System Failure Probability Research Articles

Novel reliability method for multidimensional nonlinear dynamic systems

The paper describes a novel structural reliability method, particularly suitable for multi-dimensional structural responses, either measured or numerically simulated over sufficient period of time, resulting in sufficiently long ergodic time series. Unlike other reliability methods the new method does not require to re-start simulation each time system fails, in case of numerical simulation. In case of measured structural response, an accurate prediction of system failure probability is also possible as illustrated in this study. Moreover, classic reliability methods, dealing with time series do not have an advantage of dealing easily with system high dimensionality and cross-correlation between different dimensions.As an example for this reliability study was chosen container ship subjected to large deck panel stresses and extreme roll angles occurring during sailing in harsh weather. Risk of losing containers due to extreme motions is primary concern for ship transport. Due to non-stationarity and complicated nonlinearities of both waves and ship motions, it is a considerable challenge to model such a phenomenon. In case of extreme motions, the role of nonlinearities dramatically increases, activating effects of second and higher order. Moreover, laboratory tests may also be questioned because of the scaling and the sea state choice. Therefore, data measured on actual ships during their voyages in harsh weather provides a unique insight into statistics of ship motions.The aim of this work is to benchmark state of art method, which makes it possible to extract the necessary information about the extreme response from onboard measured time histories. The method proposed in this paper opens up the possibility to predict simply and efficiently failure probability for nonlinear multi-dimensional dynamic system as a whole.

A nested single-loop Kriging model coupled with subset simulation for time-dependent system reliability analysis

Time-dependent system reliability analysis still faces severe challenges including the simultaneous consideration of time-dependent uncertainties under multiple failure modes and the accurate estimation of small failure probability. Therefore, this paper proposes a nested single-loop Kriging (NSLK) model coupled with subset simulation (SS) method, named NSLK-co-SS, for time-dependent system reliability assessment. Firstly, based on the rationale of SS method, the small time-dependent system failure probability is converted into the product of a series of large intermediate failure probabilities by introducing a series of intermediate failure events. Then, by reformulating the time-dependent system reliability problem as a nested system reliability one, the NSLK method is developed to estimate each intermediate failure probability. Meanwhile, a system reliability theory-based U (SYSU) learning function is proposed to identify both the best training sample and mode and sequentially update the Kriging models of multiple modes in a series of small intermediate sample pools. Two numerical examples and an engineering example were investigated to demonstrate the efficiency and accuracy of the proposed method.

Comparative Analysis of Two Modified Fast Simulation Methods for Evaluation of the Failure Probability of a Rank Structure System

Comparative Analysis of Two Modified Fast Simulation Methods for Evaluation of the Failure Probability of a Rank Structure System

Cross-Layer Device Authentication With Quantum Encryption for 5G Enabled IIoT in Industry 4.0

Industrial Internet of Things (IIoT), a core enabler of Industry 4.0, is evolving rapidly to tackle the challenges imposed by explosive real-time manufacturing data in the context of Internet and telecommunication industry. 5G technology is the key to addressing such challenges. This is done by bypassing upper authentication protocols and supporting small data transmission during initial access, which, however, causes serious security breaches in IIoT device authentication. To solve this, in this article propose a secure cross-layer authentication framework based on quantum walk on circles. The system performs random hash coding on multidomain physical-layer resources to encode and decode device identifiers securely, while using a quantum walk based privacy-preserving protocol to maintain code privacy at arbitrary high level, being controlled by the number of occupied physical resources. The upper bound of decoding errors is derived and a nonconvex integer programming problem of minimizing the bound is formulated to characterize the security performance. The space of one-time keys for encryption is also derived that show how high privacy and scalability advantage is maintained against classical and quantum computers. Finally, we derive novel expressions of failure probability of this new authentication system and numerically show that our scheme can bring ultrahigh level of security and privacy protection with low latency despite attack.

