Component Reliability Indices Research Articles

Effect of structural repairs on the load rating and reliability of a prestressed concrete bridge

Prestressed girders often deteriorate over time due to environmental and man-made stressors, lowering the strength and serviceability of bridge structures. Although structural repairs are implemented to improve the load carrying capacity of the structure, the presence of numerous unknowns leads to high uncertainty in estimating the adequacy of repairs. For instance, the cross-section of the remaining strands, material properties, applied external loads, and workmanship assumptions made throughout the repair process introduce ambiguities when estimating the adequacy of the repairs. This study evaluates the efficiency of re-tensioning repairs of prestressed concrete bridge span girders. The repairs include field splicing, re-tensioning, of deteriorated or damaged strands by torquing a splicing coupler. The evaluation in this study considers component, system reliability, and load ratings while accounting for several uncertainties, such as structural repair, material properties, and external loads. This paper introduces an approach to account for prestressing strands damage and repair uncertainties while also accounting for other uncertainties. In this regard, five cases are studied: as-built, repaired, and three varying degrees of damage cases. First, the distribution for structural demand and capacity accounting for uncertainty in loads, material properties, and repair process is defined for each girder in the prestressed concrete bridge span. In doing so, Monte-Carlo simulation is employed to determine the distributions. Accordingly, the limit state function of the girders is defined from the obtained distributions. Then, the component reliability of each AASHTO (American Association of State Highway and Transportation Officials) Type II girder is calculated from the obtained reliability indices based on the determined limit state functions. Finally, a system reliability model of the span is developed from the component reliability of each girder. Some advantages and disadvantages of using component and system reliability index versus load rating in damaged and repaired prestressed concrete bridge girders are also discussed. Several critical conclusions are made regarding the uncertainties in structural repair, material properties and external loads, and their impact on the load rating and the component and system reliability of the prestressed concrete bridge structure girders.

Reliability Assessment and Improvement of Electrical Distribution Systems by Using Multinomial Monte Carlo Simulations and a Component Risk Priority Index

In this paper, a method of assessing and improving the reliability of power distribution systems based on Monte Carlo simulation and a novel risk priority index is proposed. The initialization of the assessment process is carried out by using Multinomial Monte Carlo simulation with a nonsequential technique to assess system reliability in the form of SAIFI and SAIDI indices. Then, the novel per-time-based component reliability indices representing the insights obtained from root-cause analysis for each component in the system are evaluated to make suitable decisions on improvement measures. The proposed indices are derived as a component risk priority index based on the principle of the failure mode and an effect analysis to prioritize and select the implementation points by the Pareto principle. By applying the proposed method, a reliability improvement should be achieved at the correct point with minimal operations. In addition, the proposed method can be used to study the effect of uncertainty regarding some device operations on the system reliability. To verify the performance of the proposed method and demonstrate its application, three case studies were performed on the IEEE RBTS Bus-2 test system. From the first case study, the results of the proposed assessment process were validated by comparison with a standard benchmark. The second case study showed the performance of applying the entire process to improve system reliability, and the results showed that system reliability can be improved significantly. The third case study was performed to determine the effect of uncertainty in protective device operations. The results of the third case showed that there was a significant decrease in overall reliability in terms of a higher level of power outages, while the performance of the protective components was slightly reduced.

Component reliability and sensitivity analysis of anchor-pile-wall reinforcement design of a multilayer soil slope

Component reliability and sensitivity analysis of soil-slope combined-reinforcement deterministic designs are studied using a hybrid numerical-probabilistic method. Major components are qualitatively identified with numerical simulations to avoid redundancy evaluations. Quadratic polynomials as response surfaces are stepwise regressed to predict component load effects. Major component resistances of supporting structures are calculated in states of soil ultimate equilibrium and maximum allowable deformations obtained according to building and foundation types. Component performance functions (PFs) are established based on component failure models and soil-mass deformation properties. Reinforced slope stability reliabilities are calculated with first-order second-moment and design point methods. The reinforcement probability safety indicated by component reliability indices is adopted to check whether the deterministic design needs improvement. This methodology is applied to a loess slope reinforced by combined supporting. The resultant reliability indices of the slope imply some improving treatments should be made. Sensitivity analysis shows some variable variation has a more significant impact on the PFs; inversely signed sensitivity coefficients indicate that the equilibrium point between PFs should be considered when modifying parameters. Stable monitoring results of modified design implementation indicate that probabilistic analysis of component stability is necessary for some slope-treatment designs with distinct probability distribution variables.

