Optimal Smoothing Research Articles

Autonomous Driving Trajectory Optimization With Dual-Loop Iterative Anchoring Path Smoothing and Piecewise-Jerk Speed Optimization

This letter presents a free space trajectory optimization algorithm for autonomous driving, which decouples the collision-free trajectory generation problem into a Dual-Loop Iterative Anchoring Path Smoothing (DL-IAPS) problem and a Piecewise-Jerk Speed Optimization (PJSO) problem. The work leads to remarkable driving performance improvements including more robust and precise collision avoidance, higher control feasibility, higher computation efficiency and stricter driving comfort guarantee, compared with other existing algorithms. The advantages of our algorithm are attributed to our fast iterative collision checks with exact vehicle/obstacle shapes, strict non-holonomic dynamic constraints and accurate kinematics-based speed optimization. It has been validated that, through batch simulation and road experiments, compared with prior works, our algorithm is with the highest robustness and capable to maintain the lowest failure rate (~7%) at nearly all test conditions, achieves 10x faster computational speed than other planners, fulfills 100% driving-comfort standards in complex driving scenarios, and does not induce significant time increase as boundaries or obstacles scale up.

Dental Caries Prediction Based on a Survey of the Oral Health Epidemiology among the Geriatric Residents of Liaoning, China.

Background Dental caries is one of the most common chronic diseases observed in elderly patients. The development of preventive strategies for dental caries in elderly individuals is vital. Objective The objective of the present study was to construct a generalized regression neural network (GRNN) prediction model for the risk assessment of dental caries among the geriatric residents of Liaoning, China. Methods A stratified equal-capacity random sampling method was used to randomly select 1144 elderly (65-74 years) residents (gender ratio 1 : 1) of Liaoning, China. Data for the oral assessment, including caries characteristics, and questionnaire survey from each participant were collected. Multivariate logistic regression analysis was then performed to identify the independent predictors. GRNN was applied to establish a prediction model for dental caries. The accuracy of the unconditional logistic regression and the GRNN early warning model was compared. Results A total of 1144 patients fulfilled the requirements and completed the questionnaires. The caries rate was 68.5%, and the main associated factors were toothache history, residence area, smoking, and drinking. We randomly divided the data for the 1144 participants into a training set (915 cases) and a test set (229 cases). The optimal smoothing factor was 0.7, and the area under the receiver operating characteristic curve for the GRNN model was 0.626 (95% confidence interval, 0.544 to 0.708), with a P value of 0.002. In terms of consistency, sensitivity, and specificity, the GRNN model was better than the traditional unconditional multivariate logistic regression model. Conclusion Geriatric (65-74 years) residents of Liaoning, China, have a high rate of dental caries. Residents with a history of toothache and smoking habits are more susceptible to the disease. The GRNN early warning model is an accurate and meaningful tool for screening, early diagnosis, and treatment planning for geriatric individuals with a high risk of caries.

Power fluctuation and allocation of hybrid energy storage system based on optimal exponential smoothing method and energy entropy

Power fluctuation and allocation of hybrid energy storage system based on optimal exponential smoothing method and energy entropy

Deep learning with noise-to-noise training for denoising in SPECT myocardial perfusion imaging.

