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Introduction. At present, numerical methods enjoy widespread use in construction practice. They enable performing and analyzing complex non-linear, multi-factor models without excessive analytical procedures. However, as a rule, the most complex tasks, performed in a three-dimensional setting with account taken of physical, geometric and other nonlinearities, are performed in deterministic formulations without the analysis of the stochastic nature of physical processes. This seems particularly strange, given that numerical methods are well-suited for modeling stochastic processes. Numerical probabilistic and statistical approaches (PSA) can be applied to simulate and take into consideration various spatiotemporal aspects of the probabilistic nature of loads and forces, structural system resistances, materials and geological terrains. Even the most advanced numerical models of deterministic physical systems are merely a specific case of probabilistic and statistical modeling: they enable obtaining only one value (point) on the whole field of possible implementations, being unable to demonstrate an objective and exhaustive variety of probable outcomes. This article presents a case study of numerical probabilistic and statistical analyses of loads and forces. Methods of research. Materials from different sources, such as reference books, regulatory documents, laboratory test results, as well as available experimental data, were used as input parameters. The principal calculation and analysis of the integral function of loads was performed using the Monte Carlo numerical method of probabilistic and statistical modeling and various theoretical (statistical) and empirical distributions, followed by the quantitative assessment of design loads at various confidence probability values. Results. This study provides an example of the probabilistic and statistical calculation (determination) of the integral function of loads and forces with account taken of different origins of loads and varied input parameter distribution patterns, including empirical distributions. It has proven great importance of accurate description of initial distributions of a random value for the determination of reliable design load values. Conclusions. Probabilistic and statistical approaches have the ability to objectively assess the performance of structural systems based on the quantitative assessment of the probabilistic nature of load factors. These approaches have huge potential for increasing the reliability of buildings and structures and the cost effectiveness of construction projects.

The performance function of many engineering structures and mechanisms is usually complex, highly nonlinear, and described in the implicit form. The reliability analysis of these structures using common methods requires high cost and time. In this paper, a new approach for reliability analysis of engineering structures and mechanisms by using the particle swarm optimization algorithm is presented. The advantages of this method in comparison with the conventional methods are its simplicity and accuracy. In addition, the limitations of the common previously presented methods are eliminated by the proposed method. This approach is based on a new redefinition of most probable point in the reliability analysis. To evaluate the performance and validity of the proposed method, some examples in the reliability analysis of various functions are employed. Finally, the superiority of the proposed method in performance and accuracy is demonstrated and compared to the conventional methods and it can be used for reliability analysis of complicated engineering structures.

A safety performance function (SPF) is a statistical equation to predict the expected crash frequency for a certain roadway facility, mainly as a function of traffic exposure indicators. Ro...

An important challenge in structural reliability is to reduce the number of calls to evaluate the performance function, especially the complex implicit performance functions. To reduce the computational burden and improve the reliability analysis efficiency, a new active learning method is developed to consider the probability density function of samples based on the learning function U in an active learning reliability method that combines the kriging and Monte Carlo simulation. In the proposed method, the proposed active learning function contains two parts: part A is based on function U, and part B is based on the probability density function and function U. By changing the weights of parts A and B, the sample points close the limit-state function, and those in the region with a higher probability density function have more weight to be selected compared to the others. Subsequently, the kriging model can be constructed more effectively. The proposed method avoids a large number of time-consuming function evaluations, and the recommended weight is also reported. The performance of the proposed method is evaluated through three numerical examples and one engineering example. The results demonstrate the efficiency and accuracy of the proposed method.

The available robust and reliable topology optimization methods provide quick and efficient design output in an uncertain environment. However, the whole domain of performance function remains hidden during this design process. In the interest of the designer, it is required to know the overall behavior of performance functions in deterministic as well as uncertain/realistic environment. The current work achieves this by proposing an integrated methodology, which combines the design of experiments approach and reliability-based topology optimization. The proposed method enables the designer to simulate performance functions in a desired design-factors space, including uncertainties, via reliability value. For this analysis, compliance, maximum deflection, mechanical advantage, and von Mises stress values are selected as performance functions. Volume fraction, applied force, and dimensions or aspect ratio are chosen as design/control factors. The uncertainties of these design factors are captured using reliability-based topology optimization. The uncertainties due to noncontrollable factors such as material property, load direction, and magnitude are incorporated using the design of experiments approach. Under these uncertainties, the performance of topologically optimized problem is simulated for different experimental combinations of the design factors. The experimental combinations for uncertainties and design factors are generated using Taguchi's orthogonal array. Simulated results are analyzed using techniques such as analysis of mean and variance, signal-to-noise ratio, and response surface method. These analyses help in identifying statistical significance of factors and uncertainties, performance variations, and equivalence relation of performance vs. factor. The proposed methodology is illustrated by selecting monolithic structures such as, on MBB, cantilever beam, and force inverter mechanism.

