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Structural reliability assessment is of great significance for the safety and maintenance of structures. In recent years, the moment method has been rapidly developed and applied widespread for its simplicity and performance. Sometimes, the accuracy of the moment method, using only the first four moments (i.e., mean value, standard deviation, skewness, and kurtosis), is not sufficient in evaluating the reliability index of strong non-Gaussian performance functions. In this study, a method based on the quartic normal transformation (QNT) is proposed for structural reliability assessment, which enables incorporation of the first five moments, including the super-skewness, of performance function. The structural reliability index based on the QNT model is derived. The first five moments of the performance function are estimated by introducing the point estimate method. Seven engineering examples are employed to demonstrate the efficacy of the QNT. The results show that the computational efficiencies of CNT and QNT were close to each other and both superior to that of MCS. The results also show that the performance of QNT is superior to CNT in aspect of accuracy and robustness in particular to performance functions with strong non-Gaussianity., Competing Interests: Declarations. Competing interests: The authors declare no competing interests., (© 2025. The Author(s).)

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.

Because of their high electrocatalytic activity, sensitivity, selectivity, and long-term stability in electrochemical sensors and biosensors, numerous nanomaterials are being used as suitable electrode materials thanks to developments in nanotechnology. Electrochemical sensors and biosensors are two areas where two-dimensional layered materials (2DLMs) are finding increasing utility due to their unusual structure and physicochemical features. Nanosensors, by their unprecedented sensitivity and minute scale, can probe deeper into the structural integrity of piles, capturing intricacies that traditional tools overlook. These advanced devices detect anomalies, voids, and minute defects in the pile structure with unparalleled granularity. Their effectiveness lies in detection and their capacity to provide real-time feedback on pile health, heralding a shift from reactive to proactive maintenance methodologies. Harvesting data from these nanosensors, data was incorporated into a probabilistic model, executing the reliability index calculations through Monte Carlo simulations. Preliminary outcomes show a commendable enhancement in the predictability of vertical bearing capacity, with the coefficient of variation dwindling by up to 12%. The introduction of nanosensors facilitates instantaneous monitoring and fortifies the long-term stability of pile foundations. This study accentuates the transformative potential of nanosensors in geotechnical engineering., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier Inc.)

The plastic behavior of strengthened haunched beams utilizing carbon fiber-reinforced polymers (CFRP) was investigated using a probabilistic design that took into account random concrete properties, CFRP properties, and complementary strain energy values, with the reliability index serving as a limiting index, as the proposed method considers a novel method that deals with probabilistic parameters for models with limited plastic behavior designed based on the reliability index. The data used in this research were gathered and evaluated in a recent study on simply supported haunched beams reinforced with carbon fiber-reinforced polymers. The purpose of this research was to use the reliability limitation index for simulated strengthened haunched beams by taking into account randomness in concrete and CFRP properties and the complementary strain energy value, which is considered a plastic behavior controller that provides an illustration of the damage amount within the reinforcement steel bars. The results indicate how randomness affects the behavior of the presented models, which are chosen to have different numbers of CFRP strips. The variable randomness affects load and deflection values where the reliability index value increases as the corresponding load value decrease, reflecting the increased probability of failure in models subjected to higher loading conditions, while tension concrete damage percentages are reflected in the damage pattern presented in the results, showing that as the produced load increases, so does the damage intensity. It is also obvious that the reliability index served as a limitation index while taking concrete characteristics and complementary strain energy as random variables.

