Stress-strength Interference Model Research Articles

Building reliability of risk assessment of domino effects in chemical tank farm through an improved uncertainty analysis method

The severity and complexity of fire-induced domino effects have received widespread attention. The spatial and temporal evolution process modeling of domino accidents is still stuck in single crisp value, in which the uncertainty will affect the reliability of the results. In this paper, we propose a computational method for uncertainty propagation of the evolution process modeling of the domino effect called Uncertainty Propagation of Domino Evolution Model (UPDEM), aiming to increase the reliability of risk assessment results. The method is capable of obtaining ranges and corresponding probability envelopes for tiame to failure and escalation probabilities, and quantifying uncertainty for all computational models that require input parameters. The uncertainty is quantified based on the evidence theory and a parameter cropping method based on the stress-strength interference model is proposed to optimize the evidence theory. The proposed method is applied to a case study and compared with previous studies. The comparison confirms that the results are more reliable after considering uncertainty and can produce the worst possible scenario consequence. Conducting the sensitivity analysis to prioritize the treatment of parameters and identify effective measures in risk control. The methodology can provide an important reference for decision-makers to prevent and control domino effects.

Reliability analysis of aerospace planetary roller screw mechanism considering multiple failure modes

Abstract Faults in planetary roller screw mechanisms under typical aerospace operating conditions are usually caused by the combined effects of multiple coupled failure modes. Reliability analysis methods that ignore correlation often lead to significant errors. In this paper, the failure models of the planetary roller screw mechanism under fatigue elastic failure, wear failure, and fracture failure are analyzed based on the stress-strength interference model, and failure functional functions are provided. The improved O. Ditlevsen second-order reliability bound theory is used to characterize the relationships between multiple failure modes. Using this method, reliability analysis and calculation of planetary roller screw pairs considering multiple failure modes have been performed, verifying the rationality and effectiveness of this method.

Multi-Indicator Fused Resilience Assessment of Power Grids Considering Wind-Photovoltaic Output Uncertainty during Typhoon Disasters

Extreme weather events such as typhoons pose a serious threat to the safe operation of power grids. In the field of power system resilience assessment during typhoon disasters, a parametric typhoon wind field model combined with actual historical meteorological data has not been well adopted, and the conventional renewable energy uncertainty modeling methods are not suitable for typhoon disaster periods. In this paper, a multi-indicator fused resilience assessment strategy considering wind-photovoltaic uncertainty and component failure during typhoon disasters is proposed. Firstly, based on the actual historical meteorological data of typhoons, an uncertainty model of typhoon wind speed is established by a rolling non-parametric Dirichlet process Gaussian mixture model. Then, a spatial–temporal contingency set is constructed by considering the best-fit wind field model and stress–strength interference model for failure probability of transmission lines. On this basis, a holistic resilience assessment framework is established from the perspectives of priority, robustness, rapidity, and sustainability, and the entropy weight method combined with the technology for order preference by similarity to an ideal solution is leveraged to obtain the comprehensive resilience indicator. Finally, numerical studies are performed on the IEEE-30 bus test system to identify vulnerable lines and improve system resilience during typhoon disasters.

Stochastic pre‐disaster planning and post‐disaster restoration to enhance distribution system resilience during typhoons

AbstractIn recent years, extreme weather events, such as typhoons, have led to large‐scale power outages in distribution systems. As a result, developing strategies to bolster distribution system resilience has become imperative. This paper proposes a two‐stage stochastic programming model aimed at enhancing this resilience. Prior to a typhoon, the first stage establishes a comprehensive wind field model based on extreme value distribution for accurate wind speed predictions. Simultaneously, a refined stress–strength interference model is used to determine the likelihood of distribution line failures. Taking into account the uncertainty of line damage, repair crews and mobile emergency generators are then strategically positioned at staging depots. Following the typhoon, the second stage coordinates network reconfiguration, dispatches repair crews, and mobilizes mobile emergency generators to minimize load shedding and expedite repairs. This model was validated on the IEEE 33‐bus distribution system, coupled with a corresponding transportation network, utilizing data from the 2018 super typhoon Mangkhut'' in China. Simulations indicate that our approach can effectively reduce load shedding and power outage durations, thereby enhancing the resilience of distribution systems.

