An adaptive wavelet network for function learning

In this article, a wavelet neural network (WNN) model is proposed for approximating arbitrary nonlinear functions. Our WNN model structure comes from the idea of adaptive neuro-fuzzy inference system (ANFIS) which is used for obtaining fuzzy rule base from the input–output data of an unknown function. The WNN model which is called in this study as adaptive wavelet network (AWN) consists of wavelet scaling functions in its processing units whereas in an ANFIS, mostly Gaussian-type membership functions are used for a function approximation. We present to train an AWN by a hybrid-learning method containing least square estimation (LSE) with gradient-based optimization algorithm to obtain the optimal translation and dilation parameters of our AWN for model accuracy. Simulation examples are also given to illustrate the effectiveness of the method.     

二进离散小波神经网络在传感器逆向建模中的应用

给出了快速收敛的离散二进小波神经网络的初始化,构造和权值确定的详细方法。并将这类小波神经网络应用于传感器的非线性校正,并给出了仿真实验结果。相对使用随机贪心算法训练的神经网络,快速收敛小波神经网络利用离散二进小波变换的便利,采用启发式的构造算法;具有构造过程复杂度低,构造完成后高度接近目标模型,训练次数少,并可有效避免陷入局部极小点的优点。有效解决了小波神经网络尺度和平移系数在训练时需对小波函数进行求导而影响网络收敛速度的问题。     

Wavelet Neural Network for Corrections Prediction in Single-Frequency GPS Users

Accurate and reliable position determination is a vital component in Global Positioning System (GPS). GPS positioning errors occur from the cumulative effects of receiver, satellite and atmosphere, and also due to the U.S. military intentionally such as Selective Availability (SA). In order to improve the accuracy of positions provided by GPS additional correction information may be used, such as Differential GPS (DGPS) or other sensors to enhance position reliability. The DGPS has the problem of slow updates. To overcome this limitation, DGPS corrections prediction has been proposed. The ability of Neural Networks (NNs) to discover nonlinear relationships in input data makes them ideal for modeling nonlinear dynamic systems. The Wavelet Neural Network (WNN) employing nonlinear wavelet basis function, which are localized in both the time and frequency space, has been developed as an alternative approach to nonlinear fitting problem. Particle Swarm Optimization (PSO), a global optimization method, is used to train the WNN. In this paper, a WNN trained by a PSO algorithm is proposed for DGPS corrections prediction in single-frequency GPS receivers. Experimental results show the feasibility and effectiveness of the proposed method. The results are analyzed and compared with WNN trained by Back Propagation (BP) algorithm. The experimental results show that WNN, trained by the PSO algorithm, is able to reduce RMS errors to less than 1 m with SA on and 0.6 m with SA off.     

GPS orbit approximation using radial basis function networks

We present solutions for GPS orbit computation from broadcast and precise ephemerides using a group of artificial neural networks (ANNs), i.e. radial basis function networks (RBFNs). The problem of broadcast orbit correction, resulting from precise ephemerides, has already been solved using traditional polynomial and trigonometric interpolation. As an alternative approach RBFN broadcast orbit correction produces results within the accuracy range of the traditional methods. Our study shows RBFN broadcast orbit correction performs well also near the end of data intervals and for short data spans (～20 min). Regarding limitations of polynomial and trigonometric extrapolation, the most significant advantage of using RBFNs over the traditional methods for GPS broadcast orbit approximation arises from its short time prediction capability.     

A genetic algorithm with memory for mixed discrete-continuous design optimization

This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.     

离散过程神经网络在时间序列预测中的应用

为解决复杂时间序列的预测问题,针对目前过程神经网络的输入为多个连续的时变函数,而许多实际问题的输入为多个序列的离散值,提出一种基于离散输入的过程神经网络模型及学习算法;并以太阳黑子数实际数据为例对太阳黑子数时间序列进行预测,仿真结果表明该模型具有很好的逼近和预测能力。     

Computational Methods for Verification of Stochastic Hybrid Systems

Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finite-difference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.     