Objective: Current Road geometric design processes disregard stochastic aspects, resulting in inadequate traffic safety considerations. In addition, the primary sources of crash data are obtained from police department, insurance agency and hospitals, where detailed investigation is not carried out from a transportation perspective. So, the data obtained from these sources may or may not be reliable. The main objective of this study is to account uncertainties using reliability as a tool that considers slow down the vehicle while they maneuver the curve and to develop thresholds of reliability index associated with sight distance based on operating speed design consistent measure as a surrogate safety measure rather than using crash data., Methodology: This study proposes a thresholds of reliability index associated with sight distance for various operating speed ranges based on design consistent measure. In addition, established the relationship between the consistency levels, geometric characteristics and vehicle characteristics. In this study, classical topography survey was carried out on the field using total station. The data collected comprises speed data and geometric data of 18 horizontal curves (Lane based analysis was carried out). A total of 3042 free flowing vehicle speeds have been extracted from the video graphic survey and used in the analysis., Results: The threshold values of reliability indices associated with sight distance is higher as the operating speed increases for the section to be a consistent design section. The results from the Binary Logit Model show that the consistency level is significantly affected by deflection angle and operating speed. Deflection angle was negatively correlated with the in-consistency level, and the operating speed was positively correlated with in-consistency level., Conclusions: From Binary Logit Model (BLM) results, we can conclude that an increase in the value of deflection angle will significantly decrease the probability of In-Consistent level, which indicates uncertainties that cause drivers to change the path of vehicle or rate of deceleration of the vehicle while maneuvering the curve will be decreased. Whereas, increase in the operating speed will significantly increase the probability of In-Consistency level.

One of the feasible solutions for the solid waste management problem is to use recycled plastic waste as a replacement for natural aggregates in construction applications, which reduces pollution and protects natural resources from depletion. Corrosion of steel reinforcement due to carbonation is one of the important factors affecting the durability of reinforced concrete, which leads to a decrease in serviceability and safety of structures. This study aimed to compute the probability of corrosion initiation using the reliability index for concrete whose coarse aggregate was partially replaced with high impact polystyrene (HIPS). This study employed a statistical carbonation depth prediction model incorporating recycled aggregates which relate carbonation in concrete with 28-day compressive strength, cement content, aggregates' equivalent water absorption, and CO 2 content in the atmosphere. A reliability index of 1.28, which infers the probability of corrosion initiation less than 10%, has been used for inference. Results showed that a slight increase in concrete cover for concrete with HIPS replacements was required to exhibit similar service life as that of conventional concrete., (© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Bamboo structures have various types of connections, such as bolting and lashing. One crucial issue in bamboo structures is that the connection with bolts and nails has a lower load-carrying capacity associated with the bamboo failure resulting from the bolt or nail invading them. This paper focuses on the connection for raw bamboo members with steel hoops (BHC), of which the two semi-circular steel hoops are fastened to the raw bamboo with high-strength bolts. The sliding friction is controlled by the interfacial pressure, which can be increased by tightening the bolts. A push-out experiment on thirty-six specimens was conducted considering the following two parameters: the different surface conditions of raw bamboo (with or without the epidermis) and the different interfacial pressure. The test results mainly showed the two failure modes of specimens under certain conditions: continuous longitudinal slip after the vertical load reached the peak; and the steel hoop stuck in the bamboo skin after a period of slip. It is found that the sliding friction was controlled by the interfacial pressure, and the difference in the anti-sliding capacity between the epidermal bamboo specimen and the non-epidermal bamboo specimen was magnified with the increase of interfacial pressure. The contact stress on the surface of bamboo is approximately uniformly distributed based on the finite element analyses. The interfacial pressure can be predicted by the torque value of the digital electronic torque wrench and the equations established by mechanical analysis, respectively. Moreover, the design formulae of bearing capacity for BHC under three guaranteed rates (50%, 95%, and 99.9%) were developed based on probability theory, while the fourth design formula was derived by regression analysis. The reliability indices of the four design formulae were up to 0.07, 1.44, 3.09, and 0.97, respectively, and the resistance partial coefficients were suggested accordingly.

In this paper, Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), was used to conduct reliability analyses. For static-strength calculations, the MES3D module, designed by the authors, was employed. Ultimate limit state was defined as condition of non-exceedance of the capacity value, resulting from the stability criterion of the bent and compressed element. The serviceability limit state was defined as the condition of non-exceedance of allowable vertical displacement. The above conditions constitute implicit forms of random variable functions; therefore, it was necessary to build an interface between the Numpress Explore and MES3D programs. In the study, a comparative analysis of two cases was carried out. As regards the first case, all adopted random variables had a normal distribution. The second case involved a more accurate description of the quantities mentioned. A normal distribution can be adopted for the description of, e.g., the randomness in the location of the structure nodes, and also the randomness of the multiplier of permanent loads. In actual systems, the distribution of certain loads deviates substantially from the Gaussian distribution. Consequently, adopting the assumption that the loads have a normal distribution can lead to gross errors in the assessment of structural safety. The distribution of loads resulting from atmospheric conditions is decidedly non-Gaussian in character. The Gumbel distribution was used in this study to describe snow and wind loads. The modulus of elasticity and cross-sectional area were described by means of a log-normal distribution. The adopted random variables were independent. Additionally, based on an analysis of the elasticity index, the random variables most affect the failure probability in the ultimate limit state and serviceability limit state were estimated.

