and convex variables

Purpose This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment. Design/methodology/approach This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration. Findings The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice. Originality/value The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime.

Dynamic Reliability Analysis of Braced Frame Structures Considering Inter Story Correlation

Adding buckling restrained braces (BRB) of reinforced concrete frame structure can effectively improve the safety performance of the structure. The dynamic reliability analysis based on Poisson continuous process assumption and the first exceeding failure probability can be used to obtain the failure probability of the buckling restrained brace frame system under earthquake load, and the relationship between the failure probabilities of each floor of the structure is analyzed to obtain the frame system reliability interval of frame structure. The results show that the reliability of BRB frame structure is higher than that of pure frame structure, and the discrete failure probability is lower.

Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method

To improve the analysis accuracy of dynamic reliability of a nonlinear system, an equivalent nonlinear system method is presented. In this method, general nonlinear systems are converted to equivalent Duffing nonlinear systems according to the minimum mean square error criterion, whose exact analytical solution of the random steady-state responses can be determined by a FokkerPlanckKolmogorov equation. Then the exact results of stochastic responses are used to analyze structural dynamic reliability. To use the equivalent nonlinear system method to analyze structural dynamic reliability is not only convenient for calculation but highly accurate. In addition, the presented equivalent nonlinear system has a parameter ε, which controls the degree of nonlinearity. Thus, it is easy to obtain the corresponding analysis results from converting the original system to equivalent nonlinear systems with different degrees of nonlinearity by changing the value of ε. Especially, when ε is zero, the equivalent nonlinear system will degenerate to the linear system, and leading to the analysis results of the equivalent linearization method. An example shows that the analysis results of the proposed equivalent nonlinear system method are reliable, and the calculation appears to be more accurate than that of the equivalent linearization method.

Interval dynamic reliability analysis of mechanical components under multistage load based on strength degradation

AbstractTo further study the law of strength degradation, the residual strength degradation model is established based on the definition of fatigue damage, considering the interaction of various uncertain factors and time factors in service environment. Combined with equivalent damage model, a nonlinear cumulative damage model is proposed, which takes the interaction among loading loads into account and improves the accuracy of calculation. Additionally, the equivalent transformation of multistage load is studied using interval theory. According to the interval dynamic nonprobability reliability prediction model, a dynamic reliability analysis of the interval model is carried out. Dynamic reliability of the component is analyzed under multistage load accumulation damage to verify the effectiveness of the method.

Moving extremum surrogate modeling strategy for dynamic reliability estimation of turbine blisk with multi-physics fields

To improve the dynamic reliability analysis of complex structures like turbine blisk, moving extremum surrogate modeling strategy (MESMS) is proposed in respect of multi-physics coupling with various dynamics/uncertainties. In this strategy, extremum thought is adopted to handle the dynamic process of input parameters and output response, and the importance sampling (IS) method is utilized to extract efficient samples and improve the efficiency of dynamic reliability estimation, and moving least square (MLS) method is used to select good samples from training samples with local compact support region to establish a precise surrogate model. The dynamic reliability analysis of turbine blisk radial deformation with fluid-thermo-structural interaction is performed to validate the developed MESMS in approximate precision and simulation performance by comparing to other methods. As shown in this study, (i) the reliability degree of turbine blisk is 0.9975 when the allowable value of radial deformation is 2.6856 × 10−3 m subject to 3 sigma levels; (ii) the proposed MESMS processes high modeling accuracy and efficiency due to small error; (iii) the MESMS holds high simulation performance in efficiency and accuracy owing to outstanding computational consumption and simulation. These results demonstrate that the MESMS is effective and applicable in structural reliability estimation regarding dynamics and uncertainties. The efforts of this paper provide a useful insight for performing the reliability-based design optimization of complex structures besides turbine blisk.

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Bearings are the core components in various kinds of rotating machineries. With the increasing demand of reliable bearings in precision equipment, it is of great significance to analyze the motion error of bearings. In this article, a nonlinear dynamic model of angular contact ball bearings installed in pairs is constructed to describe its response characteristics. The definition of a failure mode in matched bearings is that the dynamic response of each inner race is larger than the allowed axial runout. This article introduces a feasible approach to evaluate the reliability of positioning precision of matched bearings with random geometric parameters. The statistical moments of dynamic response are calculated using stochastic perturbation method. The probability distribution function of state function relating to positioning precision is approached by Edgeworth series, from which the reliability and sensitivity are obtained. A pair of 7206B bearings is taken as an application instance of the proposed method. Monte Carlo simulation is employed to provide a benchmark on which to verify the precision and efficiency of the proposed method. In addition, the effects of mean values and variances of random geometric parameters on the positioning precision are analyzed, respectively.