Research on Reliability Index and Realization of Magnetic Resonance (MR) Based on Clinical Use Condition

Combined with the clinical use condition of MR in use in Shanghai Sixth People's Hospital, MR components are divided into scanning type I and scanning type II. At the same time, combined with the main loss force of MR components, the research divides MR components into dynamic components and electric thermal components. In this study, a complete set of MR system reliability indexes and implementation methods are given, including system reliability index determination, system reliability allocation, component reliability index realization, system reliability prediction and system reliability verification. At the same time, this study also gives the methods of reliability prediction and reliability verification, and gives the MTBF calculation method of MR system based on clinical use data statistics.

Evaluation of reliability index and probability of failure for the improvement of the Nigerian empirical mechanistic flexible pavement analysis and design system (Nempads)


 
 
 The aim of this work was to evaluate reliability index (RI) with respect to fatigue and rutting within the different seasons peculiar to Nigeria, in order to improve Empirical-Mechanistic flexible pavement design approach, using First Order Reliability Method (FORM). Flexible pavement design involves many uncertainties, variabilities, and approximations regarding the input parameters like material properties, traffic loads. Others include subgrade strength, drainage conditions, construction, compaction procedures and climatic factors such as temperature, rainfall, and snowfall, etc. The combination of the variances associated with input parameters contributes to components and system uncertainty, and this combination of variances can have a significant effect on the predicted performance of the pavement. Reliability in pavement design is introduced to consider these uncertainties. Layers thicknesses, material properties, and Equivalent Standard Axle Load (ESAL) were entered into a multi-layer elastic theory software, ELSYM-5, which in turn were used to calculate strains and stresses for different seasons. The results obtained were entered into Nigerian fitted transfer function distress models to compute allowable ESALS. Miner’s hypothesis theory equation was used to calculate the cumulative damage due to stress and strains generated. A Framework was generated for finding individual reliability index (RI), systemic reliability index (SRI), and probability of failure. The findings showed that Season I (Winter) recorded the highest component reliability index for fatigue (5.63 for Normal Distribution). Season II (Summer) recorded the lowest component reliability index (β) for rutting (5.4 for Normal Distribution). Season III (Spring) recorded the lowest component reliability index for fatigue (1.85 for Normal Distribution)
 
 

Reliability analysis and formula adjustment for shear capacity of concrete shear walls

The Unified Standard for Reliability Design of Building Structures of China (GB50068-2001) requires that the average value of a component’s reliability index should not be lower than the target reliability index. However, the newly revised code GB50068-2018 increases the partial load factor and requires that the minimum value of the component reliability index should not be lower than the target reliability index. The reliability of the shear capacity of shear walls has not been calibrated in the Chinese codes. To determine whether the reliability of the shear capacity of reinforced concrete shear walls meets the requirements of GB50068-2018, 74 shear wall test data were collected and screened. The test and calculated values of the shear capacity of the specimens were analysed to obtain statistical parameters of the uncertainty of the computational model; subsequently, the statistical parameters of the resistance could be calculated. The Rackwitz-Fiessler method was used to calculate the reliability index of the shear capacity of shear walls. This study also compared the reliability of the shear capacity of shear walls according to GB50068-2018 and GB50068-2001. The reliability index obtained in GB50068-2018 is 5.88 %–8.02 % higher than that obtained in GB50068-2001. However, the reliability index of the shear capacity of shear walls does not meet the target reliability index requirements of GB50068-2018. In this work, the formula for the shear capacity of shear walls is updated with a reliability index adjustment coefficient of 0.9 so that the reliability index calculated using the adjusted formula meets the current code’s requirements.

Time-Dependent System Reliability Analysis With Second-Order Reliability Method

AbstractSystem reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

Structural reliability assessment of offshore wind turbine support structures subjected to pitting corrosion‐fatigue: A damage tolerance modelling approach

AbstractThe structural integrity of offshore wind turbine (OWT) support structures is affected by one of the most severe damage mechanisms known as pitting corrosion‐fatigue. In this study, the structural reliability of such structures subjected to pitting corrosion‐fatigue is assessed using a damage tolerance modelling approach. A probabilistic model that ascertains the reliability of the structure is presented, incorporating the randomness in cyclic load and corrosive environment as well as uncertainties in shape factor, pit size and aspect ratio. A non‐intrusive formulation is proposed consisting of a sequence of steps. First, a stochastic parametric Finite Element Analysis (FEA) is performed using SMART© crack growth and Design Xplorer© facilities within the software package ANSYS. Secondly, the results obtained from the FEA are processed using an Artificial Neural Network (ANN) response surface modelling technique. Finally, the First Order Reliability Method (FORM) is used to calculate the reliability indices of components. The results reveal that for the inherent stochastic conditions, the structure becomes unsafe after the 18th year, before the attainment of the design life of 20 years. The FEA results are in very good agreement with results obtained from analysis steps outlined in design standard BS 7910 and other references designated as ‘theoretical analysis methods’ in this study. The results predict, for the case study, that the pit growth life is approximately 56% of the total pitting corrosion fatigue life. Sensitivity analysis results show that the aspect ratio of pits at critical size plays a significant role on the reliability of the structure.

