Variation In Probability Research Articles

Forecasting solar irradiance for the strategic integration of hybrid hydro and solar photovoltaic systems in rural Indian regions

ABSTRACT Conversion of the conventional electrical grid into a smart and sustainable grid involves several considerations. The primary factors, however, are renewable energy penetration, associated storage systems, and energy generation costs. This research endeavors to conduct a thorough survey and analysis of the solar irradiance on various hydropower locations in India, including Run-of-River (RoR), Run-of-River with Pondage (RoRP), Reservoir Storage (S), Multi-Purpose Storage (MP) and Pumped Storage Systems (PSS). The hydroelectric projects in rural Indian regions have been the subject of the proposed case study. As a preliminary study, the probabilistic variables like minimum, maximum, and mean solar irradiance are calculated for 252 High-Scale Hydropower Plant locations (HSHPs) using the past 40 years day ahead solar radiation data to identify the high-irradiance hydropower plant location in each state of India. This study concludes that the maximum mean solar irradiance location in each state as these sites are well suited for hybrid PV-hydro systems. The identified high-irradiance locations 40 years day ahead data sets are analyzed employing 8 machine learning models and 2 deep learning models. This analysis aims to forecast solar irradiance, serving as a crucial foundation for the initial phase of the implementation of hybrid PV-hydro.

An artificial neural network-based predictive model for tensile behavior estimation under uncertainty for fused deposition modeling

PurposeThis paper aims to present a predictive model approach to estimate the tensile behavior of polylactic acid (PLA) under uncertainty using the fused deposition modeling (FDM) and American Society for Testing and Materials (ASTM) D638’s Types I and II test standards.Design/methodology/approachThe prediction approach combines artificial neural network (ANN) and finite element analysis (FEA), Monte Carlo simulation (MCS) and experimental testing for estimating tensile behavior for FDM considering uncertainties of input parameters. FEA with variance-based sensitivity analysis is used to quantify the impacts of uncertain variables, resulting in determining the significant variables for use in the ANN model. ANN surrogates FEA models of ASTM D638’s Types I and II standards to assess their prediction capabilities using MCS. The developed model is applied for testing the tensile behavior of PLA given probabilistic variables of geometry and material properties.FindingsThe results demonstrate that Type I is more appropriate than Type II for predicting tensile behavior under uncertainty. With a training accuracy of 98% and proven presence of overfitting, the tensile behavior can be successfully modeled using predictive methods that consider the probabilistic nature of input parameters. The proposed approach is generic and can be used for other testing standards, input parameters, materials and response variables.Originality/valueUsing the proposed predictive approach, to the best of the authors’ knowledge, the tensile behavior of PLA is predicted for the first time considering uncertainties of input parameters. Also, incorporating global sensitivity analysis for determining the most contributing parameters influencing the tensile behavior has not yet been studied for FDM. The use of only significant variables for FEA, ANN and MCS minimizes the computational effort, allowing to simulate more runs with reduced number of variables within acceptable time.

Quantifying and enabling the resiliency of a microgrid considering electric vehicles using a Bayesian network risk assessment

With the increase in the number of natural disasters, caused by climate change, the role of emission and resilience has become more outstanding. In this paper, a novel model for quantifying and enabling the resiliency of a microgrid, using a Bayesian network risk assessment approach is presented. The three objective functions of cost, pollution, and resilience are optimized simultaneously using an improved lexicographic augmented ɛ-constraint method. It should be mentioned that these items are included in the proposed model due to the irreplaceable role of electric vehicles (EVs) and renewable energy sources (RESs) in distribution systems. Moreover, with the Bayesian network, the interaction between random variables is considered and a graphic view of casual relationships between stochastic and probabilistic variables is investigated in this study. The Monte Carlo scenario-based technique has handled the uncertainties of EVs and RESs. The proposed mixed integer linear programming (MILP) is implemented in the GAMS software environment under the CPLEX solver and finally, the results are discussed.