多项式求解的OFDM连续信号的峰均比估计算法

在OFDM信号中峰均比估计问题中,通常采用过采样的离散信号来逼近连续信号,用离散信号的峰均比来近似连续信号的峰均比。在基本过采样公式的基础上,研究了末尾补零的IFFT和中间补零的IFFT两种常用的插值过采样算法的数学关系,比较了这两种方法对于连续信号的逼近性能。同时为得到更精确的PAPR值,通过将非线性方程的求根转化为多项式方程求解,设计一种直接针对连续信号高效峰均比估计算法。仿真结果表明,这种新的估计算法是精确而有效的。     

基于节点生长k-均值聚类算法的强化学习方法

处理连续状态强化学习问题,主要方法有两类:参数化的函数逼近和自适应离散划分.在分析了现有对连续状态空间进行自适应划分方法的优缺点的基础上,提出了一种基于节点生长k均值聚类算法的划分方法,分别给出了在离散动作和连续动作两种情况下该强化学习方法的算法步骤.在离散动作的MountainCar问题和连续动作的双积分问题上进行仿真实验.实验结果表明,该方法能够根据状态在连续空间的分布,自动调整划分的精度,实现对于连续状态空间的自适应划分,并学习到最佳策略.     

The identification of electric load simulator for gun control systems based on variable-structure WNN with adaptive differential evolution

Owing to the complex nonlinearities of the electric load simulator (ELS) for the gun control system (GCS), the surplus torque plays a great negative impact on the performance of the loading system. This paper proposes a variable-structure wavelet-neural-network (VSWNN) identification strategy based on adaptive differential evolution (ADE). First of all, a mathematical model is established based on the structure and the working principle of the ELS. Then an intelligent identification method is applied, where the wavelet function is chosen as the excitation function, which improves the generalization and approximation ability of the neural network. The ADE is used to optimize the parameters, which solves the difficulty of determining the structure of the WNN. In order to reduce the computation complexity and speed up the convergence of the identification system, the adaptive laws of the pitch adjusting rate (PAR), band width (BW) and variable numbers of neurons are proposed. Finally, a pseudo random multilevel signal and a linear frequency modulation signal are chosen as input signals for the hardware-in-the-loop simulation. The test results show that the proposed ADE-VSWNN algorithm has superior validity and practicability, especially when the identification algorithm is used in the working circumstances with different inertial torque. Further, the high precision and strong robustness of the identification algorithm are further verified.     

基于小波网络的BP算法改进研究

对BP算法的特点进行了分析,在权值平衡算法的基础上,应用小波网络对其进行改造,提出了基于小波网络的BP权值平衡算法,给出了具体的算法步骤,仿真结果证明该算法既具有BP网络的简捷性,又能够提高学习速度和精度,避免了BP网络易出现的收敛速度慢、易产生局部最优解的问题,是一种较好的神经网络学习算法。     

基于GNSS的建筑塔机垂直度全圆智能检测

鉴于传统经纬仪测量方法检测塔机垂直度存在诸多弊端,提出一种基于全球卫星导航系统（Global navigation satellite system,GNSS)的建筑塔机垂直度全圆智能检测技术。基于GNSS的动态检测模型,设计一种建筑塔机垂直度全圆智能检测方法,并基于Visual Studio 2017平台,利用C#编程语言,设计并开发一种基于GNSS的建筑塔机垂直度全圆智能检测系统(GNSS-based verticality intelligent detection system in rounds, GNSS_VDS)。实验结果表明：GNSS_VDS系统全圆智能检测水平精度优于3 cm、高程精度优于4 cm,本文算法是行之有效的,可为建筑塔机抗倾翻稳定性实时监测提供一种高精度智能化解决方案。     

SSUKF-WNN算法及其在飞行器气动力建模中的应用

针对传统小波网络算法的不足,提出一种基于改进无迹Kalman滤波(UKF)的小波网络算法.该算法使用一种基于简化球形分布Sigma点的UKF(SSUKF)来训练小波网络的参数,以提高小波网络的学习性能和训练质量.飞行器气动力建模算例表明,相对于BP算法和EKF算法,SSUKF算法训练的小波网络收敛速度更快,估计精度更高,计算量更小.同时也为飞行器的气动力建模提供了一种有效可行的手段.     

