Stochastic Conditions Research Articles

On the Potential Impacts of Smart Traffic Control for Delay, Fuel Energy Consumption, and Emissions: An NSGA-II-Based Optimization Case Study from Dhahran, Saudi Arabia

Intelligent traffic control at urban intersections is vital to ensure efficient and sustainable traffic operations. Urban road intersections are hotspots of congestion and traffic accidents. Poor traffic management at these locations could cause numerous issues, such as longer travel time, low travel speed, long vehicle queues, delays, increased fuel consumption, and environmental emissions, and so forth. Previous studies have shown that the mentioned traffic performance measures or measures of effectiveness (MOEs) could be significantly improved by adopting intelligent traffic control protocols. The majority of studies in this regard have focused on mono or bi-objective optimization with homogenous and lane-based traffic conditions. However, decision-makers often have to deal with multiple conflicting objectives to find an optimal solution under heterogeneous stochastic traffic conditions. Therefore, it is essential to determine the optimum decision plan that offers the least conflict among several objectives. Hence, the current study aimed to develop a multi-objective intelligent traffic control protocol based on the non-dominated sorting genetic algorithm II (NSGA-II) at isolated signalized intersections in the city of Dhahran, Kingdom of Saudi Arabia. The MOEs (optimization objectives) that were considered included average vehicle delay, the total number of vehicle stops, average fuel consumption, and vehicular emissions. NSGA-II simulations were run with different initial populations. The study results showed that the proposed method was effective in optimizing considered performance measures along the optimal Pareto front. MOEs were improved in the range of 16% to 23% compared to existing conditions. To assess the efficacy of the proposed approach, an optimization analysis was performed using a Synchro traffic light simulation and optimization tool. Although the Synchro optimization resulted in a relatively lower signal timing plan than NSGA-II, the proposed algorithm outperformed the Synchro optimization results in terms of percentage reduction in MOE values.

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds.

Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.

Direct plastic structural design under random strength and random load by chance constrained programming

A new formulation to calculate shakedown limit load of structures under stochastic conditions of strength and loading is developed. Direct structural reliability design is based on the required failure probabilities by chance constrained programming, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem.

Generic framework for reliability assessment of offshore wind turbine jacket support structures under stochastic and time dependent variables

Offshore wind turbines (OWTs) are exposed to harsh marine environments with considerable uncertainties in the environmental loads and soil properties, constituting their integrity assessment a challenging task and qualifying reliability assessment as the most suitable approach in order to systematically account for these uncertainties. In this work, a generic framework for the reliability assessment of OWT jacket support structures is developed based on a non-intrusive formulation. More specifically, a parametric FEA (finite element analysis) model of a typical OWT jacket support structures is developed incorporating load and soil-structure interaction, in order to map its response under varying input conditions. The results from a number of deterministic FEA simulations are post-processed through multivariate regression, deriving performance functions for relevant limit states. For this analysis five limit states are considered, i.e. buckling, deflection, fatigue, frequency and ultimate limit states. The reliability index under each limit state is then calculated using FORM (first order reliability method) to allow calculation of low probability values. The proposed framework has been applied to the NREL 5 MW OWT OC4 jacket to assess the reliability of critical components of the structure. The results of the reliability assessment indicate that, for the considered stochastic conditions, the structural components of the jacket structure are found to be within acceptable reliability levels. The proposed framework, which can be applied in various complex engineering systems, has demonstrated to be capable of effectively assessing the reliability of OWT jacket structures and can be further applied to optimize jacket structures on the basis of reliability.

Expertise of Digital Reality as a Factor of Achieving Society Stability Under Stochastic Conditions (Uncertainty, Instability, Bifurcation)

Since we all live in a complex, interconnected, and interdependent world, where volumes of information grow exponentially, and many leaders recognize the challenges of operating under conditions of stochasticity and uncertainty, the relevance of the analyzed problem remains extremely significant. The purpose of the article is to conceptualize the study of digital reality concerning stochastic ambiguity based on system methodology and computer modeling. This conceptual and categorical apparatus aims to expose digital reality as both a social phenomenon and a dynamic process. The principal approach to the research problem is a synergetic methodology that includes methods of consistency, structuredness, reasoning, making it credible to unveil the essence of the analysis of digital reality as a factor in achieving societal stability in stochastic circumstances, which is an integral process. The article demonstrates that, through the ability to predict, mistakes can be avoided, success achieved, and the prosperity of organizations multiplied. The article explains that the synergetic methodology, as a complexity methodology, meets the conditions of globalization 4.0, Industry 4.0, technological progress 4.0, digital society, Enlightenment 2.0, and Agile management. It is for these complex requirements that a synergistic complexity methodology can be applied. The materials presented in the article hold practical value for experts, scientists, and leaders. The implementation of this expertise will benefit society, the state, international partners, and future generations by promoting sustainable growth. The practical significance of the article lies in solving the problems of acquiring a conceptual framework for analyzing digital reality as a factor in achieving the efficiency and sustainability of society in stochastic circumstances. This approach enables the formulation of national, regional, local, and other indicators of sustainability and contributes to overcoming crises. All mentioned indicators can manifest in absolute and relative dimensions, including indicators in the social sphere, such as health status, quality of life, social activity, demographics, and others.