Structural system reliability assessment using generalized factorized dimensional reduction method and iterative maximum entropy method

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.

An efficient reliability analysis method for structures with hybrid time-dependent uncertainty

Performing time-dependent reliability analysis is an effective way to estimate the failure probability of structural system throughout its lifetime. In the engineering practices, uncertain parameters with sufficient sample and limited sample may exist simultaneously. The uncertain parameters with limited sample data are difficult to construct its precise probabilistic characteristics during estimating the accurate time-dependent reliability. To address this issue, this paper first develops a new hybrid time-dependent reliability model involving interval processes. Then, to reduce the high dimensionality, an extension method based on equivalent stochastic process transformation approach is proposed to transform the stochastic processes and the interval processes into corresponding equivalent random variables respectively. In particular, an instantaneous reliability model is constructed to envelope all potential system failures that may occur during the time interval. In order to identify the instantaneous failure surface accurately, an active learning method is proposed based on the deep neural network model and the weighted sampling method. With the constructed deep neural network model, the new hybrid time-dependent reliability can be evaluated by performing the Monte Carlo Sampling. Three numerical examples are used to verify the accuracy and efficiency of the proposed method.

Representative slip surface identification and reliability analysis of slope systems in spatially variable soils

ABSTRACT A slope system is a series system with numerous potential slip surfaces (PSSs), and its failure probability is commonly evaluated by several significant failure surfaces, or representative slip surfaces (RSSs). Previous efforts have mainly identified the RSSs in spatially variable soils from the perspective of the correlations between different PSSs, the effects of the failure probabilities of the PSSs were rarely considered. With the goal of identifying RSSs from the perspective of the system failure probability, a method adopting the second-order reliability method (SORM) and the multimodal optimisation is proposed. In this method, the spatial variability of soil properties along the slip surface is characterised by local averaging to reduce the number of variables in SORM. Equations for calculating the correlation coefficient between different PSSs with correlated variables are derived. The task of RSS identification is transformed as a multimodal optimisation problem, and the PSSs that make great contributions to the system failure probability are determined as RSSs. The proposed method and the derived equations are demonstrated using two slope examples. The results show that the proposed method is capable of identifying RSSs with significant contributions, and it provides a proper estimate of the system failure probability.

System reliability analysis of foundation stability of gravity dams considering anisotropic seepage and multiple sliding surfaces

PurposeFor gravity dams built on foundations with directional joint sets, the seepage in the foundation possesses anisotropic characteristics and may have adverse effects on the foundation stability. A methodology for system reliability analysis of gravity dam foundations considering anisotropic seepage and multiple sliding surfaces is proposed in this paper.Design/methodology/approachAnisotropic seepages in dam foundations are simulated using finite element method (FEM) with the equivalent continuum model (ECM), and their effect on dam foundation stability is involved by uplift pressures acting on the potential sliding surfaces. The system failure probability of the dam foundation is efficiently estimated using Monte Carlo method (MCM) combined with response surface method (RSM).FindingsThe case study shows that it is necessary to consider the possibly adverse effect of anisotropic seepage on foundation stability of gravity dams and the deterministic analysis of the foundation stability may be misleading. The system reliability analysis of the dam foundation is justified, as the uncertainties in shear strength parameters of the foundation rocks and joint sets as well as aperture, connectivity and spacing of the joint sets are quantified and the system effect of the multiple potential sliding surfaces on the foundation reliability is reasonably considered.Originality/value(1) A methodology is proposed for efficient system reliability analysis of foundation stability of gravity dams considering anisotropic seepage and multiple sliding surfaces (2) The influence of anisotropic seepage on the stability of gravity dam foundation is revealed (3) The influence of estimation errors of RSMs on the system reliability assessment of dam foundation is investigated.

