Numerical Computations for Flow Patterns and Force Statistics of Three Rectangular CylindersRead the full article
Mathematical Problems in Engineering is a broad-based journal publishing results of rigorous engineering research across all disciplines, carried out using mathematical tools.
Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.
Latest ArticlesMore articles
Awareness Modeling and Computing for Quality-Aware Coordination
In this paper, we address the issues of the trade-off between QoS and QoE with an analytical analysis based on mathematical modeling under a unified normalization measurement. We model through computation the awareness of QoS and QoE with a strategy of quality-aware QoE-QoS coordination. A balanced coordination is proposed using modeling correlations between user experience and service performance. The main contributions of this paper include three main parts. First, a comprehensive mapping is modeled in a close form to illustrate the analytic correlations between QoS, QoE, and data communication. Second, an analytical method to analyze and coordinate the nonlinear trade-off between QoE and QoS is proposed based on the theoretical proof with discussions on necessary-sufficient conditions. Third, an algorithmic framework is provided to perform QoE-QoS coordination based on quality-awareness computing with a test proof. An assessment model for user experience quantification is built with the mean opinion score (MOS) test. Quality-aware QoE and QoS models are built based on the subspace learning strategy. Simulations are given to prove the feasibility and effectiveness of the proposed method. The results show that the operations with the proposed solution can be obtained analytically with balanced efficiency in both user experience performance and network performance.
A Novel Family of Exact Nonlinear Cascade Control Design Solutions for a Class of UAV Systems
In this work, a novel family of exact nonlinear control laws is developed for trajectory tracking of unmanned aerial vehicles. The proposed methodology exploits the cascade structure of the dynamic equations of most of these systems. In a first step, the vehicle position in Cartesian coordinates is controlled by means of fictitious inputs corresponding to the angular coordinates, which are fixed to a combination of computed torque and proportional-derivative elements. In a second step, the angular coordinates are controlled as to drive them to the desired fictitious inputs necessary for the first part, resulting in a double-integrator 3-input cascade control scheme. The proposal is put at test in two examples: 4-rotor and 8-rotor aircrafts. Numerical simulations of both plants illustrate the effectiveness of the proposed method, while real-time results of the first one confirm its applicability.
Dynamic Equivalent Modeling of Wind Farm Based on Dominant Variable Hierarchical Clustering Algorithm
The actual operating state of the wind turbine group is influenced by the wake effect and control mode; however, the current models cannot describe the actual operating state very well. A dynamic equivalent modeling method for a doubly fed wind power generator is proposed on the basis of ensuring the accurate description of the wind turbine group. As the clustering index, dominant variables are used in the hierarchical clustering algorithm, which are extracted by principal component analysis. Three dynamic equivalent models of 24 wind turbines are established using PSCAD software platform, which use 13 state variables, wind speed, and dominant variables as clustering indexes, respectively. Furthermore, the active power and reactive power output curves of wind farm are simulated in the case of the three-phase short-circuit fault on the system side or wind speed fluctuation, respectively. The simulation results demonstrate that it is reasonable and effective to extract slip ratio and wind turbine torque as clustering index, and the maximal relative error between the dominant variable equivalent model and 13-state-variable model is only 9.9%, which is greatly lower than that of the wind speed model, K-means clustering model, neural network model, and support vector machine model. This model is easy to implement and has wider application prospect, especially for characteristics analysis of large-scale wind farm connected to power grid.
Fault Diagnosis of Data-Driven Photovoltaic Power Generation System Based on Deep Reinforcement Learning
Aiming at the problem of fault diagnosis of the photovoltaic power generation system, this paper proposes a photovoltaic power generation system fault diagnosis method based on deep reinforcement learning. This method takes data-driven as the starting point. Firstly, the compressed sensing algorithm is used to fill the missing photovoltaic data and then state, action, strategy, and return functions from the environment. Based on the interaction rules and other factors, the fault diagnosis model of the photovoltaic power generation system is established, and the deep neural network is used to approximate the decision network to find the optimal strategy, so as to realize the fault diagnosis of the photovoltaic power generation system. Finally, the effectiveness and accuracy of the method are verified by simulation. The simulation results show that this method can accurately diagnose the fault types of the photovoltaic power generation system, which is of great significance to enhance the security of the photovoltaic power generation system and improve the intelligent operation and maintenance level of the photovoltaic power generation system.
Analysis and Evaluation of CDPR Cable Sagging Based on ANFIS
The cable sagging problem of cable-driven parallel robots (CDPRs) is very complicated, because several models for calculating cable sag based on the well-known catenary equation have been studied, but time and computational efficiency are a problem to be solved. There is still no simple mathematical model to calculate cable sag by considering all relevant conditions due to the complexity and nonlinearity of the cable sagging model, which involves many dominant variables and their influence on the position accuracy of CDPRs. In this study, we proposed an ANFIS (adaptive neuro-fuzzy inference system) architecture to estimate cable sag for large-sized CDPRs. The ANFIS model can be used to solve nonlinear functions and detect nonlinear factors online in the control system; this characteristic is consistent with the nonlinear model of cable sag. The trained data for ANFIS models were taken from calculation results by Trust-Region-Dogleg algorithm based on two cable tension calculation algorithms as Dual Simplex Algorithm and Force Distribution in Closed Form. Cable sagging data obtained from ANFIS and Trust-Region-Dogleg algorithm are compared and evaluated by statistical factors of evaluations consisting of root-mean-square error, correlation coefficients, and scatter index. The analytical results show that the ANFIS gave computed results with small errors and can be applied to predict cable sagging for any CDPR configuration, with the advantage of fast calculation time and high precision. The results of these models are also applied on a CDPR that contains two redundant actuators.
Closed-Form Solution of a Rational Difference Equation
In this paper, we study the solution of the difference equation , where the initials are positive real numbers.