Resilience enhancement of distribution network under typhoon disaster based on two-stage stochastic programming

The reliability of power supply in distribution network is vulnerable to extreme weather events such as typhoon. Pre-event preparation can effectively mitigate the deterioration of system resilience. Therefore, we propose a distribution network resilience enhancement decision-making framework which is formulated as a two-stage stochastic mixed-integer linear programming (SMILP) model. The first stage invests coordinately in four strategies, including hardening lines, installing distributed generators (DG), allocating mobile emergency generators (MEG), and deploying switches, etc. And the goal at the first stage is to minimize the investment cost of resilience enhancement strategies. The objective at the second stage is to ensure the minimum expected recourse operation cost of the comprehensive strategies for all typical scenarios. The proposed model can combine distribution network long-term resilience planning with short-term post-event recovery. Furthermore, in order to address the uncertain problems of wind field, line damage and load fluctuations under typhoon disaster, this paper proposes the following solutions. For wind field uncertainty, a detailed wind field model considering time transition, sea-land transition and extreme value distribution is established to deal with wind speed prediction. For line damage uncertainty, an improved stress-strength interference model is set up. And for the load fluctuation uncertainty, scenario generation using load random multipliers is applied to address load uncertainty. The proposed framework is tested in IEEE 33-bus distribution system using historical data from 2018 super typhoon “Mangkhut” in China and demonstrates the SMILP model can significantly reduce the post-event expected recourse operation cost and meanwhile improve the distribution network resilience.

A new calculation method of bearing reliability of tyre unloader based on heterogeneous dimensional interference model

Bearing is an important rotating support part of tyre unloader, and its fatigue reliability is an important part of the whole system reliability. Because of the huge alternating stress, the support bearing is required to have high fatigue life and reliability. In this paper, combined with stress-strength interference model and statistical theory, the life distribution of bearing steel material is predicted by using group test data; Based on the multi-rigid body dynamics and finite element numerical simulation platform, the reliability of the bearing of tyre unloader under different operating years was predicted by using the different dimensional interference model. The results show that the maximum resultant force of the bearing at the bottom rocker arm of the tyre unloader can reach 150kN, and the maximum transverse and longitudinal forces can reach 108kN and 78kN. When bearing the weight of the whole tyre and turning, the inertia force is the largest, the maximum stress value is 1316.2MPa, which occurs in the bearing inner ring and ball contact part. After the statistics, the stress amplitude distribution of the bearing conforms to Weibull distribution, and the life of the bearing follows lognormal distribution. After 105 tyre unloading, the fatigue reliability of the bearing is lower than 0.82, which is consistent with the actual working condition. Therefore, this model can be used to calculate the fatigue reliability of bearings conveniently and quickly, and provide certain theoretical support for the safety and fatigue reliability prediction of bearings.

Dynamic Reliability Evaluation and Life Prediction of Transmission System of Multi-Performance Degraded Wind Turbine

Wind power is a kind of important green energy. Thus, wind turbines have been widely utilized around the world. Wind turbines are composed of many important components. Among these components, the failure rate of the transmission system is relatively high in wind turbines. It is because the components are subjected to aerodynamic loads for a long time. In addition, its inertial load will result in fatigue fracture, wear and other problems. In this situation, wind turbines have to be repaired at a higher cost. Moreover, the traditional reliability methods are difficult to deal with the above challenges when performing the reliability analysis of the transmission system of wind turbines. To solve this problem, a stress-strength interference model based on performance degradation is introduced. Based on considering the strength degradation of each component, the improved Monte Carlo method simulation based on the Back Propagation neural network is used to obtain the curve of system reliability over time. Finally, the Miner linear cumulative damage theory and the Carten-Dolan cumulative damage theory method are used to calculate the cumulative damage and fatigue life of the gear transmission system.

