Optimal Smoothing Research Articles

Data mining and application of ship impact spectrum acceleration based on PNN neural network

The selection of the smoothing coefficient of the probabilistic neural network directly affects the performance of the network. Traditionally, all the mode layer neurons use a uniform smoothing coefficient, and then the optimal smoothing parameters suitable for this problem are searched by the optimization algorithm. In this study, the smoothing coefficients of the mode layer neurons connected by the same summation layer are set to the same value, which not only reflects the relationship between the training samples of the same pattern, but also highlights the difference between the training samples of different modes. Two probabilistic neural network models are applied to the ship impact environment prediction respectively. The results show that the classification effect of multiple smoothing factors is further improved than the single smoothing factor network.

Efficient nonlinear optimal smoothing and sampling algorithms for complex turbulent nonlinear dynamical systems with partial observations

A nonlinear optimal smoother and an associated optimal strategy of sampling hidden model trajectories are developed for a rich class of complex nonlinear turbulent dynamical systems with partial and noisy observations. Despite the strong nonlinearity and the significant non-Gaussian characteristics in the underlying systems, both the optimal smoother estimates and the sampled trajectories can be solved via closed analytic formulae. Thus, they are computationally efficient and the methods are applicable to high-dimensional systems. The nonlinear optimal smoother is able to estimate the hidden model states associated with various non-Gaussian phenomena and is particularly skillful in capturing the onset, demise and amplitude of the observed and hidden extreme events. On the other hand, the sampled hidden trajectories succeed in recovering both the dynamical and statistical features of the underlying nonlinear systems, including the fat-tailed non-Gaussian probability density function and the temporal autocorrelation function. In the situations with only a short period of partially observed training time series, the optimal sampling strategy can be used to efficiently create a sufficient number of samples in an unbiased fashion that facilitates an accurate prediction of important non-Gaussian features in both the observed and hidden variables. In addition, the information provided by the sampled trajectories based on imperfect models allows an effective way of quantifying the model error. It also offers a systematic approach to improve approximate models and stochastic parameterizations in highly non-Gaussian systems and thus advances the real-time forecasts.

Event classification using improved salp swarm algorithm based probabilistic neural network in fiber-optic perimeter intrusion detection system

Abstract To remarkably upgrade the performance of the intrusion detection system based on single-mode—multimode—single-mode (SMS) fiber structure which can effectively discriminate man-made event and natural event in zone perimeter, a novel event classification approach is presented in this paper. Firstly, the original intrusion signal is decomposed by the filter bank into four frequency channels with an interval of 11745 Hz. Then, the singular value and kurtosis extracted from each frequency channel as combinations of eigenvectors, being transferred to the probabilistic neural network (PNN) for training and classification. Finally, the weight factor and adaptive mutation operator are embedded in the salp swarm algorithm (SSA), which is utilized to optimize and search for the optimal smoothing factor of the PNN classifier and compared with the other four metaheuristic (MH) algorithms under five algorithm performance evaluation metrics. Large practical experiments exhibit that the presented scheme can accurately recognize man-made events (knocking, rattling) and natural events (wind, rain) respectively, shedding light on the feasibility and applicability of SMS fiber structure in zone perimeter.

Prediction of gas emission based on grey-generalized regression neural network

Coal mine gas is one of the main factors endangering mine safety in China, and the amount of gas emission is affected by a variety of related factors, which have the characteristics of non-linearity and uncertainty. In order to predict gas emission more quickly and accurately, a coupling algorithm of grey theory (GM (1,1) and generalized regression neural network (GRNN) is proposed. Thirteen parameters, such as coal seam gas content, depth and GM (1,1) gas emission prediction value, are used as input of the model. The input parameters are normalized and used as training and testing samples of the model. The 10 fold cross validation and minimum root mean square error (RMSE) are used to find the optimal smoothing factor (spread), then a non-linear prediction model of gas emission is established. The gas monitoring data of Qianjiaying Mining Area of Kailuan Mining Group from May 2007 to December 2008 are used in the experiment. The results show that the model has a great improvement in convergence speed and a good accuracy, which can provide theoretical basis for the prevention and control of coal mine gas disasters.