A novel multi-dimensional reliability approach for floating wind turbines under power production conditions

Floating offshore wind turbines (FOWT) generate green renewable energy and are a vital part of the modern offshore wind energy industry. Robust predicting extreme offshore loads during FOWT operations is an important safety concern. Excessive structural bending moments may occur during certain sea conditions, posing an operational risk of structural damage. This paper uses the FAST code to analyze offshore wind turbine structural loads due to environmental loads acting on a specific FOWT under actual local environmental conditions. The work proposes a unique Gaidai-Fu-Xing structural reliability approach that is probably best suited for multi-dimensional structural responses that have been simulated or measured over a long period to produce relatively large ergodic time series. In the context of numerical simulation, unlike existing reliability approaches, the novel methodology does not need to re-start simulation again each time the system fails. As shown in this work, an accurate forecast of the probability of system failure can be made using measured structural response. Furthermore, traditional reliability techniques cannot effectively deal with large dimensionality systems and cross-correction across multiple dimensions. The paper aims to establish a state-of-the-art method for extracting essential information concerning extreme responses of the FOWT through simulated time-history data. Three key components of structural loads are analyzed, including the blade-root out-of-plane bending moment, tower fore-aft bending moment, and mooring line tension. The approach suggested in this study allows predicting failure probability efficiently for a non-linear multi-dimensional dynamic system as a whole.

A nested hierarchy of second order upper bounds on system failure probability

For a coherent, binary system made up of binary elements, the exact failure probability requires knowledge of statistical dependence of all orders among the minimal cut sets. Since dependence among the cut sets beyond the second order is generally difficult to obtain, second order bounds on system failure probability have practical value. The upper bound is conservative by definition and can be adopted in reliability based decision making. In this paper we propose a new hierarchy of m-level second order upper bounds, Bm : the well-known Kounias–Vanmarcke–Hunter–Ditlevsen (KVHD) bound – the current standard for upper bounds using second order joint probabilities – turns out to be the weakest member of this family (m=1). We prove that Bm is non-increasing with level m in every ordering of the cut sets, and derive conditions under which Bm+1 is strictly less than Bm for any m and any ordering. We also derive conditions under which the optimal level m bound is strictly less than the optimal level m + 1 bound, and show that this improvement asymptotically achieves a probability of 1 as long as the second order joint probabilities are only constrained by the pair of corresponding first order probabilities. Numerical examples show that our second order upper bounds can yield tighter values than previously achieved and in every case exhibit considerable less scatter across the entire n! orderings of the cut sets compared to KVHD bounds. Our results therefore may lead to more efficient identification of the optimal upper bound when coupled with existing linear programming and tree search based approaches.

(Retracted) Research on intelligent transportation and logistics tracking of long billet based on machine vision

We solve the problems in the iron and steel industry of identifying the quantity, length, and position of billets in complex industrial environments by studying and applying machine vision algorithms, such as billet image segmentation based on optimal threshold method and billet image post-processing based on morphology. Compared with the existing technologies that rely on various sensors to realize the automatic transportation of billets or the physical marking of billets one by one to realize the billet logistics tracking, the scheme proposed here has a low one-time investment cost, especially for the billet logistics tracking of follow-up production control and quality traceability. Because the hot delivery billets only carry out virtual marking, there is no consumption cost of consumables, i.e., the higher the hot delivery rate, the lower the average marking cost of billets. Moreover, due to the non-contact of machine vision, the system failure probability is also lower. The machine vision algorithm and solution proposed here achieve the goal of intelligent transportation and logistics tracking of long billets with lower investment cost, lower consumption of consumables, fewer faults, and higher efficiency.

