Support Vector Regression Method for Wind Speed Prediction Incorporating Probability Prior Knowledge

Prior knowledge, such as wind speed probability distribution based on historical data and the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, provides much more information about the wind speed, so it is necessary to incorporate it into the wind speed prediction. First, a method of estimating wind speed probability distribution based on historical data is proposed based on Bernoulli’s law of large numbers. Second, in order to describe the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, the probability distribution estimated by the proposed method is incorporated into the training data and the testing data. Third, a support vector regression model for wind speed prediction is proposed based on standard support vector regression. At last, experiments predicting the wind speed in a certain wind farm show that the proposed method is feasible and effective and the model’s running time and prediction errors can meet the needs of wind speed prediction

Rough Set Model based on Uncertain Measure

Abstract Probabilistic rough set model based on probability measure is a new rough set model to deal with uncertain information systems. Uncertain measure is a generalization of probability measure. Based on the fundamental knowledge of rough set model and uncertain measure, a rough set model based on uncertain measure is established. Furthermore, by comparative study of the lower approximation and upper approximation, it is true that the rough set model based on uncertain measure is an extension of the probabilistic rough set model

Constructing composite search directions with parameters in quadratic interpolation models

Unconstrained optimization, Trust region method, Quadratic model, Simplex methods, Business intelligence systems,

A Novel GRA-NARX Model for Water Level Prediction of Pumping Stations

It is necessary but difficult to accurately predict the water levels in front of the pumping stations of an open-channel water transfer project because of the complex interactions among hydraulic structures. In this study, a novel GRA-NARX (gray relation analysis—nonlinear auto-regressive exogenous) model is proposed based on a gray relation analysis (GRA) and nonlinear auto-regressive exogenous (NARX) neural network for 2 h ahead for the prediction of water levels in front of pumping stations, in which an improved algorithm of the NARX neural network is used to obtain the optimal combination of the time delay and the hidden neurons number, and GRA is used to reduce the prediction complexity and improve the prediction accuracy by filtering input factors. Then, the sensitivity to changes of the training algorithm is analyzed, and the prediction performance is compared with that of the NARX and GRA-BP (gray relation analysis back-propagation) models. A case study is performed in the Tundian pumping station of the Miyun project, China, to demonstrate the reliability and accuracy of the proposed model. It is revealed that the GRA-NARX-BR (gray relation analysis—nonlinear auto-regressive exogenous—Bayesian regularization) model has higher accuracy than the model based only on a NARX neural network and the GRA-BP model with a correlation coefficient (R) of 0.9856 and a mean absolute error (MAE) of 0.00984 m. The proposed model is effective in predicting the water levels in front of the pumping stations of a complex open-channel water transfer project

Half Open Multi-Depot Heterogeneous Vehicle Routing Problem for Hazardous Materials Transportation

How to reduce the accidents of hazardous materials has become an important and urgent research topic in the safety management of hazardous materials. In this study, we focus on the half open multi-depot heterogeneous vehicle routing problem for hazardous materials transportation. The goal is to determine the vehicle allocation and the optimal route with minimum risk and cost for hazardous materials transportation. A novel transportation risk model is presented considering the variation of vehicle loading, vehicle types, and hazardous materials category. In order to balance the transportation risk and the transportation cost, we propose a bi-objective mixed integer programming model. A hybrid intelligent algorithm is developed based on the ε-constraint method and genetic algorithm to obtain the Pareto optimal solutions. Numerical experiments are provided to demonstrate the effectiveness of the proposed model. Compared with the close multi-depot heterogeneous vehicle routing problem, the average risk and cost obtained by the proposed bi-objective mixed integer programming model can be reduced by 3.99% and 2.01%, respectively. In addition, compared with the half open multi-depot homogeneous vehicle routing problem, the cost is significantly reduced with the acceptable risk

A Novel GRA-NARX Model for Water Level Prediction of Pumping Stations

It is necessary but difficult to accurately predict the water levels in front of the pumping stations of an open-channel water transfer project because of the complex interactions among hydraulic structures. In this study, a novel GRA-NARX (gray relation analysis—nonlinear auto-regressive exogenous) model is proposed based on a gray relation analysis (GRA) and nonlinear auto-regressive exogenous (NARX) neural network for 2 h ahead for the prediction of water levels in front of pumping stations, in which an improved algorithm of the NARX neural network is used to obtain the optimal combination of the time delay and the hidden neurons number, and GRA is used to reduce the prediction complexity and improve the prediction accuracy by filtering input factors. Then, the sensitivity to changes of the training algorithm is analyzed, and the prediction performance is compared with that of the NARX and GRA-BP (gray relation analysis back-propagation) models. A case study is performed in the Tundian pumping station of the Miyun project, China, to demonstrate the reliability and accuracy of the proposed model. It is revealed that the GRA-NARX-BR (gray relation analysis—nonlinear auto-regressive exogenous—Bayesian regularization) model has higher accuracy than the model based only on a NARX neural network and the GRA-BP model with a correlation coefficient (R) of 0.9856 and a mean absolute error (MAE) of 0.00984 m. The proposed model is effective in predicting the water levels in front of the pumping stations of a complex open-channel water transfer project

Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

In order to formulate water allocation schemes under uncertainties in the water resources management systems, an inexact multistage stochastic chance constrained programming (IMSCCP) model is proposed. The model integrates stochastic chance constrained programming, multistage stochastic programming, and inexact stochastic programming within a general optimization framework to handle the uncertainties occurring in both constraints and objective. These uncertainties are expressed as probability distributions, interval with multiply distributed stochastic boundaries, dynamic features of the long-term water allocation plans, and so on. Compared with the existing inexact multistage stochastic programming, the IMSCCP can be used to assess more system risks and handle more complicated uncertainties in water resources management systems. The IMSCCP model is applied to a hypothetical case study of water resources management. In order to construct an approximate solution for the model, a hybrid algorithm, which incorporates stochastic simulation, back propagation neural network, and genetic algorithm, is proposed. The results show that the optimal value represents the maximal net system benefit achieved with a given confidence level under chance constraints, and the solutions provide optimal water allocation schemes to multiple users over a multiperiod planning horizon