Flattened aggregate function method for nonlinear programming with many complicated constraints

In this paper, efforts are made to solve nonlinear programming with many complicated constraints more efficiently. The constrained optimization problem is firstly converted to a minimax problem, where the max-value function is approximately smoothed by the so-called flattened aggregate function or its modified version. For carefully updated aggregate parameters, the smooth unconstrained optimization problem is solved by an inexact Newton method. Because the flattened aggregate function can usually reduce greatly the amount of computation for gradients and Hessians, the method is more efficient. Convergence of the proposed method is proven and some numerical results are given to show its efficiency.

A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization

Nonlinear conjugate gradient methods are among the most preferable and effortless methods to solve smooth optimization problems. Due to their clarity and low memory requirements, they are more desirable for solving large-scale smooth problems. Conjugate gradient methods make use of gradient and the previous direction information to determine the next search direction, and they require no numerical linear algebra. However, the utility of nonlinear conjugate gradient methods has not been widely employed in solving nonsmooth optimization problems. In this paper, a modified nonlinear conjugate gradient method, which achieves the global convergence property and numerical efficiency, is proposed to solve large-scale nonsmooth convex problems. The new method owns the search direction, which generates sufficient descent property and belongs to a trust region. Under some suitable conditions, the global convergence of the proposed algorithm is analyzed for nonsmooth convex problems. The numerical efficiency of the proposed algorithm is tested and compared with some existing methods on some large-scale nonsmooth academic test problems. The numerical results show that the new algorithm has a very good performance in solving large-scale nonsmooth problems.

Semi-supervised optimal recursive filtering and smoothing in non-Gaussian Markov switching models

Filtering and smoothing in switching state-space models are important in numerous applications. The classic family of conditionally Gaussian linear state space models (CGLSSMs) is a natural extension of the Gaussian linear system by introducing its dependence on switches. In spite of their simplicity, recursive filtering and smoothing are no longer feasible in CGLSSMs and approximate methods must be used. Conditionally Markov switching hidden linear models (CMSHLMs) are alternative models which allow recursive optimal exact filtering and smoothing. We introduce an original family of CMSHLMs defined with copulas and we address the problem of their identification. The proposed identification method chooses a model in a family of admissible parametric models and estimates the parameters. It is applied to a learning sample containing observations and states, while the switches are unknown. The interest of the proposed ”semi-unsupervised” filtering and smoothing is validated via experiments on simulated data.

Inverse identification strategies for the characterization of transformation-based anisotropic plasticity models with the non-linear VFM

The Virtual Fields Method (VFM) is a well established inverse technique used to identify the constitutive parameters of material models using heterogeneous full-field strain data. When VFM is employed to retrieve the coefficients of advanced plasticity models, including non linear hardening and anisotropy, however, the procedure may become computationally intensive. Furthermore, the impact of experimental uncertainties is still not entirely scrutinized. In this paper, an identification strategy based on uncoupling the hardening behaviour and the anisotropic yield function is proposed. The approach, based on VFM, allows to carry on the identification with low computational time, and provides also indications on the optimal smoothing level to use in the full-field measurement.The identification framework is applied on the linear transformation-based yield condition Yld2000-2D, employing numerical data for the validation and, afterwards, using actual experimental data on a bake-hardenable steel, i.e. BH340. Moreover, several aspects of the identification procedure are investigated in dept, namely, the effect of smoothing, the influence of VFM settings (type of virtual fields used, discretization method) and the computational time. The identification results are compared with the standard calibration process, demonstrating that the proposed strategy is capable of identifying properly the material anisotropic behaviour using only three tests on notched specimens.

Contracting Proximal Methods for Smooth Convex Optimization

In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a regularization term in the form of Bregman divergence. We provide global convergence analysis for a general scheme admitting inexactness in solving the auxiliary subproblem. In the case of using for this purpose high-order tensor methods, we demonstrate an acceleration effect for both convex and uniformly convex composite objective functions. Thus, our construction explains acceleration for methods of any order starting from one. The augmentation of the number of calls of oracle due to computing the contracted proximal steps is limited by the logarithmic factor in the worst-case complexity bound.