For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function (GPF) expression is established under the strict mathematical derivation for the Profust reliability model. By constructing the GPF, the calculation of the Profust failure probability can be transformed into the calculation of the traditional failure probability. Then various existing methods for the traditional failure probability can be used to estimate the Profust failure probability. Due to the high efficiency of the Adaptive Kriging (AK) model and the universality of the Monte Carlo Simulation (MCS), AK inserted MCS (abbreviated as AK-MCS) has been proven to be an efficient method for estimating the failure probability. Therefore, the AK-MCS combined with the GPF (abbreviated as AK-MCS + GPF) is proposed for estimating Profust failure probability. The proposed method greatly reduces the computational cost while ensuring the accuracy. Finally, four examples are given to validate the proposed AK-MCS + GPF. The results of the examples show the rationality and the efficiency of the proposed AK-MCS + GPF. Keywords: Failure probability, Fuzzy-state assumption, General performance function, Kriging model, Profust reliability, Reliability

This paper proposes an efficient Kriging-based subset simulation (KSS) method for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probability. In this method, Kriging metamodel is employed to replace the true performance function, and it is smartly updated based on the samples in the first and last levels of subset simulation (SS). To achieve the smart update, a new update strategy is developed to search out samples located around the projection outlines on the limit-state surface. Meanwhile, the number of samples in each level of SS is adaptively adjusted according to the coefficients of variation of estimated failure probabilities. Besides, to quantify the Kriging metamodel uncertainty in the estimation of the upper and lower bounds of the small failure probability, two uncertainty functions are defined and the corresponding termination conditions are developed to control Kriging update. The performance of KSS is tested by four examples. Results indicate that KSS is accurate and efficient for HRA-RI with small failure probability.

In reliability analysis for the practical engineering problems with the time-consuming model, it has become an important challenge that how to obtain accurate reliability assessment with a minimum number of calls. In order to reduce the computational cost, this paper develops a new sequential surrogate method combining adaptive kriging and Markov chain Monte Carlo simulation with a novel learning strategy for reliability analysis. The proposed method is named AK-MCMC, which takes full advantage of the classification feature of reliability analysis based on the surrogate models, and it can efficiently approximate the classification boundary of the performance function. First, the learning strategy is developed to sequentially pick out the informative samples for updating the experimental design samples. Then, a new stopping criterion is adopted to guarantee the classification accuracy of the constructed kriging model. In this way, the proposed method skillfully makes reliability evaluation independent of an adaptive iterative process, which greatly improves the efficiency of model refinement. Finally, the proposed method is applied to several examples, which contain small failure probability problem, non-linearity problem, and engineering problem with an implicit performance function. In particular, the efficiency of the proposed AK-MCMC method is proved for the problems with small failure probability.

In this paper, a new analytical formula is proposed to determine the mean outcrossing rate of nonstationary non-Gaussian performance functions. The performance function is firstly transform...

Local reliability sensitivity methods aim at determining the partial derivatives of the failure probability or the reliability index with respect to model parameters. For efficient local reliability based sensitivity analysis, it is important to avoid repeated evaluations of the performance function. To this end, an extension of the moving particles method to local reliability based sensitivity analysis is presented that is completely based on the already evaluated samples for the reliability estimate and thus avoids repeated evaluations of the performance function. In order to further reduce the variance of the estimator and to increase the efficiency, a multilevel variant of the estimator is proposed. The method is discussed in detail and illustrated by means of examples.

The present work discusses an innovative approach to metamodeling in reliability that uses a field-transversal rationale. Adaptive metamodeling in reliability is characterized by its large spectra of models and techniques with different assumptions. As a result, the reliability engineer is frequently faced with the highly challenging task of selecting an appropriate model or technique with limited a priori knowledge about the performance function that defines the problem of reliability. To tackle this challenge, a complement-basis is proposed for adaptive metamodeling. It consists in using a batch of multiple metamodels or techniques that, accordingly to an activation criterion, are selected to solve the reliability analysis. This activation is set to depend on the model synergy with the problem in-hand. In the present work the leave-one-out loss is applied as evaluator of compatibility, and results show that the absolute loss successfully performs as an activator. A metamodel-independent learning approach and stopping criterion are implemented to study the proposed approach in five representative examples. Results show that the complement-basis allows to increase the efficiency of the reliability analysis through the selection of adequate metamodels, which is indicative of the untapped potential that further transversal research may add to metamodeling in reliability analysis.

