Stochastic Engineering Research Articles

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Fractional Brownian motion in financial engineering models

An application of fractional Brownian motion (fBm) is considered in stochastic financial engineering models. For the known Fokker–Planck equation for the fBm case, a solution for transition probability density for the path integral method was built. It is shown that the mentioned solution does not result from the Gaussian unit of fBm with precise covariance. An expression for approximation of fBm covariance was found for which solutions are found based on the Gaussian measure of fBm and those found based on the known Fokker–Planck equation match.

Electricity Theft Detection in Smart Grids Using a Hybrid BiGRU-BiLSTM Model with Feature Engineering-Based Preprocessing.

In this paper, a defused decision boundary which renders misclassification issues due to the presence of cross-pairs is investigated. Cross-pairs retain cumulative attributes of both classes and misguide the classifier due to the defused data samples’ nature. To tackle the problem of the defused data, a Tomek Links technique targets the cross-pair majority class and is removed, which results in an affine-segregated decision boundary. In order to cope with a Theft Case scenario, theft data is ascertained and synthesized randomly by using six theft data variants. Theft data variants are benign class appertaining data samples which are modified and manipulated to synthesize malicious samples. Furthermore, a K-means minority oversampling technique is used to tackle the class imbalance issue. In addition, to enhance the detection of the classifier, abstract features are engineered using a stochastic feature engineering mechanism. Moreover, to carry out affine training of the model, balanced data are inputted in order to mitigate class imbalance issues. An integrated hybrid model consisting of Bi-Directional Gated Recurrent Units and Bi-Directional Long-Term Short-Term Memory classifies the consumers, efficiently. Afterwards, robustness performance of the model is verified using an attack vector which is subjected to intervene in the model’s efficiency and integrity. However, the proposed model performs efficiently on such unseen attack vectors.

Optimization and Simulation Analysis of Loader Driving Stability System based on Differential Connection

Taking wheel loader as the research object, for the vibration problem under the driving condition of wheel loader, study an optimized differential connection loader driving stability system, model the whole vibration system of wheel loader with three degrees of freedom dynamics, and establish the mathematical model by using Lagrange's equation, combine with the stochastic engineering road excitation model under E-class road surface, and carry out the simulation analysis of the vibration system by MATLAB/Simulink module. Simulation analysis of the vibration system is carried out, and the results show that the body droop acceleration, body angular acceleration and work device angular acceleration under the driving condition of the wheel loader are significantly reduced after adding the driving stability system, and the three kinds of acceleration are further reduced after optimizing to the differential connection driving stability system, which indicates that the differential connection loader driving stability system further improves the driving smoothness of the loader.

Three-dimensional surface fatigue crack growth life assessment model of steel welded joints and structures

To investigate the fatigue crack growth of surface cracks in steel welded joints, a three-dimensional surface fatigue crack growth life assessment model considering both the surface crack growth period and the following through crack growth period is proposed. The fatigue crack growth life of a standard steel butt joint specimen is predicted considering the effect of welding residual stress and it is compared with fatigue test results. An example of a welded beam-to-column connection in a steel high-rise building under wind is selected to demonstrate the improvement of the model to make it applicable to stochastic loading and real engineering structures. The life results are compared with those obtained by other fatigue assessment approaches. The mesh sensitivity analysis is made and the effect of extreme welding imperfections and corrosion environment are both discussed. Guidance to select the fatigue life assessment approaches is also proposed. The results show that the growth shape of the edge crack remains a quarter of a circle while that of the center crack remains a quarter of an ellipse during the growth; When the surface crack grows through the plate thickness and becomes a through crack, the remaining fatigue crack growth life is unneglectable for real engineering components especially for the ones with a large plate width; The effect of welding residual stress on the fatigue crack growth life of real engineering component is complex and it depends on the distribution of the residual stress itself; The proposed three-dimensional surface crack engineering model can acquire accurate life results and is applicable to stochastic loading and engineering structures.