On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods

This paper studies the class of nonsmooth nonconvex problems in which the difference between a continuously differentiable function and a convex nonsmooth function is minimized over linear constraints. Our goal is to attain a point satisfying the stationarity necessary optimality condition, defined as the lack of feasible descent directions. Although elementary in smooth optimization, this condition is nontrivial when the objective function is nonsmooth, and, correspondingly, there are very few methods that obtain stationary points in such settings. We prove that stationarity in our model can be characterized by a finite number of directions and develop two methods, one deterministic and one random, that use these directions to obtain stationary points. Numerical experiments illustrate the benefit of obtaining a stationary point and the advantage of using the random method to do so.

Using singular spectrum analysis for inference on seasonal time series with seasonal unit roots

The problem of optimal linear filtering, smoothing and trend extraction for m-period differences of processes with a unit root is studied. Such processes arise naturally in economics and finance, in the form of rates of change (price inflation, economic growth, financial returns) and finding an appropriate smoother is thus of immediate practical interest. The filter and resulting smoother are based on the methodology of singular spectrum analysis (SSA). An explicit representation for the asymptotic decomposition of the covariance matrix is obtained. The structure of the impulse and frequency response functions indicates that the optimal filter has a 'permanent' and a 'transitory component', with the corresponding smoother being the sum of two such components. Moreover, a particular form for the extrapolation coefficients that can be used in out-of-sample prediction is proposed. In addition, an explicit representation for the filtering weights in the context of SSA for an arbitrary covariance matrix is derived. This result allows one to examine the specific effects of smoothing in any situation. The theoretical results are illustrated using different datasets, namely US inflation and real GDP growth.

Using singular spectrum analysis for inference on seasonal time series with seasonal unit roots

The problem of optimal linear filtering, smoothing and trend extraction for m-period differences of processes with a unit root is studied. Such processes arise naturally in economics and finance, in the form of rates of change (price inflation, economic growth, financial returns) and finding an appropriate smoother is thus of immediate practical interest. The filter and resulting smoother are based on the methodology of singular spectrum analysis (SSA). An explicit representation for the asymptotic decomposition of the covariance matrix is obtained. The structure of the impulse and frequency response functions indicates that the optimal filter has a 'permanent' and a 'transitory component', with the corresponding smoother being the sum of two such components. Moreover, a particular form for the extrapolation coefficients that can be used in out-of-sample prediction is proposed. In addition, an explicit representation for the filtering weights in the context of SSA for an arbitrary covariance matrix is derived. This result allows one to examine the specific effects of smoothing in any situation. The theoretical results are illustrated using different datasets, namely US inflation and real GDP growth.

Adaptive Fading Bayesian Unscented Kalman Filter and Smoother for State Estimation of Unmanned Aircraft Systems

This paper proposes an adaptive fading Bayesian unscented Kalman filter (AF-BUKF) and explores its application for state estimation of unmanned aircraft systems (UASs). In the AF-BUKF, the state and noise densities are approximated as finite Gaussian mixtures, in which the mean and covariance for each component are recursively estimated using the UKF. To avoid the prohibitive computational complexity caused by the exponential growth of mixture components, a Gaussian mixture simplification algorithm is employed. Moreover, the AF-BUKF algorithm employs a novel adaptive fading strategy to recursively update the Gaussian components, so that the adverse effect of inexact knowledge of the state and measurement noise covariance can be mitigated. An AF-BUK Smoother (AF-BUKS) is also proposed by extending the AF-BUKF algorithm using the concept of optimal Bayesian smoothing and the Rauch-Tung-Striebel Smoother to improve estimation accuracy. Experimental results on simulated and real UAS data show that the proposed AF-BUKF/S algorithms can achieve better performance compared with the conventional methods. Thus, they can serve as attractive alternative approaches for nonlinear state estimation of UASs and other problems.

