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Due to the complexity of the transmission tower structure and the correlation between wind and ice loads in the actual project, it is difficult to analyze the reliability of transmission towers with traditional methods. To solve this problem, the unscented transformation (UT) principle is presented concisely and used in the reliability analysis of transmission towers in this paper. Moreover, the finite element model of the target transmission tower is created. The reliability indices of the transmission tower under various loading cases are evaluated using UT and analyzed relative to the outcomes of the Monte Carlo method (MCS). Lastly, by analyzing and validating a wine-cup shape tangent tower, the simulation results show that the UT yields reliability indices with less than 6% relative error compared with MCS results for the transmission towers with lower reliability, which are more important in engineering. Variations in error caused by the change in correlation coefficients among variables are small. Consequently, the efficiency of calculations is improved by the UT-based reliability calculations for transmission towers in the case of correlated variables, which better meet engineering application requirements. It is proved that the method of reliability analysis for transmission towers based on the UT is applicable.

This paper presents a finite element analysis (FEA) of and reliability study on concrete-filled steel tube (CFST) members under the combined effects of corrosion and compressive loading. First, a stochastic-based FE model is established through the proposed secondary development program based on ABAQUS 2021 software. The model could account for the uncertainties of material, geometric, and corrosion effect on CFST members. The reliability of the built model was validated through experimental data of corroded CFST members under compression loading. Subsequently, the compressive performance of CFST under a combination of corrosion and loading was further investigated by numerical parameter analysis. A total of 1800 models were created to clarify the coupling mechanism among the core concrete strength, the steel tube strength, the steel ratio, and the maximum strength of the CFST member. Three theoretical formulas presented in classical design standards were used to calculate the axial compressive strength of the corroded CFST, and the uncertainty parameters μkp and δkp were also obtained for the discussed design formulas. Finally, the First Order and Second Moment (FOSM) method was employed to estimate the reliability indices β across different standards. The calculations revealed that the reliability indices β according to European standard ranges from 2.93 to 5.52, with some results falling below the target reliability index βT of 3.65. In addition, the multi-parameter coupling effects on reliability index β were investigated, and the main influencing factors were obtained. By leveraging the reliability analysis, reasonable design requirements can be proposed for CFST members under the coupling effects of corrosion and external load, which provides a design basis for the CFST member.

Digital image correlation (DIC), a widely used non-contact measurement technique, often requires empirical tuning of several algorithmic parameters to strike a balance between computational accuracy and efficiency. This paper introduces a novel uncertainty analysis approach aimed at optimizing the parameter intervals of a DIC algorithm. Specifically, the method leverages the inverse compositional Gauss–Newton algorithm combined with a prediction-correction scheme (IC-GN-PC), considering three critical parameters as interval variables. Uncertainty analysis is conducted using a non-probabilistic interval-based multidimensional parallelepiped model, where accuracy and efficiency serve as the reliability indexes. To achieve both high computational accuracy and efficiency, these two reliability indexes are simultaneously improved by optimizing the chosen parameter intervals. The optimized algorithm parameters are subsequently tested and validated through two case studies. The proposed method can be generalized to enhance multiple aspects of an algorithm’s performance by optimizing the relevant parameter intervals.

Fibre-reinforced polymer (FRP) reinforcement has been employed as an alternative to conventional steel reinforcement in concrete structures, which is attributed to its excellent strength and corrosion resistance. However, one drawback is that FRP reinforcements are brittle and affect the ductility of concrete structures. One of the recent effective techniques proposed to overcome ductility issues is the compression yielding (CY) concept. The CY mechanism allows the structure to fail differently than the conventional FRP-reinforced concrete structure. Thus, the existing design recommendations as per the current codes for FRP-reinforced concrete structures are not appropriate. Hence, reliability studies are crucial for the development of a functional CY beam design in order to emphasise the structure’s lifetime performance and to guarantee safety requirements. In this study, a reliability-based design approach is developed for a compression-yielded FRP-reinforced concrete beam (CY beam) using load and resistance factor design (LRFD). Firstly, the flexural failure modes of CY beams are discussed. The uncertainties involved in the development of the probabilistic model for the CY beam are defined. A case study is consequently conducted for a CY beam with random variables that are associated with the statistical characteristics of material properties and load. The reliability analysis method employed in this research is the Hasofer–Lind method. The results suggest the importance of choosing appropriate design variables and stochastic parameters for CY blocks that contribute to a higher level of reliability. The reliability index and resistance factors of a CY beam are then evaluated using the Monte Carlo Simulation computational method. The reliability index value of 3.336 is obtained from the simulation, which indicates that the CY beam demonstrates ductile behaviour. The results not only demonstrate ductile behaviour but also contribute to a possible reduction in material costs and a substantial safety margin. When compared to conventional FRP-reinforced concrete beams, for different load ratios, CY beams showed higher resistance and better reliability levels.

