Interval Distribution Parameters Research Articles

Reliability analysis for air-breathing hypersonic vehicles based on a new dynamic PHI2 method

Purpose This paper aims to present a novel dynamic reliability model that considers the interval mixed uncertainty for the air-breathing hypersonic flight vehicle (AHFV) to guarantee flight safety and structural reliability. Design/methodology/approach Initially, the force condition of the fuselage is analyzed based on the longitudinal elastic model of an AHFV. Subsequently, a new high-efficiency dynamic reliability model is presented to describe the failure probability evolution of the fuselage structure. For the random uncertainty problem with interval distribution parameters, the interval PHI2 method of time-dependent reliability is used to obtain the time-dependent reliability interval of the AHFV. Finally, the key variables that affect the failure probability accumulation are determined, which provide an important reference for ensuring structural reliability and improving the life span of AHFVs. Findings It is demonstrated that the proposed reliability model can obtain more accurate dynamic reliability results for the fuselage, and it is confirmed the key variables that affect the failure probability accumulation. The results also provide an important reference for the reliability analysis of hypersonic vehicles. Originality/value The novelty of this work comes from the first application of the PHI2 method (considering the interval mixed uncertainty) in the AHFV and the development of a new reliability model for the entire body of AHFVs. The proposed analysis scheme is implemented on the dynamic model of the AHFV, which provides a more accurate reference for improving the structural reliability and life span of AHFVs.

Data-driven reliability assessment with scarce samples considering multidimensional dependence

This study proposes a data-driven method for assessing reliability, based on the scarce input dataset with multidimensional correlation. Since considering the distribution parameters estimated from the scarce dataset as those of the population may lead to epistemic uncertainty, the bootstrap resampling algorithm is adopted to infer the distribution parameters as interval parameters. To account for the variable dependence, vine copula theory is utilized to construct the joint probability density function (PDF) of input variables, and maximum likelihood estimation (MLE) and Akaike information criterion (AIC) analysis are employed to select optimal copulas based on the samples for the vine structure. Subsequently, the failure probability bounds of a response function are calculated based on the constructed joint PDF with interval distribution parameters by the active learning Kriging (AK) method combining the sparse grid integration (SGI) method. Finally, several examples are provided to demonstrate the feasibility and efficiency of the proposed method.

A novel method for reliability analysis with interval parameters based on active learning Kriging and adaptive radial‐based importance sampling

AbstractFor the reliability analysis of complex engineering structures, the estimation of the bounds of failure probability with interval distribution parameters is an important task when the perfect information of random variables is unavailable and the corresponding probability distributions are imprecise. The present work proposes an active learning Kriging‐based method combining with adaptive radial based importance sampling to compute the bounds of failure probability. For computing the bounds, the classical double‐loop optimization model is always investigated in the standard normal space. To decouple the computation, the inner‐loop optimization is addressed with the monotonicity of the commonly used probability distributions. When suffering the high dimensional problem, the dimension reduction method is introduced in monotonic analysis. While for the outer‐loop optimization, the normal space is decomposed with spheres, then the proposed method with an adaptive updated procedure is given. With this method, the bounds of failure probability can be estimated efficiently, especial for the rare event. Numerical examples are investigated to validate the rationality and superiority of the proposed method. Finally, the proposed method is applied to the reliability analysis of turbine blade and aeronautical hydraulic pipeline system with interval distribution parameters.

An Extended SORA Method for Hybrid Reliability-Based Design Optimization

In many practical engineering problems, distributions of some random variables may not be precisely known or even only the variation ranges can be given, due to which the Reliability-Based Design Optimization (RBDO) methods cannot be applied directly. In this paper, a hybrid RBDO model is established to deal with hybrid uncertainties including random variables with interval distribution parameters and coexistence of random and interval variables. The hybrid uncertainties lead to an interval of reliability, thus giving rise to a triple-loop optimization problem, which burdens the computational effort significantly. Therefore, an extended Sequential Optimization and Reliability Assessment (SORA) method is proposed, where the worst-case point over the bounded domain of interval uncertainty is employed to replace reliability constraint with deterministic optimization. Therefore, the hybrid RBDO problem can be efficiently solved by a series of deterministic optimization procedures. The efficiency and accuracy of the proposed method are illustrated through several numerical examples.