Dynamic reliability analysis for the reusable thrust chamber: A multi-failure modes investigation based on coupled thermal-structural analysis

To evaluate the dynamic reliability of the thrust chamber in the reusable rocket engine (RRE) under multi-failure modes, a reliability analysis based on the coupled thermal-structural finite element model and the multiple response surface (MRS) is proposed. Through the deterministic thermal-structural simulation, two major failure modes, the static strength failure and cyclic cumulative damage, are examined. While the random variables are introduced concerning working loads, geometrical dimensions, and material properties. The reliability of a typical reusable LOX/H2 rocket engine thrust chamber is examined by the proposed method. The feasibility of the proposed method is validated by comparing our results with that from the traditional Monte Carlo simulation and the influences of sampling methods as well as set sizes are investigated. This study provides an efficient and steadfast approach to evaluate the reliability of thrust chambers in the reusable rocket engine and quantifies the importance ranking of working loads, geometrical dimensions, and material properties for the chamber reliability, which provides a valuable insight into the reliability-based design and optimization process for reusable rocket engines

A novel dynamic impact pressure model of debris flows and its application on reliability analysis of the rock mass surrounding tunnels

Assessing the influence of the impact pressure exerted on surrounding rock mass by potential debris flows is one of the challenges in a mountain tunnel construction project. This paper proposes an effective mathematical model for the assessment of impact pressure exerted by debris flows on obstacles. The characteristics of the new model are analyzed, and the parameters determination method for the new model are deduced. Also, a new method for dynamic reliability analysis of the rock mass surrounding tunnels is proposed and is constituted into three key steps. First, by inputting impact pressure of debris flows generated by the aforementioned new model, the FLAC3D is used as the dynamic analysis engine to obtain the time-varying stress distribution of surrounding rock mass during the impact of debris flow. Second, the factor of safety (FOS) contours of surrounding rock mass are generated based on element states using the maximum tensile stress criterion and the Mohr-Coulomb yield criterion. Third, by using the time-varying contours of the FOS, a failure probability and a reliability index are obtained from a reliability perspective. A case study shows the complete analysis process and confirms the effectiveness of the above methodology. In sum, this paper provides new ideas, new methods, and a reference example for evaluating the influence of dynamic impact exerted by debris flows on the rock mass surrounding tunnels.

Dynamic Model-based Saddle-point Approximation for Reliability and Reliability-based Sensitivity Analysis

Dynamic reliability analysis must consider both dynamic performance and parametric randomness to evaluate system safety in operation. The saddle-point approximation method is utilized to establish the dynamic probability distribution for known or unknown types of random variables. The cumulative distribution function is used to establish the approximation dynamic reliability model based on a simplified formula with high accuracy. Dynamic reliability analysis is investigated to describe the system safety of the moving operation process. Additionally, dynamic reliability-based sensitivity is used to represent the influence of the parameters on the system's dynamic performance. The fixed-threshold model and load-strength interference model are considered to develop computational formulas of reliability analysis and the degree of effect of each parameter's fluctuation. Finally, the proposed method is evaluated and demonstrated by means of four numerical examples to analyse the system performance and the parameters’ effects. The crude Monte Carlo simulation is performed to provide benchmark results.

Fatigue dynamic reliability and global sensitivity analysis of double random vibration system based on Kriging model

ABSTRACT In this paper, the dynamic reliability and global sensitivity analysis method of double random vibration system is proposed, considering structure uncertainty and excitation uncertainty of complex mechanical and structural systems under random load. Based on the Miner criterion of fatigue failure of structures, the dynamic responses of structures under the condition of double random vibration are analyzed, and the dynamic reliability analysis method is established. Furthermore, the moment-independent global sensitivity index of random structures is proposed, which can quantitatively reflect the effects of random structure parameters on dynamic reliability under random excitation and provide reference for structure reliability optimization design. Based on the proposed dynamic reliability moment-independent global sensitivity analysis (GSA) index, this paper combines the computationally efficient active learning Kriging (ALK) method to establish the solving method. Finally, the rationality and correctness of the dynamic reliability GSA index and the ALK method proposed in this paper are illustrated by comparing the results with those gained by Monte Carlo simulation (MCS) method. The results prove that the GSA has significantly guided meaning and referenced value in the dynamic reliability design and optimization for the double random vibration system, especially for the engineering practice.