Reliability Of Dynamic Systems Research Articles

Data-Based Estimation of the Dynamic Reliability and Performance Indicator of an Industrial Manufacturing System

The aim is to develop a more simple and effective method's performance and dynamic reliability assessment for complex industrial systems. By using the operating data of the industrial system characterized by a strong desynchronization and applying to it prediction algorithms of artificial intelligence applied to the time series, the model will have learned from the behavior of the complex manufacturing system allowing the operator or decision-maker to better orientate the maintenance, production, and quality policies. Furthermore, we propose this approach to avoid tedious mathematical methods related to dynamic reliability calculations and performance evaluation to make forecasts of the company's operation over a long period by identifying future bottlenecks in the system's behavior. The low-performance indicators and irrelevant reliability presented by many third-generation industries are due to the lack of efficient and simple tools for reliability assessment taking into account the dynamic aspect of the different elements of the production chain, maintenance department, production department, and quality department. We propose to develop a model that will abstract from conventional, complex, and inefficient mathematical methods for systems subject to combinatorial explosion problems in the manufacturing industry.

System dynamic reliability evaluation of multiple failure modes of earth dams subjected to strong earthquake excitation

System dynamic reliability evaluation of multiple failure modes of earth dams subjected to strong earthquake excitation

MAntRA: A framework for model agnostic reliability analysis

We propose a novel model-agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach – referred to as MAntRA – combines Bayesian inference and stochastic differential equations to evaluate the reliability of stochastically-driven dynamical systems for which the governing physics is a priori unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output-only data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data and aleatoric uncertainty because of environmental effects and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme, and the probability of failure is computed. The efficacy of the proposed approach is illustrated in four numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.

Stability of nonlinear vibrations induced by rolling force in a precise cold mill system

This paper investigates the stability of horizontal nonlinear vibration of four-high cold mill under the effects of gyro-precession and eccentricity between rolls. The threshold value of chaos about Smale horseshoe commutation is given from Melnikov method, and the correctness of the result is verified by the fractal process of the attraction basin. Through the analyzes of bifurcation, maximum Lyapunov exponents and bi-parameter bifurcation, it is revealed for the effect of different parameters variation on the nonlinear dynamic behavior of horizontal vibration in rolling system. The results show, the fluctuation amplitude of horizontal force increases, the stable domain decreases, and once its value ≥3.5, it is necessary to prefer to the adjustment of parameter-exciting stiffness; meanwhile, it is noticeable that the critical points of damping and average force of the system with bifurcation or chaos appear hysteresis. The evolutions of system dynamics with four pairs of parameter changes confirm the quantitative optimal couple of one structural plus one process parameter in the system. Based on this, we can also find a balance between the average horizontal force and eccentricity, so as to optimize the structural design so that there is a proper and reliable eccentricity between the rolls. The results provide a theoretical reference for service stability and dynamic reliability of the rolling mill system.

Stochastic dynamic response and seismic fragility analysis for high concrete face rockfill dams considering earthquake and parameter uncertainties

The multiple uncertainties of soil properties and ground motions significantly affect the seismic response of high concrete face rockfill dams (CFRDs). Three types of randomness (the material parameter randomness, stochastic seismic excitation, and their coupling) are generated by stochastic ground motion model and generalized F-discrepancy (GF-discrepancy) method. The generalized probability density evolution method (GPDEM) is used to analyze the influence of randomness on the stochastic dynamic response and system reliability of high CFRDs. The limit state of CFRD is defined according to the crest subsidence and the stress of face-slab, and a performance-based reliability evaluation framework is established. The results show that the randomness of ground motions dominates stochastic dynamic response of the CFRD and the dynamic reliability at different safety thresholds can be obtained by the above methods. Moreover, the proposed seismic safety evaluation framework provides a significant guidance for designing and analyzing practical engineering projects.

Proposal of quantification method of dynamic system reliability model of digital RPS using Markov state-transition model

ABSTRACT In safety systems of the latest nuclear power plants such as the Advanced Boiling Water Reactor (ABWR) and the latest Pressurized Water Reactor (PWR), digital circuits are used for start-up signals of a reactor protection system (RPS) and emergency core cooling systems (ECCS). And several studies have been conducted to develop the method to build a system reliability model of RPS to be combined with probabilistic risk assessment (PRA) so far. However, these studies have not been sufficiently progressed in terms of the quantitative evaluation and coupling with the conventional PRA method. Despite of the efforts of Task group of Digital system reliability failure mode taxonomy (DIGREL, later becoming Working Group on Digital Instrumentation and Control [WGDIC]) of Organization for Economic Co-operation and Development (OECD)/Nuclear Energy Agency (NEA) in this field, the situation has not changed sufficiently. From these backgrounds, this paper presents a rational quantitative evaluation method of the dynamic system reliability model of the digital RPS which can represent time-dependency and is consistent with the conventional PRA method.

