Probabilistic Reliability Analysis Research Articles

Hybrid fault tolerant control for air–fuel ratio control of internal combustion gasoline engine using Kalman filters with advanced redundancy

In this paper, a hybrid fault tolerant control system is proposed for air–fuel ratio control of internal combustion gasoline engines based on Kalman filters and triple modular redundancy. Hybrid fault tolerant control system possesses properties of both active fault tolerant control system and passive fault tolerant control system. As part of active fault tolerant control system, fault detection and isolation unit is designed using Kalman filters to provide estimated values of the sensors to the engine controller in case of faults in the sensors. As part of passive fault tolerant control system, a dedicated proportional–integral feedback controller is incorporated to maintain air–fuel ratio by adjusting the throttle actuator in the fuel supply line in faulty and noisy conditions for robustness to faults and sensors’ noise. Redundancy is proposed in the sensors and actuators as a simultaneous failure of more than one sensor, and failure of the single actuator will cause the engine shutdown. Advanced redundancy protocol triple modular redundancy is proposed for the sensors and dual redundancy is proposed for actuators. Simulation results in the MATLAB Simulink environment show that the proposed system remains stable during faults in the sensors and actuators. It also maintains air–fuel ratio without any degradation in the faulty conditions and is robust to noise. Finally, the probabilistic reliability analysis of the proposed model is carried out. The study shows that the proposed hybrid fault tolerant control system with redundant components presents a novel and highly reliable solution for the air–fuel ratio control in internal combustion engines to prevent engine shutdown and production loss for greater profits.

Imprecise Probabilistic Reliability Analysis Method for Mechanism Based on Ellipsoid Model

Imprecise Probabilistic Reliability Analysis Method for Mechanism Based on Ellipsoid Model

PROBABILISTIC RELIABILITY ASSESSMENT OF GATEWAY HEADS BY THE CRITERIA OF STABILITY AGAINST DISPLACEMENT ON THE EXAMPLE OF HYDRO SCHEMES OF THE DNIEPER CASCADE

When calculating and designing modern hydraulic structures, it becomes necessary to assess their reliability and safety based on probabilistic methods. This work further develops the method for assessing reliability of gateway heads by the criteria of stability loss against displacement and overturning.The work considers the random nature of the external loads and impacts, which the gateway heads bear during operation, as well as correlations between them. It also considers the random nature of mechanical properties of the foundation soils and correlations between them. The suggested method allows assessing reliability by the criterion of stability loss against displacement of the gateway heads located both on rock and non-rock foundations. For solving this problem, the method of statistical tests (Monte Carlo method) was applied, which is widely used for assessing probabilistic reliability of complex technical systems.A numerical probabilistic assessment of the risk when the gateway heads on rock and non-rock foundations at hydro schemes of the Dnieper Cascade reach the boundary conditions has been performed. Confidence limits of the probability of losing stability of the gateway heads against displacement are determined; a number of statistical tests required to achieve confident accuracy is determined.Correctness of the obtained results is confirmed by their correspondence with the reliability assessment of the gateway heads of the Dnieper cascade by deterministic analyses using the method of boundary conditions.In the future, the proposed method could be used in probabilistic reliability analyses of hydraulic structures and cascades of hydro schemes, taking into account the correlations between natural factors: hydrological characteristics, wind, and ice, as well as temperature loads and impacts.

PROBABILISTIC RELIABILITY ASSESSMENT OF GRAVITY ABUTMENTS ON ROCK AND NON-ROCK FOUNDATIONS BY THE CRITERIA OF STABILITY AGAINST DISPLACEMENT OF THE GRAVITY ABUTMENTS ON THE EXAMPLE OF HYDRO SCHEMES OF THE DNIEPER CASCADE

When calculating and designing modern hydraulic structures, it becomes necessary to assess their reliability and safety based on probabilistic methods. This work further develops the method for assessing reliability of gravity abutments by the criteria of stability loss against displacement. The work considers the random nature of the external loads and impacts, which the gravity abutments bear during operation, as well as correlations between them. It also considers the random nature of mechanical properties of the foundation soils and correlations between them. For solving this problem, the method of statistical tests (Monte Carlo method) was applied, which is widely used for assessing probabilistic reliability of complex technical systems. In applying the method of statistical tests to assess the reliability of a complex technical system, it is necessary to perform a significant number of statistical tests. This implies determination of internal parameters of the system during each statistical test. A numerical probabilistic assessment of the risk when the gravity abutments on rock and non-rock foundations at hydro schemes of the Dnieper Cascade reach the boundary conditions has been performed. Confidence limits of the probability of losing stability of the gravity abutments against displacement are determined; a number of statistical tests required to achieve confident accuracy is determined. Correctness of the obtained results is confirmed by their correspondence with the reliability assessment of the gravity abutments of the Dnieper cascade by deterministic analyses using the method of boundary conditions. In the future, the proposed method could be used in probabilistic reliability analyses of hydraulic structures and cascades of hydro schemes, taking into account the correlations between natural factors: wind, ice, and hydrological characteristics, as well as temperature loads and impacts.