Structural reliability analysis involving highly nonnormally distributed performance functions or relatively small failure probabilities is still a challenging problem in engineering practi...

The existing step size methods aim to success in the convergence of searching the minimum performance target point in the reliability analysis. However, these methods cannot guarantee that the performance function value is smaller than that of previous point. This results in the redundant computation during the search process. In this paper, a new step method called hybrid directional step method is proposed to improve the efficiency of search process. The proposed method can keep the performance function values of iterations presenting a decreasing sequence and quickly converge to the minimum performance target point. The proposed method is compared with some existing methods through several numerical examples. The results show that the proposed hybrid directional step method presents good robustness and more efficient computation in practical application.

A dynamic process model based on a base metal refinery including critical control layers has been developed. The critical control layers include sensors, actuators, regulatory controllers, alarm systems, safety interlocks and supervisory control. With the help of expert knowledge, a fault (abnormal event) library was incorporated into the dynamic model. Fault diagnosis methods are used to detect and identify abnormal process conditions. With the use of the dynamic process model, fault detection and identification methods can be more rigorously and accurately evaluated for hydrometallurgical industry use. An economic performance function is developed from expert knowledge. Once the fault diagnosis is complete, an economic impact analysis based on the fault diagnosis results is completed. A possible economic case for fault diagnosis is concluded from the results.

This paper studies a fully distributed optimal formation flying problem for a multi-satellite system with a chief satellite and some deputy satellites, in order to seek the optimal formation via si...

A new reliability analysis method for tunnels was developed by integrating an adaptive Radial Basis Function (RBF) metamodeling technique with a First-Order Reliability Method (FORM). In each iteration of the adaptive RBF (A-RBF) technique, an explicit metamodel of the performance function was constructed using an augmented RBF, before an alternate FORM was applied. Additional sample points were then added in the neighborhood of the design point in order to improve the accuracy of the metamodel. Three examples were solved and the proposed approach worked well. This work provides an efficient and effective reliability analysis method for practical tunnel engineering problems.

Based on reliability theory, the value of the standard normal distribution integral can be obtained by calculating the probability of the failure domain of the linear performance function. After th...

Accurate determination of the failure probability of oil and gas pipeline is very important in integrity assessment and work conditions of such structure. In this paper, the failure probability of the corroded pipelines which is made by X60 steel grade is evaluated. The burst corroded performance function is developed using the M5 model tree for this complex real engineering failure problem. The structural reliability of a the pressurized gas pipeline containing external corrosion defects has been evaluated using hybrid reliability method combined by the M5 model tree and Monte Carlo simulation. The results indicated that increasing the defects depth are strongly reduced the safety levels of this problem.

This paper proposes a sampled-data $H_\infty $ fuzzy observer technique for nonlinear uncertain oscillating systems that are represented by the Takagi–Sugeno fuzzy model. The observers are designed for two cases: a measurable premise variable and an immeasurable premise variable. The error system between the nonlinear uncertain system and the sampled-data observer is constructed. The $H_\infty $ performance function for the oscillating system is defined and is guaranteed in the Lyapunov sense. Sufficient conditions for the $H_\infty $ sampled-data fuzzy observer are given in terms of linear matrix inequalities. Finally, the feasibility of the proposed technique is shown using two simulation examples.

The first–order reliability method (FORM) is widely used in structural reliability analysis for its simplicity and efficiency. It can be solved by gradient–based algorithms, on which the nonlinear degree of performance functions may have a great influence. On the other hand, evolutionary algorithms could achieve convergence solutions even for highly nonlinear performance function, usually with expensive computational cost. To overcome their drawbacks, we propose a new reliability analysis method called PMA–IACC to search the most probable failure point (MPP). As the inverse reliability analysis and reliability analysis are reversible each other, the performance measure approach (PMA) of the inverse reliability analysis could be used for the reliability analysis based on the multi–objective optimization theory. To enhance the efficiency and robustness of the inverse reliability, the improved adaptive chaos control (IACC) method is proposed and then it is integrated into the PMA reliability analysis strategy. Five illustrative examples, including three two–dimensional problems and two multi–dimensional problems, demonstrate the outstanding efficiency and robustness of the PMA–IACC over other prevalent approaches.