Plastic deformation-based rolling bearing reliability and sensitivity analysis under incomplete probability information

It is currently difficult to adequately characterize the probability distribution information of rolling bearings, and research on the reliability of rolling bearings based on plastic deformation is lacking. To address this problem, the Latin hypercube design, BP neural networks, and higher-order moment method are combined, fully considering the randomness of the load, geometry, and material parameters of the rolling bearing. The dynamics model of the rolling bearing was constructed by using the Hertz contact theory and Jones model, combined with a Latin hypercube design to obtain neural network training samples. Based on the rational construction of the neural network structure, the mapping relationship between the equivalent stress and the design variables is obtained. The state function of the rolling bearing is constructed according to the stress–strength interference model, and then, the reliability index and reliability of the rolling bearing are obtained using the higher-order moment method, followed by a reliability sensitivity analysis. Finally, the proposed method is applied to the reliability analysis of a certain type of angular contact ball bearing, and the calculation results are compared with the Monte Carlo method results to demonstrate the correctness and effectiveness of the proposed method.

A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure

Traditional dynamic stress-strength interference (SSI) models usually assume that a failure occurs when the magnitude of a shock exceeds the strength. The assumption holds in most circumstances, while it is not applicable for self-healing protective structure which go through a recovery process after each shock. In this paper, a generalized dynamic SSI model combined with the δ-failure criterion is proposed to analyze the reliability for self-healing protective structure. Particularly, the shock is modeled as a non-homogenous Poisson process with stochastic time-varying magnitude, and the strength is modeled as a stochastic degradation path. Two different initial states (i.e., intact state and healing state) are considered under the δ-failure criterion. Then, a Gauss-Legendre-based hierarchical iteration algorithm is established to solve the complex reliability function including multiple internal and external nested integrations. Numerical solutions which can significantly improve the computational efficiency are provided. Finally, a simulation study and a real application to spur gear reducer are provided to illustrate the effectiveness of the proposed model and method.

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.

Dynamic Fatigue Analysis of High-Speed Trains Gearbox Using Copula Function

As a key component of the transmission system of high-speed trains, the reliability of gearbox is crucial to the overall reliability and driving safety of high-speed trains. In this work, a comprehensive reliability model for the key parts of the gearbox including the driving and driven gears, bearings, and gearbox housing is developed, which combines the strength degradation parameters obtained by P-S-N curves of the corresponding material, and a stress-strength interference model based on the Poisson distribution of random stress and the Wiener strength degradation process. Further, a nested Copula function reliability model of the gearbox series system is developed using the binary Frank Copula function considering the correlation of failures of different parts and different failure modes. This model realizes the dynamic reliability analysis of the gearbox under different failure modes. The reliability analysis of the key parts of the gearbox and the gearbox series system of high-speed train achieved with this model are in line with the engineering practice. This method enables dynamic tracking and monitoring of gearbox reliability during the service life of high-speed train.

The Time-Dependent Reliability Analysis of Brake Piston Special-Shaped Seal of the Caliper Disc Brake

To solve the brake caliper disc brake piston sealing ring in the high temperature, pressure, and changeful, complex working environments, such as vibration failure cause brake short service life, low reliability, in the original brake piston O seal ring and cross section, the research, based on the standard of sealing ring, such as special-shaped seal structure is put forward in order to improve the reliability of the caliper disc brake piston sealing performance. Based on the basic concept of time-varying reliability and the theoretical basis of stress-strength interference model, the time-varying reliability model of the plum blossom seal ring of the brake piston under shear stress failure and leakage failure modes was established. The reliability of the plum blossom seal ring under single failure mode and multiple failure modes is obtained. The results show that under the same conditions, the reliability of the plum blossom seal ring is greater than that of the O seal ring, and its sealing performance is better than that of the O seal ring.

