Function Approximation Method Research Articles

A Time-Domain Calculation Method for Gust Aerodynamics in Flight Simulation

Gusts have a significant impact on aircraft and need to be analyzed through flight simulations. The solution for time-domain gust aerodynamic forces stands as a pivotal stage in this process. With the increasing demand for flight simulations within gusty environments, traditional methods related to gust aerodynamics cannot fail to balance computational accuracy and efficiency. A method that can be used to quickly and accurately calculate the time-domain gust aerodynamic force is needed. This study proposes the fitting strip method, a gust aerodynamic force solution method that is suitable for real-time flight simulations. It only requires the current and previous gust information to calculate the aerodynamic force and is suitable for different configurations of aircraft and different kinds of gusts. Firstly, the fitting strip method requires the division of fitting strips and the calculation of the aerodynamic force under calibration conditions. In this study, the double-lattice method and computational fluid dynamics are used to calculate the aerodynamic force of the strips. Then, the amplitude coefficients and time-delay coefficients are obtained through a fitting calculation. Finally, the coefficients and gust information are put into the formula to calculate the gust aerodynamic force. An example of a swept wing is used for validation, demonstrating congruence between the computational results and experimental data across subsonic and transonic speeds, which proves the accuracy of the fitting strip method in both discrete gusts and continuous gusts. Compared with other methods, the fitting strip method uses the shortest time. Furthermore, the results of a calculation for normal-layout aircraft show that this method avoids the shortcomings of the rational function approximation method and is more accurate than the gust grouping method. Concurrently, gust aerodynamic force calculations were performed on aircraft with large aspect ratios and used in a real-time flight simulation.

E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network. Based on PINN, an extended PINN(E-PINN) is proposed, which is a mixture of the polynomial function approximation method and PINN's learning framework. A preprocess layer is added before the classical PINN, using Legendre polynomials as the polynomial basis function. Therefore, E-PINN not only has the excellent approximation ability of the polynomial basis function, but also inherits the learning framework of the neural network method. In numerical experiments, the proposed E-PINN algorithms have high accuracy in solving 1D, 2D high-order nonlinear Fredholm equations and equations system, including the forward and inverse problems.

E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network. Based on PINN, an extended PINN(E-PINN) is proposed, which is a mixture of the polynomial function approximation method and PINN's learning framework. A preprocess layer is added before the classical PINN, using Legendre polynomials as the polynomial basis function. Therefore, E-PINN not only has the excellent approximation ability of the polynomial basis function, but also inherits the learning framework of the neural network method. In numerical experiments, the proposed E-PINN algorithms have high accuracy in solving 1D, 2D high-order nonlinear Fredholm equations and equations system, including the forward and inverse problems.

Parallel event-triggered dynamic output feedback control for nonlinear networked systems with randomly occurring multiple communication delays

This paper investigates the issue of parallel event-triggered (PET) dynamic output feedback control for networked control systems (NCSs) built by the discrete-time T–S fuzzy model. Initially, a novel PET dynamic output feedback controller is designed. Based on saving network resources and enhancing transmission efficiency, the PET strategy makes full use of relative and absolute triggering condition information. And the dynamic output feedback control can not only address unmeasurable states but also provide a better response to the internal information of the system. The random multiple communication delays and the ℓth-order Rice fading model with different channel coefficients, meanwhile, are both applied in the system. It is closer to the actual situation. Subsequently, new sufficient conditions of membership function dependence are proposed via the staircase function approximation method combined with Lyapunov stability. It guarantees that the system is exponentially mean square stable (EMSS) with H∞ performance. Ultimately, the presented results are validated using two examples. In the future, we will explore the correlative research of T–S fuzzy Markov jump NCSs.