Active extremum Kriging-based multi-level linkage reliability analysis and its application in aeroengine mechanism systems

To improve the computational efficiency and accuracy of dynamic multi-component system reliability analysis involving complex characteristics like dynamic traits, high-nonlinearity, and failure correlation, an active extremum Kriging-based multi-level linkage method (AEK-MLL) is proposed by incorporating the benefits of extremum selection technique, active learning Kriging model, and the multi-level linkage strategy. In AEK-MLL modeling, the extremum selection technique first converts the dynamic candidate sample domain into a steady-state candidate sample domain, and the active learning technique searches for the best training samples, to build the active extremum Kriging model of component-level limit state functions (LSFs); moreover, the multi-level linkage strategy is adopted to take failure correlation into account, to establish a reliability framework for complex dynamic multi-component systems. The proposed method is first validated by a dynamic numerical case and three system numerical cases, and then applied to the dynamic multi-component reliability analysis of a typical aero-engine mechanism system. The numerical cases and engineering case show that the AEK-MLL holds the high-accuracy and high-efficiency in dealing with the complex dynamic multi-component system reliability analysis.

Dynamic reliability analysis of gear transmission system based on sparse grid numerical integration and saddle‐point approximation method

AbstractGear systems are widely used in various mechanical transmission systems. This paper aims to develop an effective and practical method for dynamic reliability analysis of gear transmission system. The proposed method can comprehensively evaluate the dynamic reliability of gear transmission system by adopting the fourth‐moment SPA method. First, a nonlinear dynamics model of a single‐stage spur gear transmission system is established, which simultaneously takes into account the nonlinear backlash, time‐varying meshing stiffness, and static transmission error. After that, a dynamic reliability model for the tooth surface contact fatigue failure of gear system is established with the uncertainty of the motion, structure, and material parameters using stress‐strength interference (SSI) theory. To be specific, the sparse grid numerical integration (SGNI) method is applied to solve the statistical characteristic parameters of the dynamic reliability of the system. The probability distribution of the performance function is obtained with the fourth‐moment SPA method. Test examples show that the results of the proposed method are consistent with the results obtained by the Monte Carlo simulation (MCS) and superior to the maximum entropy with fractional moments (ME‐FM) method, which verifies the effectiveness of this approach. Finally, the dynamic reliability of the gear transmission system with respect to load times is evaluated.

Dynamics research on gear transmission system of oscillating float wave energy generator

Aiming at the problem of dynamic characteristics and dynamic reliability of gear transmission system in point wave acquisition system, combined with the characteristics of randomness and instability of waves, the dynamic model of gear transmission system is established based on the simulation of actual wave excitation, and the dynamic response of gear transmission system is solved. Using rain flow counting method, the time history of gear contact stress is statistically analyzed, and the contact stress spectrum and probability distribution function of each gear pair are obtained. Based on the random process function of the stress-strength interference model, the Monte Carlo method is used to calculate and analyze the change law of the reliability of the gear transmission system over time. The results show that the reliability of the gear transmission system gradually decreases with the increase of time within 20 years, and finally the reliability is 0.8. Speed increasing gear has the greatest impact on the reliability of the transmission system.

Stochastic dynamic analysis of nonlinear MDOF systems under combined Gaussian and Poisson noise excitation based on DPIM