Based on the clinical application data of medical X-ray computed tomography (CT) in the Shanghai Sixth People's Hospital, this study transformed it into the product reliability index requirements, and took the mechanical representative component-examination table (hereinafter referred to as "patient table") and the electronic representative component-DCB (data control board) as examples. Based on the relationship between failure characteristics and clinical application data, a complete set of closed-loop implementation methods from reliability index requirements to reliability design and verification are discussed.

This paper presents an efficient method of shield tunneling reliability analysis using spatial random fields. We introduced two stochastic methods into numerical simulation. The first one computes the maximal ground surface settlement using classical statistics, in which the response surface method is utilized to calculate the failure probability by first-order second moment. Cohesion, internal friction angle, Young's modulus and mechanical model factor are considered as random variables. The second method is the spatial random fields of aforementioned three key geotechnical parameters. Using these two methods, similar multiple soil layers are converted into a stationary random field by local regression as the first step, and then the process is followed by the spatially conditional discretization of multivariate. Failure probability of maximal ground surface settlement is calculated by a subset Monte-Carlo Algorithm. This approach is applied into the four-overlapping shield tunnels of the 5 th and 6 th metro lines intersecting at Huanhu W Rd station, Tianjin China. The failure analysis results indicated that classical statistics of geotechnical parameters showing higher variability than spatial random fields, which substantially support the complex shield tunneling project., (© 2019 The Authors.)

Medial Tibial Stress Syndrome MTSS is frequently diagnosed as a severe clinical issue which occurs due to the cycle loadings (fatigue failure). Since the mechanical properties of the bones are random variables, therefore, there is a need for a probabilistic approach to rationally assess the reliability level of the fatigue failure of the tibia. The main contribution of this paper is to introduce a novel limit state function to determine the fatigue damage state and the reliability index of MTSS based on the different loading and aging conditions. In this study, the tibias of the several people at the different ages are subjected to the fatigue loadings. The load carrying capacities of the considered specimen are determined based on the reliability analysis. Indeed, several 3D finite element analyses are performed to find out the damage states of the tibias. Accordingly, the reliability-based stress analysis is accomplished to localize the most vulnerable zone of the bone. As it was expected, the higher loading cycles associated with the elder bones is related to the lowest fatigue reliability level. Finally, the target reliability level of MTSS is proposed to deliberate the safe level of the loading condition on the tibia in terms of the walking distance., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Purpose: The head-mounted automated perimeter imo ® is a new portable perimeter that does not require a dark room and can be used to examine patients in any setting. In this study, imo 24plus (1-2) AIZE examinations were compared with previous Humphrey Field Analyzer (HFA) 30-2 (SITA standard) examinations within the same patient., Patients and Methods: imo examinations (either head-mounted [i-H] or fixed [i-F] type) were performed in patients with glaucoma or suspected glaucoma who had already experienced HFA five or more times. Measurement time and correlations of mean deviation (MD) and visual field index (VFI) values were compared between groups for HFA, i-H, i-F, and imo total (i-T). Fixation loss (FL), false-positive (FP), and false-negative (FN) detection rates were compared. The percentage of binocular random single-eye tests under possible non-occlusion conditions using imo was determined. Mann-Whitney U test was performed, and Spearman's rank-order correlation coefficient was calculated., Results: The inclusion period was July to December 2016. Among 273 subjects (543 eyes), 147 (292 eyes) were tested with i-H type and 126 (251 eyes) with i-F type. Mean MD values for HFA and i-T were -6.1±7.8 and -6.2±7.1 dB, respectively. Mean measurement times for HFA, i-H, i-F, and i-T were 15.23±2.07, 10.47±2.11, 11.04±2.31, and 10.54±2.19 minutes, respectively ( P <0.01 for HFA vs i-H/i-F). Total mean measurement time was shorter by 30.8% for i-T vs HFA. Correlation coefficients of MD and VFI were R 2 >0.81 for HFA vs i-H and i-F. FP and FN detection rates were significantly higher with i-T than HFA; there was no significant difference in FL. Binocular random single-eye tests were possible in 85% of cases., Conclusion: imo reduced measurement time by 30.8%. imo VFI and MD values were highly correlated with HFA. As i-F and i-H types produced similar results, imo can be used in accordance with the patient's situation., Competing Interests: Disclosure The authors report no conflicts of interest in this work.