Nonprobabilistic Reliability Evaluation for In-Service Gravity Dam Undergoing Structural Reinforcement

Influenced by many factors such as material performance attenuation, structural defect repair, and reinforcement, the structural reliability of a gravity dam changes in different periods, which are called dynamic effects. Traditional methods are inclined to calculate and analyze the structural probability reliability from the random or fuzzy uncertain characteristics of parameters. However, in practice, it is difficult to obtain the probability distribution of uncertain parameters as well as the performance function, which is too nonlinear to be expressed. In addition, gravity dam failures are low probability events. Thus, a reliability calculation model and method for the gravity dam system considering dynamic effects under the practice of reinforcement are studied by integrating the theory of interval mathematics and nonprobability reliability. First, with the help of the monitoring data, and physical model and numerical simulation results of the gravity dam before and after the reinforcement, we establish a nonprobabilistic reliability (N-PR) calculation model for the gravity dam element and system based on the bounds of uncertain parameters and propose an inversion method for the bounds of uncertain parameters. Subsequently, by combining the response surface method with the central composite design technique, an N-PR index calculation method for gravity dams considering dynamic effects is developed. It turns out that the given model and method can effectively pave the way to avoid falling into the limitations of classical probabilistic reliability analysis of which the uncertain parameters require to be randomly changed and the results are highly sensitive to the parameters. In addition, it can better adapt to the characteristic of gravity dam performance function, which is too nonlinear to be expressed explicitly. When employing this method to analyze the reliability of gravity dam services, we are able to evaluate and predict the changing process and the trend of it more objectively, and have a closer look at the comprehensive influence and contribution of reinforcement to dam service reliability.

Reliability Evaluation of Hydraulic Conductivity Characteristics of Waste Wood Ash Treated Lateritic Soil

Probabilistic reliability analysis of suitability of compacted waste wood ash (WWA) treated lateritic soils for use as liners and covers in waste containment structures was assessed using FORTRAN-based First Order Reliability Method. This is based on the predictive model developed from regression analysis and statistical analyses (descriptive statistics and regression) of the results of geotechnical properties of both natural and WWA modified samples in which WWA, water content (WC), percentage fine, plasticity index (PI), degree of saturation (Sr) and compactive effort are the independent variables and hydraulic conductivity (k) the dependent variable. In sensitivity, reliability indices (β) decreased with variations in the coefficient of variation for all the variables at West African Standard and British Standard Heavy (BSH) compactive efforts, but increased at British Standard light except WWA which has no effect by remaining constant. Also, reliability indices increased with increase in compactive efforts. However, apart from WWA, PI has the most significant influence in sensitivity followed by Sr and then WC. Analysis of variance showed that compactive effort has significant effect on the outcome of the results. Stochastic assessment of the reliability indices shows that none of the variables has the reliability index values between 2.5 and 4.0 which is the safety margin in structural reliability; however, the use of reliability index value of 1 according to NKB Report (Recommendation for loading and safety regulations for structural design. Nordic Committee on Building Regulation 1978) was favourable only at BSH compactive efforts. Therefore, only BSH could be used successfully to actualize reliable minimum hydraulic conductivity of 1 × 10−9 m/s in the field using WWA treated lateritic soil.

Optimising Monitoring: Standards, Reliability Basis and Application to Assessment of Roof Snow Load Risks

This paper addresses the optimisation of monitoring and decision-making criteria regarding the future use of structures. The current state of practice in standards and reliability framework are initially summarised. A general methodology for obtaining cost-optimal decisions is then presented on the basis of limit state design, probabilistic reliability analysis and cost estimates. The implementation of the risk-based approach is illustrated in a case study dealing with the roof of a stadium located in northern Italy. As the roof fails to comply with the requirements of the Eurocodes, the installation of a permanent monitoring system is recommended to allow for a real-time reliability assessment. The results demonstrate the potential of monitoring systems and probabilistic reliability analysis for supporting decisions regarding safety measures such as snow removal or temporary closure of the stadium, as well as reflecting the need to implement the discussed procedures in future standards.

Early quantification of reliability for a safety critical and control system: a case study of reactor core cooling system

Using Probabilistic Reliability analysis for Quantifying reliability of a system is already a common practice in Reliability Engineering community. This method plays an important role in analyzing reliability of nuclear plants and its various components. In Nuclear Power Plants Reactor Core Cooling System is a component of prime importance as its breakdown can disrupt Cooling System of power plant. In this paper, we present a framework for early quantification of Reliability and illustrated with a Safety Critical and Control System as case study which runs in a Nuclear Power Plant.