Random vibration analysis of structures subjected to combined Gaussian and Poisson white noise excitation is a challenging issue. In this paper, a novel direct probability integral method (DPIM) is suggested to address stochastic responses and dynamic reliability of nonlinear multi-degree-of-freedom (MDOF) systems under combined excitation. Firstly, probability density integral equation (PDIE) of MDOF system under combined excitation is derived based on the principle of probability conservation. Then, DPIM is proposed to achieve the probability density function of stochastic response by solving deterministic motion equation of MDOF system and PDIE in sequence. To solve PDIE, two techniques, i.e., partition of input probability space and smoothing of Dirac delta function, are introduced. From the perspective of probability conservation, furthermore, the equivalent relationship between the PDIE and the corresponding probability density differential equation of a Markov system under combined Gaussian and Poisson noise is established. Since Dirac delta function is analytically integrated as Heaviside function, the first-passage dynamic reliability of MDOF system under combined excitation is readily evaluated by introducing the extreme value mapping of stochastic response. Finally, two nonlinear MDOF systems, including multiple-span bridge under combined vehicle load and non-stationary seismic excitation, are solved. Results demonstrate that the proposed DPIM is effective for random vibration and dynamic reliability analyses of MDOF structures excited by combined Gaussian and Poisson noise, and considering the randomness of vehicle load and seismic excitation simultaneously in the bridge design benefits the safe operation of bridge.

Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method

Analyzing the reliability of a stochastic dynamical system represents one of the most challenging problems in stochastic dynamics. In this paper, the reliability of dynamical systems excited by combined Gaussian and Poisson white noise is investigated by adapting the path integral (PI) method. We derive the PI solutions for the reliability based on the reliability density function (RDF), where the short-time transition probability density function (TPDF) for the PI method is derived based on the Fourier transformation. And the impact of the combined noise on the reliability is analyzed theoretically for the one-dimensional case. We prove that the reliability for the system excited by combined noise will approach that for the system excited by Gaussian white noise when the mean arrival rate goes to infinite and jump amplitude for the Poisson white noise satisfies certain conditions. Then, one-dimensional and single-degree-of-freedom (SDOF) dynamical systems excited by combined Gaussian and Poisson white noise are worked out to show the application of the PI method on the reliability. Reliability under different system parameters is calculated and presented. The roles of jump amplitude with different distributions on the reliability are calculated and compared, which verifies the theoretical results. Moreover, it is discovered that the first passage of the system is more easily caused by the Gaussian white noise compared with the combined Gaussian and Poisson white noise when the noise intensity is the same.

Study on dynamic reliability of permanent magnet gear transmission system with wear and failure correlation

To reveal the features of the gear wear and failure correlation on the system reliability, comprehensive consideration of PMSM characteristics, gear internal structure and load torque, the permanent magnet gear transmission system dynamic model is established based on the motor theory and Maxwell equation. The gear variable amplitude fatigue load spectrum is statistically analyzed by rain flow counting method and Goodman theory. On this basis of nonlinear damage theory and modified P-S-N curve, the dynamic reliability of gear single failure mode considering the number of random loads and strength degradation is predicted. Finally, based on the Copula function, the change regularities of the system dynamic reliability are analyzed by using the relationship between the correlation function and reliability.

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.

Dynamic reliability modeling for general standby systems

General standby systems with component lifetimes following independent and nonidentical phase-type (PH) distributions are presented in a state-space model using state transition block matrices. The model is constructed by identifying a block matrix representing each system state and a block matrix that causes a transition from one system state to another. This general model is applicable to hot, warm, or cold standby and any combination of them in K-out-of-N general standby structures. The resulting model becomes a PH representation of the system lifetime distribution and is thus useful for exact dynamic system reliability analysis. The advantage is that many functional system reliability measures, such as the reliability, hazard, and mean residual life functions, can be obtained by simple matrix algebra. These functions are shown to be useful for determining optimal component ordering. Comparisons with other methods from previous publications are presented.

Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations

In practical geotechnical engineering of slopes, it is well-known that the uncertainty of soil properties and ground motions need to be considered for the safety of the project. The effect of uncertain parameters and stochastic ground motions on seismic responses as well as dynamic failure probabilities of slopes are analyzed and discussed in this study. A recently proposed generalized probability density evolution method (GPDEM) is formulated to investigate the system reliability of complex slopes with consideration to uncertainty in multiple slope parameters and in ground motions. Firstly, the fundamental theory of dynamic stability, GPDEM, dynamic system reliability, generation of random samples and stochastic ground motion model are described. Then, the efficiency and accuracy of proposed GPDEM are verified and a novel evaluating index is presented. Four complex slopes, each with multi-parameter uncertainties, are examined in separate study cases. Each study case uses GPDEM to study the random dynamic responses as well as probability responses of slopes while considering deterministic ground motion. The efficiency and accuracy of GPDEM used in complex slopes are validated by comparing with the Monte Carlo method (MCM). In addition, a novel evaluating index called the average large failure probability Pff, is proposed to describe the failure probability of the slopes, and can take the probability time histories intoaccount. Finally, the seismic system reliability of complex slopes is evaluated using the time-history method, and randomness in earthquakes, parameters and their coupling are investigated. The stochastic dynamic responses and probability responses of deterministic parameters subjected to stochastic earthquake excitations, and random parameters subjected to stochastic earthquake excitations are also discussed and are compared based on study case 3. The results demonstrate the high accuracy and validity of the GPDEM. Furthermore, the probability of failure and the degree of safety for the slopes can be directly estimated through probability analysis. In addition, the results also indicate that randomness in ground motions have a much larger influence than randomness in slope parameters, but randomness in slope parameters cannot be completely neglected.