A single-loop method for reliability-based design optimization with interval distribution parameters

The Reliability-Based Design Optimization (RBDO) provides an effective way to obtain the optimum design in the presence of random uncertainties which follow the precise probability distribution function in the structural optimization design. However, in many practical engineering problems, the probability distribution which describes the stochastic nature of the uncertainties cannot be precisely obtained due to limited information. To quantify this kind of imprecise uncertainties, a probability-interval hybrid model emerged, where all uncertain variables are treated as random variables while some distribution parameters can only be given variation intervals. For such kind of uncertainties, this paper establishes a hybrid reliability-based design optimization model and proposes a single-loop solution algorithm. The interval parameters lead to an interval of reliability for each constraint function, thus giving rise to a triple-loop optimization problem for the hybrid RBDO, which is difficult to solve due to the unaffordable computational effort and the hinder of convergency. In this paper, the Karush–Kuhn–Tucker (KKT) optimality conditions of the inner loops are imposed as equivalent deterministic equality constraints. The original triple-loop optimization is thus converted into an equivalent single-loop problem, which alleviates the computational demand significantly. The efficiency and accuracy of the proposed Single-Loop Method (SLM) is verified through several practical engineering problems.

Time-dependent mechanism reliability analysis with imprecise probability distributions based on envelope function

The time-dependent mechanism reliability and sensitivity analysis with imprecise probability distributions is investigated in this article. First, the interval model is employed to describe the uncertainty of the parameters of input variables due to the lack of data and knowledge. Next, the form of time-dependent failure probability and global reliability sensitivity (GRS) main effect index in the case of interval distribution parameters is analyzed. Then, the calculation methods of failure probability and GRS main effect index under the above circumstance are discussed. Finally, combined with the optimization algorithm, the Monte Carlo simulation (MCS) method and the method based on envelope function (MEVF) are proposed. By comparing with the MCS results, several numerical and engineering examples are analyzed to demonstrate the significance as well as the effectiveness of MEVF.

Effectiveness of Containment Measures Against COVID-19 in Singapore: Implications for Other National Containment Efforts.

We hypothesize that comprehensive surveillance of COVID-19 in Singapore has facilitated early case detection and prompt contact tracing and, with community-based measures, contained spread. We assessed the effectiveness of containment measures by estimating transmissibility (effective reproduction number, (Equation is included in full-text article.)) over the course of the outbreak. We used a Bayesian data augmentation framework to allocate infectors to infectees with no known infectors and determine serial interval distribution parameters via Markov chain Monte Carlo sampling. We fitted a smoothing spline to the number of secondary cases generated by each infector by respective onset dates to estimate (Equation is included in full-text article.)and evaluated increase in mean number of secondary cases per individual for each day's delay in starting isolation or quarantine. As of April 1, 2020, 1000 COVID-19 cases were reported in Singapore. We estimated a mean serial interval of 4.6 days [95% credible interval (CI) = 4.2, 5.1] with a SD of 3.5 days (95% CI = 3.1, 4.0). The posterior mean (Equation is included in full-text article.)was below one for most of the time, peaking at 1.1 (95% CI = 1.0, 1.3) on week 9 of 2020 due to a spreading event in one of the clusters. Eight hundred twenty-seven (82.7%) of cases infected less than one person on average. Over an interval of 7 days, the incremental mean number of cases generated per individual for each day's delay in starting isolation or quarantine was 0.03 cases (95% CI = 0.02, 0.05). We estimate that robust surveillance, active case detection, prompt contact tracing, and quarantine of close contacts kept (Equation is included in full-text article.)below one.

