Linear Time-varying Parameters Research Articles

Online public opinion prediction based on a novel conformable fractional discrete grey model

PurposeAs social networks have developed to be a ubiquitous platform of public opinion spreading, it becomes more and more crucial for maintaining social security and stability by accurately predicting various trends of public opinion dissemination in social networks. Considering the fact that the dissemination of online public opinion is a dynamic process full of uncertainty and complexity, this study establishes a novel conformable fractional discrete grey model with linear time-varying parameters, namely the CFTDGM(1,1) model, for more accurate prediction of online public opinion trends.Design/methodology/approachFirst, the conformable fractional accumulation and difference operators are employed to build the CFTDGM(1,1) model for enhancing the traditional integer-order discrete grey model with linear time-varying parameters. Then, to improve forecasting accuracy, a base value correction term is introduced to optimize the iterative base value of the CFTDGM(1,1) model. Next, the differential evolution algorithm is selected to determine the optimal order of the proposed model through a comparison with the whale optimization algorithm and the particle swarm optimization algorithm. The least squares method is utilized to estimate the parameter values of the CFTDGM(1,1) model. In addition, the effectiveness of the CFTDGM(1,1) model is tested through a public opinion event about “IG team winning the championship”. Finally, we conduct empirical analysis on two hot online public opinion events regarding “Chengdu toddler mauled by Rottweiler” and “Mayday band suspected of lip-syncing,” to further assess the prediction ability and applicability of the CFTDGM(1,1) model by comparison with seven other existing grey models.FindingsThe test case and empirical analysis on two recent hot events reveal that the CFTDGM(1,1) model outperforms most of the existing grey models in terms of prediction performance. Therefore, the CFTDGM(1,1) model is chosen to forecast the development trends of these two hot events. The prediction results indicate that public attention to both events will decline slowly over the next three days.Originality/valueA conformable fractional discrete grey model is proposed with the help of conformable fractional operators and a base value correction term to improve the traditional discrete grey model. The test case and empirical analysis on two recent hot events indicate that this novel model has higher accuracy and feasibility in online public opinion trend prediction.

An online auction-based mechanism for pricing and allocation of instant delivery services

Recently, instant delivery has been growing rapidly, with numerous platforms emerging to offer such services. Requestors dynamically arrive at the platform to place delivery service requests that detail their pickup locations, recipient locations, package weights, departure times, and willingness-to-pay (WTP). The platform then uses its dedicated riders, scattered in different places, to fulfill these requests. Given the dynamic and fluctuating characteristics of the demand, coupled with limited rider resources and heterogenous pickup costs, the platform faces the critical problem of dynamically pricing the requests and assigning the riders to maximize social welfare. To address this problem, we propose an online auction-based transaction mechanism. Specifically, we first propose a scoring function to evaluate the values of the requests over multi-period operations taking into account the requests’ attributes, riders’ delivery costs, and resource availability. Based on the scoring function, we design a time-varying Vickrey–Clarke–Groves (VCG)-like payment rule that can reflect the impacts of fluctuating supply-demand imbalances. Under this rule, a requestor will pay more during undersupply periods than during oversupply periods. To carve out the different impact degrees of the supply-demand imbalances, we further consider the linear, quadratic, and exponential time-varying resource parameters to construct the payment rule. In addition, we develop an online instant delivery resource allocation model to efficiently assign the riders to fulfill the accepted requests. We show that the proposed mechanism has desirable properties (individual rationality, budget balance, and incentive compatibility) and is computationally efficient. Furthermore, we give a lower bound for the mechanism efficiency. To validate the practicality of our mechanism and get some managerial insights into the operations of the instant delivery platform, we conduct numerical studies to compare the performance of our mechanism to the First-in, first-out (FIFO) allocation mechanism and to investigate the impacts of pricing functions, rolling horizon configurations, and rider numbers on the mechanism's performance.

Forecasting carbon emissions using a multi-variable GM (1,N) model based on linear time-varying parameters

Faced with serious growing global warming problem, it is important to predict carbon emissions. As there are a lot of factors affecting carbon emissions, a novel multi-variable grey model (GM(1,N) model) based on linear time-varying parameters discrete grey model (TDGM(1,N)) has been established. In this model, linear time-varying function is introduced into the traditional model, and dynamic optimization of fixed parameters which can only be used for static analysis is carried out. In order to prove the applicability and effectiveness of the model, this paper compared the model with the traditional model and simulated the carbon emissions of Anhui Province from 2005 to 2015. Carbon emissions in the next two years are also predicted. The results show that the TDGM(1,N) model has better simulation effect and higher prediction accuracy than the traditional GM(1,N) model and the multiple regression model(MRM) in practical application of carbon emissions prediction. In addition, the novel model of this paper is also used to predict the carbon emissions in 2018–2020 of Anhui Province.