Hierarchical response surface method for reliability analysis of a pile-slope system

Stabilizing piles have been widely used as an effective measure to reinforce slopes. In this paper, a hierarchical response surface method is presented to evaluate the reliability of a pile-slope system efficiently. The suggested method can be used to identify the minimum reliability indexes of different types of failure modes. It can also be used to identify the representative failure modes governing the failure probability of the pile-slope system. This study found that the most critical sliding surface of an unreinforced slope and a reinforced slope is different. It may be nonconservative to design a pile-slope system according to the representative sliding surface of the slope without reinforcements. Even if many failure modes may exist, the reliability index of the pile-slope system is often controlled by several representative failure modes. For the slope examined in this paper, the reliability index of the pile-slope system is controlled by the reliability index of first representative failure mode. The first representative failure mode may vary with the reinforcement ratio, pile length, pile spacing, and location of the piles. The approach presented in this study provides a practical means to quantify the effect of such factors on the design of a pile-slope system.

Characterization of the terminal area of standard arrival routes using the queueing system

The article solves the problem of determining the probabilistic characteristics of the STARs legs which specify a sequencing technique of “point merge” and “trombone”-type considering the intensity of the air traffic flow and the formation of a queue. This task is closely related to the airspace efficiency, as well as to the limit values of flight safety performance. An application of the queueing system makes it possible to optimize the elements of the airspace structure on an objective basis, and in the event of considering the inverse problem to establish limit values for the air traffic flow characteristics. The characteristics of the “point merge” and “trombone”-type schemes become of prime importance in the air hub, where several airfields function of each other in a relatively small volume of airspace – as it happens in the Moscow air hub, so it is the given hub that is taken as a practical example. In this problem the basic model is the queueing system with limited-size queues where the optimal number of service channels in a stationary air traffic flow is determined in a probabilistic way. The stated model encapsulates the essence of the “trombone” or “point merge”-type scheme, where the number of service channels corresponds to the number of flight levels on the arc of the “point merge” or on the horizontal flight segment of the “trombone”. Now, the number of such flight levels, as a rule, corresponds to the number of standard arrival routes involved in the formation of a “trombone” (“point merge”), which, from a practical point of view, is excessive. The task of using the mathematical apparatus of the queueing system is to determine the optimal number of flight levels – service channels of the model while establishing the required probability of its failure. As a mathematical model of the queueing system, the “trombone”-type scheme is used, and in the mentioned above example, the structure of the airspace is presented using the “point merge”-type scheme as a regulator of the aircraft sequence for landing. All the computations are performed for the certain intensity of air traffic flow for a specified airfield, considering the full-scale application of continuous descent operations and continuous climb operations (CDO, CCO). As a result of solving the problem, the value for the optimal number of flight levels on the “trombone” or “point merge”-type scheme was obtained, and the dependence of the number of service channels (flight levels on the “trombone” or “point merge”) on the value of the given probability of the queueing system failure was shown. The proposed approach to the airspace structure formation has prospects for implementation.

Fuzzy fault tree analysis of chlorine gas release hazard in Chlor-Alkali industry using [formula omitted]-cut interval-based similarity aggregation method

In chemical industries, the release of toxic gases and chemicals is always a serious concern as it has the potential to harm human life and the environment, leading to significant losses. Risk assessment in chemical industries is essential to identify and prevent such type of unwanted hazards. Conventional fault tree analysis has been used effectively to identify the system failure causes and evaluate the system reliability, but it requires quantitative historical failure data of system components. In many real-world applications, it can be difficult to obtain precise and sufficient quantitative failure data of system components. This research paper proposes a novel fuzzy set theory-based fault tree analysis to evaluate system failure probability by utilizing the available qualitative data such as expert opinions/views when quantitative historical failure data of system components is unavailable or insufficient. To aggregate the different opinions of selected experts, a new similarity aggregation method is developed by using interval distance-based similarity measure function. The proposed fuzzy fault tree analysis applies system fault tree, α-cut intervals of fuzzy membership functions, and interval arithmetic operations. To validate the applicability and effectiveness of proposed approach, the basic event probabilities in fault tree analysis of chlorine release from storage and filling facility are generated using proposed approach and then compared with the known probabilities. Further, importance analysis is performed to evaluate the contribution of each basic event in top event “chlorine release” occurrence that would help the decision makers to identify the risk factor of chlorine release. The obtained results may be helpful for decision makers to decide whether and where to take protective actions in the risk management process.