Transfer reinforcement learning for multi‐agent pursuit‐evasion differential game with obstacles in a continuous environment

AbstractIn this paper, we study the multi‐pursuer single‐evader pursuit‐evasion (MSPE) differential game in a continuous environment with the consideration of obstacles. We propose a novel pursuit‐evasion algorithm based on reinforcement learning and transfer learning. In the source task learning stage, we employ the Q‐learning and value function approximation method to overcome the challenges posed by the large‐scale storage space required by the conventional Q‐table solution method. This approach expands the discrete space to the continuous space by value function approximation and effectively reduces the demand for storage space. During the target task learning stage, we utilize the Gaussian mixture model (GMM) to classify the source tasks. The source policies whose corresponding state‐value sets have the highest probability densities are assigned for the agent in the target task for learning. This methodology not only effectively avoids negative transfer but also enhances the algorithm's generalization ability and convergence speed. Through simulation and experiment, we demonstrate the algorithm's effectiveness.

Method of calculation of temperature parameters and service life of 10 kv cable lines

This study is based on the analysis of the methodology for calculating the temperature parameters of 10 kV cable lines and calculating the service life of insulation under various operating conditions, as well as identifying dependencies that allow the most accurate selection of cable parameters during operation at industrial facilities. The results of the study can be used to improve the energy efficiency of enterprises, and contribute to reducing the number of emergency failures of cable lines that may occur due to thermal breakdowns caused by incorrect choice of cable parameters under certain operating conditions, which may cause an increase in production costs in general. Conducting research and calculations of temperature parameters of cable lines at a voltage of 10 kV with different laying methods and with different capacity factors according to the climatology of the Republic of Tatarstan, as well as identifying key dependencies that will enable to draw appropriate conclusions on the operation of cables in the conditions under consideration. The article uses methods for calculating temperature parameters and cable service life, as well as methods for processing the data obtained as a result of calculations, including the method of function approximation. Special software is also used to visualize the results obtained after the calculations. The results of calculations of temperature parameters of 10 kV cable lines for various laying methods, with different types of insulation and with different capacity factors according to climatology of the Republic of Tatarstan are presented. Calculations of the service life of cable lines under the conditions under study have been made and conclusions have been drawn on optimal cable loads that will not lead to premature thermal aging of insulation under certain operating conditions. The initial data for the calculations and the methodology used comply with GOST standards for cable lines. The results of the study and the calculations performed can be used to evaluate and select the optimal load of cable lines under selected conditions at the design stage of power supply systems.

A 0–1 linear relaxation and stochastic approximation method for real-time pricing in a smart grid with non-convex constraints

In this article, real-time pricing (RTP) for a smart grid with complicated non-convex and/or non-smooth constraints is explored. First, piecewise linear functions are adopted to approximate any kinds of utility function and RTP is formulated into bilevel non-convex programming. Then, a 0–1 relaxation method is used to linearize sparse constraints and piecewise linear utility functions, to obtain mixed integer linear programming. Finally, a distributed simultaneous perturbation stochastic approximation (DSPSA) method is designed to solve the bilevel non-convex programming. The RTP strategy is generalizable because sparse constraints and non-differentiable and/or non-concave utility functions are widespread in practice, and the piecewise linear functions approximation method is applicable to all kinds of utility function, not just to non-smooth and/or non-concave utility functions. In addition, the 0–1 linear relaxation and stochastic approximation method make the bilevel non-convex programming easily solvable by DSPSA, which converges rapidly while maintaining the high accuracy of solutions.

Doping effect on electronic and magnetic properties of Ag-doped single-walled (6,0) GaN nanotubes: First-principles study

The electronic and magnetic properties of GaN wurtzite, un-doped, and Ag-doped single-walled (6,0) chiral GaN nanotubes (SWGaNNT) were investigated using Density Functional Theory and Local Spin Density Approximation methods within Hubbard U semiempirical correction (DFT-LSDA + U). In a consecutive DFT-LSDA + U electronic structure simulation, the effects of defects on the nature and origin of ferromagnetism (FM) are studied for an Ag-doped SWGaNNT system. For the Ag-doped GaN nanotube configurations, the energy gap decreases with increasing concentration of impurity. The total energy calculations for doped systems show the stability of the ferromagnetic phase. In the case of the Ag-doping GaN NT system, the wide energy gap is decreasing and the total magnetic moment of this system is ∼2.0 μB. From first-principles calculations, an Ag-doped GaN nanosystem can be made into a magnetic ferromagnetic material, and it is an important candidate for spintronics device applications.