For the purpose of reliability quantitative assessment of the surrounding rock of the deeply embedded karst tunnel and the geological body around the cavern in the case of the cavern in the forepart of the tunnel face, on the basis of the upper bound limit analysis method, the energy dissipation theory, as well as the reliability theory, the dimensionless performance function of each damage area of the deeply buried karst tunnels could be established in the case of the cavern in the front of the tunnel face. Subsequently, the probability of failure and the reliability index of each damage region of the deep–bedded karst tunnel in the case of the cavern in the front of this tunnel face should be calculated through the Monte Carlo simulation sampling approach. The investigation has demonstrated that the larger the cohesion of the geotechnical body and the larger the internal friction angle within the geotechnical body, the larger the reliability indexes of the geotechnical bodies around the tunnel. The larger the diameter of the cavern and the larger the tunnel burial depth, the greater the probability of failure in the left part of the geotechnical body around this cavern, and the smaller the reliability indexes of these damage areas.

This paper employs probability methods to evaluate the fire safety performance of prestressed steel–concrete beam bridges based on simulation experimental research. Firstly, fire simulation experimental sample analysis was conducted on actual small box girder bridges to assess the structural response of prestressed steel–concrete structures to fire, as is in line with engineering practice. Next, we constructed a reliability analysis model to investigate the fire resistance performance of prestressed steel–concrete beam bridges. Combining reliability theory with the finite element method, we established a reliability analysis method for the fire resistance performance of prestressed steel–concrete beam bridges. Subsequently, we proposed a safety factor evaluation model for the fire resistance performance of prestressed steel–concrete beam bridges and then established a safety factor evaluation method for the fire resistance performance of prestressed steel–concrete beam bridges based on reliability back analysis. Finally, based on the analysis of the post-fire structural response in the specific case of a steel–concrete continuous beam bridge project moving from conditions of being simply supported to continuously prestressed, a structural resistance sample of the prestressed steel–concrete beam bridge was generated via the uniform design method, and statistical analysis was conducted. Subsequently, probability methods were used to evaluate the safety of the prestressed steel–concrete beam bridge after a fire. Through analysis, we concluded that the duration of the fire had a significant impact on the structural performance of prestressed steel–concrete beam bridges and that the randomness of parameters had a significant impact on the safety reserve of prestressed steel–concrete beam bridges following the fire. Going forward, it is necessary to pay attention to this factor in specific engineering practices and strengthen the monitoring and statistical analysis of structural random characteristics.

The reliability of the electricity supply is important since any interruption to the supply has direct and indirect consequences for its users. A reliable electricity supply requires a reliable electrical grid system to transmit and distribute the power from the generating plants to the consumers. This study reviewed the literature to find out how the reliability concept has been understood with a special focus on grid electricity reliability, what factors influence grid electricity reliability, what measures have been used to measure grid electricity reliability, which theories and methodologies have been applied to study grid electricity reliability and what are the likely research gaps that require future address. This review found that the literature documents four categories of factors that influence grid electricity reliability, and these are environmental, security, organizational and technical. The biggest influencers of grid electricity reliability were the technical-related factors followed by the environmental-related factors. In addition, we found that sixty studies focused on one subsystem, eleven on two subsystems while seven studies considered three subsystems. Most studies were found to address the distribution of subsystem reliability. As per the methodology adopted, this review found that eleven studies used a qualitative approach, forty-five studies used a quantitative approach, while eleven studies used a case study approach to study the concept of grid electricity reliability. In addition, we found that thirty-seven studies used the duration and frequency of power outages to measure grid electricity reliability.