Reliability analysis of a collective decision-making scheme by Co-operation of NPP operators and automatic diagnosis system

With the continuous improvement of hardware equipment performance, human error of operation team has become the major factor threatening the safe operation of nuclear power plants. The argument of the extent to which computerized automatic diagnosis can reduce human error of operation team in decision-making has become a major concern in the actual engineering practice. This paper presents a decision-making scheme of HPR1000 nuclear power plant under accident conditions. An automatic diagnosis (AD) system is designed to assist the operation team in emergency decision-making under accident conditions. The fault modes and effects of the AD system are identified. Aiming at the fault modes of the AD system, a collective decision-making scheme coordinated by the AD system and the operation team is presented. The reliability of the proposed scheme is analyzed by using the Probabilistic Safety Assessment (PSA) approach. The analysis results are compared with the other two schemes. The weakness of the proposed scheme and the corresponding countermeasures are identified. On the premise of operator error probability and decision-making mode set in this paper, the analysis results show that the reliability of the collective decision-making scheme proposed in this paper is higher than that of the traditional team decision-making scheme in the main control room. While ensuring the stability of diagnosis results, the proposed scheme reduces the dependence of decision-making on personal roles. Quantitative analysis results also show that when the failure probability of an AD system is lower than 0.01, it will bring a positive benefit to reduce the probability of wrong decision-making. It also implies an acceptable standard of the failure probability of a fully automatic decision-making system.

Reliability Analysis of Serviceability Limit State for Braced Excavation Considering Multiple Failure Modes in Spatially Variable Soil

High uncertainty is an inherent behavior of geotechnical materials. Nowadays, random field theory is an advanced method to quantify the effect of high uncertainty on geotechnical engineering. This study investigates the effect of spatial variable soil layers on deformations of deep excavation via the random finite element method. A procedure based on PLAXIS 2D software was developed to generate two-dimension random finite element models including multiple variables. Via the K-S test and S-W test, the excavation deformations basically followed lognormal distribution. With the growth of standard deviation of soil properties parameters, the distribution of excavation deformations becomes wider, and the failure probability increases. When the vertical scale of fluctuation ranges from 1 m to 25 m, the distribution of excavation deformations becomes wider. To analyze system reliability, this study proposed a fitted multiple lognormal distribution methods, which was a method with higher efficiency. The results indicated that system reliability was lower than single failure probability and sensitive to design level. The system failure probability will be over-evaluated or under-evaluated if the correlation between excavation responses is ignored. This study provided a novel method to quantify the effect of high uncertainty of soil layer on excavation responses and proposed an efficient method for system reliability analysis, which is meaningful for excavation reliability design.

A Flood Risk Management Model to Identify Optimal Defence Policies in Coastal Areas Considering Uncertainties in Climate Projections

Coastal areas are particularly vulnerable to flooding from heavy rainfall, sea storm surge, or a combination of the two. Recent studies project higher intensity and frequency of heavy rains, and progressive sea level rise continuing over the next decades. Pre-emptive and optimal flood defense policies that adaptively address climate change are needed. However, future climate projections have significant uncertainty due to multiple factors: (a) future CO2 emission scenarios; (b) uncertainties in climate modelling; (c) discount factor changes due to market fluctuations; (d) uncertain migration and population growth dynamics. Here, a methodology is proposed to identify the optimal design and timing of flood defense structures in which uncertainties in 21st century climate projections are explicitly considered probabilistically. A multi-objective optimization model is developed to minimize both the cost of the flood defence infrastructure system and the flooding hydraulic risk expressed by Expected Annual Damage (EAD). The decision variables of the multi-objective optimization problem are the size of defence system and the timing of implementation. The model accounts for the joint probability density functions of extreme rainfall, storm surge and sea level rise, as well as the damages, which are determined dynamically by the defence system state considering the probability and consequences of system failure, using a water depth–damage curve related to the land use (Corine Land Cover); water depth due to flooding are calculated by hydraulic model. A new dominant sorting genetic algorithm (NSGAII) is used to solve the multi-objective problem optimization. A case study is presented for the Pontina Plain (Lazio Italy), a coastal region, originally a swamp reclaimed about a hundred years ago, that is rich in urban centers and farms. A set of optimal adaptation policies, quantifying size and timing of flood defence constructions for different climate scenarios and belonging to the Pareto curve obtained by the NSGAII are identified for such a case study to mitigate the risk of flooding and to aid decision makers.