Node-bound communities for partition of unity interpolation on graphs

Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based on the underlying graph structure, employing an algorithm that relies exclusively on centrality measures and modularity, without requiring the input of the number of subdomains. Subsequently, we integrate PUMs with a local graph basis function (GBF) approximation method to develop cost-effective global interpolation schemes. We also discuss numerical experiments conducted on both synthetic and real datasets to assess the performance of this presented technique.

Radial Basis Functions Approximation Method for Time-Fractional FitzHugh–Nagumo Equation

In this paper, a numerical approach employing radial basis functions has been applied to solve time-fractional FitzHugh–Nagumo equation. Spatial approximation is achieved by combining radial basis functions with the collocation method, while temporal discretization is accomplished using a finite difference scheme. To evaluate the effectiveness of this method, we first conduct an eigenvalue stability analysis and then validate the results with numerical examples, varying the shape parameter c of the radial basis functions. Notably, this method offers the advantage of being mesh-free, which reduces computational overhead and eliminates the need for complex mesh generation processes. To assess the method’s performance, we subject it to examples. The simulated results demonstrate a high level of agreement with exact solutions and previous research. The accuracy and efficiency of this method are evaluated using discrete error norms, including L2, L∞, and Lrms.

Piecewise reconstruction of membership function approximation errors for Takagi–Sugeno fuzzy control

We propose a conservative relaxed control method to stabilize Takagi–Sugeno (TS) fuzzy systems. First, a conventional piecewise linear function approximation method is adopted to consider the membership functions’ information in the closed-loop system’s stability analysis. Subsequently, a model reconstruction method is proposed to reformulate linear approximation error terms in the TS fuzzy form, which can effectively introduce more information into stability conditions and achieve better robust control effects. Then, based on a fuzzy Lyapunov function approach, control design conditions are derived in terms of linear matrix inequalities, with less conservatism for related results in the literature. Finally, via a benchmark experiment, it is verified that the proposed method can show better robustness with fewer decision variables in robust convex conditions.

Bayesian approach for radial kernel parameter tuning

In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In particular, we propose a statistical technique, called Bayesian optimization, that consists in modeling the error function with a Gaussian process, by which, through an iterative process, the optimal shape parameter is selected. The process is step by step self-updated resulting in a relevant decrease in search time with respect to the classical leave one out cross validation technique. Numerical results deriving from some test examples and an application to real data show the performance of the proposed method.

A Policy Gradient Algorithm to Alleviate the Multi-Agent Value Overestimation Problem in Complex Environments

Multi-agent reinforcement learning excels at addressing group intelligent decision-making problems involving sequential decision-making. In particular, in complex, high-dimensional state and action spaces, it imposes higher demands on the reliability, stability, and adaptability of decision algorithms. The reinforcement learning algorithm based on the multi-agent deep strategy gradient incorporates a function approximation method using discriminant networks. However, this can lead to estimation errors when agents evaluate action values, thereby reducing model reliability and stability and resulting in challenging convergence. With the increasing complexity of the environment, there is a decline in the quality of experience collected by the experience playback pool, resulting in low efficiency of the sampling stage and difficulties in algorithm convergence. To address these challenges, we propose an innovative approach called the empirical clustering layer-based multi-agent dual dueling policy gradient (ECL-MAD3PG) algorithm. Experimental results demonstrate that our ECL-MAD3PG algorithm outperforms other methods in various complex environments, demonstrating a remarkable 9.1% improvement in mission completion compared to MADDPG within the context of complex UAV cooperative combat scenarios.