The paper presents a High order stochastic response surface method (HOSRSM) for reliability and reliability-based sensitivity analyses of transmission mechanism of a shearer in heavy and impulsive environments. Dynamic analysis is affected by several sources of uncertainty, and it is important to quantify their combined effect on performance of the mechanism in order to aid risk assessment, risk mitigation, and decision-making. A dynamic transmission model of the traction unit is established under the condition of low speed and impulsive load. A performance function is proposed to evaluate the system transmission accuracy. The effects of basic variables in HOSRSM are investigated on calculation efficiency and computation cost of system precision reliability. The results indicate that structure parameters of a sun gear are more sensitive than others. The tooth width is a more sensitive geometric parameter than the diameter of the center hole. The targets are proposed to manufacture and inspect the sun gear in traction unit for safety.

The time-variant system reliability analysis is a significant topic in the field of reliability engineering. Although progress has been made, there remain multiple challenges in the existing methods including the explosive number of possible failure modes, requiring correlation information, and excessive computational efforts. In the present work, an improved moment method with high accuracy, efficiency and robustness is proposed for system reliability analysis of deteriorating structures. First, by introducing the complete system failure process, an equivalent time dependent performance function describing a deteriorating structural system is obtained. Second, a point estimate method based on the adaptive trivariate dimensional decomposition is adopted to calculate the first six moments of the performance function. And third, a saddlepoint approximation involving the first six moments is developed to estimate the system failure probability. Several examples are investigated to verify the accuracy, efficiency and stability of the proposed method.

Simulation based structural reliability analysis suffers from a heavy computational burden, as each sample needs to be evaluated on the performance function, where structural analysis is performed. To alleviate the computational burden, related research focuses mainly on reduction of samples and application of surrogate model, which substitutes the performance function. However, the reduction of samples is achieved commonly at the expense of loss of robustness, and the construction of surrogate model is computationally expensive. In view of this, this paper presents a robust and efficient method in the same direction. The present method uses radial-based importance sampling (RBIS) to reduce samples without loss of robustness. Importantly, Kriging is fully used to efficiently implement RBIS. It not only serves as a surrogate to classify samples as we all know, but also guides the procedure to determine the optimal radius, with which RBIS would reduce samples to the highest degree. When used as a surrogate, Kriging is established through active learning, where the previously evaluated points to determine the optimal radius are reused. The robustness and efficiency of the present method are validated by five representative examples, where the present method is compared mainly with two fundamental reliability methods based on active learning Kriging.

Practically, the performance of many engineering problems can be defined using a complex implicit limit state function. Approximation of the accurate failure probability is very time-consuming and inefficient based on Monte Carlo simulation (MCS) for complex performance functions. M5 model tree (M5Tree) model is robust approach for simulation and prediction phenomena, which provides ability to dealing with complex implicit problems by dividing them into smaller problems. By improving the efficiency of reliability method using accurate approximated failure probability, an efficient reliability method using the MCS and M5Tree is proposed to calibrate the performance function and estimate the failure probability, respectively. The superiorities including simplicity and accuracy of M5Tree meta-model are investigated to evaluate the actual performance function through five nonlinear complex mathematical and structural reliability problems. The proposed reliability method-based MCS and M5Tree improved the computational efforts for evaluating the performance function in reliability analysis. The M5Tree significantly increased the efficiency of reliability analysis with accurate failure probability.

Consider a system composed of several units. The performance of each unit can be affected by providing a portion of a limited amount of costly resources available. An allocation of resources to a unit results in a unit's response that depends on the level of resources allocated to it and some of its random parameters. In this paper we consider cases where each unit has one or two random parameters. The overall performance of the system is mapped by a function on the vector of responses generated by all the units in the system. Our interest is in identifying the conditions on the response function of the units, the system performance function and the random parameters under which the random system performance as a function of the resource allocation has stochastic arrangement increasing property. This allows one to substantially reduce the number of allocation that needs to be searched to identify an optimal allocation that maximizes the expected utility derived from the system response as a result of the resource allocation.

In this presentation, we propose to use the expertise gained in the cluster community in unbiased optimization to identify materials with optimal properties. Specifically, we present an inverse-design method that automatically identifies atoms or functional groups to be placed at pre-defined positions. Which groups are placed at which positions is identified automatically by optimizing a so called performance function. In the present work, we study, as a simple example, mixed Si-Ge clusters whereby their performance in solar-energy harvesting is optimized. We demonstrate that the proposed method is capable of identifying a larger number of very good candidate structures, although there are cases where not the best (but ‘only’ the 2nd best) structure is identified. It is also demonstrated that it can be difficult to predict the optimal system based on simple chemical and/or physical ideas. Finally, extensions and challenges of the present approach are being briefly discussed.