Expertise of Digital Reality as a Factor of Achieving Society Stability Under Stochastic Conditions (Uncertainty, Instability, Bifurcation)

Since we all live in a complex, interconnected, and interdependent world, in which the volumes of exponential information growth are increasing; since many leaders realize they are operating under conditions of stochasticity and uncertainty, the relevance of the analyzed problem remains extremely significant. The purpose of the article is to conceptualize the study of digital reality in matters of stochastic ambiguity based on system methodology and computer modeling. This conceptual and categorical apparatus aims to expose digital reality as a social phenomenon and a dynamic process. The principal approach to the research problem is a synergetic methodology that includes methods of consistency, structuredness, reasoning, and makes it credible to unveil the essence of the analysis of digital reality as a factor in achieving societal stability in circumstances of stochasticity, which is an integral process. The article demonstrates that through the ability to predict, mistakes can be avoided, success can be achieved, and the prosperity of organizations can be multiplied. The article explains that the synergetic methodology, as a methodology of complexity, meets the conditions of globalization 4.0, Industry 4.0, technological progress 4.0, digital society, Enlightenment 2.0, and Agile management. It is for these complex requirements that a synergistic complexity methodology can be applied. The materials presented in the article hold practical value for experts, scientists, and leaders. Implementation of this expertise will benefit society, the state, international partners, and future generations by promoting sustainable growth. The practical significance of the article lies in solving the problems of acquiring a conceptual framework for analyzing digital reality as a factor in achieving the efficiency and sustainability of society in circumstances of stochasticity. This approach enables the formulation of national, regional, local, and other indicators of sustainability and contributes to overcoming crises. All indicators mentioned can be manifested in absolute and relative dimensions, including indicators in the social sphere, such as health status, quality of life, social activity, demographics, and others.

Bio-objective long-term maintenance scheduling for wind turbines in multiple wind farms

Abstract Maintenance scheduling (MS) for wind turbines (WTs) is an emerging investigation area in recent years. The MS of WTs is more complex than that of traditional thermal generators, because maintenance activities of WTs are affected by stochastic weather conditions, e.g., wind speed and precipitation. This paper proposes a long-term MS method to obtain the joint preventive maintenance plan during the whole warranty period of WTs on multiple wind farms. Both the labour cost and production loss are used as objective functions of the MS. Historical weather data are analysed, and a statistical model is developed to describe the weather conditions. Then, the MS problem is formulated compactly as a mixed integer linear programming model. Finally, a detailed practical case study is demonstrated to validate the effectiveness of the proposed MS method. The result confirms that cost-effective joint preventive maintenance (PM) plans of three wind farms can be derived through the proposed MS method. Compared with the periodic PM plan, the expected labour cost and production loss are reduced by approximately 30% and 20%, respectively.

Distributed model predictive control of positive Markov jump systems

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

Random ecological networks that depend on ephemeral wetland complexes

Wetlands provide diverse ecosystem services: they create habitats, provide hydrological control, and regulate biogeochemical cycles of flora and fauna through interaction with surrounding wetlands. These services vary temporally, depending primarily on hydro-climatic conditions and the type of wetland. To better understand the functions of wetlands, it is necessary to analyze the effect of stochastic hydro-climatic conditions on the dynamics of wetland surface area and the resulting dispersal of species. In this study, we analyzed the dynamics of the connectivity and efficiency of ecological networks according to (1) the characteristics of the wetland area distribution, which varies by season, and (2) dispersal models (threshold distance, exponential kernel, and heavy-tailed movement). The results indicate that hydrologically sensitive small wetlands were often the primary elements that characterize wetland area distribution. Consequently, during dry seasons, the corresponding ecological network topology, measured by mean degree, network efficiency, and clustering coefficient decreased in all dispersal models we tested. We also found that while the correlation of hubs between dispersal models was strong, the levels of network vulnerability, evaluated by removing those hubs, were different, with the heavy-tailed model showing the highest vulnerability. Moreover, we observed the possibility of regime shift in ecological networks when a chronic, high dryness induced significant reduction of large wetlands. Our network modeling approach based on hydrologic systems will provide a new decision-making process and perspectives for conservation and restoration planning including the conditions regarding climate change.