Reliability-based analysis method of fluid dynamics for turbomachinery with interval distribution parameters

Machining level and manufacturing accuracy have an important influence on the reliability of turbomachinery flow physics and dynamic performance. This article proposes a hybrid uncertainty analysis method for fluid dynamics problems with manufacturing constraints. The parameters with sufficient and insufficient experimental samples are processed by the stochastic method and interval method, respectively, which can quickly solve the difficulties of epistemic uncertainty modelling caused by the lack of experimental samples. On this basis, an efficient iterative algorithm is proposed to solve the hybrid reliability model based on the update response surface, and the interval of the failure probability of fluid dynamics for turbomachinery is calculated. Two examples of cooling axial flow and centrifugal turbomachinery are given to verify the validity of the proposed method. The results show that the reliability of the turbomachinery flow performance can be significantly improved by increasing the uncertainty level of key parameters.

Surrogate model-based reliability analysis for structural systems with correlated distribution parameters

Uncertainties are usually modeled by random variables, and the values of distribution parameters are estimated from the collected samples. In practical engineering, point and interval samples are possibly available for the estimation of distribution parameters; then, their values are intervals instead of point values. In view of the fact that all distribution parameters are estimated from the same set of samples, they must be correlated rather than mutually independent. In this study, the correlation among interval distribution parameters is considered and modeled using ellipse models, and the Monte Carlo simulation (MCS)-based reliability method for correlated distribution parameters, denoted as D–MCS, is first proposed. Performance functions are usually implicit functions involving simulation that are expensive-to-evaluate evaluate in real applications; hence, an efficient adaptive surrogate model-based reliability method for structural systems with correlated interval distribution parameters is proposed to reduce computational burden. A new and efficient learning function based on the U function is developed to adaptively add the best new training samples at each iteration. The corresponding stopping criterion to terminate the proposed algorithm is also developed. The lower and upper bounds of probability of failure are calculated based on the final constructed surrogate model. The proposed method is effective because it can provide more accurate reliability results compared with traditional independence assumption reliability methods, and it can be used for structural systems with mixed variables. The proposed method is easy to code and understand. Three numerical examples are investigated to show the applicability of the proposed method.

Toward the Effect of Dependent Distribution Parameters on Reliability Prediction

Random variables are commonly encountered in engineering applications, and their distributions are required for analysis and design, especially for reliability prediction during the design process. Distribution parameters are usually estimated using samples. In many applications, samples are in the form of intervals, and the estimated distribution parameters will also be in intervals. Traditional reliability methodologies assume independent interval distribution parameters, but as shown in this study, the parameters are actually dependent since they are estimated from the same set of samples. This study investigates the effect of the dependence of distribution parameters on the accuracy of reliability analysis results. The major approach is numerical simulation and optimization. This study demonstrates that the independent distribution parameter assumption makes the estimated reliability bounds wider than the true bounds. The reason is that the actual combination of the distribution parameters may not include the entire box-type domain assumed by the independent interval parameter assumption. The results of this study not only reveal the cause of the imprecision of the independent distribution parameter assumption, but also demonstrate a need of developing new reliability methods to accommodate dependent distribution parameters.

Reliability analysis of motion mechanism under three types of hybrid uncertainties

Hybrid reliability analysis of motion mechanism, in which the inputs contain both random variables and interval variables, is investigated in this paper. Firstly, the hybrid uncertainty is divided into three categories. In the first category, the inputs that include both random variables and interval variables are considered. In the second category, the inputs that include random variables with interval distribution parameters are considered. In the third category, the inputs that include both random variables with interval distribution parameters, and interval variables are considered. The above three types of uncertainties outline the general situation of hybrid uncertainties. In order to achieve the reliability analysis of motion mechanism under the above three hybrid uncertainties, this paper presents a method of combining the Poisson's assumption-based first passage method and a double loop iterative algorithm. The specific calculation process is described in detail by a numerical example. Simultaneously, the accuracy and efficiency of the proposed is also shown and discussed by comparing the Monte Carlo simulation (MCS) results in this numerical example. Finally, the proposed method is applied to two practical engineering examples, a crank slider mechanism and a rack-and-pinion steering linkage.