In this paper, a robust tracking control scheme is proposed for wheeled mobile robots with skidding, slipping, and input disturbance. Considering the existing skidding and slipping, a desired disturbance-observer-based virtual velocity control law is first designed. Then, the robust tracking control scheme is developed by considering the prescribed tracking performance requirement and using the disturbance observer. In the tracking control scheme design, the prescribed performance function method is employed to guarantee the desired tracking performance. To handle the skidding, slipping, and input disturbance, the disturbance observer is developed in the control scheme design. Experiment results demonstrate the effectiveness of the proposed tracking control scheme for wheeled mobile robots with skidding, slipping, and input disturbance.

Probability of failure sensitivity analysis is a subject of major interest in uncertainty based optimization. However, the computational effort required to obtain accurate results is frequently very high. In this work we present a novel strategy for probability of failure sensitivity analysis, that is based on polynomial expansions of both the performance function and its derivatives. Sensitivity analysis is then made using the obtained polynomial expansions together with standard expressions. Since the simulation step requires only evaluation of closed form polynomials, very large samples can be used to obtain accurate results with small computational effort. The proposed approach is expected to be efficient when polynomial expansion methods are suitable. Four numerical examples are presented in order to show the effectiveness of the proposed approach.

This paper proposes a new terminal homing guidance law with line-of-sight angle constraint for a missile to intercept a noncooperative maneuvering target by integrating prescribed performance control with sliding mode control. The newly proposed guidance law is derived analytically with a prescribed performance controller in combination with the continuous nonsingular terminal sliding mode manifold and the disturbance observer. The prescribed performance controller is designed with a new prescribed performance function to avoid undesired abrupt change in the derivative of prescribed performance variable. In addition to its robustness and preciseness, this new homing guidance law is able to attenuate a largely abrupt change in guidance commands due to driving the sliding mode variable whose initial derivative is close to zero to a desired residual set at the beginning of the terminal homing phase. Furthermore, the time-varying control gain of the new guidance law is analytically determined by terminal tolerance. Theoretical analysis and numerical simulations are conducted to demonstrate the effectiveness of this new guidance law.

In order to solve the problem of multi-sensor multi-objective configuration, a management algorithm based on Simulated Annealing Genetic Algorithm (SA-GA) is proposed. Firstly, Analytic Hierarchy Process (AHP) is used to quantify the sensor’s spatial information perception ability. Secondly, target’s priority is calculated. Finally, SA-GA is used to allocate sensor resources. It can be seen from the simulation results that this algorithm achieves the maximum performance function in solving the multi-objective distribution. And it has certain engineering significance.

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.

To address the problem of control surface redundancy for compound high-speed rotorcraft in multi-mode conversion process, a hybrid multi-objective control allocation strategy based on adaptive particle swarm optimization (PSO) algorithm is proposed. First, the control allocation problem is converted to a hybrid multi-objective optimization problem to solve the control redundancy, and a hybrid multi-objective optimization performance function is designed to satisfy the multiple requirements of flight mission. Second, a preference matrix is designed to determine the weight coefficients of the optimization performance function. The preference matrix can simplify the complexity of hybrid multi-objective optimization problem. Finally, an adaptive PSO algorithm is designed to solve the hybrid multi-objective control allocation dynamically. The simulation verifies the feasibility and effectiveness of the control allocation strategy, which eliminates the need of extra controllers in the mode conversion, reduces the difficulty of flight control system design and improves the system security.

Aiming at the longitudinal motion model of the air-breathing hypersonic vehicles (AHVs) with parameter uncertainties, a new prescribed performance-based active disturbance rejection control (PP-ADRC) method was proposed. First, the AHV model was divided into a velocity subsystem and altitude system. To guarantee the reliability of the control law, the design process was based on the nonaffine form of the AHV model. Unlike the traditional prescribed performance control (PPC), which requires accurate initial tracking errors, by designing a new performance function that does not depend on the initial tracking error and can ensure the small overshoot convergence of the tracking error, the error convergence process can meet the desired dynamic and steady-state performance. Moreover, the designed controller combined with an active disturbance rejection control (ADRC) and extended state observer (ESO) further enhanced the disturbance rejection capability and robustness of the method. To avoid the differential expansion problem and effectively filter out the effects of input noise in the differential signals, a new tracking differentiator was proposed. Finally, the effectiveness of the proposed method was verified by comparative simulations.