Reliability investigation of steam turbine critical components

Several aspects of maintaining and operating steam turbines at the palm oil mill areas have historically resulted in unreliable performance and repetitive failures. The reliability analysis using Weibull probability distribution for various components of steam turbine is discussed extensively. The objective of this reliability assessment is to identify the potential failure path of steam turbine components. The intent herein is to focus on critical components of steam turbine to successfully improve the integrity and reliability of turbines in those components. Areas discussed will be bearing failures, Shaft Seal failures, Control/stop Valve, Main Oil Pump, and Reducing Gear. It is necessary to improve the reliability indices of the steam turbine components by taking some measures such as well-planned and routine maintenance of equipment’s as well as training and retraining of technical human resources of the major equipment like steam turbine.

Design of agricultural machinery upon reliability indices

Introduction. The formation of an algorithm for designing mechanical systems machines in terms of reliability is considered. The algorithm is built with account for the latest publications on the standardization of reliability indices of machines and components at the initial stages of the project. The recovery cost technique, free from the need to use the exponential law when distributing reliability indices between system elements, is presented. The concepts of the required and achieved reliability factors and methods for obtaining them at different stages of the project are introduced. The possibilities of the project modification to provide a given level of reliability are considered. Research objective is to combine modern scientific developments on the standardization of reliability indices of machines, components, and methods for obtaining the required operation life with the design drafting stages.

Effects of post-failure material behaviour on redundancy factor for design of structural components in nondeterministic systems

This paper investigates the effects of post-failure material behaviour on redundancy factor for the design of structural components in nondeterministic systems. The procedure for evaluating the redundancy factors of components of ductile and brittle nondeterministic systems is demonstrated using systems consisting of two to four components. The effects of the number of brittle components in a mixed (ductile–brittle) system and the post-failure behaviour factor on the redundancy factor are also studied using these systems. An efficient approach for simplifying the system model in the redundancy factor analysis of brittle systems with a large number of components is proposed. In order to generate standard tables to facilitate the design process, the redundancy factors and the associated component reliability indices of nondeterministic ductile and brittle systems with large number of components are calculated considering three correlation cases and two probability distribution types. Finally, a bridge example is used to demonstrate the application of the redundancy factor in the design of steel girders taking into account their post-failure behaviour.

Reliability Analysis of Half-Through Concrete-Filled Steel Tubular Arch Bridge

The object of this paper analyzes the reliability of half-through concrete-filled steel tubular arch bridges. Load and resistance parameters are treated as random variables. The statistical parameters are based on the available literature, test data and survey results. Reliability indices of main components of the bridge structure are calculated by iterations using the first-order second-moment method. The half-through concrete-filled steel tubular arch bridge is the typical series system and the reliability index of the system is calculated by the PNET method. The study shows that the reliability indices of suspenders are relatively larger than others, and the correlation coefficients among the same members have high relativity index.

The Software Reliability Increase Method

Our investigation purpose is to create the software reliability increase method. The proposed method allows creators to calculate statistic, probabilistic and valuating reliability indices of software components which contain defects. The method’s aim is to take into consideration the statistic components complexity by means of composite metrics. The use of received indices provides for components finding which contain much more defects for refactoring and the first testing process. It contributes to increase identified and corrected defects quantity and improve the software reliability on average about 8%.

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example.

Load path uncertainty in a wood structure and the effect on structural reliability

The roof truss bearing points of a light-framed wood house were instrumented with load cells. It was found that under dead load alone, symmetric and theoretically identical truss reactions have significant variation. A similar degree of reaction discrepancy was found under the application of uplift pressures caused by hurricane winds. Analysis revealed that the majority of this discrepancy is caused by inherent uncertainties in load path. Although uncertainties in load magnitude and material resistance are accounted for in design by use of appropriate load and resistance factors, load path is generally taken to be deterministic. In this study, load path uncertainty in a test structure is statistically quantified and the effect on the reliability of wood structural members is investigated. Although large uncertainties in reactions were present, it was found that the resulting influence on reliability was modest, with decreases in component reliability index ranging from 5% to 15%.