The management of disaster waste is one of the most critical tasks associated with recovery after a disaster. Having a general idea of the required capacity, cost and target clean-up time while considering the uncertainties involved in the system before the detailed plan of a disaster waste clean-up system is significant. Reliability analysis is a method to judge the performance of a system and deal with uncertainties in the system. Evaluating the reliability of the system, which can indicate the possibility to complete the clean-up within the target time and cost, and optimising the system to maximise the reliability to provide information to decision-makers regarding the capacity, cost and time required to finish the clean-up is the purpose of this paper. A mathematical model is developed applying the First Order Reliability Method (FORM) to address the problem. Additionally, a non-linear optimisation model is developed to improve the reliability of the disaster waste clean-up system with consideration of the total cost and clean-up time constraints, and solved using a Genetic Algorithm. The proposed models are implemented to solve a case study in Queensland, Australia. It is shown that the models have the capability of maximising the reliability and minimising the total clean-up costs by optimising the arrangement of vehicles during the clean-up process., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

The severity of roadway departure crashes mainly depends on the roadside features, including the sideslope, fixed-object density, offset from fixed objects, and shoulder width. Common engineering countermeasures to improve roadside safety include: cross section improvements, hazard removal or modification, and delineation. It is not always feasible to maintain an object-free and smooth roadside clear zone as recommended in design guidelines. Currently, clear zone width and sideslope are used to determine roadside hazard ratings (RHRs) to quantify the roadside safety of rural two-lane roadways on a seven-point pictorial scale. Since these two variables are continuous and can be treated as random, probabilistic analysis can be applied as an alternative method to address existing uncertainties. Specifically, using reliability analysis, it is possible to quantify roadside safety levels by treating the clear zone width and sideslope as two continuous, rather than discrete, variables. The objective of this manuscript is to present a new approach for defining the reliability index for measuring roadside safety on rural two-lane roads. To evaluate the proposed approach, we gathered five years (2009-2013) of Illinois run-off-road (ROR) crash data and identified the roadside features (i.e., clear zone widths and sideslopes) of 4500 300ft roadway segments. Based on the obtained results, we confirm that reliability indices can serve as indicators to gauge safety levels, such that the greater the reliability index value, the lower the ROR crash rate., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The crystallographic reliability index [Formula: see text] is based on a method proposed more than two decades ago. Because its calculation is computationally expensive its use did not spread into the crystallographic community in favor of the cross-validation method known as [Formula: see text]. The importance of [Formula: see text] has grown beyond a pure validation tool. However, its application requires a sufficiently large dataset. In this work we assess the reliability of [Formula: see text] and we compare it with k-fold cross-validation, bootstrapping, and jackknifing. As opposed to proper cross-validation as realized with [Formula: see text], [Formula: see text] relies on a method of reducing bias from the structural model. We compare two different methods reducing model bias and question the widely spread notion that random parameter shifts are required for this purpose. We show that [Formula: see text] has as little statistical bias as [Formula: see text] with the benefit of a much smaller variance. Because the calculation of [Formula: see text] is based on the entire dataset instead of a small subset, it allows the estimation of maximum likelihood parameters even for small datasets. [Formula: see text] enables maximum likelihood-based refinement to be extended to virtually all areas of crystallographic structure determination including high-pressure studies, neutron diffraction studies, and datasets from free electron lasers.