This paper, on the one hand, aims to identify significant crash risk factors at unsignalized three-leg intersections connecting rural two-lane two-way roads and minor roads with a STOP control on the approaches (3ST) and, on the other, to make adjustments to the Highway Safety Manual (HSM) procedure, fine-tuning its Safety Performance Function (SPF) based on observation of the local context. Over an 8-year period of study, a total of 240 crashes on 35 3ST intersections were observed, with no geometric-infrastructure adjustments or changes in the Annual Average Daily Traffic (AADT) and surrounding context noted at the intersections investigated. To obtain reliable results, the study period was divided into two groups: (a) 5 years to calibrate a new SPF, and (b) the remaining 3, not included in the first dataset, were used to validate the results. A negative binomial regression model was adopted to calibrate the new SPF. It was found that the AADT on the major and minor roads, the intersection skew angle, the co-occurrence of left and right-turn lanes on the major roads, and lighting seriously affect the crash scenario.

The structural failure of a tunnel is a process that evolves from local damage to overall destruction. The system reliability analysis method can be useful for analyzing the evolutionary law of local structural failure. In many complex stress environments, the structural performance function may be very complicated or even impossible to solve. This paper establishes a response surface function to represent the implicit tunnel performance function. The reliability of the shear capacity of a tunnel is considered. The critical parts and critical failure paths of the tunnel system are determined using the β-unzipping method. Failure evolution is analyzed to obtain the failure process of the tunnel system. Different failure modes are shown under different cases. Based on the partial failure probability and impact on the tunnel system, the risk levels of the critical parts at each stage of the failure history are evaluated. Therefore, the tunnel failure tree model obtained by combining the response surface method and β-unzipping method plays an important role in tunnel reliability evolution, and can evaluate tunnel safety comprehensively.

This paper presents a cost-effective probabilistic approach to be used in engineering applications. The proposed approach consists of an improved Kriging-based method aiming at reducing to a minimum the number of evaluations of the true performance function when computing a failure probability. It is a kind of variant of the classical Active learning method combining Kriging and Monte Carlo Simulation (AK-MCS) developed by Echard et al. (2011) [1], where some improvements are introduced to enhance the learning process. Some illustrative and practical examples are presented and discussed. The proposed approach has shown a great efficiency as compared to the classical AK-MCS approach.

A resilient system should have the ability to mitigate the disruption caused by unfavorable environment and to rapidly recover to an acceptable performance level. In this paper, a detailed model to assess resilience of shield tunnel is presented. The performance robustness under disruption and the subsequent recovery rapidity are emphasized in this model. The tunnel horizontal convergence is selected as the performance indicator. The resilience index (Re) is defined by the ratio of the integral of the performance transition function over the integral of the normal performance function. The rationality and applicability of the model is validated by a real case of extreme surcharge on Shanghai metro tunnel. In this case, the performance transition and the normal performance degradation are characterized by the measured data. 70–80% of the normal performance is disrupted due to the surcharge, but only 1% is recovered by unloading of the surcharge in 9 days and 12.4% is recovered after 4 years by the soil grouting in 38 days. It results in a resilience index (Re) between 0.28 and 0.45. The lesson learned from the case indicates that the high vulnerability of lining convergence due to the severe surcharge and the long time duration between recovery measures could result in weak resilient abilities for shield tunnels. The value of resilience index Re could be significantly increased by 73% on average if the recovery duration were shortened.

According to the National Highway Traffic Safety Administration's Fatality Analysis Report System, more than 25 percent of fatal crashes occur on horizontal curves. High Friction Surface Treatments are an innovative, cost-effective, and sustainable means of improving roadway safety, which could improve the safety of this alignment. This research involved a comprehensive review of crash data to identify the correlation between pavement skid number, roadway curvature degree, crash rate, and crash severity. The dataset showed that greater injury occurred on higher degrees of curvature, and lower skid numbers correlated to a higher percent of wet road crashes. Also, around a skid number of 55, an increase in skid number no longer resulted in decreased crash rates. The goal of this research is to use these correlations to develop Crash Modification Factor that would integrate pavement friction and horizontal curvature, to enhance the accuracy of the current Highway Safety annual performance function.

Civil infrastructure can be subjected to different deterioration scenarios (e.g., continuous deterioration and sudden events) during its service life. Time-dependent reliability analysis of a deteriorating system is of vital importance in the structural design, assessment, and management process. In this paper, a general and novel probability density function-informed framework for time-dependent reliability analysis is developed, considering different deterioration processes and system-level performance. Both continuous deterioration and sudden events are considered within the proposed framework. For the scenario with random sudden drops and/or significant differences in deterioration rates, a novel two-step translation method is proposed to assess the probability density of the performance function within the service life of a structure. In this method, translation operation is conducted twice; the first time to build a virtual and differentiable performance function, and the second, to solve the actual probability density function based on the results from the first step. Then, three illustrative examples are assessed: a simple deteriorating case, a component-level case, and a system-level case. The relevant results demonstrate the feasibility and efficiency of the proposed method.

