Dynamic Reliability Analysis Research Articles

Time-varying reliability analysis of compressor blisk based on particle swash optimization extreme Kriging model

In order to effectively realize the dynamic time-varying reliability analysis of the radial deformation of the aero-engine low pressure compressor, based on Kriging model combined with particle swarm optimization (PSO) and extreme value idea, a particle swarm optimization extremum Kriging model (PSOEKM) method was proposed. Firstly, the analysis principle of PSOEKM method is expounded. Secondly, the modeling idea of PSOEKM method is discussed. Then, the implementation approach of time-varying reliability analysis based on PSOEKM is explored. Finally, taking the aero-engine low pressure compressor blisk as an example, the dynamic reliability analysis is carried out by using PSOEKM. The analysis results show that the reliability is 99.76% when the allowable value of radial deformation of the compressor blisk is 1.594×10-3 m. Compared with the traditional Kriging model and the extreme response surface model, the PSOEKM method has high analysis accuracy and calculation efficiency. The method presented in this paper provides a new research idea for time-varying reliability analysis of complex structures.

Structural dynamic reliability analysis of super large-scale lattice domes during earthquakes using the stochastic finite element method

For large-scale dome structures subjected to earthquake ground motions, the need for accurate and efficient approaches that account for uncertainties in design, material properties, loads, damping, and manufacturing processes has grown significantly. In uncertainty analyses, the theory of probability, uncertainty quantification, and reliability analysis approaches are commonly used. However, because of computing efficiency and capability, the space scale of dome structures is severely limited. As a result, the computational issues of the complex dynamic reliability that super-large-scale dome structures encounter during earthquakes are challenging. The uncertainties of the dynamic demands of a super-large-scale lattice dome with multiple variables are quantified using a stochastic finite element method (SFEM) with nonlinear time-history analysis developed in this paper, and this method can consider the randomness of variables in more detail for a structure. The dynamic reliability is investigated in depth using the efficient Latin hypercube sampling (LHS) technique to reduce the number of repetitive time-consuming calculations. To improve the efficiency and accuracy of the analysis, an optimization approach based on the genetic algorithm (GA) is used to obtain the probability of structural failure and the reliability index. The results show that these methods are highly efficient for super-large-scale structures. Finally, a sensitivity analysis based on variable randomness is conducted to further evaluate the effects of variables on structural performance using various evaluation methods. This paper provides an efficient solution for structural dynamic reliability problems of super-large-scale structures in the SFEM framework.

Dynamic reliability analysis approach based on fault tree and new process capability index

AbstractThis paper proposes a dynamic reliability analysis approach based on fault tree (FT) and new process capability index (PCI). This work has three contributions. First, new PCIs, namely, Cp‐R, Cpk‐R, Cpm‐R, and Cpmk‐R, are proposed on the basis of traditional PCI prototypes, and the data stability analysis results converge to (0∼1] interval. These new PCI advantages and defects are compared, and the result shows that Cpmk‐R can identify the stability of the dynamic data effectively. Second, fault risk index (FRI) based on Cpmk‐R index, namely, Rpmk‐R, is proposed to approximate the probability of basic events (BEs) for FT. Third, FRI and FT are used to analyze fault transmission and assess dynamic fault risk of equipment. A circulating cooling water heat exchange system is used for simulation to verify the practicability of the approach. Results show that the FT based on Rpmk‐R can assess the dynamic fault risk of equipment accurately.

Dynamic reliability analysis framework using fault tree and dynamic Bayesian network: A case study of NPP

The Emergency Diesel Generator (EDG) is a critical and essential part of the Nuclear Power Plant (NPP). Due to past catastrophic disasters, critical systems of NPP like EDG are designed to meet high dependability requirements. Therefore, we propose a framework for the dynamic reliability assessment using the Fault Tree and the Dynamic Bayesian Network. In this framework, the information of the component's failure probability is updated based on observed data. The framework is powerful to perform qualitative as well as quantitative analysis of the system. The validity of the framework is done by applying it on several NPP systems.

Markov/CCMT: Towards an integrated platform for dynamic reliability and risk analysis

An integration Markov/CCMT analytics platform for dynamic reliability and risk analysis of digital process control system is presented in the paper. The Markov/CCMT analytics platform is integrated with a simulation-based testing and matrix-based coding paradigm for automatic generation and unsupervised learning update of probabilistic mapping model and a versatile Markov/CCMT algorithm for multiway search analysis. The capabilities of the integrated Markov/CCMT analytics tool are validated with an example case study of water level control system. The results demonstrate that the features for convenient modeling, updating, and high-performance computing allows the practical and scalable use of Markov/CCMT analytics platform to risk-based reliability modeling and analysis of large complex dynamic systems.

