Time-variant Reliability Model Research Articles

Time-varying Reliability Analysis of Contact Fatigue Strength for Nutation Face Gear Transmission

Background: Nutation face gear transmission is a patent about a new type of transmission based on meshing between two face gears. It replaces spur gear with internal face gear to form a “faceface” meshing gear pair and actualizes its deceleration function by combining the nutation principle, which has the advantages of both face gear and nutation drive. Objective: The purpose of this paper is to establish the time-varying reliability calculation model of contact fatigue strength based on fractal contact theory, so as to improve the reliability, safe service and further optimization design of the nutation face gear transmission. Methods: The time-varying uncertainties of the contact stress and the allowable contact stress of the face gear teeth are analyzed respectively, and then the time-varying reliability model of the contact fatigue strength is established. Finally, the drift rate and fluctuation rate of each random variable are simulated using the Monte Carlo simulation method to obtain the time-varying reliability of the contact fatigue strength for the nutation face gear drive. Results: The results show that the general trend of geometric Brownian motion locus of each random variable is consistent with the actual situation. Conclusion: For the given example of the nutation face gear transmission device, the reliability of the contact fatigue strength of the planetary face gear meshing with the fixed face gear and the rotating face gear within one year is calculated to be 0.9912 and 0.9856 respectively, and the maximum vibration noise is about 68dB, which meets the expected value.

A Reliability-Based Robust Design Optimization Method for Rolling Bearing Fatigue under Cyclic Load Spectrum

Reliability-based robust design methods have been widely used in the field of product design; however, they are difficult to apply to the fatigue reliability design process of rolling bearings due to the problems of determining fatigue accumulated damage caused by the internal cyclic time-varying load distribution of rolling bearings and the computational cost of time-varying reliability. Therefore, a reliability-based robust design method for rolling bearing fatigue failure is proposed, which derives the formula for fatigue accumulated damage of a rolling bearing under cyclic load spectrum and significantly reduces the computational cost of rolling bearing time-varying reliability compared with existing methods. First, the state response of a rolling bearing under random design parameters is obtained by finite element simulation. Then, the adaptive kriging method is used to characterize the correlation between the random parameters and the state response. The Miner fatigue cumulative damage theory is improved and the rolling bearing fatigue time-varying equation of state under cyclic load spectrum is derived. Subsequently, a fatigue time-varying reliability model based on an improved fourth-order moment method is developed, and a reliability robust optimization design method is proposed. Finally, a rolling bearing example is presented to demonstrate that the method achieves time-varying fatigue reliability design under cyclic load spectrum and effectively improves the reliability and robustness of the product design.

Service Life Prediction of Flexible Concrete Mattresses (FCMs) in the Yangtze River

Many scholars have studied the failure mechanism of waterway regulating structures, but there is still a need to improve research on their reliability and service life in the industry. Currently, flexible concrete mattresses (FCMs) are the regulating structure widely used on the Yangtze River Golden Waterway, so it is important to study their service life. The stability function has been built based on the mechanism of stability against sliding and a time-varying reliability model. Experiments have been conducted to analyze the critical failure load of FCMs, determine the influence parameters, and derive a service life calculation formula. Finally, the middle reaches of the Yangtze River were taken as an example for analysis.

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.

Dynamic reliability evaluation of buried corroded pipeline under rockfall impact

Load impact, such as the rockfall, may bring significant threats to the integrity management of pipeline. This study is intended to evaluate the reliability of buried pipeline under rockfall impact, and so as to reduce the possible failure and unnecessary downtime. Firstly, the dynamic response of the buried pipeline under load is analyzed by Euler Bernoulli foundation beam. After that, the process of rockfall impact on buried corroded pipeline is simulated with nonlinear finite element method. Furthermore, the influence of rockfall’s parameters (including rockfall mass, impact velocity, impact position, etc.) on the pipeline’s equivalent stress is quantitatively analyzed. Eventually, a time-varying reliability model is established to calculate the failure probability. The results indicate that the mass and velocity of the rockfall have obvious influence on the pipeline’s failure probability, and the change of impact’s position has small influence. The proposed method can provide a theoretical reference for the design and maintenance of buried pipeline.