Uncertainty Quantification Across Design Space Using Spatially Accurate Polynomial Chaos

In the last decade, the demand for stochastic engineering results has increased substantially. Concurrently, improvements in computing hardware, access to large computing clusters, and efficient statistical methods have made uncertainty quantification studies feasible for complex, computationally expensive simulations such as computational fluid dynamics or finite element methods. In current practice, uncertainty may be quantified at particular locations within a flight envelope or design space, but an ongoing challenge remains to interpolate or extrapolate this information to predict the uncertainty at untested or unsimulated locations. The goal of this paper is to introduce a spatially accurate polynomial chaos method, which can interpolate both aleatory and epistemic uncertainty throughout a flight envelope or design space. An additive correction is also presented, which improves accuracy at a small additional sample cost. Interpolation of polynomial chaos expansion coefficients is achieved using established regression techniques, allowing for a spatially accurate uncertainty propagation method which is agnostic to the characterization of parametric input uncertainties. As a demonstration of the method, results are shown for an analytic test function and for simulations of the NASA Common Research Model. The results indicate that Spatially Accurate Polynomial Chaos and its additive correction can provide accurate interpolated estimates of uncertainty.

Hybridized Extreme Learning Machine Model with Salp Swarm Algorithm: A Novel Predictive Model for Hydrological Application

The capability of the extreme learning machine (ELM) model in modeling stochastic, nonlinear, and complex hydrological engineering problems has been proven remarkably. The classical ELM training algorithm is based on a nontuned and random procedure that might not be efficient in convergence of excellent performance or possible entrapment in the local minima problem. This current study investigates the integration of a newly explored metaheuristic algorithm (i.e., Salp Swarm Algorithm (SSA)) with the ELM model to forecast monthly river flow. Twenty years of river flow data time series of the Tigris river at the Baghdad station, Iraq, is used as a case study. Different input combinations are applied for constructing the predictive models based on antecedent values. The results are evaluated based on several statistical measures and graphical presentations. The river flow forecast accuracy of SSA-ELM outperformed the classical ELM and other artificial intelligence (AI) models. Over the testing phase, the proposed SSA-ELM model yielded a satisfactory enhancement in the level accuracies (8.4 and 13.1 percentage of augmentation for RMSE and MAE, respectively) against the classical ELM model. In summary, the study ascertains that the SSA-ELM model is a qualified data-intelligent model for monthly river flow prediction at the Tigris river, Iraq.

A Stochastic Simulation-Optimization Method for Generating Waste Management Alternatives Using Population-Based Algorithms

While solving difficult stochastic engineering problems, it is often desirable to generate several quantifiably good options that provide contrasting perspectives. These alternatives should satisfy all of the stated system conditions, but be maximally different from each other in the requisite decision space. The process of creating maximally different solution sets has been referred to as modelling-to-generate-alternatives (MGA). Simulation-optimization has frequently been used to solve computationally difficult, stochastic problems. This paper applies an MGA method that can create sets of maximally different alternatives for any simulation-optimization approach that employs a population-based algorithm. This algorithmic approach is both computationally efficient and simultaneously produces the prescribed number of maximally different solution alternatives in a single computational run of the procedure. The efficacy of this stochastic MGA method is demonstrated on a waste management facility expansion case.

Stochastic engineering framework for timber structural elements and its application to glued laminated timber beams

Due to the natural growth process of trees, wooden boards show a high amount of random fluctuation in their mechanical properties. Currently, in engineering practice, a homogeneous material behaviour is assumed within wooden boards and uncertainties in loading and load-bearing capacity are considered through design procedures based on partial safety factors. These partial safety factors are not directly linked to the individual mechanical behaviour of the considered structural system/element. Thus, a stochastic framework opening up the possibility to establish such links, by combining structural analysis tools with probabilistic descriptions of wooden boards, could be an important step in timber design, also to improve the competitiveness of wood against other building materials.In this study, a framework able to consider the impact of random stiffness fluctuations of wooden boards on the performance of glued laminated timber (GLT) is presented. A 2D finite element model is employed to depict the interactions between individual laminations. It is tightly integrated into a commercial robustness analysis and optimisation software package.The mechanical properties of each board are obtained on basis of measurements collected during the grading process and are condensed into so-called stiffness and strength profiles. Based thereon, a probabilistic material model is developed for the random generation of an arbitrary number of stiffness and strength profiles. On basis of the probabilistic material model and the mechanical FE model, the sensitivity to changes in the design can be explored. Subsequently, an adaptive response surface approach leads to the optimal design parameters of the user-defined structure.An exemplary application scenario shows the workflow for determining the optimum hole dimensions and location in a GLT beam. The material model indicates large scatter in the mechanical properties, leading to conservative results. Nonetheless, and although only bending failure of GLT beams and no finger joints are taken into account, the example shows the strengths of the employed workflow from sensitivity analysis to best designs.