The low order Taylor’s series expansion was employed in this study to estimate the reliability indices of the failure criteria for reliability-based design optimization of a linear static structure subjected to random loads and boundary conditions. By taking the advantage of the linear superposition principle, only a few analyses of the structure subjected to unit-loads are needed through the entire optimization process to produce acceptable results. Two structural examples are presented in this study to illustrate the effectiveness of the proposed approach for reliability-based design optimization: one deals with a truss structure subjected to random multiple point constraints, and the other conducts shape design optimization of a plane stress problem subjected to random point loads. Both examples were formulated and solved by the finite element method. The first example used the penalty method to reformulate the multiple point constraints as external loads, while the second example introduced an approach to propagate the uncertainty linearly from the nodal displacement vector to the nodal von Mises stress vector. The final designs obtained from the reliability-based design optimization were validated through Monte Carlo simulation. This validation process was completed with only four unit-load analyses for the first example and two for the second example.

One issue to consider while designing and constructing steel girders reinforced with carbon fiber-reinforced polymer (CFRP) plates in bridges is debonding failure. Previous studies showed that the parameters such as characteristics of material, load, adhesive, and CFRP plates have an effect on the failure probability of steel girder, which is represented by the reliability index. Therefore, this study analyzes the reliability indices of steel girders in bridges strengthened with CFRP plates to clarify the effects of debonding failure. Debonding and strength limit states are used to compare differences in reliability indices of different design scenarios. Strength and debonding margin the functions for the strength limit state and debonding limit state will be established in this study. The probability of failure is determined by a Monte Carlo simulation (MCS). It is found that the reliability index of debonding limit state is much lower than that of the strength limit state. This shows that the debonding failure should be considered significant in the reliability analysis of steel bridge girders strengthened with CFRP plate.

An alternative probabilistic assessment of buildings excited by multi-level seismic loading is presented in this paper. This evaluation is developed for both steel and reinforced concrete buildings using the Performance-Based Seismic Design (PBSD) concept. The methodology implements Probability Density Functions (PDFs) of inter-story drifts to extract structural risk in terms of the reliability index. Ten buildings of steel and reinforced concrete, respectively, are designed considering different locations in Mexico. Then, each structure is excited by ground motions representing different earthquake intensity levels for three performance levels: immediate occupancy, life safety, and collapse prevention. The deterministic seismic response of buildings is extracted using the finite element software OpenSees. Based on the results, it can be stated that the probabilistic assessment technique represents an efficient approach for extracting the seismic risk of structures using PDFs of inter-story drifts. Lastly, it is demonstrated that the evaluation of buildings following PBSD is a step in the right direction, moving from traditional deterministic design concepts to probabilistic philosophies.

Data collected using sensors plays an essential role in active bridge health monitoring. When analyzing a large number of bridges in the U.S., the National Bridge Inventory data as been widely used. Yet, the database does not provide information about live loads, one of the most indeterminate variables for monitoring bridges. Such asymmetric information can lead to an adverse selection problem in making maintenance, rehabilitation, and repair decisions. This study proposes a data-driven reliability analysis to assess probabilities of bridge failure by synthesizing NBI data and Weigh-In-Motion (WIM) data for a large number of bridges in Georgia. On the resistance side, tree ensemble methods are employed to support the hypothesis that the NBI operating load rating represents the distribution of bridge resistance capacities which change over time. On the loading side, the live load distribution is derived from field data collected using WIM sensors. Our results show that the proposed WIM data-enabled reliability analysis substantially enhances information symmetry and provides a reliability index that supports monitoring of bridge conditions, depending on live loads and load-carrying capacities.