Practical dynamic reliability analysis with spatiotemporal features in geotechnical engineering

ABSTRACT In recent years, improvements to the design of earth structures to ensure soil robustness against accidental disaster load conditions has gained considerable importance. In this paper, we propose a practical reliability analysis scheme that can enable the development of a robust design based on dimensionality reduction; this scheme employs input parameters, and it uses numerical analysis results as multidimensional information while preserving the spatiotemporal information to the maximum extent. Further, the proposed design scheme has practical design functions similar to those of conventional reliability analysis methods, such as the first-order second-moment method and first-order reliability method. Finally, the effectiveness of the proposed design scheme and its significant contribution to the practical design of earth structures are demonstrated via a time series seismic deformation analysis of simple embankments on liquefiable sand ground.

Parametric Vibration Analysis of a Six-Degree-of-Freedom Electro-Hydraulic Stewart Platform

Electro-hydraulic Stewart 6-DOF platform is a 6-DOF parallel mechanism combined with the electro-hydraulic servo control system, which is widely used in the field of construction machinery. In actual working conditions, the flow and pressure pulsation of the hydraulic oil output from the hydraulic leg of the electro-hydraulic Stewart platform are inevitable, so the equivalent stiffness of the platform leg will change, and the stiffness parameters of the transmission system will change, resulting in vibration, which will affect the accuracy of the platform. This paper considering the fluid unit equivalent stiffness cyclical fluctuations and leg, on the basis of the relationship between hydraulic stiffness, constructs the electric hydraulic Stewart platform machine vibration dynamics equation, fluid coupling parameters of vibration parameters using the method of the multiscale approximate analytic formula of the main resonance and combination resonance are derived, and the system parameters vibration time-domain response and frequency response under two different poses are discussed. Results show that the system first to six order natural frequency and the first to the sixth order natural frequency and frequency of hydraulic oil equivalent stiffness of the combination of frequency will have an effect on the parameters of the system vibration. In the main resonance, the dominant frequency is mainly the first to sixth order natural frequency of the system; in the combined resonance, the dominant frequency is the combined frequency. Through the parameter vibration analysis of two different positions of the platform, it is concluded that when the platform is in an asymmetric position, each leg of the system is more involved in vibration. This study can provide the reference for the subsequent dynamic optimization and reliability analysis of the electro-hydraulic Stewart platform.

A New Approach for Fatigue Reliability Analysis of Thin-Walled Structures with DC-ILSSVR.

Fatigue analysis is of great significance for thin-walled structures in the spacecraft industry to ensure their service reliability during operation. Due to the complex loadings of thin-walled structures under thermal–structural–acoustic coupling conditions, the calculation cost of finite element (FE) simulations is relatively expensive. To improve the computational efficiency of dynamic reliability analysis on thin-walled structures to within acceptable accuracy, a novel probabilistic approach named DC-ILSSVR was developed, in which the rotation matrix optimization (RMO) method was used to initially search for the model parameters of least squares support vector regression (LS-SVR). The distributed collaborative (DC) strategy was then introduced to enhance the efficiency of a component suffering from multiple failure modes. Moreover, a numerical example with respect to thin-walled structures was used to validate the proposed method. The results showed that RMO performed on LS-SVR model parameters provided competitive prediction accuracy, and hence the reliability analysis efficiency of thin-walled pipe was significantly improved.

Overturning assessment of railway vehicles under cross winds

The overturning issues in a strong wind are extremely critical to the railway vehicles, which have attracted a great deal of attention over the years. To address such problems, this paper introduces a dynamic reliability approach to evaluate the overturning risk of vehicles in crosswinds. Starting from the aerodynamic model, a novel prediction formula of unsteady crosswind forces with a consideration of the complete turbulent field effect is derived. Using the pseudo-excitation method (PEM), the power spectrum of vehicle responses is then calculated by the established vehicle model, and finally the corresponding results are used to assess the probabilistic overturning of vehicles in terms of the dynamic reliability analysis. It is found from the calculations that the time-dependent failure probability curves are related to the vehicle speed, wind speed, and crosswind direction, and the probabilistic characteristic wind curves (PCWCs) at different failure probabilities are more useful and reasonable for evaluating the overturning risk in comparison with the traditional characteristic wind curves (CWCs) in previous investigations. Furthermore, the probabilistic characteristic wind surface (PCWS) that considers the effect of crosswind direction, is developed, and it reveals that the vehicle is most vulnerable at a condition of perpendicular crosswind direction.