Stochastic engineering framework for timber structural elements

AbstractDue to the natural growth process of trees, the resulting wooden boards show a high amount of random fluctuation in their mechanical properties. In this work, a framework able to consider the impact of random stiffness fluctuations of wooden boards on the performance of glued laminated timber (GLT) is presented. A 2D finite element model is employed to depict the interactions between individual laminations and is integrated into a commercial robustness analysis and optimisation software package.The mechanical properties of each board are obtained during the grading process and are condensed into so‐called stiffness and strength profiles. Based thereon, a probabilistic material model is developed for the random generation of an arbitrary number of stiffness and strength profiles. On basis of the probabilistic material model and the mechanical FE model, the sensitivity to changes in the design can be explored. Subsequently, the optimal design parameters of the user‐defined structure are identified.An exemplary application scenario shows the workflow for determining the optimum hole dimensions and location in a GLT beam. The material model indicates large scatter in the mechanical properties, leading to conservative results. Nonetheless, the example shows the strengths of the employed workflow from sensitivity analysis to best designs.

Incorporation of stochastic engineering models as prior information in Bayesian medical device trials

ABSTRACTEvaluation of medical devices via clinical trial is often a necessary step in the process of bringing a new product to market. In recent years, device manufacturers are increasingly using stochastic engineering models during the product development process. These models have the capability to simulate virtual patient outcomes. This article presents a novel method based on the power prior for augmenting a clinical trial using virtual patient data. To properly inform clinical evaluation, the virtual patient model must simulate the clinical outcome of interest, incorporating patient variability, as well as the uncertainty in the engineering model and in its input parameters. The number of virtual patients is controlled by a discount function which uses the similarity between modeled and observed data. This method is illustrated by a case study of cardiac lead fracture. Different discount functions are used to cover a wide range of scenarios in which the type I error rates and power vary for the same number of enrolled patients. Incorporation of engineering models as prior knowledge in a Bayesian clinical trial design can provide benefits of decreased sample size and trial length while still controlling type I error rate and power.

The Theory of Optimal Stochastic Control as Applied to Insurance Underwriting Cycles

We use the theories of optimal stochastic control and engineering process control to analyze the well-known phenomenon of insurance underwriting cycles in continuous time. We show in a continuous time framework that underwriting cycles can be explained with a model where premiums are set rationally, but where there are various reporting and regulatory lags. We find that the observed cycle length depends on the length of these underlying lags. Our result can be seen as consistent with previous empirical work showing underwriting cycles varying across countries and lines of insurance. In the event that no lags exist, our result is also consistent with more recent literature suggesting that insurance cycles may not exist.

Optimal representation of multi-dimensional random fields with a moderate number of samples: Application to stochastic mechanics

A significant amount of problems and applications in stochastic mechanics and engineering involve multi-dimensional random functions. The probabilistic analysis of these problems is usually computationally very expensive if a brute-force Monte Carlo method is used. Thus, a technique for the optimal selection of a moderate number of samples effectively representing the entire space of sample realizations is of paramount importance. Functional Quantization is a novel technique that has been proven to provide optimal approximations of random functions using a predetermined number of representative samples. The methodology is very easy to implement and it has been shown to work effectively for stationary and non-stationary one-dimensional random functions. This paper discusses the application of the Functional Quantization approach to the domain of multi-dimensional random functions and the applicability is demonstrated for the case of a 2D non-Gaussian field and a two-dimensional panel with uncertain Young modulus under plane stress.