The main aim of this paper was to propose a new reliability index for steel structure assessment and to check it using the example of a popular Pratt truss girder. Structural analysis was completed in the finite element method system Autodesk ROBOT, and probabilistic analysis was implemented in the computer algebra software MAPLE. The stochastic finite element method (SFEM) was contrasted here with the Monte Carlo simulation and the girder span was selected as the input structural uncertainty source. Both methods were based on the same structural polynomial response functions determined for extreme deformation, for extreme stresses and also for the structural joint exhibiting the largest effort. These polynomials were statistically optimized during the additional least squares method experiments. The first four basic probabilistic characteristics of the structural responses, the first-order reliability method (FORM) index, and as the new proposition for this index were computed and presented. This new index formula follows the relative probabilistic entropy model proposed by Bhattacharyya. The computer analysis results presented here show a very strong coincidence of both probabilistic numerical techniques and confirms the applicability of the new reliability index for the input coefficient of variation not larger than 0.15. These studies should be continued for other engineering systems’ reliability and, particularly, for large-scale and multiscale computer simulations. The results presented in this paper may serve in different applied sciences, from biology through to econometrics, experimental physics and, of course, various branches of engineering.

In this paper a modification of the reliability-based robust geotechnical design (RGD) method is proposed. The intention of the proposed modifications is to simplify the method, make it less computationally expensive, and harmonise of the results with Eurocode 7. The complexity of the RGD method mainly stems from the calculation of the design’s robustness measure, which is the feasibility robustness index (ββ). Due to this fact, the replacing of the existing robustness measure with a generalised reliability index (β) is considered. It was demonstrated that β fits into the robustness concept, and is traditionally used as a construction reliability measure, making it intuitive and “user friendly”. It is proposed to conduct a sensitivity analysis using Soboli indices, with the aim of freezing the variables whose contribution to the system response variance is negligible, which will further simplify the method. By changing the robustness measure, the number of the required reliability analyses is significantly decreased. Further reduction is achieved by conducting analyses only for the designs chosen in the scope of the genetic algorithm. The original RGD method is used as an extension of traditional reliability-based design. By applying the proposed modifications, the RGD method can be used as an alternative to the classic and reliability-based design method.

The seismic performance of the aged-concrete gravity dam (aged-CGD) by safety assessment based on the reliability-index is the main focal point of this study. Determination of reliability-index has been handled by the site seismic hazard analysis with the help of PSHRisk-tool (developed by the authors) and risk assessment. Incorporated with the uncertainties, the failure probability has been carried out by the IDA and fragility analysis. For the nonlinear finite element model of the CGD, the concrete damage plasticity (CDP) model is adopted. To investigate the aging effect, the hygro-chemo-mechanical model has been taken for different years consideration. Through the failure risk assessment of serviceability and safety level, the target reliability index has been determined here for an existing CGD in Korea. Despite several types of research on the CGD safety assessment, the main novelty of this proposed approach will help the dam operator to check the safety barrier for the aged-CGD. A safety index is investigated by comparing the target reliability-index of the age-CGD with the reliability-index for two potential earthquake levels. However, the proposed approach can implement to check the safety range of any seismic site for any set of earthquakes.

A geotechnical structure’s reliability index calculated using identical input parameters and assumptions can significantly vary as a function of the used method. The different approaches to solving the reliability problem could result in an error which depends on many factors. The most important error sources are the complexity of the performance function, the number of random variables, their mutual correlations, and marginal statistical distributions. A review of relevant literature in the field of reliability in geotechnical engineering revealed a lack of information on the errors of individual reliability methods for geotechnical problems and general criteria for assessing their suitability concerning the error size. The paper defines the reliability method error and proposes criteria for assessing the suitability of reliability methods in geotechnical engineering. Based on the proposed criteria, the suitability of common reliability methods was evaluated in the example of a shallow foundation, analysed according to Eurocode 7, DA 3, such that Ed=Rd. It is shown that due to the mathematically complex expression of the reliability integral, methods that are easier to use result in a larger error and are not suitable for a reliability analysis of shallow foundations. Sophisticated methods are more accurate but require specific knowledge and resources that are not often used in daily engineering practice.