Reliability analysis of autonomous underwater vehicle aft pressure shell for optimal design and strength

The lightweight design of the autonomous underwater vehicle (AUV) is a means to improve its resistance. In order to meet reliability requirements of AUV, the lightweight optimization design of aft pressure shell (APS) with sandwich structure is studied. A multi-objective optimization mathematical model is established for the mass and maximum stress as objectives and the strength as constraint condition, which is efficiently adopted by NSGA-II based on Kriging surrogate model. In the reliability analysis, the statistical distributions of the yield strength and the maximum stress is obtained according to the random variable sample and finite element method and then the stress-strength interference model is established. The result shows that the APS with sandwich structure meets the strength requirements and the maximum stress appears near outer skin. The thickness of the sandwich structure has a great influence on the mass and maximum stress. The reliability index of the optimized APS is 5.02, which satisfies three sigma level of random variables and ensures safety and reliability of AUV. The analysis provides reference and technical support for lightweight of pressure shell.

Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence

Multiple failure modes and strength degradation are usually inherent in the gear transmission system, which brings new challenges for conducting fatigue reliability analysis and design. This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of the Copula function and Gamma process. Firstly, the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history. The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model. The marginal distribution functions of tooth contact fatigue and dedendum bending fatigue are calculated respectively based on the dynamic interference model. Finally, the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence, and so the dynamic fatigue reliability considering failure dependence can be estimated. The effectiveness of the proposed method is illustrated with examples. The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.

Importance measure for K-out-of-n: G systems under dynamic random load considering strength degradation

Taking the importance analysis of the compressor rotor system as an opportunity and combining the structural characteristics of the blade, this paper proposes a dynamic importance measure considering component strength degradation for the k-out-of-n: G system under dynamic random load. The k-out-of-n: G system consists of n components, and it works if and only if at least k components are functioning. As an effective analytical tool in the reliability field, the application of importance measures in critical equipment and complex systems is a problem worthy of study. Based on the stress-strength interference (SSI) model, the two most common degradation patterns are incorporated into the modeling of importance measure, i.e., the component strength degrades with the times of load action or degrades with time. The dynamic importance measure not only provides a continuous and dynamic analysis method for the computation of the component importance but also effectively reflects the effects of strength degradation, which will help to identify the weaknesses of systems comprehensively and accurately. A numerical case is presented to illustrate the application of the importance measure and shows some unique properties. Meanwhile, a Monte Carlo (MC) simulation method is developed to validate the results of the proposed importance measure.

Reliability analysis of wind turbine based on degradation threshold

The time-dependent reliability model of the structure was established by using the Gamma process and combined with the stress-strength interference model to describe the product strength degradation process. The characteristics of the failure threshold based on strength degradation was analyzed, and the life distribution of the product can be calculated under the condition of given degradation threshold was pointed out. Taking a vertical axis wind turbine as an example, ANSYS finite element analysis software was used to calculate the load at the stress concentration of the shaft end of the wind turbine. According to the distribution of load and based on the threshold of product degradation, the product lifetime distribution subject to Gamma degradation was analyzed, the variation law of reliability at the shaft end of the wind turbine with time was studied, and the probability distribution of lifetime under a given threshold of degradation was solved. By using this method, the product reliability subject to Gamma degradation and the lifetime distribution under a given threshold could be obtained, which provides a method for product reliability evaluation with difficulty in obtaining reliability data.