基于WNN的BP算法的多传感器数据融合研究

小波神经网络（WNN）是将小波理论和神经网络理论结合起来的一种神经网络,有较强的函数学习能力和推广能力及广阔的应用前景。采用基于WNN的BP权值平衡算法对多传感器测量的结果进行特征级的数据融合,融合结果提供给决策级判断。该融合算法避免了BP网络收敛速度慢,易产生局部最优解等缺点,提高了学习的速度、精度。仿真结果表明了该方法的有效性。     

Interval analysis based robust truss optimization with continuous and discrete variables using mix-coded genetic algorithm

The problem of optimizing truss structures in the presence of uncertain parameters considering both continuous and discrete design variables is studied. An interval analysis based robust optimization method combined with the improved genetic algorithm is proposed for solving the problem. Uncertain parameters are assumed to be bounded in specified intervals. The natural interval extensions are employed to obtain explicitly a conservative approximation of the upper and lower bounds of the structural response, and hereby the bounds of the objective function and the constraint function. This way the uncertainty design may be performed in a very efficient manner in comparison with the probabilistic analysis based method. A mix-coded genetic algorithm (GA), where the discrete variables are coded with binary numbers while the continuous variables are coded with real numbers, is developed to deal with simultaneously the continuous and discrete design variables of the optimization model. An improved differences control strategy is proposed to avoid the GA getting stuck in local optima. Several numerical examples concerning the optimization of plane and space truss structures with continuous, discrete or mixed design variables are presented to validate the method developed in the present paper. Monte Carlo simulation shows that the interval analysis based optimization method gives much more robust designs in comparison with the deterministic optimization method.     

A quasi-Newton method for unconstrained non-smooth problems

We present a method, based on a variational problem, for solving a non-smooth unconstrained optimization problem. We assume that the objective function is a Lipschitz continuous and a regular function. In this case the function of our variational problem is semismooth and a quasi-Newton method may be used to solve the variational problem. A convergence theorem for our algorithm and its discrete version is also proved. Preliminary computational results show that the method performs quite well and can compete with other methods.     

Discrete approximation of multivariate densities with application to Bayesian estimation

A procedure is presented for finding a discrete approximation to a continuous multivariate density function. It is based on a previously developed algorithm [2] for determining the L₁ optimal discrete approximation to a univariate density. Results of approximating continuous bivariate density functions, which represent distributions of the parameters of a pharmacokinetic model, show good agreement between the mean and covariance matrix of the approximated and approximating densities. The distribution of a predicted drug conceptration was also calculated using a continuous density and discrete approximations with both 25 and 81 points. The expected values of the predicted concentration, as well as selected percentile points, obtained using each density are in close agreement.     

基于遗传小波神经网络的冷轧轧制力预报研究

依据小波函数的非线性逼近能力和神经网络的自学习特性，提出一种适合高维输入的小波神经网络建模方法，这种网络结构类似于多层感知器，不同的是隐层神经元的激励函数为小波基函数．为使小波神经网络具有更高的学习精度和更快的收敛速度，将遗传算法、小波神经网络和梯度下降算子结合起来，提出一种遗传小波神经网络．将该网络应用于冷轧轧制力的预报，仿真结果表明预报精度大为提高．     

基于强化学习的海洋移动观测网络观测路径规划方法

合理有效地对移动海洋环境观测平台进行规划,有利于海洋环境观测网络的设计和海洋环境信息的采集.针对庞大的海洋环境,在有限的观测资源下,使用深度强化学习算法对海洋环境观测网络进行规划.针对强化学习算法求解路径规划问题中的离散和连续动作设计问题,分别使用DQN和DDPG两种算法对该问题进行单平台和多平台实验,实验结果表明,使...     

基于法矢控制的B样条曲面逼近的PIA方法

提出了一种基于法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)算法。一方面该方法将离散数据点的切失、曲率、法矢等几何特征充分应用到离散数据点的逼近问题上,利用数据点两个方向的切矢构造出数据点的法矢约束来控制逼近曲面形状,相比于无法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)方法,逼近曲面更光顺,可获得更好的逼近效果。另一方面由于该算法选取主特征点作为控制顶点,所以允许在曲面拟合中控制顶点的数目小于数据点的数目。而且PIA算法的每次迭代过程中的各个步骤都是独立的,很容易被应用到并行计算上,可提高计算效率。本文还给出了一些实例来验证该算法的有效性。