Sensitivity analysis of ranked data: from order statistics to quantiles

In this paper we provide the mathematical theory for sensitivity analysis of order statistics of continuous random variables, where the sensitivity is with respect to a distributional parameter. Sensitivity analysis of order statistics over a finite number of observations is discussed before addressing sensitivity analysis of quantiles. In particular, we provide a central limit theorem and related confidence intervals for the proposed sensitivity estimators, and we improve the known convergence results for IPA. Our analysis provides guidelines for sensitivity analysis of order statistic related performance measures such as basic order-statistics or quantiles. Our findings are corroborated by a series of numerical examples from different areas of operations research: stochastic activity networks, queues, reliability, and financial engineering.

Development of application-specific adjacency models using fuzzy cognitive map

Neural regression provides a rapid solution to modeling complex systems with minimal computation effort. Recurrent structures such as fuzzy cognitive map (FCM) enable for drawing cause–effect relationships among system variables assigned to graph nodes. Accordingly, the obtained matrix of edges, known as adjacency model, represents the overall behavior of the system. With this, there are many applications of semantic networks in data mining, computational geometry, physics-based modeling, pattern recognition, and forecast. This article examines a methodology for drawing application-specific adjacency models. The idea is to replace crisp neural weights with functions such as polynomials of desired degree, a property beyond the current scope of neural regression. The notion of natural adjacency matrix is discussed and examined as an alternative to classic neural adjacency matrix. There are examples of stochastic and complex engineering systems mainly in the context of modeling residential electricity demand to examine the proposed methodology.

The use of Petri nets and a two-zone model for fire scene reconstruction

Fire scene investigation relies on in situ investigation (observations that take place where the fire occurred) and laboratory analysis. Nowadays the role and place of fire modelling in fire forensic investigation are debated within the forensic community. The main objective of this work is to propose a methodology to consider the stochastic aspect of fire development in a specific case by using fire modelling. Therefore, a stochastic fire safety engineering tool so-called SCHEMA-SI (Stochastic Computation and Hybrid Event Modelling Approach-Sécurité Incendie) developed at the CSTB (French Scientific and Technical Construction Centre) has been used to reconstruct a fire scene that occurred in 2007 in a senior care facility situated in the Paris suburb (France). In this case study, several fire scenarios were generated with SCHEMA-SI from probabilistic data in order to perform fire scene investigation. Each scenario is composed on one hand by a succession of dated events and on the other hand by physical quantities time-evolution at different locations in the building (heat release rate, temperature, interface height…). The objective of this work was to find the scenarios which allow getting an acceptable agreement between the calculated values and the observations from the real situation in the fire scene. Among the thousands of fire scenarios generated, 20% were compliant with the fire scene observations. The analysis of these compliant scenarios gave a better idea of what might have happened in the care facility. At the end, the contribution of numerical simulation in a fire scene analysis is discussed.

Optimal splitting for rare-event simulation

Simulation is a popular tool for analyzing large, complex, stochastic engineering systems. When estimating rare-event probabilities, efficiency is a big concern, since a huge number of simulation replications may be needed in order to obtain a reasonable estimate of the rare-event probability. The idea of splitting has emerged as a promising variance reduction technique. The basic idea is to create separate copies (splits) of the simulation whenever it gets close to the rare event. Some splitting methods use an equal number of splits at all levels. This can compromise the efficiency and can even increase the estimation variance. This article formulates the problem of determining the number of splits as an optimization problem that minimizes the variance of an estimator subject to a constraint on the total computing budget. An optimal solution for a certain class of problems is derived that is then extended to the problem of choosing the better of two designs, where each design is evaluated via rare-event simulation. Theoretical results for the improvements that are achievable using the methods are provided. Numerical experiments indicate that the proposed approaches are efficient and robust.