Optimal design and strength reliability analysis of pressure shell with grid sandwich structure

This study focuses on lightweight optimum design of head pressure shell of an autonomous underwater vehicle (AUV) with reliability requirements. The grid sandwich structure is applied to the pressure shell for lightweight. An optimal mathematical model is established, which takes weight and the maximum von-Mises stress as objective and strength requirement as a constraint condition. This optimization model is solved by genetic algorithm (GA) based on back propagation (BP) neural network surrogate model, which is optimized by particle swarm optimization (PSO) for improving accuracy. Additionally, the randomness of geometry sizes, material properties and loads are considered to ensure reliability. A stress-strength interference model is established for obtaining failure probability and reliability according to statistical regularity of yield strength and the maximum von-Mises stress. The result shows that the weight of grid sandwich structure pressure shell is reduced by 38.26% compared with the solid pressure shell. The width of transverse grid has more influence on the maximum von-Mises stress than longitudinal grid. The critical load factor is 21.611 and buckling deformation will not occur under given conditions. The pressure shell with grid sandwich structure meets three sigma level with random variables, which can ensure enough reliability of AUV. The above analysis shows that application of grid sandwich structure to the pressure shell of AUV head is feasible.

Reliability model for wind turbine blade composites under alternate action of normal and extreme wind loads

Wind turbine blade is the key component to capture wind power, and it is mainly composed of glass fiber reinforced polymer (GFRP). Due to the randomness and volatility of wind speed in nature, wind turbine blade is usually subjected to the alternate action of normal and extreme wind loads during its long-term service. In this study, a reliability model that considering the stochastic wind loads and strength degradation of GFRP is proposed. Firstly, a residual strength model is developed based on the Palmgren-Miner (P-M) damage theory and the same damage state (SDS) principle, which is capable of characterizing the strength degradation law of GFRP under the normal wind load. Then, the alternate actions of normal and extreme wind loads are considered, and a dynamic reliability model is presented based on Poisson process and mathematical derivation. Finally, the traditional discrete stress-strength interference (DSSI) model is extended to calculate the dynamic reliability when probability distributions of stochastic wind loads and residual strength of GFRP are unknown. The wind load data and GFRP test data are utilized to demonstrate the effectiveness of the proposed model. The result shows that the reliability of GFRP keeps at a high level in the early stage, then it rapidly decreases due to the accumulation of fatigue damage.

Research on solder joint stress damage evaluation method based on discrete SSI model

Based on the discrete SSI(Stress-strength-interference) model, this paper establishes a stress damage evaluation method for the through-hole insertion process. First, based on the Monte Carlo sampling method, the mean value of solder joint stress was clarified, and a stress-strength interference model for through-hole insertion was established. Secondly, after calculating the shape of the solder joints of the through-holes, the simulated load input curve is determined and the stress simulation is performed to obtain the stress and strain simulation results. The stress and strain of the PCB board are measured through experiments. Finally, a random stress model of solder joints was established by Monte Carlo sampling, and a constant strength model of through-hole solder joints was established in combination with material strength. According to the stress strength interference model, the failure probability of process stress damage was calculated, and the stress damage evaluation of solder joints in through-hole insertion process was realized.

Reliability Engineering Design Method based on Generalized Margin Design theory

Traditional reliability indexes in engineering are statistic parameters of failure time or failure rates, these reliability parameters are not related to products’ design parameters directly. In fact, reliability design in engineering process is margin design, for instance, the safety factors approach, the derating design approach, and even the selection of the high quality components carried out by enhancing the margin of resisting the sense stress of failures. This paper proposes a reliability engineering design method based on the general margin theory, and the quantification relationships between the statistic reliability parameters and general margin parameters are established. The general margin proposed in this paper contains the stress margin and function margin. The margin design rules and requirements are defined according to the products(or concepts design) ‘s loads in the predicted lifecycle; and then the stress margin parameters that satisfying the reliability could be determined based on the stress-strength interference model, and these margin parameters could support the products concepts selection; if the stress margin parameters could not satisfy the requirements, then the function margin parameters are analyzed to guide the key function redundancy design until the reliability of the products are meet. This method could improve the suitability of reliability theory in engineering field. This paper demonstrates the availability of this design method with a case study.