Post-reconstruction filtering is often applied for noise suppression due to limited data counts in myocardial perfusion imaging (MPI) with single-photon emission computed tomography (SPECT). We study a deep learning (DL) approach for denoising in conventional SPECT-MPI acquisitions, and investigate whether it can be more effective for improving the detectability of perfusion defects compared to traditional postfiltering. Owing to the lack of ground truth in clinical studies, we adopt a noise-to-noise (N2N) training approach for denoising in SPECT-MPI images. We consider a coupled U-Net (CU-Net) structure which is designed to improve learning efficiency through feature map reuse. For network training we employ a bootstrap procedure to generate multiple noise realizations from list-mode clinical acquisitions. In the experiments we demonstrated the proposed approach on a set of 895 clinical studies, where the iterative OSEM algorithm with three-dimensional (3D) Gaussian postfiltering was used to reconstruct the images. We investigated the detection performance of perfusion defects in the reconstructed images using the non-prewhitening matched filter (NPWMF), evaluated the uniformity of left ventricular (LV) wall in terms of image intensity, and quantified the effect of smoothing on the spatial resolution of the reconstructed LV wall by using its full-width at half-maximum (FWHM). Compared to OSEM with Gaussian postfiltering, the DL denoised images with CU-Net significantly improved the detection performance of perfusion defects at all contrast levels (65%, 50%, 35%, and 20%). The signal-to-noise ratio (SNRD ) in the NPWMF output was increased on average by 8% over optimal Gaussian smoothing (P<10-4 , paired t-test), while the inter-subject variability was greatly reduced. The CU-Net also outperformed a 3D nonlocal means (NLM) filter and a convolutional autoencoder (CAE) denoising network in terms of SNRD . In addition, the FWHM of the LV wall in the reconstructed images was varied by less than 1%. Furthermore, CU-Net also improved the detection performance when the images were processed with less post-reconstruction smoothing (a trade-off of increased noise for better LV resolution), with SNRD improved on average by 23%. The proposed DL with N2N training approach can yield additional noise suppression in SPECT-MPI images over conventional postfiltering. For perfusion defect detection, DL with CU-Net could outperform conventional 3D Gaussian filtering with optimal setting as well as NLM and CAE.

POST-FIRE HAZARD DETECTION USING ALOS-2 RADAR AND LANDSAT-8 OPTICAL IMAGERY

Abstract. This study investigates the use of Advanced Land Observing Satellite 2 (ALOS-2) equipped with an enhanced L-band SAR sensor imagery alongside with Landsat-8 optical sensor in detection and mapping of burnt and unburnt scars occurring after a bushfire in Victoria, Australia. The bushfires had recently occurred in the period of 2018–2019. The analysis was explored using a contextual classifier Support Vector Machine (SVM), as SVM allows us to integrate spectral information and spatial context through the optimal smoothing parameter without degrading image quality. The training and test set datasets consisting of burnt and unburnt pixels were created from Landsat-8 scenes used as reference data. The backscatter intensity maps (acquired before and after the forest fires) from ALOS-2 data were compared and investigated, with a special concern on topographic influence removal. The dual polarizations (HH and HV) have been used to improve the forest fire mapping capability. These change detection techniques were based on image feature differences, index calculation such as normalized burn ratio. The burnt area and unburnt area were then classified via a threshold given by the pre- and post- disaster differences. The classification result achieved an accuracy of 80% Landsat-8 and 89% ALOS-2. This result shows the limitations of burnt area mapping with ALOS-2 due to effect local incidence angle and topography were of greater impact resulting in shadows. Nevertheless, the results in both areas verify the use of satellite SAR sensors and optical in forestry application.

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

In this paper, we study the inverse problem of recovering the spatially varying material properties of a solid polycrystalline object from ultrasonic travel time measurements taken between pairs of points lying on the domain boundary. We consider a medium of constant density in which the orientation of the material's lattice structure varies in a piecewise constant manner, generating locally anisotropic regions in which the wave speed varies according to the incident wave direction and the material's known slowness curve. This particular problem is inspired by current challenges faced by the ultrasonic non‐destructive testing of polycrystalline solids. We model the geometry of the material using Voronoi tessellations and study two simplified inverse problems where we ignore wave refraction. In the first problem, the Voronoi geometry itself and the orientations associated to each region are unknowns. We solve this nonsmooth, nonconvex optimisation problem using a multistart non‐linear least squares method. Good reconstructions are achieved, but the method is shown to be sensitive to the addition of noise. The second problem considers the reconstruction of the orientations on a fixed square mesh. This is a smooth optimisation problem but with a much larger number of degrees of freedom. We prove that the orientations can be determined uniquely given enough boundary measurements and provide a numerical method that is more stable with respect to the addition of noise.