Identification of Linear Time-Varying Parameters of Nonstationary Systems

The paper considers the identification algorithm for unknown parameters of linear non-stationary control objects. It is assumed that only the object output variable and the control signal are measured (but not their derivatives or state variables) and unknown parameters are linear functions or their derivatives are piecewise constant signals. The derivatives of non-stationary parameters are supposed to be unknown constant numbers on some time interval. This assumption for unknown parameters is not mathematical abstraction because in most electromechanical systems parameters are changing during the operation. For example, the resistance of the rotor is linearly changing, because the resistance of the rotor depends on the temperature changes of the electric motor in operation mode. This paper proposes an iterative algorithm for parameterization of the linear non-stationary control object using stable LTI filters. The algorithm leads to a linear regression model, which includes time-varying and constant (at a certain time interval) unknown parameters. For this model, the dynamic regressor extension and mixing (DREM) procedure is applied. If the persistent excitation condition holds, then, in the case the derivative of each parameter is constant on the whole time interval, DREM provides the convergence of the estimates of configurable parameters to their true values. In the case of a finite time interval, the estimates convergence in a certain region. Unlike well-known gradient approaches, using the method of dynamic regressor extension and mixing allows to improve the convergence speed and accuracy of the estimates to their true values by increasing the coefficients of the algorithm. Additionally, the method of dynamic regressor extension and mixing ensures the monotony of the processes, and this can be useful for many technical problems.

Fractional-Order Accumulative Linear Time-Varying Parameters Discrete Grey Forecasting Model

Traditional discrete grey forecasting model can effectively predict the development trend of the stabilizing system. However, when the system has disturbance information, the prediction result will have larger error, and there will appear significant downward trend in the stability of the model. In the presence of disturbance information, this paper presents a fractional-order linear time-varying parameters discrete grey forecasting model to deal with the system that contains both linear trend and nonlinear trend. The modeling process of the model and calculation method are given. The perturbation bounds of the new model are analyzed by using the least-squares method of perturbation theory. And it is compared with that of the first-order linear time-varying parameters discrete grey forecasting model. Finally, two real cases are given to verify the effectiveness and practicality of the proposed method.

Improved PSO Algorithm based Optimal Operation in Power Systems Integrating Solar and Wind Energy Sources

This paper proposes an improved particle swarm optimization (PSO) algorithm for optimal operation of a power system including the solar and wind energy sources. The algorithm is to minimize operating costs of the hybrid power system. The proposed PSO algorithm is one of the standard PSO algorithm variants, which modifies the acceleration coefficients of the cognitive and social components in the velocity update equation of the PSO algorithm as linear time-varying parameters. The acceleration coefficients are varied during the evolution process of the PSO algorithm to improve the global search capability of particles in the early stage of the optimization process and direct the global optima at the end stage. Additionally, the inertia weight which is considered as a trade-off factor for the local and global search abilities of the PSO algorithm is also linearly decreased instead of a fixed constant value to improve its performance. The improved PSO algorithm based optimal operation of the hybrid power system with and without solar and wind powers is considered on a standard IEEE 30-bus 6-generator 41transmission line test power system. The numerical results demonstrate the capabilities of the proposed algorithm to generate optimal solutions of a hybrid power system considering the solar and wind energy resources. The comparison with the standard PSO algorithm demonstrates the superiority of the proposed algorithm and confirms its potential to optimize the operating costs of the hybrid power system.

Optimal Generation Rescheduling of Power Systems with Renewable Energy Sources Using a Dynamic PSO Algorithm

1 Abstract: This paper proposes a dynamic particle swarm optimization (PSO) algorithm for optimal generation rescheduling of a power system including renewable energy sources such as the solar and wind energy sources. The algorithm is to minimize total operating costs of this hybrid power system. The proposed dynamic PSO algorithm is one of the standard PSO algorithm variants, which modifies the acceleration coefficients of the cognitive and social components in the velocity update equation of the PSO algorithm as linear time-varying parameters. The acceleration coefficients are varied during the evolution process of the PSO algorithm to improve the global search capability of particles in the early stage of the optimization process and direct the global optima at the end stage. The dynamic PSO algorithm based optimal generation rescheduling of the power system with and without solar and wind powers is considered on the standard IEEE 30-bus 6-generator 41-transmission line test power system. The numerical results demonstrate the capabilities of the proposed algorithm to generate optimal solutions of the power system considering the renewable energy resources. The comparison with the standard PSO algorithm demonstrates the superiority of the proposed algorithm and confirms its potential to reschedule an optimal generation of the power system including the solar and wind energy sources.

Research Cage Wind Turbines’ Dynamic Characteristics Based on Time-varying Parameters

According to the characteristics of cage wind turbines’ dynamic characteristics which change following the wind speed changes, the dynamic mathematical models of cage wind turbines major subsystems have been established, including the aerodynamic subsystem model, drive train subsystem model and generator subsystem model. Then these nonlinear dynamic models with time-varying parameters have been integrated and linearized to obtain the whole linear time-varying parameters dynamic mathematical model. To take the 2MW cage wind turbines wind turbine as example, the proposed model is validated by the study on the dynamic characteristics of cage wind turbines with wind speed variation , and the results show that the proposed model could provide a theoretical support for optimal control of the cage wind turbines.