Structural reliability assessment of offshore wind turbine support structures subjected to pitting corrosion‐fatigue: A damage tolerance modelling approach

AbstractThe structural integrity of offshore wind turbine (OWT) support structures is affected by one of the most severe damage mechanisms known as pitting corrosion‐fatigue. In this study, the structural reliability of such structures subjected to pitting corrosion‐fatigue is assessed using a damage tolerance modelling approach. A probabilistic model that ascertains the reliability of the structure is presented, incorporating the randomness in cyclic load and corrosive environment as well as uncertainties in shape factor, pit size and aspect ratio. A non‐intrusive formulation is proposed consisting of a sequence of steps. First, a stochastic parametric Finite Element Analysis (FEA) is performed using SMART© crack growth and Design Xplorer© facilities within the software package ANSYS. Secondly, the results obtained from the FEA are processed using an Artificial Neural Network (ANN) response surface modelling technique. Finally, the First Order Reliability Method (FORM) is used to calculate the reliability indices of components. The results reveal that for the inherent stochastic conditions, the structure becomes unsafe after the 18th year, before the attainment of the design life of 20 years. The FEA results are in very good agreement with results obtained from analysis steps outlined in design standard BS 7910 and other references designated as ‘theoretical analysis methods’ in this study. The results predict, for the case study, that the pit growth life is approximately 56% of the total pitting corrosion fatigue life. Sensitivity analysis results show that the aspect ratio of pits at critical size plays a significant role on the reliability of the structure.

Drag Prediction of Nasa Common Research Model Under Stochastic Inflow Conditions

Numerical investigations of NASA Common Research Model under stochastic inflow conditions are analysed in this paper by Non-intrusive Polynomial Chaos (NIPC) method. Reynolds number, Mach number and temperature of inflow conditions are assumed to be independent stochastic variables. It is found that predicted drag mainly depends on Mach number of incoming flow. The contribution of Reynolds number and temperature to the variance of drag is negligible. The mean value of drag shows consistent convergence with grid refinement. The investigation of this paper quantitates the uncertainty induced by stochastic inflow conditions to drag prediction and recognizes the most significant input variable. This will help the validation of numerical methods with experiment.

Distributed active disturbance rejection control for Ackermann steering of a four-in-wheel motor drive vehicle with deception attacks on controller area networks

This paper investigates the network-based modeling and distributed active disturbance rejection control (ADRC) to address the Ackermann steering problem of a four-in-wheel motor drive electric vehicle with deception attacks on controller area networks (CAN). The distributed ADRC can achieve the independent steering, ensure a small steering radius and improve the stability and robustness of the vehicle under unknown tyre longitudinal forces and network attacks. Using an independent driving strategy and Ackermann steering geometry, a state-space model for rotational velocity tracking of each wheel is established, where a virtual external disturbance that consists of the tyre longitudinal force and the expected rotational velocity is imposed on the model. Considering the effect of deception attacks on measurement outputs, sampled-data-driven extended state observers are designed to estimate the tracking error and the external disturbance. To capture the interactions among four wheels, a distributed controller based on ADRC is proposed and the resulting system is formulated as a stochastic linear system with input delay and composite disturbance, where the composite disturbance is composed of false signals, a discretized disturbance error and the derivative of the longitudinal forces. A lemma is obtained to prove the discretized disturbance error to be energy-limited. Some stochastic stability conditions with H∞ performance are derived by constructing a new discontinuous augmented Lyapunov–Krasovskii functional, and a design algorithm of the observer gain and the controller gain is presented. The effectiveness of the results is exemplified by two examples.

Stability analysis and control design of singular Markovian jump systems via a parameter-dependent reciprocally convex matrix inequality

Abstract This paper is concerned with the problems of stochastic stability and control design for singular Markovian jump systems (SMJSs) with time varying delay. The derivative coefficient is considered to be mode dependent. A parameter-dependent reciprocally convex matrix inequality (PDRCMI) is constructed, which covers some existing ones as its special cases. Different from some existing ones, the introduced parameters are completely known, which can be optimized by an iteration algorithm. To decrease the redundant decision variables, a mild assumption is given for the case of mode-dependent coefficient such that the considered system is decomposed into differential equations and algebraic ones. In this case, the components of state vectors of the subsystem are applied to construct a new augmented Lyapunov-Krasovkii functional (LKF). Based on the PDRCI and the new augmented LKF, a novel stochastic stability condition with both less computational demands and less conservativeness is derived. Based on the decomposed subsystems and the stability condition, a set of state feedback controller is designed in terms of linear matrix inequalities (LMIs). Some numerical examples are introduced to illustrate the effectiveness of the proposed results.