Multiaxial fatigue damage and reliability assessment of aero-engine compressor blades made of TC4 titanium alloy

This paper discusses the multiaxial fatigue damage and reliability evaluation of aero-engine compressor blades using an improved strength degeneration scheme based on Chaboche damage model combined with stress-strength interference (SSI) approach. Firstly, the multiaxial proportion and non-proportion fatigue tests of TC4 (Ti-6Al-4V) alloy under a series of loading paths are carried out. The nonlinear fatigue damage calculation and life prediction of TC4 alloy is described by combining the Chaboche nonlinear damage criterion and critical plane method with proposed damage control parameter. Secondly, a nonlinear strength degradation model based on accumulative damage is further developed, and it is proved that the model can get greater precision under different loading conditions. Finally, a revised time-varying reliability model is established by viewing mechanical characteristic of compressor blade set as interconnected system with variant load component on each blade. According to the results of Monte Carlo simulation, the proposed revised model has a better prediction precision, with the error controlled less than 5%.

On the use of probabilistic and non-probabilistic super parametric hybrid models for time-variant reliability analysis

Due to having a large number of uncertain variables originating from various sources in time-variant reliability problem, the methods for taking account of these uncertainties are of high significance in engineering. In this study, a novel hybrid time-variant reliability model is established based on a probabilistic model and a super parametric convex model. The probabilistic and non-probabilistic parameters can be addressed simultaneously using this model. The stochastic processes are discretized using the expansion optimal linear estimation method to capture the correlation among different time nodes. In addition, the hybrid reliability iteration method is presented to obtain the upper and lower bounds of failure probability simultaneously. Subsequently, a new relaxed reliability iteration method is proposed to solve the hybrid time-variant reliability model. The relaxed method is adopted to ensure the robustness and efficiency of the proposed method. Three examples are discussed to demonstrate the validity and usage of the presented methodology.

A dynamic time-varying reliability model for linear guides considering wear degradation

This paper devotes to providing a dynamic reliability model for linear guideways for the whole life. Since a linear guide is always worn, the wear degradation of the linear guide is established. Moreover, the profile error of rail is considered. To get the dynamic behavior of linear guides precisely, we developed a dynamic stiffness model of the system in terms of different load conditions and operation time. The reliability model with variant stochastic parameters is proposed according to the contact characteristics of linear guides. The Monte Carlo method is adopted to solve the reliability of linear guides. The simulation results show the reliability curve agrees with the experimental results, as well as the engineering experience in practice. The proposed model can be well applied to the reliability prediction for linear guideways.

Design of Concrete Building Structure in Marine Corrosion Zones

Zhao, H.R., 2020. Design of concrete building structure in marine corrosion zones. In: Al-Tarawneh, O. and Megahed, A. (eds.), Recent Developments of Port, Marine, and Ocean Engineering. Journal of Coastal Research, Special Issue No. 110, pp. 266–270. Coconut Creek (Florida), ISSN 0749-0208.Building structures in offshore areas are extremely susceptible to chloride ion erosion in seawater or marine atmospheric environment, causing problems such as corrosion and swelling of steel rebar, spalling of concrete protective layer, etc., reducing the service life of the structure, and increasing the maintenance and operating costs of the structure. This paper attempts to enhance the design concrete building structures in the marine corrosion zones from the two aspects of durability and service life. To this end, it summarizes the principles of chloride ion erosion of reinforced concrete structures in coastal areas based on existing research, and explores the destruction mechanism of reinforced concrete structures under the action of chloride ions and external loads. Finally, the new method suitable for durability design of reinforced concrete structures in marine corrosion zone was proposed. The study found that the chloride-induced corrosion to the structure in the marine environment can cause the corrosion of the steel bars and accelerate the corrosion rate; a time-varying reliability model of the reinforced concrete structure was proposed; the increase in the thickness of the steel protective layer in the concrete can effectively improve the durability and service life of the structure. The research findings provide a theoretical basis for the durability design of concrete structures in offshore environments or marine corrosion zones.

Time-varying reliability prediction modeling of positioning accuracy influenced by frictional heat of ball-screw systems for CNC machine tools

Thermally induced elongation of a screw is the primary cause of deterioration in the positioning accuracy of half-closed-loop screw systems in machine tools. The failure mode of ball-screw feed-drive systems in relation to the positioning accuracy is defined as the response error of the carriage exceeding the axial tolerance. It is still challenging to accurately predict the thermal errors using conventional methods because the randomness of the influencing factors is not considered. This paper presents an improved random thermal network model subjected to dynamic thermal excitation for calculating real-time transient temperatures of ball-screw systems. Furthermore, a time-varying reliability model is proposed for estimating the gradual reliability of the thermally induced positioning accuracy of ball-screw systems with random thermal boundary parameters using the random thermal network. A ball-screw system of a computerized numerical controlled lathe is used as an example to show the practical application of the proposed model. Repeated experiments demonstrate the accuracy retaining ability and robustness of this method. This work provides the theoretical and practical method for real-time monitoring of the positioning accuracy reliability index for ball-screw systems and it has high accuracy considering the random parameters.