Reliability-based design optimization for problems with interval distribution parameters

Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.

An efficient uncertainty propagation method for parameterized probability boxes

In the response analysis of uncertain structural models with limited information, parameterized p-boxes are used to quantify the uncertain variables. In this study, a new technique is developed to compute the probability bounds of the structural response. Monotonicity analysis is performed on probability transformations of the random variables, revealing the relations between the interval distribution parameters and probability bounds of the structural response. Based on the monotonicity analysis, an algorithm for parameterized p-boxes is developed for computing the structural response. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.

The interval PHI2 analysis method for time-dependent reliability

The uncertainty modeling and time-dependent reliability analysis for time-dependent structures with a large number of inherently uncertain parameters is very important in engineering. When evaluating the reliability of structures under stochastic loadings through traditional methods, the distribution parameters of random variables, such as strength, stiffness and damping, are usually determined, but the accurate value of distribution parameters can hardly be known in practical engineering. In this paper an interval PHI2 (I-PHI2) method is proposed to solve the time-dependent reliability for random problems with the interval distribution parameters. I-PHI2 method can provide the reliability interval for assessing design reliability over the whole lifecycle of uncertain structures. Firstly, the time-dependent reliability analysis model is built for uncertain problem of interval distribution parameters. Secondly, the interval distribution parameters of random variables and stochastic processes are determined by use of the interval analysis method and then transferred into the standard coordinate space. Thirdly, the analytical expression of out-crossing rate in which there are many interval parameters are derived and the corresponding upper and lower bounds of out-crossing rate can be obtained. Finally, based on the traditional time-independent reliability tools such as FORM, an efficient algorithm for time-dependent structure is developed to obtain the upper and lower bounds of time-dependent reliability index and failure probability. Two numerical examples are presented for verification of the validity of I-PHI2 method.

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.

Importance measures for imprecise probability distributions and their sparse grid solutions

For the imprecise probability distribution of structural system, the variance based importance measures (IMs) of the inputs are investigated, and three IMs are defined on the conditions of random distribution parameters, interval distribution parameters and the mixture of those two types of distribution parameters. The defined IMs can reflect the influence of the inputs on the output of the structural system with imprecise distribution parameters, respectively. Due to the large computational cost of the variance based IMs, sparse grid method is employed in this work to compute the variance based IMs at each reference point of distribution parameters. For the three imprecise distribution parameter cases, the sparse grid method and the combination of sparse grid method with genetic algorithm are used to compute the defined IMs. Numerical and engineering examples are employed to demonstrate the rationality of the defined IMs and the efficiency of the applied methods.

Phoneme recognition using zerocrossing interval distribution of speech patterns and ANN

The speech signal is modeled using zerocrossing interval distribution of the signal in time domain. The distributions of these parameters are studied over five Malayalam (one of the most popular Indian language) vowels. We found that the distribution patterns are almost similar for repeated utterances of the same vowel and varies from vowel to vowel. These distribution patterns are used for recognizing the vowels using multilayer feed forward artificial neural network. After analyzing the distribution patterns and the vowel recognition results, we realize that the zerocrossing interval distribution parameters can be effectively used for the speech phone classification and recognition. The noise adaptness of this parameter is also studied by adding additive white Gaussian noise at different signal to noise ratio. The computational complexity of the proposed technique is also less compared to the conventional spectral techniques, which includes FFT and Cepstral methods, used in the parameterization of speech signal.

A Hybrid Reliability Approach Based on Probability and Interval for Uncertain Structures

Abstract Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.