An isogeometric framework for the optimal design of variable stiffness shells undergoing large deformations

The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions to provide a smooth description of the deformed shapes, thereby reducing the number of degrees of freedom with respect to standard finite elements. The stiffness variation is obtained by exploiting the same NURBS interpolation to describe lamination parameters, employed as intermediate optimisation variables. This choice allows the design space to be thoroughly explored with relatively few design variables in a smooth optimisation space. Therefore, the optimisation strategy is divided into two stages. Firstly, the optimal distribution of lamination parameters is determined using a gradient based algorithm. Afterwards, an actual distribution of fibre orientation is retrieved. The viability of the tool is tested firstly onto a cylindrical panel under compressive loading. Then, the postbuckling optimisation of a composite wingbox is given. For both structures, the optimised postbuckling response is compared with those of the corresponding quasi-isotropic baselines showing significant improvements.

Assessment of the performance of carrier-phase and Doppler smoothing code for low-cost GNSS receiver positioning

With the wide civil applications of low-cost Global Navigation Satellite System (GNSS) receiver, precise positioning based on low-cost receiver attracted extensive attention. Because the noise of pseudo-range measurement is one of the important factors affecting the performance of GNSS positioning, carrier-phase smoothed code and Doppler smoothed code have been generally used to reduce the effect of pseudo-range noise and improve the positioning accuracy. In view of this, we will focus on the analysis of Carrier-phase smoothed code and Doppler smoothed code with low-cost GNSS receiver to improve the positioning performance. Firstly, we investigated the optimal smoothing window of Carrier-phase smoothed code and Doppler smoothed code. Secondly, some static and kinematic positioning experiments were carried out in an open environment and under environment with obvious obstruction by low-cost receiver, respectively. The experiment results illustrated that the Carrier-phase smoothed code and Doppler smoothed code can improve positioning accuracy of meter-lever. In the static experiment, the positioning accuracy of Carrier-phase smoothed code with the optimal smoothing window is better than that of Doppler smoothed code in the open sky while it is not as good as the Doppler smoothed code with the optimal smoothing window with obvious obstruction. In the kinematic experiment, the positioning accuracy of Carrier-phase smoothed code with the optimal smoothing window was slightly improved compared with the Doppler smoothed code in an open environment, but was significantly degraded compared with the Doppler smoothed code under environment with obvious obstruction.

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Accelerated Methods for Saddle-Point Problem

Recently, it has been shown how, on the basis of the usual accelerated gradient method for solving problems of smooth convex optimization, accelerated methods for more complex problems (with a structure) and problems that are solved using various local information about the behavior of a function (stochastic gradient, Hessian, etc.) can be obtained. The term “accelerated methods” here means, on the one hand, the presence of some unified and fairly general way of acceleration. On the other hand, this also means the optimality of the methods, which can often be proved rigorously. In the present work, an attempt is made to construct in the same way a theory of accelerated methods for solving smooth convex-concave saddle-point problems with a structure. The main result of this article is the obtainment of in some sense necessary and sufficient conditions under which the complexity of solving nonlinear convex-concave saddle-point problems with a structure in the number of calculations of the gradients of composites in direct variables is equal in order of magnitude to the complexity of solving bilinear problems with a structure.

A Novel Bayesian Framework With Enhanced Principal Component Analysis for Chemical Fault Diagnosis

Fault diagnosis is of great importance to enhance the reliability and security of the complex chemical processes. However, many fault diagnosis methods cannot extract correlation information among attributes in the feature extraction procedure, resulting in the degradation of diagnosis performance. In this article, a novel framework is proposed for fault diagnosis of the chemical processes. First, in the framework, an enhanced kernel principal component analysis (eKPCA) is proposed to obtain the key features of the fault based on Hotelling’s $T^{2}$ and squared prediction error (SPE) statistics. Second, to learn the correlation information of the features, an enhanced naive Bayesian model (eNBM) is constructed with a multivariate Gaussian kernel function. Third, the dragonfly algorithm (DA) is employed to find the optimal smoothing parameter to improve the performance of eNBM. The framework is applied to make a fault diagnosis of Tennessee Eastman (TE) process. The experimental results show that the proposed framework is more effective compared with the already existed traditional approaches, such as deep learning.