Second-Order Guarantees of Distributed Gradient Algorithms

We consider distributed smooth nonconvex unconstrained optimization over net- works, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned distributed gradient descent algorithm likely converges to a neighborhood of a second-order stationary (SoS) solution; and (ii) the more recent class of distributed algorithms based on gradient tracking---implementable also over digraphs---likely converges to exact SoS solutions, thus avoiding (strict) saddle points. Furthermore, new convergence rate results for first-order critical points is established for the latter class of algorithms.

A Computation Approach to Chance Constrained Optimization of Boundary-Value Parabolic Partial Differential Equation Systems

Abstract This work studies chance constrained optimization of boundary-value parabolic partial differential equations (CCPDE) with random data, where the PDE model is treated as equality constraint and chance constraints are imposed on inequality constraints involving state variables. Since such a CCPDE problem is generally non-smooth, non-convex and difficult to solve directly, we use our recently proposed smoothing approximation method to solve the problem. As a result, the probability function of the chance constraints is approximated in two different ways by a family of differentiable functions. This leads to two smooth parametric optimization problems IAτ and OAτ, where the feasible sets of IAτ are always subsets (inner approximation) and the feasible sets of OAτ always supersets (outer approximation). The feasible sets of IAτ (resp. OAτ ) converge asymptotically to the feasible set of the CCPDE. Moreover, any limit point of a sequence of optimal solutions of IAτ (resp. OAτ ) is a stationary point of CCPDE. The viability of the approximation approach is numerically demonstrated by optimal thermal cancer treatment as a case study.

Decentralized Accelerated Gradient Methods With Increasing Penalty Parameters

In this article, we study the communication, and (sub)gradient computation costs in distributed optimization. We present two algorithms based on the framework of the accelerated penalty method with increasing penalty parameters. Our first algorithm is for smooth distributed optimization, and it obtains the near optimal $O(\sqrt{\frac{L}{\epsilon (1-\sigma _2(W))}}\log \frac{1}{\epsilon })$ communication complexity, and the optimal $O(\sqrt{\frac{L}{\epsilon }})$ gradient computation complexity for $L$ -smooth convex problems, where $\sigma _2(W)$ denotes the second largest singular value of the weight matrix $W$ associated to the network, and $\epsilon$ is the target accuracy. When the problem is $\mu$ -strongly convex, and $L$ -smooth, our algorithm has the near optimal $O(\sqrt{\frac{L}{\mu (1-\sigma _2(W))}}\log ^2\frac{1}{\epsilon })$ complexity for communications, and the optimal $O(\sqrt{\frac{L}{\mu }}\log \frac{1}{\epsilon })$ complexity for gradient computations. Our communication complexities are only worse by a factor of $(\log \frac{1}{\epsilon })$ than the lower bounds. Our second algorithm is designed for nonsmooth distributed optimization, and it achieves both the optimal $O(\frac{1}{\epsilon \sqrt{1-\sigma _2(W)}})$ communication complexity, and $O(\frac{1}{\epsilon ^2})$ subgradient computation complexity, which match the lower bounds for nonsmooth distributed optimization.

Estimating Regression Function of Multi-response Semiparametric Regression Model Using Smoothing Spline

The article describes a new estimation method of regression functions in a multi-response semiparametric regression model based on smoothing spline. The multi-response semiparametric regression model is a combined model between a parametric regression model and a nonparametric regression model, where there is a correlation between responses. The proposed estimation method enhances the flexibility of the multi-response semiparametric regression model by combining a goodness of fit function and a penalty function to calculate an estimation which not only considers the goodness of fitting of the model, but also the smoothness of the estimation model curve. The optimal trade-off between goodness and smoothness can be achieved by selecting the optimal smoothing parameters. The article discusses a theoretically proposed method for estimating this multi-response semiparametric regression model regression function of parametric and nonparametric components. We use the weighted least squares method to estimate the parametric component parameters, we determine the goodness of fit and penalty functions using the reproducing kernel Hilbert space method, and then take the result of penalized weighted least squares optimization to obtain an estimate of the nonparametric component. The new research results are a weighted least squares estimator of parameters of parametric components, and a weighted partial smoothing spline estimator of the nonparametric component. The result shows that the estimated multi-response semiparametric regression model is linear to the observation, and is a combination of the estimations of the parametric and nonparametric components. The research results of the estimation of this model can be applied to medical fields for predictive purposes.