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.

Active learning and relevance vector machine in efficient estimate of basin stability for large-scale dynamic networks.

The interconnectivity between constituent nodes gives rise to cascading failure in most dynamic networks, such as a traffic jam in transportation networks and a sweeping blackout in power grid systems. Basin stability (BS) has recently garnered tremendous traction to quantify the reliability of such dynamical systems. In power grid networks, it quantifies the capability of the grid to regain the synchronous state after being perturbated. It is noted that detection of the most vulnerable node or generator with the lowest BS or N-1 reliability is critical toward the optimal decision making on maintenance. However, the conventional estimation of BS relies on the Monte Carlo (MC) method to separate the stable and unstable dynamics originated from the perturbation, which incurs immense computational cost particularly for large-scale networks. As the BS estimate is in essence a classification problem, we investigate the relevance vector machine and active learning to locate the boundary of stable dynamics or the basin of attraction in an efficient manner. This novel approach eschews the large number of sampling points in the MC method and reduces over 95% of the simulation cost in the assessment of N-1 reliability of power grid networks.

An X-shaped-switching-network high-step-up converter for grid integration of renewable energy sources

Power converters play a pivotal role in forming modern renewable energy sources integrated power grids. Among all grid-forming converters, high step-up converters with great nonlinear dynamic responses and fault recovery abilities have been sought after and developed in recent decades. This study proposes a novel X-shaped switching network (X-net)-based high-step-up converter. Specifically, an X-shaped switching network is designed to realize energy conversion of the converter, which, different from traditional impedance networks, only comprises switches and diodes. With this radically new X-shaped network, the proposed X-net converter is able to realise additional voltage pumping and low capacitor stress, hence improving dynamic responses and system reliability. In this study, the theory, analysis and simulation and prototype experiments of the proposed X-net converter with additional voltage pumping are presented in detail. Extensive comparisons between the X-net converter and its traditional counterparts are also presented which verifies the superiority of the proposition. The proposed X-net based high step-up converter bears significant potential as future grid-forming converters.

Research on Reliability Analysis Method Based on Dynamic Fault Tree

Due to the development of digital technology, digital I&C systems have replaced analog I&C systems and become the mainstream I&C systems for nuclear power plants and marine nuclear power plants. However, there is still a lack of effective and recognized analysis methods for the reliability analysis of digital I&C systems. Based on the commonly used dynamic fault tree analysis method for dynamic system reliability analysis, this paper uses Markov transition matrix to achieve quantitative analysis. Reliability analysis of the digital I&C system, through the improved dynamic fault tree analysis method, provides an effective analysis method for the reliability analysis of the digital I&C system.

An Inductive Coupler Array for In-Motion Wireless Charging of Electric Vehicles

An inductive power transfer (IPT) system is envisaged as the best solution to conveniently charge electric vehicles (EVs). While stationary IPT systems are becoming commercialized, significant research is being conducted to address the challenges related to dynamic IPT systems. Dynamic or in-motion IPT systems require a fully electrified roadway with embedded inductive couplers with accompanying circuitry. The large number of electronic components required, however, increases the system complexity, reducing the reliability and economic viability of dynamic IPT systems proposed to-date. This article proposes a simple yet robust push-pull driven coupler array (PPCA), aiming to decrease the number of switches required to drive the in-road couplers. This article is the first to report a configuration where only N+1 switches are required to independently energize N primary IPT couplers. Any number of couplers can be activated simultaneously in the array without proportionally increasing the current stress on the switches. A state-space model is developed and implemented in PLECS to investigate the efficiency and power transferred to an EV traveling over the proposed PPCA while considering the variation in the coupling and the self-inductances of the couplers. A 3.3-kW scaled prototype PPCA consisting of three primary couplers and two secondary couplers has been implemented to validate the performance of the proposed configuration.