Stochastic finite element-based reliability of corroded pipelines with interacting corrosion clusters

The performance of corroded carbon steel pipelines over the course of their design life is generally assessed by probabilistic variables with explicit limit state functions, rather than the realistic representation with stochastic spatial variability and implicit failure considerations. This could be due to the complexities associated with the uncertainty quantification and performance estimation approaches. The consideration of random process representation of corrosion defect propagation and material properties, along with computationally effective implicit formulation is expected to lead to accurate reliability outcomes. This paper proposes a stochastic-based reliability framework considering suitable failure modes represented with surrogate models, that lead to time-variant reliability estimation. The approach combines surrogate computational model with scalar random variables and random field discretisation of underlying characteristics to generate experimental designs and corresponding surrogate models over a time period, which are used to derive reliability estimates. The outcomes of this approach are compared with the results of explicit time-dependent functions. It was observed that reliability estimates of the corroded pipeline change rapidly after the fifth year, providing a much lesser probability of failure (of 3.08×10−3 at 30th-year) compared to the existing models (of 1.80×10−2 at 30th-year), thereby providing an effective pathway for risk-based maintenance and management.

An Efficient Evolution-Based Technique for Moving Target Search with Unmanned Aircraft Vehicle: Analysis and Validation

Recent advances in technology have led to a surge in interest in unmanned aerial vehicles (UAVs), which are remote-controlled aircraft that rely on cameras or sensors to gather information about their surroundings during flight. A UAV requires a path-planning technique that can swiftly recalculate a viable and quasi-optimal path in flight if a new obstacle or hazard is recognized or if the target is moved during the mission. In brief, the planning of UAV routes might optimize a specific problem determined by the application, such as the moving target problem (MTP), flight time and threats, or multiobjective navigation. The complexity of MTP ranges from NP-hard to NEXP-complete because there are so many probabilistic variables involved. Therefore, it is hard to detect a high-quality solution for this problem using traditional techniques such as differential calculus. Therefore, this paper hybridizes differential evolution (DE) with two newly proposed updating schemes to present a new evolution-based technique named hybrid differential evolution (HDE) for accurately tackling the MTP in a reasonable amount of time. Using Bayesian theory, the MTP can be transformed into an optimization problem by employing the target detection probability as the fitness function. The proposed HDE encodes the search trajectory as a sequence of UAV motion pathways that evolve with increasing the current iteration for finding the near-optimal solution, which could maximize this fitness function. The HDE is extensively compared to the classical DE and several rival optimizers in terms of several performance metrics across four different scenarios with varying degrees of difficulty. This comparison demonstrates the proposal’s superiority in terms of the majority of used performance metrics.

Hybrid‐driven‐based resilient control for networked T‐S fuzzy systems with time‐delay and cyber‐attacks

AbstractThis work investigates design problem of the hybrid‐triggered‐based resilient controller for a class of Takagi–Sugeno (T‐S) fuzzy systems subject to nondeterministic cyber‐attacks, probabilistic time‐delay, controller gain variations and actuator failures in which nondeterministic cyber‐attacks and hybrid‐triggered mechanism are implemented by probabilistic variables gratifying the Bernoulli distributions. To save the network resources, a new kind of hybrid‐triggered‐based resilient controller design is introduced. By employing Lyapunov technique together with improved Wirtinger's integral inequalities and event‐generator function, new delay‐dependent sufficient conditions are constructed which assures that the resulting closed‐loop system is mean square asymptotically stable and satisfies a prescribed performance. At last, two numerical examples are provided to display the effectiveness and advantage of the constructed method.

Optimal Plastic Reliable Design of Reinforced Concrete Beams Considering Steel Bars Volume Probability

This paper aims to investigate the plastic response of reinforced concrete tapered beams when subjected to random steel reinforcement volumes, using both deterministic and probabilistic analyses, with the complementary strain energy as a boundary in the first case, and the reliability index as a boundary in the second. The first step in this study was to use a previously studied model and perform a deterministic analysis, assuming that the complementary strain energy is a limiting factor and controller of the plastic behaviour. Next, a probabilistic analysis is applied, with the reliability index as a limitation. At the same time, the volume of the reinforcement steel used, and the complementary strain energy were treated as probabilistic variables with mean values and specific standard deviations. This novel method highlighted the plastic behaviour limiting procedure and provided results that highlighted the nature of the model’s changed behaviour when the complementary strain energy was controlled and when applying probabilistic properties with reliability index limitation.

Probabilistic linguistic evolutionary game with risk perception in applications to carbon emission reduction decision making

Carbon emission reduction, an effective way to facilitate carbon neutrality, has gained increasing attention in government policy and scientific research. However, the establishment of a sustainable carbon emission reduction market is a complex game between governments and enterprises. In addition, it is difficult to obtain precise evaluations of the political and environmental factors in most cases. Irrational enterprises with a profit-seeking nature bring challenges to the strategy selection. To bridge this gap, we propose a probabilistic linguistic evolutionary game to model strategic behavior in carbon emission reduction assistant decision making. First, we introduce a probabilistic linguistic payoff matrix to describe the uncertain payoffs of players. A new distance measure for the probabilistic variables is also proposed to construct the prospect payoff matrix in the prospect theory framework. Then, the evolutionary dynamics and the probabilistic linguistic evolutionary stability of the proposed methods are analyzed. A comprehensive case study for carbon emission reduction with comparisons is presented for validation.