Using statistical and interval-based approaches to propagate snow measurement uncertainty to structural reliability

Observations are inevitably contaminated with measurement uncertainty, which is a predominant source of uncertainty in some cases. In present practice probabilistic models are typically fitted to measurements without proper consideration of this uncertainty. Hence, this study explores the effect of this simplification on structural reliability and provides recommendations on its appropriate treatment. Statistical and interval-based approaches are used to quantify and propagate measurement uncertainty in probabilistic reliability analysis. The two approaches are critically compared by analysing ground snow measurements that are often affected by large measurement uncertainty. The results indicate that measurement uncertainty may lead to significant (order of magnitude) underestimation of failure probability and should be taken into account in reliability analysis. Ranges of the key parameters are identified where measurement uncertainty should be considered. For practical applications, the lower interval bound and predictive reliability index are recommended as point estimates using interval and statistical analysis, respectively. The point estimates should be accompanied by uncertainty intervals, which convey valuable information about the credibility of results.

Using statistical and interval-based approaches to propagate snow measurement uncertainty to structural reliability

Observations are inevitably contaminated with measurement uncertainty, which is a predominant source of uncertainty in some cases. In present practice probabilistic models are typically fitted to measurements without proper consideration of this uncertainty. Hence, this study explores the effect of this simplification on structural reliability and provides recommendations on its appropriate treatment. Statistical and interval-based approaches are used to quantify and propagate measurement uncertainty in probabilistic reliability analysis. The two approaches are critically compared by analysing ground snow measurements that are often affected by large measurement uncertainty. The results indicate that measurement uncertainty may lead to significant (order of magnitude) underestimation of failure probability and should be taken into account in reliability analysis. Ranges of the key parameters are identified where measurement uncertainty should be considered. For practical applications, the lower interval bound and predictive reliability index are recommended as point estimates using interval and statistical analysis, respectively. The point estimates should be accompanied by uncertainty intervals, which convey valuable information about the credibility of results. Copyright © 2018 Inderscience Enterprises Ltd.

PROBABILISTIC RELIABILITY ASSESSMENT OF GATE CHAMBERS ON ROCK FOUNDATION BY THE CRITERIA OF STRENGTH, OVERTURNING AND STABILITY AGAINST DISPLACEMENT OF THE GATE CHAMBERS ON THE EXAMPLE OF HYDRO SCHEMES OF THE DNIEPER CASCADE

This work further develops the method for assessing reliability of gate chambers by the criteria of stability loss against displacement and overturning, as well as floating up. The work considers the random nature of the external loads and impacts, which the gate chambers bear during operation, as well as correlations between them. It also considers the random nature of mechanical properties of the foundation soils and correlations between them.For solving this problem, the method of statistical tests (Monte Carlo method) was applied, which is widely used for assessing probabilistic reliability of complex technical systems. A numerical probabilistic assessment of the risk when the gate chambers on rock foundation at hydro schemes of the Dnieper Cascade reach the boundary conditions has been performed.In the future, the proposed method could be used in probabilistic reliability analyses of hydraulic structures and cascades of hydro schemes, taking into account the correlations between natural factors: hydrological characteristics, ice, and wind, as well as temperature loads and impacts.

PROBABILISTIC RELIABILITY ASSESSMENT OF POWERHOUSES BY THE CRITERION OF STABILITY LOSS AGAINST DISPLACEMENT ON THE EXAMPLE OF HYDRO SCHEMES OF THE DNIEPER CASCADE

This work further develops the method for assessing reliability of powerhouses by the criteria of stability loss against forward and slanting displacement along flat and inclined surfaces. It also considers the random nature of mechanical properties of the soil in the foundation and correlations between mechanical properties of the soil . In the future, the proposed method of probabilistic risk assessment of stability loss of powerhouses could be used in probabilistic reliability analyses of hydraulic structures and cascades of hydro schemes, taking into account the correlations between natural factors: hydrological characteristics, ice, and wind, as well as temperature loads and impacts.

Reliability Analysis of Fatigue Fracture of Wind Turbine Drivetrain Components

One of the main challenges for the wind turbine industry currently, is to reduce the cost of levelized energy, especially for offshore wind. Failures in the wind turbine drivetrain generally result in the second largest down times of the wind turbine, hence significantly increasing the cost of operation and maintenance. The manufacturing of casted drivetrain components, like the main shaft of the wind turbine, commonly result in many smaller defects through the volume of the component with sizes that depend on the manufacturing method. This paper considers the effect of the initial defect present in the volume of the casted ductile iron main shaft, on the reliability of the component. The probabilistic reliability analysis conducted is based on fracture mechanics models. Additionally, the utilization of the probabilistic reliability for operation and maintenance planning and quality control is discussed.