In production environments, failure data of a complex system are difficult to obtain due to the high cost of experiments; furthermore, using a single model to analyze risk, reliability, availability and uncertainty is a big challenge. Based on the fault tree, fuzzy comprehensive evaluation and Markov method, this paper proposed a fuzzy Markov method that takes the full advantages of the three methods and makes the analysis of risk, reliability, availability and uncertainty all in one. This method uses the fault tree and fuzzy theory to preprocess the input failure data to improve the reliability of the input failure data, and then input the preprocessed failure data into the Markov model; after that iterate and adjust the model when uncertainty events occur, until the data of all events have been processed by the model and the updated model obtained, which best reflects the system state. The wellhead connector of a subsea production system was used as a case study to demonstrate the above method. The obtained reliability index (mean time to failure) of the connector is basically consistent with the failure statistical data from the offshore and onshore reliability database, which verified the accuracy of the proposed method.

Due to increasing load and characteristic stagnation and fluctuations of existing generation systems capacity, the reliability assessment of generation systems is crucial to system adequacy. Furthermore, a rapid load increase could amount to a consequent sudden deficit in the generation supply before the next scheduled assessment. Hence, a reliability assessment is conducted at regular and close intervals to ensure adequacy. This study simulates and establishes the relationship between the load growth and generation capacity using the generation and load data of the IEEE reliability test system (IEEE RTS ‘96 standard). The generation capacity states and the risk model were obtained using the sequential Monte Carlo simulation (MCS) method. The load was gradually increased stepwise and is simulated against the constant generation capacity. In each case, the reliability index was recorded in terms of loss-of-load evaluation (LOLE). The recorded reliability index was thereafter fitted with the load-growth trend by the linear regression approach. A predictive assessment approach is thereafter proffered through the obtained fitting equation. In addition, a reliability threshold is effectively determined at a yield point for a reliability benchmark.

Risk in a power system’s ability to survive imminent disturbances without recourse to low operational cost and non-interruptive energy delivery remains the responsibility of every grid operator. Intermittencies in renewable energy and dynamic load variations influence the quality of power supply. The sudden changes affect the system frequency, compromising the reliability of the system grid; generation response to frequency regulation is momentous in such an incident. Slower response or smaller reserve capacity may cause a power shortage. This paper proposes a novel predictive scheme for a short-term operational reliability evaluation for system operations planning. The proposed method evaluates the operational reliability of system frequency whiles considering high renewable power penetration and energy storage system incorporation. Required energy generations, and other grid parameters, are modelled as stochastic inputs to the framework. We formulate a reliability index as a frequency distribution considering system frequency control dynamics and processes. The IEEE Reliability Test System (RTS) is used to prove the efficacy of the proposed model.

Offshore wind turbines (OWTs) are deployed in harsh environments often characterized by highly stochastic loads and resistance properties, thus necessitating the need for structural reliability assessment (SRA) to account for such uncertainties systematically. In this work, the SRA of an OWT jacket-type support structure is conducted, applying two stochastic methods to predict the safety level of the structure considering various design constraints. The first method refers to a commercial finite element analysis (FEA) package (DesignXplorer© from ANSYS) which employs direct simulations and the six sigma analysis function applying Latin hypercube sampling (LHS) to predict the probability of failure. The second method develops a non-intrusive formulation which maps the response of the structure through a finite number of simulations to develop a response surface, and then employs first-order reliability methods (FORM) to evaluate the reliability index and, subsequently, the probability of failure. In this analysis, five design constraints were considered: stress, fatigue, deformation, buckling, and vibration. The two methods were applied to a baseline 10-MW OWT jacket-type support structure to identify critical components. The results revealed that, for the inherent stochastic conditions, the structural components can safely withstand such conditions, as the reliability index values were found acceptable when compared with allowable values from design standards. The reliability assessment results revealed that the fatigue performance is the design-driving criterion for structural components of OWT support structures. While there was good agreement in the safety index values predicted by both methods, a limitation of the direct simulation method is in its requirement for a prohibitively large number of simulations to estimate the very low probabilities of failure in the deformation and buckling constraint cases. This limitation can be overcome through the non-intrusive formulation presented in this work.