Second virial coefficient, Boyle temperature and equation of state of van Hove fluids with a downward concavity attractive parabolic-well

The second virial coefficient, the Boyle temperature and the equation of state of van Hove fluids with a relatively short ranged attractive parabolic-well of downward concavity are considered. The analytic second virial coefficient for this fluid is obtained explicitly and it is used to compute the Boyle temperature of the fluid as a function of the range of the potential. Further, an equation of state is derived using the second-order thermodynamic perturbation theory of Barker and Henderson in the macroscopic compressibility approximation, with the hard-sphere fluid being the reference fluid. For this latter we profit from the fully analytical expression of the radial distribution function, consistent with the Carnahan-Starling equation state, derived within the so-called rational function approximation method up to a range twice the size of the hard-core diameter. The results for the reduced pressure of the fluid as a function of the packing fraction and two values of the range of the potential well at different temperatures are compared with Monte Carlo simulation data. Estimates of the values of the critical temperature are also provided.

Adaptive fault-tolerant fixed-time cruise control for virtually coupled train set

In the cruise control of the virtual coupled train set (VCTS), the control algorithm with high stability, high accuracy, and fast convergence speed is the basic requirement for the smooth and efficient operation of the VCTS. To this end, this paper studies the problem of fixed-time cruise control for VCTS. To begin with, by analyzing the dynamic evolution of the VCTS in an actual environment, a second-order VCTS train-following dynamic model is formulated with considering actuator faults, uncertain resistance, unknown disturbances, and control input saturation. Then, an improved barrier functions-based fixed-time sliding model control method is proposed to deal with the state constraints (i.e., safe distance and speed limit). To deal with parametric uncertainty, adaptive fault-tolerant control and core function technologies are integrated into the same framework. Furthermore, by using a function approximation method to handle the control input saturation, an adaptive fault-tolerant fixed-time cruise controller is designed which not only guarantees the fixed-time stability of the VCTS but also copes with parametric uncertainty, state constraints, and input saturation. Finally, the effectiveness of the proposed method is validated in simulation analysis.

N-Oktanol karışımlarıyla çalışan bir dizel motorun ısı yayılımı oranının değişimi için yeni matematiksel korelasyonlar: Sayısal, deneysel ve karşılaştırmalı bir analiz

The current literature reports a few papers regarding the prediction of heat release rate of a diesel engine fuelled with n-octanol blends using numerical methods. To address this gap, the main objective of presented study is to derive new correlations for estimating the variation in heat release rate of a diesel engine fuelled with diesel fuel and diesel fuel-biodiesel-n-octanol blends. For this purpose, three different ternary blends were prepared by varying the n-octanol concentration to 6% (OCT6), 8% (OCT8), and 10% (OCT10) by volume. The estimation of heat release rate was accomplished using the least-squares regression (sine, piecewise, and rational equations) and the function approximation (Padé approximation) methods. The ignition delay and peak heat release rate increased by 3.8462%, 5.9501% for OCT6; 7.6923%, 3.7125% for OCT8; and 8.9744%, 3.0755% for OCT10, respectively, compared to diesel fuel. The peak cylinder pressure of OCT6 and OCT8 was observed to be higher by 2.4378% and 1.3982%, respectively, whereas that of OCT10 is found to be lower by 1.9458%, compared to diesel fuel. Compared to the others, the suggested rational equation qualitatively and quantitatively achieved the best correlation with all experimental heat release rate data measured by both the author and some other authors.