The PDEM-based time-varying dynamic reliability analysis method for a concrete dam subjected to earthquake

A time-varying dynamic reliability analysis method based on the generalized probability density evolution method (GPDEM) is proposed for a concrete gravity dam under seismic loading. Characterized by considering both randomness and time-variability, the method could be applied to predict the time-varying seismic performance of concrete dams from the perspective of probability. Two probability density evolution equations (PDEEs) are established in the method: the extreme value distribution-based PDEE.1 considering the randomness of material parameters under seismic loading and the PDEE.2 considering the deterioration of material properties during the service life. To solve the PDEE.2, a novel initial condition is derived from the PDEE.1 for the first time. The numerical implementation is illustrated by a concrete gravity dam. The results show that the abundant and continuous probability evolution information of the time-varying seismic performance could be captured. Then, the continuous time-varying reliabilities are obtained through the specified thresholds. The accuracy and effectiveness of the newly proposed method are compared with those of the MCS. Finally, the proposed method is verified to be efficient and be suitable for complex nonlinear structures under seismic loading, which could provide a potential tool for the life-cycle seismic design.

Dynamic reliability analysis for non-stationary non-Gaussian response based on the bivariate vector translation process

Calculation of probability of exceedance for nonstationary non-Gaussian responses remains a great challenge to researchers in the field of structural reliability. In this paper, an analytical solution is proposed for calculating the mean upcrossing rate (MCR) of the non-stationary non-Gaussian responses by approximating the displacement and velocity responses with the bivariate vector translation process, in which the unified Hermite polynomial model (UHPM) is selected as the mapping function. The first four moments (i.e., mean value, standard deviation, skewness, and kurtosis) and cross-correlation function of the displacement and velocity responses needed in UHPM are estimated from some representative samples generated by random function-spectral representation method (RFSRM) and time-domain analysis. Under the Poisson assumption of the upcrossing events, the calculation of extreme value distribution or probability of exceedance for structural response can be determined with the proposed method. The proposed method is applicable to a wide range of structural responses, including asymmetric and hardening or softening responses. Three numerical examples are provided to demonstrate the efficiency and accuracy of the proposed method. It can be concluded that the proposed method provides an accurate and useful tool for dynamic reliability assessment in engineering applications.

Efficient reliability analysis based on deep learning-enhanced surrogate modelling and probability density evolution method

An improved method, termed as the AL-DLGPR-PDEM, is presented to address high-dimensional reliability problems. The novelty of this work lies in developing a complete framework for combining the deep learning (DL) architectures, serving as the utility of dimension reduction, and the Gaussian process regression (GPR), resulting in the so-called DLGPR model. First, the parameters of both the DL and the GPR are inferred using a joint-optimization scheme, rather than the traditional two-step, separate-training scheme. Second, the network configuration of the DLGPR is optimally determined by using a grid-search procedure involving cross-validation, instead of an empirical setting manner. On this basis, the DLGPR is adaptively refined via an active learning (AL)-based sampling strategy, so as to gain the desired DLGPR using as fewer training samples as possible. Eventually, the finalized DLGPR is evaluated at the whole representative point set, thereby the probability density evolution method (PDEM) is conducted accordingly. Two numerical examples are investigated. The first one tackles with the static reliability analysis of a planner steel frame, where the case of small failure probabilities is also considered; the second one addresses the dynamic reliability analysis of the steel frame under fully non-stationary stochastic seismic excitation. Comparisons against other existing reliability methods are conducted as well. Results demonstrate that the proposed AL-DLGPR-PDEM achieves a fair tradeoff between accuracy and efficiency for dealing with high-dimensional reliability problems in both static and dynamic analysis examples.

Dynamic reliability analysis of mechanical system with wear and vibration failure modes

The wear and vibration of machine tool system are coupled and time-variant, which have significant influences on the dynamic performance of machine tool feed drive system in different time scales. In this study, the coupling effects between the wear of linear guide and the vibration of machine worktable system are studied based on the infinitesimal method. A nonlinear dynamic model is developed to analyze the wear and vibration failure mechanisms considering the uncertainty of parameters. To evaluate the dynamic reliability of the machine worktable system under multi-failure modes, a time-variant and conditional reliability approach based on the active learning Kriging model and Monte Carlo Simulation is proposed. The approach gets rid of repeated calculating of the real limit state function values and the calculation efficiency is enhanced greatly. Additionally, reliability-based sensitivity indices are presented to investigate the significance of random parameters to the reliability of the system. Besides of the reliability analysis for machine worktable systems, the proposed framework and corresponding method are also suitable for the reliability evaluation of other complex mechanical systems with the conditional multi-failure modes.