Reliability-based layout optimization of concentrically braced in 3D steel frames

For an economical and safe design of building systems with concentrically braced frames, the layout of the braces should be done by considering all limitations. The current study proposes an approach for a reliability-based optimal design of concentric bracing layouts in 3D steel frames. The objective function was considered to be a reduction in the total weight. The layout of the braces was considered as the variable of the optimization problem. The deterministic design constraints of limitations of strength, drift and torsional irregularities were considered according to AISC 360-16 and ASCE 7-16. The distance between the center of mass and the center of rigidity was defined as the probability constraint. The probabilistic variables were the intensity of the distributed loads and the cross-sectional area of the braces and columns. The reliability index was evaluated using the Monte Carlo simulation method. The reliability-based design optimization (RBDO) problem was solved for 4-, 5- and 9-story steel space frames using the EVPS algorithm. To investigate the effect of the probabilistic constraint on the optimal design, numerical examples were solved without applying this constraint and the solutions to the RBDO and deterministic design optimization problems were compared.

A probability box representation method for power flow analysis considering both interval and probabilistic uncertainties

In the modern power system, the uncertainties such as renewable generation and electric vehicles are usually modelled as either interval or probabilistic variables for the power flow analysis. It is meaningful to study the mixed impacts of the interval and probabilistic variables on the power flow, but the existing methods considering the mixed impacts lack accuracy. This paper proposes a novel power flow analysis method considering both interval and probabilistic uncertainties, in which the probability box (P-box) model is established to investigate the power flow influenced by multi-type uncertainties. A probability-interval sample classification method combined with interpolation is proposed to achieve an accurate P-box representation of the power flow. Also, the correlation of uncertainties is fully considered where a novel extended optimizing-scenario method is proposed for obtaining the P-box model considering the multi-dimensional correlation of interval variables. Three test cases are carried out to verify the effectiveness of the proposed method. The P-box represented results clearly reflect the fluctuation range and the corresponding probability of the power flow. The specific influences of the sample size, correlation, capacity of multi-type uncertainties on the power flow and the P-box model are also determined and summarized.

ALLOCATION OF CAPITAL INVESTMENTS OF AN OIL COMPANY BASED ON INDEPENDENT OPPORTUNITY INFORMATION

To solve the problem of investment allocation with optimization of the total level of return on investment for projects under conditions of risk associated with uncertainty of project income, a linear combination with non-negative coefficients of two loss-making models was used: the model of the usual minimax loss-making and the model of the minimax loss-making level. The problem of probabilistic programming obtained as a result of this combination, provided that the probabilistic variables characterizing the profitability of investments in projects are independent (unrelated), is reduced to a linear programming problem. The solution of this problem by the simplex method gives a vector of the equity distribution of investments that determine the total return of investments by the criterion of the minimum of the loss function. On the basis of the proposed approach to the optimal solution of the problem of investment allocation, an algorithm for project investment planning has been developed using a database of invested and returned funds for projects in previous planning periods, according to which distributions of possible investment returns are modeled. The numerical implementation of the algorithm is illustrated by the example of investment planning in an oil company for oil and gas production projects. Keywords: probability programming, investments, investment portfolio, minimax criterion, loss-making function, return on investment, income, concentrated distribution, probability distribution, measure of opportunity, measure of necessity, fractile model, probability variable, fuzzy variable membership function.

Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications

This study investigates a variety of novel estimations involving the expectation, variance, and moment functions of continuous random variables by applying a generalized proportional fractional integral operator. Additionally, a continuous random variable with a probability density function is presented in context of the proportional Riemann–Liouville fractional integral operator. We establish some interesting results of the proportional fractional expectation, variance, and moment functions. In addition, constructive examples are provided to support our conclusions. Meanwhile, we discuss a few specific examples that may be extrapolated from our primary results.