Reliability Based LRFD Approach for External Stability of Reinforced Soil Walls

The main objective of reinforced soil wall design is to ensure safety and performance requirements of a wall for target reliability levels. Analysis is conducted to evaluate the external stability of reinforced soil walls. As this must be accomplished under conditions of uncertainties associated with reinforced backfill, retained backfill, foundation soil and surcharge load acting on the wall, probabilistic analyses are necessary in the development of such reliability based design for external stability of reinforced soil wall. A methodology for developing load and resistance factor design guidelines for reinforced soil walls is outlined in this paper. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. A first order reliability method is used to determine appropriate ranges for the values of the load and resistance factors. Load and resistance factors needed to maintain the stability against three modes of failure by targeting component reliability indices of 2, 2.5, 3, 3.5 and 4 are obtained for various values of coefficients of variation of friction angle of backfill and foundation soil, distributed dead load surcharge, live load surcharge and cohesion of the foundation soil.

Optimal reliability planning for a composite electric power system based on Monte Carlo simulation using particle swarm optimization

A methodology for planning the optimal reliability indices of system components for a composite electric power system based on state sampling non-sequential Monte Carlo simulation using particle swarm optimization (PSO) algorithm is presented. The indices designed are forced outage rate of system components and expected demand not served (EDNS) of the system. The optimal reliability planning problem has been formulated as an optimization problem of minimizing the system interruption cost and the component investment cost. The cost functions are modeled as a function of forced outage rate and EDNS. The EDNS of the system for a particular system reliability level is evaluated based on state sampling non-sequential–Monte Carlo simulation and the dc load flow based load curtailment model. PSO algorithm is employed to minimize the reliability planning model. The applications of the proposed methodology are illustrated through case studies carried out using Modified Stagg and El-Abiad 5-bus system and IEEE 14-bus system. The effectiveness of this approach is validated by comparing the results obtained with the solution of reliability planning model using genetic algorithm optimizer.

Load and resistance factor design (LRFD) approach for the reliability-based seismic design of bridge abutments

The paper presents a study on the application of a load and resistance factor design (LRFD) approach to reliability based seismic design of bridge abutments. The failure criteria for defining the performance functions are overturning failure about the toe point, eccentricity failure of the resultant force, sliding failure along the base and bearing capacity instability. Using a pseudo-static limit equilibrium method, analysis is conducted to evaluate the stability of bridge abutments subjected to earthquake loads. The first-order reliability method (FORM) is used to estimate the probability of failure in four modes of failure. Load and resistance factors needed to maintain stability against four modes of failure by targeting various component reliability indices (2.0–4.0) are obtained for various values of coefficients of variation (COV) of unit weights of concrete and backfill (γ w and γ), friction angle of backfill and foundation soil (φ and φ b ), cohesion of foundation soil (c), vertical load acting on abutment (V) and horizontal seismic acceleration coefficient (k h ). The results have been provided in a tabular form. A comparative study between LRFD and ASD is also presented with a design example at the end.

Optimum Design of Bridge Abutments under Seismic Conditions: Reliability-Based Approach

The paper focuses on the reliability-based design optimization of gravity wall bridge abutments when subjected to active condition during earthquakes. An analytical study considering the effect of uncertainties in the seismic analysis of bridge abutments is presented. Planar failure surface has been considered in conjunction with the pseudostatic limit equilibrium method for the calculation of the seismic active earth pressure. Analysis is conducted to evaluate the external stability of bridge abutments when subjected to earthquake loads. Reliability analysis is used to estimate the probability of failure in three modes of failure viz. sliding failure of the wall on its base, overturning failure about its toe (or eccentricity failure of the resultant force) and bearing failure of foundation soil below the base of wall. The properties of backfill and foundation soil below the base of abutment are treated as random variables. In addition, the uncertainties associated with characteristics of earthquake ground motions such as horizontal seismic acceleration and shear wave velocity propagating through backfill soil are considered. The optimum proportions of the abutment needed to maintain the stability are obtained against three modes of failure by targeting various component and system reliability indices. Studies have also been made to study the influence of various parameters on the seismic stability.

Operational reliability assessment of power systems considering condition-dependent failure rate

Failure rate of a system component is usually assumed to be constant in conventional reliability evaluation of power systems. It has been realised from the real-time operation that a component will experience more failures during heavy loading condition than those during light loading condition, which means that the failure rate of a component in real-time operation is not constant and varies with loading condition. In order to evaluate system operational reliability related to load condition, the factors affected condition-dependent failure rate (CDFR) are investigated and a basic CDFR model is proposed in this study. In predictive operational reliability study, equipment loading condition for a given load period is determined using AC power flow based on the corresponding load level with considering load uncertainty. A four-state model has been proposed to represent a system component. The equations for determining the probability of each state for the four-state model have been derived. A technique based on these equations and models has been developed to evaluate operational and annual reliability indices of components, load points and system. The IEEE-RTS has been analysed to illustrate the proposed models and technique.