Determination of the optimal strength of contact interaction of the tool and the part during finishing-hardening treatment by diamond smoothing

The main factors of the process of diamond smoothing are considered in the work: the force of the contact interaction of the tool and the part in the deformation zone and the friction on the contact surface of the part and the smoother. The technique of analytical determination of the optimal smoothing force for the finishing-hardening treatment mode is presented. The calculated values were obtained for some characteristic grades of materials of small and medium hardness (≤ 210 HB, indenter radius 3.4 mm) and a number of hardened steels of high hardness (indenter radius 2.0 mm). The force values are also determined using expressions for the deformation component of the friction coefficient. A comparative analysis of the results indicates that the calculation options are adequate for practical purposes. On specific examples of processed materials, graphical dependencies are shown, which reflect the relationship between the coefficient of friction, including its deformation component, and the smoothing force. With an increase in the leveling force, the friction coefficient increases, this is explained by an increase in the depth of penetration of the diamond tip and, consequently, an increase in the deformation component. The depth of penetration of the indenter into the surface to be treated, and therefore the coefficient of friction during ironing, depends on the hardness of the material being processed. With increasing hardness, the penetration depth decreases, which leads to a decrease in the deformation component and in general the coefficient of friction. The friction coefficient is also affected by the radius of the working part of the tool, since the indenter penetration depth also depends on its value. The research results can be used in the development of technology for finishing and hardening diamond smoothing, the development of the process and its introduction into production.

A directional Gaussian smoothing optimization method for computational inverse design in nanophotonics

Local-gradient-based optimization approaches lack nonlocal exploration ability required for escaping from local minima in non-convex landscapes. A directional Gaussian smoothing (DGS) approach was proposed in our recent work and used to define a truly nonlocal gradient, referred to as the DGS gradient, in order to enable nonlocal exploration in high-dimensional black-box optimization. Promising results show that replacing the traditional local gradient with the nonlocal DGS gradient can significantly improve the performance of gradient-based methods in optimizing highly multi-modal loss functions. However, the current DGS method is designed for unbounded and unconstrained optimization problems, making it inapplicable to real-world engineering design optimization problems where the tuning parameters are often bounded and the loss function is usually constrained by physical processes. In this work, we propose to extend the DGS approach to the constrained inverse design framework in order to find a better design. The proposed framework has its advantages in portability and flexibility to naturally incorporate the parameterization, physics simulation, and objective formulation together to build up an effective inverse design workflow. A series of adaptive strategies for smoothing radius and learning rate updating are developed to improve the computational efficiency and robustness. To enable a clear binarized design, a dynamic growth mechanism is imposed on the projection strength in parameterization. The methodology is demonstrated by an example of wavelength demultiplexer. Our method shows superior performance compared to the state-of-the-art approaches. By incorporating volume constraints, the optimized design achieves an equivalently high performance but significantly reduces the amount of material usage.

A note on the worst-case complexity of nonlinear stepsize control methods for convex smooth unconstrained optimization

ABSTRACT In this paper, we analyse the worst-case complexity of nonlinear stepsize control (NSC) algorithms for solving convex smooth unconstrained optimization problems. We show that, to drive the norm of the gradient below some given positive ε, such methods take at most iterations, which shows that the complexity bound for these methods is in parity with that of gradient descent methods for the same class of problems. As NSC algorithm is a generalization of several methods such as trust-region and adaptive cubic with regularization methods, such bound holds automatically for these methods as well.

Accelerated and Unaccelerated Stochastic Gradient Descent in Model Generality

A new method for deriving estimates of the rate of convergence of optimal methods for solving problems of smooth (strongly) convex stochastic optimization is described. The method is based on the results of stochastic optimization derived from results on the convergence of optimal methods under the conditions of inexact gradients with small noises of nonrandom nature. In contrast to earlier results, all estimates in the present paper are obtained in model generality.