Finite state machine and Markovian equivalents of the <i>lac</i> Operon in <i>E. coli</i> bacterium

<abstract> <p>The <italic>lac</italic> operon in <italic>E. coli</italic> has been extensively studied by computational biologists. The bacterium uses it to survive in the absence of glucose, utilizing lactose for growth. This paper presents a novel modeling mechanism for the <italic>lac</italic> operon, transferring the process of lactose metabolism from the cell to a finite state machine (FSM). This FSM is implemented in field-programmable gate array (FPGA) and simulations are run in random conditions. A Markov chain is also proposed for the <italic>lac</italic> operon, which helps study its behavior in terms of probabilistic variables, validating the finite state machine at the same time. This work is focused towards conversion of biological processes into computing machines.</p> </abstract>

Power distribution network design considering the distributed generations and differential and dynamic pricing

In this study, a power distribution network design model is developed considering voltage control, as well as differential and dynamic pricing schemes. The objective is to maximize power distribution network profits under uncertain demands and parameters, such as power generation capacity, investment and generation cost of renewable distributed generation units, and the penalty budget for unsatisfied demands. The model determines the percentage of the power supply to the customer groups, the amount of power supplied to each customer group, the technology and capacity of renewable distributed generation units, and the prices offered. The proposed pricing scheme is differential for different types of customers with allowable voltage limits. The price is dynamic according to the planning time, including low, medium, and peak times. A fuzzy stochastic programming approach is developed to solve this problem. By simultaneously using triangular crisp numbers and probabilistic variables, the fuzzy stochastic programming integrates the fuzzy and stochastic approaches to deal with the uncertainty of demand and parameters. The numerical analysis shows that, as the confidence level decreases, the capacity of renewable distributed generation units and the profit increase. The results also show that when the decision maker responds to the uncertainty in demand with a high confidence level, the optimum profit can be obtained; approximately 55.90% of the power is supplied to low-demand customers.

Robust Topology Optimization of Graphene Platelets Reinforced Functionally Graded Materials Considering Hybrid Bounded Uncertainties

Abstract An efficient scheme for the robust topology optimization considering hybrid bounded uncertainties (RTOHBU) is proposed for the graphene platelets (GPLs) reinforced functionally graded materials (FGMs). By introducing the concept of the layer-wise FGMs, the properties of the GPLs reinforced FGMs are calculated based on the Halpin-Tsai micromechanics model. The practical boundedness of probabilistic variables is naturally ensured by utilizing a generalized Beta distribution in constructing the robust topology optimization model. To address the issue of lacking the information of critical loads in existing topology optimization approaches considering hybrid uncertainties, a gradient-attributed search is carried out at first based on the hypothesis of linear elasticity to determine the critical loads leading to the worst structural performance. Subsequently, the statistical characteristics of the objective structural performance under such critical loads are efficiently evaluated by integrating the univariate dimension reduction method and the Gauss–Laguerre quadrature, the accuracy of which is verified by the comparison analyses utilizing the results of Monte Carlo simulation as references. Furthermore, a novel realization vector set is constructed for the bounded probabilistic uncertainties to parallelize the sensitivity analysis and accelerate the optimization process. All the proposed innovations are integrated into the robust topology optimization scheme, the effectiveness and efficiency of which are verified by both numerical and realistic engineering examples.

Numerical study of reliability index of structure rehabilitated with steel shear wall

Uncertainties in seismic demand and structural capacity create conservatism in the acceptance criteria of structural performance levels. This conservatism can be reduced and designs optimised by considering and reducing uncertainties. In seismic rehabilitation, a secondary system added to an existing structure has probabilistic parameters that can lead to changes in existing uncertainties. In this work, a steel moment frame was rehabilitated with a steel shear wall (SSW). Structural uncertainties were investigated by considering probabilistic variables of the force–deformation relationship of the SSW. The results showed that structural uncertainty increased the total uncertainty by 2.0–9.3%. Previous studies that have not considered structural uncertainty due to the force–deformation relationship and may not provide results with appropriate conservatism. As a result, the dispersion of the total uncertainties of a structure rehabilitated with a SSW is close to the dispersion value of a moment frame equipped with a brace, but is more than the dispersion value of the moment frame structure. A parametric study of the reliability index was performed based on probabilistic variables. Based on the results, the structural uncertainty reduced the reliability index by 0.57–1.28%.