A synthesis framework for robust gain-scheduling controllers

We present a general framework for the systematic synthesis of robust gain-scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations. We distinguish between linear time-varying parameters, which are assumed to be available online as scheduling parameters for the controller, and genuine uncertainties, not necessarily time-varying, parametric or linear, that are not available online. Under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints, this paper reveals how controller synthesis can be turned into a genuine semi-definite program. The design framework is shown to encompass a rich class of concrete scenarios.

Research Doubly-fed Induction Generator Dynamic Characteristics Based on Time-varying Parameters

According to the dynamic characteristics of doubly-fed induction generator (DFIG) which is changing with the wind speed, the dynamic mathematical models of DFIG wind turbines major subsystems’ have been established, which includes the aerodynamic subsystem, drive train subsystem and generator subsystem. The whole nonlinear time-varying parameters dynamic mathematical model would be obtained to integrate the major subsystems’ dynamic mathematical models, and the whole linear time-varying parameters dynamic mathematical model can be obtained to linearize the whole linear time-varying parameters dynamic mathematical model. To take the 2MW DFIG wind turbine as example, the proposed model is validated by the study on the dynamic characteristics of DFIG with wind speed variation, and the results show that the proposed model could provide a theoretical support for optimal control of the DFIG wind turbines.

De Saint-Venant equations-based model assessment in model predictive control of open channel flow

Model predictive control (MPC) is a model-based control technique that uses an optimization algorithm to generate optimal control actions. Based on the model used in optimization, MPC approaches can be categorized as linear or nonlinear. Both classes have advantages and disadvantages in terms of control accuracy and computational time. A typical linear model in open channel water management is the Integrator Delay (ID) model, while a nonlinear model usually refers to the Saint-Venant equations. In earlier work, we proposed the use of linearized Saint-Venant equations for MPC, where the model is formulated in a linear time-varying format and time-varying parameters are estimated outside of the optimization. Quadratic Programming (QP) is used to solve the optimization problem. However, the control accuracy of such an MPC scheme is not clear. In this paper, we compare this approach with an MPC scheme that uses Sequential Quadratic Programming (SQP) to solve the optimization problem. Because the estimation of the time-varying parameters is integrated in the optimization in SQP, the solutions from SQP-based MPC are expected to be superior to the solutions of QP-based approach. However, SQP can be computationally expensive. A simulation experiment illustrates that the QP-based MPC approach using a linearized Saint-Venant model has an accurate approximation of the control performance of SQP.

Ellipsoid based L_2 controller design for LPV systems with saturating actuators

This paper addresses the L_2 gain control problem for disturbance attenuation in Linear Parameter Varying (LPV) Systems having saturating actuators when the system is subjected to L_2 disturbances. In the presented method, saturating actuator is expressed analytically with a convex hull of some linear feedback which let us construct L_2 control problem via Linear Matrix Inequalities (LMIs) which are obtained by some ellipsoids. It is shown that the stability and disturbance rejection capabilities of the control system are all measured by means of these nested ellipsoids where the inner ellipsoid covers the initial conditions for states whereas the outer ellipsoid designates the L_2 gain of the system. It is shown that the performance of the controller is highly related by the topology of these ellipsoids. Finally, the efficiency of the proposed method is successfully demonstrated through simulation studies on a single-track vehicle dynamics having some linear time-varying parameters.

LPV Control of Actuator Saturated Systems: A Case Study on Single-Track Vehicle Control

The 2 gain control problem for disturbance attenuation in Linear Parameter Varying (LPV) Systems with saturating actuators has been addressed where the systems handled in the study are subjected to 2 disturbances. The aim in the presented method is to express saturating actuator analytically with a convex hull of some linear feedback. This point of view allows us to construct 2 control problem via Linear Matrix Inequalities (LMIs). Nested ellipsoids have been used to measure the stability and disturbance rejection capabilities of the control system. At the end, the proposed controller scheme has been simulated on a single-track vehicle dynamics with some linear time-varying parameters and a wind disturbance.

Parameter identification and convergence analysis for a class of non-linear systems with time-varying random parameters

New developments for parameter identification are presented for discrete stochastic non-linear systems with linear time-varying random parameters, which include bilinear systems. Hammerstain systems, Volterra systems, etc. These identification algorithms arc based on the least square method. Convergence of both identifying parameters and output error are studied and preliminary persistent exciting conditions arc given. Under some conditions, it is proved that identifying parameters and the mean square value of the difference between identifying parameters and random parameters are ensured converging to expectations of these random parameters and the averaging square derivation value of random paramctes, respectively.