Stochastic traffic engineering for real-time applications over wireless networks

In this work, we focus on the Stochastic Traffic Engineering (STE) problem arising from the support of QoS-demanding real-time media-streaming applications over fading and congestion affected TCP-friendly/IP multiantenna wireless pipes. First, after recasting the tackled STE problem in the form of a suitable cross-layer nonlinear stochastic optimization problem, we develop a traffic analysis of the overall underlying multiple-input multiple-output (MIMO) wireless pipe that points out the relative effects of both fading-induced errors and congestion-induced packet losses on the goodput offered by the resulting end-to-end connection. Second, we develop an optimal cross-layer resource management policy that allows a joint scheduling of the media encoding rate (i.e., playin rate), transmit energy and delivery rate (i.e., playout rate) of each end-to-end connection active over the considered access network. Salient features of the presented joint scheduling policy are that: (i) it is self-adaptive; (ii) it is able to provide hard (i.e., deterministic) QoS guarantees, in terms of hard limited playout delay and playout rate-jitter; and (iii) it explicitly accounts for the performance interaction of the protocols implemented at all layers of the considered stack.

QoS Stochastic Traffic Engineering for the wireless support of real-time streaming applications

In this work, the Stochastic Traffic Engineering (STE) problem arising from the support of QoS-demanding real-time (e.g., delay and delay-jitter sensitive) media-streaming applications over unreliable IP-over-wireless pipes is addressed. Two main contributions are presented. First, we develop an optimal resource-management policy that allows a joint scheduling of the source rate, transmit energy and playout rate. Salient features of the proposed scheduling policy are that: (i) it is self-adaptive; and, (ii) it is able to provide hard (i.e., deterministic) QoS guarantees, in terms of hard limited playout delay, playout rate-jitter and pre-roll delay. Second, by referring to power and bandwidth limited access scenarios, we develop a traffic analysis of the underlying IP-over-wireless pipes that allows us to analyze the effects of both fading-induced errors and congestion-induced packet’s losses on the end-to-end performance of the proposed scheduler.

Sergio E. Serrano: Engineering uncertainty and risk analysis: balanced approach to probability, statistics, stochastic modeling, and stochastic differential equations

Uncertainty and risk analyses are becoming more and more important in engineering sciences due to increasing climatic variation and other types of natural hazards. On average, every year infrastructure damages caused by earthquakes, floods, typhoons and other catastrophic events induce costs corresponding to hundreds of billions of dollars besides thousands of lives lost. Consequently, uncertainty and risk analyses are some of the most important subjects for engineers. In line with this, the author, Prof. Sergio E. Serrano, Temple University, has issued a second, completely revised text book on the subject. The book is a comprehensive collection of stochastic and statistical engineering techniques with uncertainty and risk analyses that are applicable in a broad range of problems. The focus is clearly on engineering applications rather than on theoretical derivation. Even rather advanced techniques involving nonlinear differential equations are solved analytically in supplied codes and presented with illustrative examples. The strong and very useful aspect of this text book is that it contains a multitude of solved examples as well as problems with answers. Consequently, the potential reader of this book might be engineering students as well as professional engineers. The book consists of fourteen chapters starting with a discussion of engineering uncertainty analysis and ending with a summary and discussion on seven steps for analysis of engineering problems. Chapter 2 introduces concepts of probability and frequency. Chapter 3 clarifies the concept of random variables with discrete and continuous variables. Chapter 4 then introduces the basics of random system modeling and Monte Carlo simulation. Chapter 5 presents the concept of several random variables and Chapter 6 introduces basic ideas of statistics. Chapter 7 shows how to fit probabilistic models to experimental data and then follows linear regression in Chapter 8. Chapter 9 explains how to develop models for reliability of engineering systems and Chapter 10 shows how to design engineering experiments. In Chapter 11 methods for testing experimental data are introduced together with ANOVA techniques. Chapter 12 is a synthesis of previous chapter in the way that it explains and visualizes random processes using explained Maple codes. Finally, Chapter 13 introduces novel techniques to solve linear and nonlinear differential equations by means of analytical methods. The above shows that it is a very comprehensive text book on uncertainty and risk. This together with solved examples and included Maple codes makes it one of the most useful books on the market for teaching engineering students as well solving practical engineering problems involving risk and uncertainty estimation. I am sure that the book will have a significant positive impact on improving engineering solving during coming decades.