Failure accidents of casings, designed obeying traditional design standards that have been amended for many times, are still happening nowadays, and existing reliability analysis methods mostly have not considered the dependence structures of variables, it's badly necessary to seek other methods to compensate these two problems and defects. This study proposes a copula-based risk analysis framework of casing in a casing-formation composite system (CFCS). Firstly, a mechanical analysis model of casing under CFCS is established and verified by the simulation method. Secondly, random data sets of the formation parameters are obtained by using logging data, meanwhile, the acquisition methods of statistical data of casing are also provided. Thirdly, the best uncertainty parameters in the given five copulas are inferred by using Bayesian-based Markov chain Monte Carlo (MCMC) likelihood algorithm, which are compared with those from other algorithms; the optimal copula is determined by the Bayesian-based MCMC-estimated method and the squared Euclidean distance (SED), respectively; the posterior joint probability isolines of the copulas are depicted, and isolines from the optimal copula are compared with that of the empirical copula method; the correlation coefficients of variables in CFCS, relative to performance function value, are sorted in magnitude. Finally, a division method of safety level is adopted, and based on the optimal copula, the risk analysis of casing is conducted with considering the bivariate dependence. The proposed framework can provide unique insights into the risk analysis of casing in CFCS with correlations considered and can also be programmed to use in risk management and decision-making systems of petroleum engineering.

The behaviour of unsaturated soils is governed by the soil-water characteristic curve (SWCC). The suction in unsaturated soil has a significant impact on the stability of infinite slopes. The measured SWCC and suction values in the soil are inherently variable and uncertain. Due to these uncertainties, the results generated by conventional deterministic approaches render unrealistic factors of safety of the slope. Therefore, it is highly appropriate to develop a reliability based design optimization (RBDO) for stability analysis of unsaturated infinite slopes. The effect of variability associated with fitting parameters, af, mf, and nf on the reliability index of infinite slopes is presented It is noted from the present study that the maximum values of COV's for af, mf and nf are 489.2, 412.5, and 297.4% respectively for different types of soils. The reliability analysis is presented based on RBDO using four different models to predict the unsaturated soil shear strength. The mean and standard deviation associated with suction, cohesion, unit weight, and internal angular friction are considered for the probabilistic optimisation. A performance function is formulated against sliding slope failure. The influence of the coefficients of variation (COV) of unsaturated soil parameters on the reliability index is also discussed.

A multilevel moving particles method is developed for the estimation of failure probabilities that are computed from numerical approximations of the performance function. The algorithm balances the statistical error of the estimate and the approximation error. This is achieved by computing a telescoping sum of estimates for the difference in the number of moves at subsequent levels of the approximation error. The sample variance of these estimates decreases with decreasing approximation error. Thus, the number of samples that has to be evaluated with high accuracy is reduced compared to a single level computation. Therefore, the proposed algorithm is very efficient for structural reliability analysis problems, in which highly accurate evaluations of the performance function are necessary and require a huge computational effort.

This paper presents a reliability study of a pile foundation design in soft soils that are consolidating under a surcharge. Both limit and serviceability states are considered in the design study. The load and soil properties are assumed to possess variances that can be described by lognormal distributions. The influence of these variances on pile capacity and settlement are evaluated in terms of reliability level using the concept of reliability index of performance function that describes the design problem. Two design loads that correspond to different conventional mean factors of safety are considered, and relevant results are used to show the relationship of reliability levels of design with mean factor of safety and variance of soil properties. The results from reliability analysis for limit and serviceability states can be used in decision making process for the final design of pile foundation in soft soils.

The multi-state manufacturing system was used to study the influence of the system performance on the reliability of the system, such as the performance status of the manufacturing system, the influence degree of the fault correlation, the complexity of the reliability analysis process and the reliability of the system. The performance of the unit was analyzed by Markov theory, and the structural decomposition of the polymorphic manufacturing system was carried out according to the fault correlation. The Copula function and the gray model were used to quantitatively analyze the influence of the failure correlation, and the fault correlation coefficient and the correlation coefficient between the subsystems and the units related to the existence of faults was given. The performance function of the polymorphic manufacturing system based on the fault correlation coefficient was given. Using the mapping method from the unit to the system, Fault-related performance of the performance of the function was obtained, and the system reliability model was built to achieve the reliability of the entire polymorphic system analysis.