Stochastic Optimization of Microgrids With Hybrid Energy Storage Systems for Grid Flexibility Services Considering Energy Forecast Uncertainties

This paper presents a stochastic framework for the optimization of microgrids that has the functionality of providing flexibility services to System Operators (SOs) considering uncertainties in the energy forecast. The methodology is developed with the aim of being applied to complex microgrids composed of different distributed energy resources and hybrid energy storage systems (ESS). The associated optimization problem is operated in two stages: the first one performs a stochastic optimization of the microgrid in order to reserve an up/down regulation capacity with which to deal with the energy forecast uncertainties of the microgrid. The different microgrid devices are optimized by considering their operational costs in order to achieve their optimal operation in the Day-Ahead Market (DM). The second stage is used to re-schedule the initial planning according to the signal request and an economic offer from the SO. The control problem is developed using Stochastic Model Predictive Control (SMPC) techniques and Mixed-Integer Quadratic Programming (MIQP), owing to the presence of logic, integer, mixed and probabilistic variables. The simulation results show that the proposed methodology reduces the risk of undergoing up/down-penalty deviations in the Regulation Service Market (RM), also being able to provide flexibility services to the SOs, despite being subject to uncertainties in the energy forecast carried out for the microgrid.

Influence of the appendicular skeletal muscle mass index on the bone mineral density of postmenopausal women

BackgroundThe appendicular skeletal muscle mass index (ASMI) is an important risk indicator for osteoporosis because of the anatomical proximity and metabolic connection between muscle and bone mass. The present study investigated the relationship between ASMI and the bone mineral density (BMD) categories of postmenopausal women.MethodsIn this cross-sectional study with a probabilistic sample, sociodemographic, lifestyle, menopause time, anthropometric, and physical activity variables were collected. ASMI and BMD were assessed by dual-energy X-ray absorptiometry (DXA). Participants were grouped according to BMD values into normal density, osteopenia, and osteoporosis. Multivariate logistic regression models were applied to verify the influence of ASMI on BMD. Data were analyzed using the SPSS statistical software, version 22. The significance level for all tests was set at 5%.ResultsOf the 114 women analyzed, most were between 60 and 69.9 years of age (62.3%), on menopause for ≤19.0 (51.8%), self-declared brown race/color (49.1%), had < 4 years of education (41.2%), never smoked (69.0%) or drank alcohol (62.8%). Of these, 52.6% were classified as sufficiently active and 52.2% had regular sun exposure. Women with osteoporosis were older (p = 0.035), on menopause for a longer time (p = 0.011), underweight (p = 0.004), had adequate waist circumference (p = 0.017), and low ASMI values (p = 0.002). There was an association between the 1st tertile of ASMI and osteoporosis. However, after adjustments for age, race/color, and body mass index, the strength of association between BMD and ASMI was not maintained.ConclusionsASMI was not associated with the BMD of the postmenopausal women evaluated. Total body and muscle mass, in addition to bone mass, should be monitored during menopause treatment. Longitudinal studies must be conducted to elucidate the mechanisms and gaps in this relationship.

The similarity about the probability distributions of variables in the Bayesian regression model and application

The linear regression model as well as the time series model is applied in many fields, in which the mean of the dependent variable is one function of the mean of the independent variables. However, to consider the regression model following in the Classical Statistics (the Frequent Statistics), it means that the parameters are the constants, in many situations, the regression model does not describe the fluctuation of both the dependent variable and the independent variables. Therefore, we need to modify the parameters following the random variable form, not the constant form, like as the regression in Bayesian Statistics. The other side, when the parameters considered as the random variables, computations in the regression model becomes very complex, because we need to compute the product of the probability distributions. So, we must evaluate about to vary of the variables' probability distributions not only the normal distribution, the Student distribution t, the Poisson distribution, the binomial distribution… In this paper, we estimated the dependent variable's probability distribution form through the simple Bayesian regression model in cases having many the probability distribution forms of the independent variable. In addition, we apply the results to real stock price data, proving that the most appropriate probability distribution with the data is a mixture of probability distributions, not a single normal distribution.

Failure-based sealing reliability analysis considering dynamic interval and hybrid uncertainties

In the reliability analysis of a sealing structure, radial clearance of the contact surface is usually regarded as a failure criterion, and the sample size is usually quite small, which brings great challenges to uncertainty quantification. Therefore, this paper proposes a reliability analysis method based on the leakage mechanism of the sealing. With the application of dynamic interval, the proposed method can be used to deal with problem of degradation in small sample to evaluate reliability. Moreover, the dynamic reliability with the mixture of the probabilistic and non-probabilistic variables can be obtained using the proposed method. An illustrative numerical case study of a spool valve is conducted in order to validate the proposed method and the implemented reliability sensitivity analysis. The proposed method is of great help in evaluating and predicting reliability with small degradation sample and hybrid uncertainties.