The main objective of the current paper is to determine fatigue critical details of wave-energy converters (WECs) and to evaluate their reliability. For this purpose, a new model of a water-hydraulic drive WEC is designed based on the IPS (company Interproject Service) buoy working principle, and the hydrodynamic frequency domain analysis method is carried out accordingly. A reliability assessment method, which combines the stress-number (SN) curves approach and linear damage cumulative theory, has been developed specifically for the proposed WEC. In order to obtain the stochastic wave load spectrum, 22 years of wave data of the intended deployment site (South China Sea), covering the span of 1988−2009, were analyzed, discussed and processed. A finite element analysis model is also established to calculate the maximum Von Mises stress of the fatigue critical component. The reliability indices and configuration parameters of the water hydraulic-drive WEC are obtained by applying first order reliability method, considering the uncertainty of the model parameters and the fatigue limit state. Optimization of configuration parameters is also developed based on the reliability method for the sake of approaching the expected service life. The results show that the fatigue life of the water turbine can reach the design service life of 20 years as the configuration parameters meet the specific condition. The cumulative reliability index and annual reliability index are recommended as 2.1 and 3.5, respectively.

Reinforced bar corrosion induced by chloride ingression is one of the most significant threats to the durability of concrete structures in marine environments. The concrete cover thickness, compressive strength, chloride diffusion coefficient, and surface defects of reinforced concrete in the Jiaozhou Bay sea-crossing railway bridge were measured. The temperature and relative humidity in the concrete and the loading applied onto the reinforced concrete were monitored. Based on the DuraCrete model, a revised model for the service life prediction of concrete structures was established, considering the effects of temperature and loading on the chloride diffusion coefficient. Further, the reliability indexes of the reinforced concrete box girder, pier, and platform, located in the marine and land sections, in relation to service lives lasting various numbers of years, were calculated. The measured and calculated results show that the mean cover thicknesses of concrete piers in the marine and land sections are 52 mm and 36 mm, respectively, and the corresponding standard deviations are 5.21 mm and 3.18 mm, respectively. The mean compressive strengths of concrete in the marine and land sections are 56 MPa and 46 MPa, respectively. The corresponding standard deviations are 2.45 MPa and 2.67 MPa, respectively. The reliability indexes of the reinforced concrete box girder and platform in the marine section, under the condition of a service life of 100 years, are 1.81 and 1.76, respectively. When the corrosion-resistant reinforced bar was used in the pier structure in the marine section, its reliability index increased to 2.01. Furthermore, the reliability index of the reinforced concrete damaged by salt fog in the land section was 1.71.

This study is an attempt to assess the effect of node location imperfections on the reliability dome. The analysis concerns a single-layer steel lattice dome that is very sensitive to node snap-through. The load-displacement path of the structure was determined using the program, Finite Element Method-Krata. To determine the failure probability, reliability index, and elasticity index, the first-order reliability method approximation method was employed. The reliability analysis was conducted with Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw. In this paper, it is shown how large differences in the assessment of the safety of a structure can appear when we incorrectly estimate the standard deviation of the random variable responsible for the imperfections of node locations.

This paper concerns the system reliability analysis of steel truss towers. Due to failures of towers, the assessment of their reliability seems to be a very important problem. In the analysis, two cases are examined: when the buckling coefficient is a deterministic value and when it is a random variable. The impact of failures of single elements on the structure reliability was investigated. Calculations of the standard deviation of the capacity and reliability indexes were made using author-developed programs in the Mathematica environment.

Due to the volatile and correlated nature of wind speed, a high share of wind power penetration poses challenges to power system production simulation. Existing power system probabilistic production simulation approaches are in short of considering the time-varying characteristics of wind power and load, as well as the correlation between wind speeds at the same time, which brings about some problems in planning and analysis for the power system with high wind power penetration. Based on universal generating function (UGF), this paper proposes a novel probabilistic production simulation approach considering wind speed correlation. UGF is utilized to develop the chronological models of wind power that characterizes wind speed correlation simultaneously, as well as the chronological models of conventional generation sources and load. The supply and demand are matched chronologically to not only obtain generation schedules, but also reliability indices both at each simulation interval and the whole period. The proposed approach has been tested on the improved IEEE-RTS 79 test system and is compared with the Monte Carlo approach and the sequence operation theory approach. The results verified the proposed approach with the merits of computation simplicity and accuracy.