Expert judgment-based reliability analysis of the Dutch flood defense system

The Wettelijk Beoordelingsinstrumentarium (WBI) is the legal set of instruments for flood risk analysis in the Netherlands. Often, engineers have the impression that some failure probabilities of flood defenses resulting from these instruments are overestimated. In an effort to better estimate the failure probabilities of dikes along the Dutch river Rhine, this study sets out to assess them with experts and compare them to model results. We used Cooke’s method for combining experts’ estimates in a structured way and follow two approaches to estimate a system failure probability. In the first approach, experts estimate discharges that lead to at least one dike failure. This gives plausible results; failure probabilities between 1/30 and 1/17.000 in a year. The second approach is based on adjusting existing model-based assessment results, by estimating the model-bias and incorporating additional dependencies. This mostly leads to large, implausible, failure probabilities: Experts tend to give more conservative answers as they are asked for detailed estimates without clear reference values. This results in large uncertainty and consequently (too) high failure probabilities. Our research shows that when applied in a clear frame of reference, structured expert judgments can be successfully used for estimating the reliability of Dutch flood defenses.

Adaptive ensemble learning of radial basis functions for efficient geotechnical reliability analysis

Surrogate models can provide an effective tool to improve the computational efficiency for geotechnical reliability analysis when direct evaluations of the original performance function (OPF) of a geotechnical structure are time-consuming. However, selection of a proper surrogate model is often problem dependent. A particular surrogate model may not suitable for different geotechnical structures. Meanwhile, training of the surrogate model sometimes can also cost significant computational time. To address these issues, this paper proposes an efficient and robust geotechnical reliability analysis method based on the adaptive ensemble model of radial basis functions (AERBF) and Monte Carlo simulation (MCS). The ensemble of multiple radial basis functions (RBFs) is constructed to replace the OPF of a geotechnical system, which can improve the robustness of the surrogate model. The ensemble model does not need to select a certain RBF but automatically determines the weight coefficients of each component RBF through the training process, which can avoid the possible selection of an improper RBF. An active learning function is adopted to select the most suitable training samples to train the ensemble model, which can improve the efficiency significantly. Several representative examples are illustrated to validate the accuracy and efficiency of the proposed method. The results show that the approach is robust to different kinds of geotechnical systems. It can accurately estimate the failure probability of geotechnical systems with a small number of evaluations of the OPF.

Reliability analysis of composite sandwich structure for fuselage skin based on surrogate model

Composite structures are characterized by multiple source uncertainties in mechanical properties, geometric dimension, etc., and multiple failure modes, which bring challenges to their design and application. In order to explore the reliability analysis method of composite sandwich structures with multi-source uncertainties and multi-failure modes, a parametric finite element model and an acoustic boundary element model were established for deterministic analysis of a fuselage skin sandwich structure. Considering the randomness of the mechanical properties of composite materials and the laminate thickness, the structural reliability models were established for three typical failure modes of sandwich structures: static strength failure, global buckling and vibration noise. In order to reduce the computational effort, the Kriging surrogate models of failure modes were constructed, and the subset simulation method was used to predict the system failure probability of the sandwich structure of fuselage skin. The proposed computational framework provides support and tool for the fine design of composite sandwich structure.