RELIABILITY OF GLULAM BEAMS SUBJECTED TO BENDING

This paper presents probabilistic reliability analyses of glulam beams by using level I semiprobabilistic procedure according to Eurocode standards and level II first-order reliability method. The analyses were performed for normal design situations on two groups of girders: roof and ceiling girders. The girders were first dimensioned for the ultimate limit state of bending according to Eurocode 5, after which the limit state equations were set with stochastic values of basic variables. A sensitivity analysis showed that the effect of strength variation is not significant when the coefficient of strength variation is approximately 15%: the recommended value from previous literature. The reliability indices obtained in this study are compared with the corresponding standard values for structural categories RC2 and RC3 according to Eurocode 0.

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing well-developed and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

Probabilistic reliability analysis of multiple slopes with genetic algorithms

Uncertainty estimation and consideration in engineering is an important practice to design reliable structures especially in geotechnics since the level of control with regards to the material parameters is relatively low. The definition of reliability indices to approximate the probability of failure allows for a better assessment of stability with fewer computations than using alternative methods. Nonetheless, yet an optimisation problem needs to be solved. In this work, a genetic algorithm is developed to solve this optimisation problem considering the limit equilibrium method to search for multiple critical failures. Study cases are presented to illustrate the capabilities of the method.

An intelligent method for contact fatigue reliability analysis of spur gear under EHL

To complete the contact fatigue reliability analysis of spur gear under elastohydrodynamic lubrication (EHL) efficiently and accurately, an intelligent method is proposed. Oil film pressure is approximated using quadratic polynomial with intercrossing term and then mapped into the Hertz contact zone. Considering the randomness of the EHL, material properties and fatigue strength correction factors, the probabilistic reliability analysis model is established using artificial neural network (ANN). Genetic algorithm (GA) is employed to search the minimum reliability index and the design point by introducing an adjusting factor in penalty function. Reliability sensitivity analysis is completed based on the advanced first order second moment (AFOSM). Numerical example shows that the established probabilistic reliability analysis model could correctly reflect the effect of EHL on contact fatigue of spur gear, and the proposed intelligent method has an excellent global search capability as well as a highly efficient computing performance compared with the traditional Monte Carlo method (MCM).

Probabilistic reliability analysis of dynamic behavior of human driver

The aim of this work was to develop a methodology for measuring and evaluation of dynamic behavior of the driver, to determine the differences between the behavior of unwearied and fatigued driver and to propose a development of a mechanism for continuous detection of dangerous situations, like going out of the traffic line. The most suitable characteristics for fatigue detection were determined and used for comparison with data obtained from test drives performed within 24 Hours. In the given environment if certain parameters are known for a given unwearied driver, characteristics of fatigue can be detected by the means of measurement, analysis and comparison.

Space Shuttle Rudder/Speed Brake Actuator—A Case Study. Probabilistic Fatigue Life and Reliability Analysis

The U.S. Space Shuttle fleet was originally intended to have a life of 100 flights for each vehicle, lasting over a 10-year period, with minimal scheduled maintenance or inspection. The first space shuttle flight was that of the Space Shuttle Columbia (OV-102), launched April 12, 1981. The disaster that destroyed Columbia occurred on its 28th flight, February 1, 2003, nearly 22 years after its first launch. In order to minimize risk of losing another Space Shuttle, a probabilistic life and reliability analysis was conducted for the Space Shuttle rudder/speed brake actuators to determine the number of flights the actuators could sustain. A life and reliability assessment of the actuator gears was performed in two stages: a contact stress fatigue model and a gear tooth bending fatigue model. For the contact stress analysis, the Lundberg-Palmgren bearing life theory was expanded to include gear-surface pitting for the actuator as a system. The mission spectrum of the Space Shuttle rudder/speed brake actuator was combined into equivalent effective hinge moment loads including an actuator input preload for the contact stress fatigue and tooth bending fatigue models. Gear system reliabilities are reported for both models and their combination. Reliability of the actuator bearings was analyzed separately, based on data provided by the actuator manufacturer. As a result of the analysis, the reliability of one half of a single actuator was calculated to be 98.6% for 12 flights. Accordingly, each actuator was subsequently limited to 12 flights before removal from service in the Space Shuttle.

Interval Reliability Analysis of Parameters of Section of Main Beam

In the calculation of the reliability of hydraulic, due to extensive uncertainties, there are lots of errors in probabilistic reliability analysis. In this paper, by comparing the non-probabilistic reliability index of different function, we get the advantages and disadvantages of one-dimensional optimization algorithm and method of Monte Carlo, and compare the functions of each variable of main beam to obtain the influence of the precision of the variables.