An Efficient Monte-Carlo Simulation for the Dynamic Reliability Analysis of Jacket Platforms Subjected to Random Wave Loads

The growing demand for the application of jacket platforms in deep water requires more attention on the assessment of structural reliability. This paper is devoted to the dynamic reliability analysis of jacket platforms subjected to random wave loads with the Monte-Carlo simulation (MCS), in which a sample size of the order of magnitude of 104 to 105 for repeated time–history analyses is required for small failure probability problems, and a duration time up to three hours needs to be considered in the time–history analyses for a specific sea condition. To tackle the difficulty involved in the MCS, the explicit time-domain method (ETDM) is used for the required time–history analyses of jacket platforms, in which truncated explicit expressions of critical responses with regards to the contributing loading terms are first established and then used for numerous repeated sample analyses. The use of ETDM greatly enhances the computational efficiency of MCS, making it feasible for the dynamic reliability analysis of jacket platforms under random wave loads. A jacket platform with 11,688 degrees of freedom was analyzed for the evaluation of dynamic reliability under a given sea condition, indicating the accuracy and efficiency of the present approach and its feasibility to practical structures.

Dynamic Reliability Assessment of PEM Fuel Cell Systems

In this paper, a novel model for the dynamic reliability analysis of a polymer electrolyte membrane fuel cell system is developed to account for multi-state dynamics and ageing. The modelling approach involves the combination of physical and stochastic sub-models with shared variables. The physical model consists of deterministic calculations of the system state described by variables such as temperature, pressure, mass flow rates and voltage output. Additionally, estimated component degradation rates are also taken into account. The non-deterministic model is implemented with stochastic Petri nets which model the failures of the balance of plant components within the fuel cell system. Using this approach, the effects of the operating conditions on the reliability of the system were investigated. Monte Carlo simulations of the process highlighted a clear influence of both purging and load cycles on the longevity of the fuel cell system.

Computer Analysis of Dynamic Reliability of Some Concrete Beam Structure Exhibiting Random Damping

An efficiency of the generalized tenth order stochastic perturbation technique in determination of the basic probabilistic characteristics of up to the fourth order of dynamic response of Euler-Bernoulli beams with Gaussian uncertain damping is verified in this work. This is done on civil engineering application of a two-bay reinforced concrete beam using the Stochastic Finite Element Method implementation and its contrast with traditional Monte-Carlo simulation based Finite Element Method study and also with the semi-analytical probabilistic approach. The special purpose numerical implementation of the entire Stochastic perturbation-based Finite Element Method has been entirely programmed in computer algebra system MAPLE 2019 using Runge-Kutta-Fehlberg method. Further usage of the proposed technique to analyze stochastic reliability of the given structure subjected to dynamic oscillatory excitation is also included and discussed here because of a complete lack of the additional detailed demands in the current European designing codes.

Mixed uncertainty analysis for dynamic reliability of mechanical structures considering residual strength

Aiming at the uncertainty of parameters in structural dynamic reliability analysis model, such as randomness, interval and fuzziness, a dynamic reliability model with mixed uncertain parameters is proposed in this paper. Based on entropy equality information, random and fuzzy variables are transformed. And the different possible uncertainties of parameters are analyzed, four reliability index analysis models are given under different parameters. Probability and interval reliability analysis are adopted to solve the reliability index, and the influence of parameter type on reliability index is discussed. The dynamic reliability index of 45# steel (test specimens) under fatigue load is calculated to verify the feasibility of the proposed method.

Discrete time dynamic reliability modeling for systems with multistate components

This study proposes modeling techniques for the exact dynamic reliability analyses of systems with the lifetimes of all components following independent and nonidentical discrete phase-type (DPH) distributions. The systems may have series, parallel, standby, K-out-of-N, and bridge structures with any combinations of them. The models produce numerical formulas and algorithms for generating system reliability and hazard functions; thus, they are applicable to the dynamic reliability analysis of systems, including networks. The approach is by showing that the system lifetime follows a DPH distribution. For network reliability analysis, the DPH distribution is generalized into a matrix-geometric (MG) distribution. The use of the DPH distribution makes the models suitable for systems with multistate components and simplifies the calculations of the system reliability measures. Its effectiveness is illustrated using results from complex structure systems.

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.