Propagation of uncertainty in a rotating pipe mechanism to generate an impinging swirling jet flow for heat transfer from a flat plate

In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (\textit{Simulation 1}) impinging on a flat plate to provide convective heat transfer (\textit{Simulation 2}). The first approach is the Stochastic Collocation Method (SCM) with Clenshaw-Curtis sparse grids. The conclusion drawn from the analysis is that the simulated system does not exhibit a significant sensitivity to stochastic variations of model input parameters, over the tested uncertainty ranges. Additionally, a set of non-linear regression models for the stochastic velocity and turbulent profiles for the pipe nozzle are created and tested, since impinging jets at Reynolds number of $Re=23000$ are very frequent in the literature, but stochastic inlet conditions have never been provided. Numerical results demonstrate a negligible difference in the predicted convective heat transfer with respect to the use of the profiles simulated via CFD. These suggested surrogate models can be directly embedded onto other CFD applications (e.g arrays of jets or jet flows impinging on plates with different shapes) in which a realistic swirling flow under uncertainty can be of interest.

BSDEs driven by normal martingale

The aim of this paper is to study backward stochastic differential equation driven by a class of normal martingale. We prove the existence and uniqueness results of the solution under the stochastic Lipschitz condition by mean the martingale representation theorem. In addition, we show that the solution of these equations provides a viscosity solution of the associated system with partial differential equations.

Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity

This paper is concerned with on the event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity. Firstly, the principle of the global convergence in fixed time with respect to nonlinear systems with semi-Markov switching is developed. Secondly, in order to realize the global stochastic synchronization goal in fixed time, a novel hybrid controller, which is composed of the event-triggered controller and the switching state-feedback controller, is designed. Under Filippov differential inclusion framework, by applying Lyapunov functional method and inequality analysis technique, the global stochastic synchronization conditions in fixed time are achieved in the form of linear matrix inequalities (LMIs). In addition, the upper bound of the stochastic settling time, which is adjusted in advance by choosing the controller parameters, is estimated accurately. Finally, the correctness of the theoretical results and the feasibility of the designed controller are verified by an example.

Prescribing transient and asymptotic behaviour to deterministic systems with stochastic initial conditions

We study a containment control problem (CCP) and a shape control problem (SCP) for systems whose initial condition is a random variable with known distribution. The two control problems both require exponential convergence to a desired trajectory, which is complemented by either; (i) a required cumulative distribution over a prescribed containment set at a specific transient time for the CCP, or; (ii) a maximum distance between an attained and a desired probability density function of the state for the SCP. For the CCP, we obtain solutions for both linear and nonlinear systems by designing the closed-loop such that the initial pdf shrinks or contracts to a desired trajectory. For the SCP, we obtain solutions for linear systems and an admissible desired pdf, by designing the closed-loop such that the evolution of the pdf at the transient time is similar to the target pdf.

Coordination Supply Chain Management Under Flexible Manufacturing, Stochastic Leadtime Demand, and Mixture of Inventory

The necessity of coordination among entities is essential for the success of any supply chain management (SCM). This paper focuses on coordination between two players and cost-sharing in an SCM that considers a vendor and a buyer. For random demand and complex product production, a flexible production system is recommended. The study aims to minimize the total SCM cost under stochastic conditions. In the flexible production systems, the production rate is introduced as the decision variable and the unit production cost is minimum at the obtained optimal value. The setup cost of flexible systems is higher and to control this, a discrete investment function is utilized. The exact information about the probability distribution of lead time demand is not available with known mean and variance. The issue of unknown distribution of lead time demand is solved by considering a distribution-free approach to find the amount of shortages. The game-theoretic approach is employed to obtain closed-form solutions. First, the model is solved under decentralized SCM based on the Stackelberg model, and then solved under centralized SCM. Bargaining is the central theme of any business nowadays among the players of an SCM to make their profit within a centralized and decentralized setup. For this, a cost allocation model for lead time crashing cost based on the Nash bargaining model with the satisfaction level of SCM members is proposed. The cost allocation model under Nash bargaining achieves exciting results in SCM coordination.

Anticipated backward doubly SDEs with generators in stochastic Lipschitz condition

In this paper, we prove the well-posedness of the solutions to anticipated backward doubly SDEs (ABDSDEs for short) with stochastic Lipschitz coefficients, where the generators (drivers) of equations not only rely on the prospective values of the pair of solutions, but also satisfy a certain type of Lipschitz condition. This type of equation has a practical background in financial mathematics.

VICTORIA transform, RESPECT and REFORM methods for the proof of the G-Elliptic Law under G-Lindeberg condition and twice stochastic condition for the variances and covariances of the entries of some random matrices

AbstractThe G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.