The most past research on storage reliability of electromagnetic relay (EMR) only focuses on the measurement of contact resistance. The relay time parameters which reflect main performance function were not monitored. So, in this study the relay time parameters and relay contact resistance were detected simultaneously. The method of prognostics and health management (PHM) was used. According to the analysis on test results of contact resistance, relay time parameters, the degradation phenomena of EMR in long-term storage are investigated, and the storage failure mechanism is analyzed. The microscopic morphology and changes in chemical elements for relay contact surface was analyzed, which provide references for the relay storage failure mechanisms.

This paper proposes a robust H∞ controller based on Multi-objective genetic algorithms (MOGAs) to control the active magnetic bearings (AMBs) with application to superfluid helium cryogenic centrifugal compressor (CCC). Basic weighting function formulas with seven parameters in all are suggested for H∞ controller, whose physical connections with system performance are clearly explained. Weighting function parameters are defined in a relatively narrow range according to actual operating feature of AMB systems. Then, based on these priori information, such as search-domain and weights expression, tuning and optimizing of the design performance function is carried out applying a MOGA. The control strategy avoids time consuming task in the progress of tuning parameters and provides a complete and versatile method to obtain weighting functions for a H∞ controller. Simulation results demonstrate that the optimized H∞ controller guarantees AMB system better closed-loop behavior performance while retaining low value of control signals.

The sensitivity of the cumulative distribution function CDF of the response with respect to the input parameters is studied in this work, to quantify how the model output is affected by input uncertainty. To solve the response CDF sensitivity more efficiently, a novel method based on the sparse grid integration SGI is proposed. The response CDF sensitivity is transformed into expressions involving probability moments, which can be efficiently estimated by the SGI technique. Once the response CDF sensitivity at one percentile level of the response is obtained, the sensitivity values at any other percentile level can be immediately obtained with no further call to the performance function. The proposed method finds a good balance between the computational burden and accuracy, and is applicable for engineering problems involving implicit performance functions. The characteristics and effectiveness of the proposed method are demonstrated by several engineering examples. Discussions on these examples have also validated the significance of the response CDF sensitivity for the purpose of variable screening and ranking.

This work investigates the attitude tracking control problem of spacecraft under strong external disturbances and parameter uncertainties. A novel appointed-time stable control scheme is proposed with guaranteed transient and steady-state performance. First, an appointed-time reachable performance function (ARPF) is presented, and its reach time can be arbitrarily selected by the users. Then, a double-ARPFs strategy is introduced, that is, by imposing two ARPFs on the attitude and the system output, respectively, all system states will be appointed-time stable. Furthermore, a robust controller with implementable structure is proposed to guarantee the performance functions under strong external disturbances and parameter uncertainties. And the attitude tracking errors as well as the angular velocity errors are proved to be appointed-time stable. Last, three groups of simulations are organized to verify the effectiveness, robustness and appointed-time stability of the proposed control scheme.

In this paper, high precision motion control of piezo-actuated stage is discussed. In order to cope with the nonlinear characteristic of the piezoelectric actuator (PEA) and get high tracking performance, this paper proposes a new approach to design the discrete time sliding mode control (DSMC) with an ability to maintain the tracking error in a known region described by a performance function. The effectiveness of the proposed method is verified by experiments. The results show that the system not only performs well with complicated desired trajectories but also robust against external disturbances.

The CNC machine is controlled by manipulating cutting parameters that could directly influence the process performance. Many optimization methods has been applied to obtain the optimal cutting parameters for the desired performance function. Nonetheless, the industry still uses the traditional technique to obtain those values. Lack of knowledge on optimization techniques is the main reason for this issue to be prolonged. Therefore, the simple yet easy to implement, Optimal Cutting Parameters Selection System is introduced to help the manufacturer to easily understand and determine the best optimal parameters for their turning operation. This new system consists of two stages which are modelling and optimization. In modelling of input-output and in-process parameters, the hybrid of Extreme Learning Machine and Particle Swarm Optimization is applied. This modelling technique tend to converge faster than other artificial intelligent technique and give accurate result. For the optimization stage, again the Particle Swarm Optimization is used to get the optimal cutting parameters based on the performance function preferred by the manufacturer. Overall, the system can reduce the gap between academic world and the industry by introducing a simple yet easy to implement optimization technique. This novel optimization technique can give accurate result besides being the fastest technique.