Optimal Synthesis of Sum and Difference Beam Patterns With a Common Weight Vector for Symmetric and Asymmetric Antenna Arrays

To alleviate the complexity of feeding network design and reduce the dependence of sum and difference beam pattern synthesis on the central symmetric antenna arrays, a method generating a common weight vector to simultaneously produce these two beam patterns for symmetric and asymmetric antenna arrays is proposed. By considering the main-lobe radiation power of the sum beam pattern, sidelobe level (SLL), null depth of the difference beam pattern at the direction of the target, and difference-to-sum ratio as design parameters in the beam pattern synthesis, a new optimization problem with a nonconvex objective function and two quadratic fractional constraints is formulated. To tackle it, we first use the variant penalty method to convert the original constrained optimization problem into a nonsmooth unconstrained one and then adopt smooth functions to approximate the nonsmooth components to obtain a smooth unconstrained optimization problem that is then solved by steepest descent. Four representative examples, namely, symmetric linear, asymmetric linear, asymmetric rectangular, and symmetric flower arrays, are implemented to demonstrate that our algorithm can simultaneously synthesize the sum and difference beam patterns with accurately controlled SLLs even in asymmetric array configurations.

Understanding Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions

Many contemporary applications in signal processing and machine learning give rise to structured nonconvex nonsmooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon-and, in fact, a very difficult conundrum even for experts-lies in the study of points of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there are myriad definitions of stationarity in nonsmooth optimization. In this article, we provide an introduction to different stationarity concepts for several important classes of nonconvex nonsmooth functions, discuss the geometric interpretations of these concepts, and further clarify their relationships. We then demonstrate the relevance of these constructions in some representative applications and indicate how they could affect the performance of iterative methods for addressing these applications.

Complexity analysis for optimization methods

The subject on convergence analysis of optimization methods is an importantarea in optimization theory. However, convergence is not sufficient as a criterion forcomparing the efficiency of different algorithms. Therefore, we need another theoryto measure the difficulty of optimization problems and the efficiency of optimizationalgorithms. This theory is called complexity analysis theory of optimizationalgorithms.This paper is divided into five parts. The first section introduces the basic setups of complexity analysisframeworks, gives the definition, methods and examples of complexity analysis,and summarizes the complexity results. In the secondsection, the complexity analysis for the smooth optimization problem is introduced.We give the upper and lower complexity bounds for different optimization problems,and also introduce the framework of convergence analysis for the accelerated gradientmethod. In the third section, the upper bounds of the complexity of nonsmoothoptimization problems are introduced. We present the complexity analysisfor the subgradient method, the mirror descent method, the center-of-gravity method,and the ellipsoid method. In the fourth section, we introduce the complexity analysis for theconditional gradient method, study its upper and lower bounds of complexity andpresent the framework of the acceleratedconditional gradient method. In the fifth section, we introduce the complexity analysisof the stochastic optimization algorithm, and compare the confidence level for theconvergence under convex and nonconvexsettings.

A global QP-free algorithm for mathematical programs with complementarity constraints

In this paper, a primal–dual interior point QP-free algorithm for mathematical programs with complementarity constraints is presented. Firstly, based on Fischer–Burmeister function and smoothing techniques, the investigated problem is approximated by a smooth nonlinear constrained optimization problem. Secondly, combining with an effective penalty function technique and working set, a QP-free algorithm is proposed to solve the smooth constrained optimization problem. At each iteration, only two reduced linear equations with the same coefficient matrix are solved to obtain the search direction. Under some mild conditions, the proposed algorithm possesses global convergence. Finally, some numerical results are reported.

An asymptotic and empirical smoothing parameters selection method for smoothing spline ANOVA models in large samples.

Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for smoothing spline ANOVA models in large samples. The idea of our approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational burden of selecting smoothing parameters in high-dimensional and large samples. We show that smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimize a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacy and running time. In an application to molecular dynamics data containing nearly one million observations, the proposed method has the best prediction performance.