Estimation of fastener pull-through resistance of composite laminates based on generalized regression neural network

The fastener pull-through resistance is a key performance index of composite laminates used for engineering application, and increasing research attention is being paid to developing methods for its calculation or estimation. The currently available research methods mainly focus on the standard test and the finite element analysis for determining the pull-through resistance of composite laminates suffering transverse load by the fasteners. Based on the results of the fastener pull-through resistance experiment performed on X850 composite laminates, a model for estimating the maximum affordable load of composite laminates for the fastener pull-through resistance is proposed, using generalized regression neural network technology. The inputs of this model are simplified to six parameters: the proportion of the ±45° layer of the laminates, the number of the layers, the thickness of the laminates, the bolt head shape, whether the bolt has a washer or not, and the nominal diameter of the bolt; the Gauss function is used as the hidden layer function. The model uses a large portion of the experimental data to train for finding the optimal smoothness factor, which is used to reconstruct the model, and simulation is performed with the remainder of the experimental data. The comparison between the estimated results using the model and the experimental results shows that the generalization ability of the proposed model can meet the estimation requirements. Moreover, the pull-through resistance of composite laminates under transverse load from a fastener can be estimated with high accuracy after some standard fastener pull-through resistance tests of the composite laminates.

An Optimal Wavelet Packets Basis Method for Cascade Hydro-PV-Pumped Storage Generation Systems to Smooth Photovoltaic Power Fluctuations

Due to the volatility of natural resources, the power fluctuations of photovoltaic (PV) generation have serious negative impacts on the power quality. This paper reports a novel approach to resolve this problem in a combined cascade hydro-PV-pumped storage (CH-PV-PS) generation system through appropriate power distribution on a small time scale. According to the characteristics of power generation systems and multi-constraints, how to obtain the optimal smoothing effects with the small cost is a key challenge. For this purpose, wavelet packet decomposition is modified by constructing cost function and ideal power trajectory sequences to obtain a new adaptive power distribution method for the CH-PV-PS generation system considering the boundary conditions of the system in this paper. At the same time, to meet the real-time control requirements of actual systems, an additive function is presented to improve the optimization speed of the adaptive power distribution method. In the meantime, a fuzzy controller is designed to optimize the inevitable delay time of the power scheduling system, and the starting threshold is set to avoid the frequently mode conversion of pumped storage. Finally, the performance of the method is evaluated based on the PV station data in Xiaojin County, Sichuan Province, China. Simulation results based on Matlab-simulink indicate that the proposed method can effectively suppress PV power fluctuations and ensure normal operation of the CH-PV-PS generation system within the multiple constraints.

Fault Diagnosis of Complex Chemical Processes Based on Enhanced Naive Bayesian Method

Fault diagnosis is crucial for the stable and reliable operation of chemical processes. However, faced with the complexity of chemical processes, conventional diagnosis methods suffer from the expertise of feature extraction and classifier design. They also lack extracting effective features from raw data whose attributes are correlated and coupled. This article proposes an enhanced naive Bayesian classifier (ENBC) for fault diagnosis of the complex chemical processes. Assuming that all attributes are related, ENBC can utilize a joint probability density function (pdf) based on multivariate Gaussian kernel function and adaptively extract the related information from the raw data. ENBC can estimate the class-conditional pdf based on the optimal smoothing parameter, which is the crucial part of the joint pdf estimation. ENBC seeks an optimal smoothing parameter by minimizing the mean integrated squared error (MISE) between the true pdf and the estimated pdf. The benchmark Tennessee Eastman (TE) process is used to illustrate the performance of ENBC. The experimental results demonstrate that ENBC is more effective than other methods.