Modeling and Experimental Study of a Water Solar Collector Coupled to Optimized Solar Water Still

This work presented the modeling and the experimental study of a water solar collector coupled with an optimized solar still developed in order to boost fresh water produced in a solar distillation system. The desalination process is currently operated under the climatological conditions of Sfax, Tunisia. To numerically simulate the water solar collector, we developed a dynamic model based on heat and mass transfer from the water solar collector. The obtained set of ordinary differential equations was converted to a set of algebraic system of equations by the functional approximation method of orthogonal collocation. The aim of this study was to present the mathematical model and experimental study of this water solar collector

Predicting wing-pylon-nacelle configuration flutter characteristics using adaptive continuation method

In this study, the aeroelastic response of a wing-pylon-nacelle system in subsonic and low supersonic flow regimes is analyzed using the continuation method in conjunction with an adaptive step size control algorithm. Idealizing the pylon and nacelle as a point mass, the computed effects of a standard structural analysis of the wing together with the pylon and nacelle are compared with those of a clean wing to build a reduced-order model for analysis. The aerodynamic forces relating to different reduced frequencies are assessed using the Doublet Lattice Method (DLM) in the subsonic flow regime and supersonic lifting surface theory relying on the unsteady linearized small-disturbance potential flow model in the low supersonic flow regime. The Rational Function Approximation (RFA) method is then utilized for the state-space formulation of the system equations, appended with the continuation method for flutter prediction. Thereafter, the linearized aeroelastic equations are resolved using the continuation method with adaptive step size, the results of which are matched with those obtained from the traditional p-k method to emphasize that the continuation method exhibits a distinct advantage in achieving better accuracy in estimating the flutter speed and identifying the “mode switching” phenomenon.

Solution for Pursuit-Evasion Game of Agents by Adaptive Dynamic Programming

The paper studies a novel method for real-time solutions of the two-player pursuit-evasion game. The min-max principle is adopted to confirm the Nash equilibrium of the game. As agents in the game can form an Internet of Things (IoT) system, the real-time control law of each agent is obtained by taking a linear-quadratic cost function in adaptive dynamic programming. By introducing the Lyapunov function, we consider the scenario when capture occurs. Since most actual systems are continuous, the policy iteration algorithm is used to make the real-time policy converge to the analytical solution of the Nash equilibrium. Furthermore, we employ the value function approximation method to calculate the neural network parameters without directly solving the Hamilton–Jacobi–Isaacs equation. Simulation results depict the method’s feasibility in different scenarios of the pursuit-evasion game.

Physics-guided identification of Euler–Bernoulli beam PDE model from full-field displacement response with SimultaNeous basis function Approximation and Parameter Estimation (SNAPE)

Full-field measurements of the continuous spatiotemporal response of the physical processes such as structural vibration or fluid flow generate large datasets. In many scientific fields, such continuous spatiotemporal dynamic models are represented by partial differential equations (PDEs). In the past, attempts have been made to identify the PDE models from the measured response by inferring its parameters by the use of either regression or deep learning-based techniques. But the previously presented regression-based methods fail to estimate the parameters of the higher-order PDE models in the presence of moderate noise. Likewise, the deep learning-based methods lack the much-needed property of repeatability and robustness in the identification of PDE models from the measured response. The authors introduced the method of SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE) in a recent paper which addresses such drawbacks by fitting basis functions to the measured response and simultaneously infer the parameters of the PDE model. In this paper the theory and formulation of SNAPE is presented to perform physics-guided identification of the Euler–Bernoulli beam PDE model which is widely applied in the modeling of large scale infrastructures to nanoscale structures.The domain knowledge of the physics is used as a constraint in the formulation of the optimization framework. The alternating direction method of multipliers (ADMM) algorithm is used to simultaneously optimize the loss function over the parameter space of the PDE model and coefficient space of the basis functions. The proposed method not only infers the parameters but also estimates a continuous function that approximates the solution to the PDE model. The efficacy of the method is both numerically and experimentally validated on noise corrupted full-field vibration response. The method neither requires the knowledge of the initial or boundary conditions of the beam nor comprises of model discretization error as in the case of finite element model updating. SNAPE demonstrates its applicability on various homogeneous and time-varying nonhomogeneous boundary conditions.