Time-variant reliability analysis of motor-hanger connecting bolts in electric trains

Due to variables in design, manufacturing and working conditions, the working loads of connecting bolts for motor hangers in electric-multiple-unit trains are uncertain. To reduce this uncertainty and improve the reliability of connecting bolts, a novel time-variant reliability analysis method has been developed. First, a parametric finite-element model of a motor hanger was established. The probability distribution of working loads for connecting bolts was then obtained by Monte Carlo simulation. Second, a one-dimensional Brownian differential equation considering the uncertainty of bolt working loads was derived based on Itō’s lemma, and expressions of the mean and variance of bolt stresses under time-variant conditions were given. The time-variant reliability model of the bolts was then constructed based on a time-variant stress–strength interference model and solved by the most-probable-point method. The results showed that the reliability calculated by this method was lower than that of the traditional method and therefore safer. It was concluded that the uncertainty of the working load has a great impact on reliability.

Non-Probabilistic Time-Varying Reliability-Based Analysis of Corroded Pipelines Considering the Interaction of Multiple Uncertainty Variables

Reliability analysis of corroded pipelines is critical to the integrity and safe working of pipeline infrastructure. Aiming at less probability information is obtained for corrosion pipeline engineering, and the mechanical properties of pipeline with corrosion defects deteriorate caused by the accumulative effect of corrosion growth. Based on the quasi-static analysis method and non-probability theory, this paper presents a reliability model for assessing corroded pipelines with corrosion growth. In fact, reliability analysis of corroded pipelines needs to consider the interaction of multiple uncertainty variables. By introducing interaction theory, a mathematical model of corrosion defects considering the interaction of variables is put forward. Moreover, this paper develops a non-probabilistic time-varying reliability method for pipeline systems with multiple defects. Thus, several numerical examples are investigated to discuss the effectiveness of the proposed methodology. The results show that a two-dimensional or even three-dimensional ellipsoid model with correlation has more accurate results to evaluate corroded pipelines under the interaction of multiple corroded defects with poor information. Furthermore, a non-probabilistic time-varying reliability model is established according to the time-varying characteristics of the corroded pipeline under the influence of multiple factors. An effective complement to the theory of non-probabilistic reliability analysis of system is investigated. The analysis of the results suggests that interaction of corroded pipeline has a negligible impact on reliability. It also provides a theoretical basis for maintenance and is of great significance for risk- and reliability-informed decisions regarding buried oil and gas pipelines.

A Time-Variant Reliability Model for Copper Bending Pipe under Seawater-Active Corrosion Based on the Stochastic Degradation Process.

In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion.

Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process

The study on reliability of an aging structure requires taking into account the influence of time. Typical approaches for performing time-variant reliability assessment are always based upon the random process model, where the dynamic distributions of uncertain parameters are determined by a substantial number of samples. In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which we describe the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times. By combining with the set-theory approach and the classical first-passage theory, a new non-probabilistic model of safety evaluation for time-dependent structures is established, and its measure index is then analytically calculated. The proposed model of time-variant reliability is suitable for both the cases of stationary process and non-stationary process. Moreover, the Monte Carlo method is also presented as a means of verification. The comparison between the presented model and the Monte Carlo-based model is eventually carried out on two application examples; the usage, efficiency and accuracy of the developed approach can be demonstrated.

Long-Term Maintenance Scheduling of Smart Distribution System through a PSO-TS Algorithm

Asset management of distribution systems is an important issue for smart grid. Maintenance scheduling, as an important part of asset management, affects the reliability of distribution equipment and power supply. This research focuses on long-term distribution system maintenance scheduling aided by available operation information, which is a prominent advantage of smart grid over conventional distribution systems. In this paper, the historical and future operation information in smart grid is taken into account through a decoupled time-varying reliability model of equipment. Based on distribution system reliability assessment, a maintenance scheduling model is proposed to determine the optimal implementation time of maintenance activities to minimize distribution systems’ total cost, while satisfying reliability requirements. A combined algorithm that consists of particle swarm optimization and tabu search is designed and applied to the optimization problem. Numerical result verifies that the proposed method can schedule long-term maintenance of distribution systems in smart grid economically and effectively.

Modeling for Time-Variant Reliability of Mechanism

A novel time-variant reliability model is developed after studying the traditional dynamic performance of mechanism. The expression of reliability is given based on stochastic process. A two-dimensional description of the error generating process is established by studying mechanism output kinematic accuracy. The reliability of mechanism output kinematic accuracy can be obtained according to this description. The model proposed can be used to calculate the reliability of mechanism directly, if the distribution of mechanism output kinematic accuracy is known.