Optimal Smoothing Research Articles

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization (SBESO), as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load. A weighted function is introduced to regulate the mass and stiffness matrix of an element, which has the inefficient element gradually removed from the design domain as if it were undergoing damage. Aiming at maximizing the natural frequency of a structure, the frequency optimization formulation is proposed using the SBESO technique. The effects of various weight functions including constant, linear and sine functions on structural optimization are compared. With the equivalent static load (ESL) method, the dynamic stiffness optimization of a structure is formulated by the SBESO technique. Numerical examples show that compared with the classic BESO method, the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function. It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Effects of polishing press-on force on surface roughness and gloss of CAD-CAM composites

The aim of this study was to determine the effect of polishing press-on force on surface roughness and gloss of computer-aided design-computer-aided manufacturing (CAD-CAM) composites. The materials evaluated included a CAD-CAM ceramic, a polymer-infiltrated ceramic, and three filler-based CAD-CAM composites. The CAD-CAM blocks were sectioned, embedded in self-cured resin, finished with abrasive papers and ultrasonically cleaned. Specimens were subsequently polished using the Sof-Lex disk system with 0.5, 1.0, 1.5, and 2.0 N press-on force by means of a custom-made apparatus. Contour arithmetic mean deviation (Ra) and gloss value (GU) data were acquired with a profilometer and glossmeter, respectively, and analyzed using ANOVA/Bonferroni post hoc test and Pearson's correlation (α = 0.05). Representative samples of the various materials at baseline and after each polishing step were examined under scanning electron microscope. Mean Ra and GU values ranged from 0.096 ± 0.004 μm to 0.295 ± 0.045 μm and 13.4 ± 1.9 to 67.6 ± 11.3 correspondingly for the various material-force combinations. Surface roughness and gloss were found to be press-on force and material dependent. A moderately strong and negative correlation (rs = -0.69) existed between Ra and GU values. For optimal smoothness and gloss, ceramic and polymer-infiltrated ceramic CAD-CAM materials must be polished with a 2.0 N force, while filler-based CAD-CAM composites should, in general, be polished using a 1.0 to 1.5 N force.

Robot Pose Optimization and Joint Path Smoothing Method for Aero-engine Complex Casing Deep Cavity Measurement

Robot Pose Optimization and Joint Path Smoothing Method for Aero-engine Complex Casing Deep Cavity Measurement

Digital Marketing Ecosystem Perspective of Regional Featured Product in North Sulawesi Province, Indonesia

The industrial sector that develops along with technological developments certainly has an impact on the economy of a country. Indonesia is a country that has great potential for the development of the digital economy with a high level of digital media penetration and a large market share. Strengthening local products based on the digital economy seems to be one way to maintain the positive momentum for post-pandemic national economic improvement. This is done by encouraging the marketing digitalization ecosystem to SMEs. This article is constructed based on literature studies that have been carried out previously by mapping articles, research journals, and related data to be able to provide a real picture regarding the role of the digital marketing ecosystem in encouraging marketing penetration of regional superior products. Some of the aspects that are used as barometer like consumer ecosystem, producer ecosystem, and core communication. These three things are collaborated with the facilitation of stakeholders such as the government, suppliers, consumers and business owners, who work together to encourage the smooth running and optimization of digital marketing operations in North Sulawesi Province, Indonesia. However, several obstacles remain, namely not all regional superior products have been reached in digital marketing. As a result, the role of actors in the local digital marketing ecosystem still needs to be carried out with various empowerment efforts. Stakeholders like the government and banking must creating more synergy with local business owners to maximize regional superior products that have enormous potential.

Variance-Reduced Shuffling Gradient Descent With Momentum for Finite-Sum Minimization

Finite-sum minimization is a fundamental optimization problem in signal processing and machine learning. This paper proposes a variance-reduced shuffling gradient descent with Nesterov’s momentum for smooth convex finite-sum optimization. We integrate an explicit variance reduction into the shuffling gradient descent to deal with the variance introduced by shuffling gradients. The proposed algorithm with a unified shuffling scheme converges at a rate of O(1T), where T is the number of epochs. The convergence rate independent of gradient variance is better than most existing shuffling gradient algorithms for convex optimization. Finally, numerical simulations demonstrate the convergence performance of the proposed algorithm.

Intelligent decision support in the optimization of irrigation systems in agriculture

The issues of determining the optimal values of the regulatory parameters of irrigation systems engaged in the cultivation of agricultural crops are considered. Following the requirements of a market economy, the main emphasis is placed on taking into account two types of criteria: maximizing the yield of agricultural crops and minimizing monetary costs. The proposed method for solving the multi-criteria optimization problem is based on the combination of the minimax criterion and the medium-step convolution, which makes it possible to scalarize the vector optimality criterion with access to smooth optimization methods. Concerning the case of priority uncertainty according to particular optimality criteria, an intelligent algorithm is proposed based on the approximation of the preference function of the decision-maker by the fuzzy Mamdani model. The multi-criteria optimization of the irrigation system used for growing cotton results differ favorably from the average values. The one hectare yield in the republic- increased by 2%, monetary costs - reduced by 4.5%. It could be concluded that the developed methodology makes it possible to bypass the computational difficulties that arise when solving problems of multi-criteria optimization of irrigation systems engaged in the cultivation of agricultural crops and to obtain real results in conditions of certainty and uncertainty goals.

Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography

We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure to characterize the state of a quantum system, which we formulate as a stochastic non-convex smooth optimization problem. Physically, the estimation of a low-rank density matrix helps characterizing the amount of noise introduced by quantum computation. Theoretically, we prove the local convergence of Local SFGD for a general class of restricted strongly convex/smooth loss functions. Local SFGD converges locally to a small neighborhood of the global optimum at a linear rate with a constant step size, while it locally converges exactly at a sub-linear rate with diminishing step sizes. With a proper initialization, local convergence results imply global convergence. We validate our theoretical findings with numerical simulations of QST on the Greenberger-Horne-Zeilinger (GHZ) state.

OFFO minimization algorithms for second-order optimality and their complexity

An Adagrad-inspired class of algorithms for smooth unconstrained optimization is presented in which the objective function is never evaluated and yet the gradient norms decrease at least as fast as \(\mathcal{O}(1/\sqrt{k+1})\) while second-order optimality measures converge to zero at least as fast as \(\mathcal{O}(1/(k+1)^{1/3})\). This latter rate of convergence is shown to be essentially sharp and is identical to that known for more standard algorithms (like trust-region or adaptive-regularization methods) using both function and derivatives’ evaluations. A related “divergent stepsize” method is also described, whose essentially sharp rate of convergence is slighly inferior. It is finally discussed how to obtain weaker second-order optimality guarantees at a (much) reduced computational cost.

Optimal Estimation of the Peak Wave Period using Smoothing Method

In this study, a smoothing method was applied to improve the accuracy of peak wave period estimation using the water surface elevation observed from the Oceanographic and Meteorological Observation Tower located on the west coast of the Korean Peninsula. Validation of the application of the smoothing method was performed using variance of the surface elevation and total amount wave energy, and then the effect on the application of smoothing was analyzed. As a result of the analysis, the correlation coefficient between variance of the surface elevation and total amount wave energy was 0.9994, confirming that there was no problem in applying the method. Thereafter, as a result of reviewing the effect of smoothing, it was found to be reduced by about 4 times compared to the confidence interval of the existing estimated spectrum, confirming that the accuracy of the estimated peak wave period was improved. It was found that there was a statistically significant difference in probability density between 4 and 6 seconds due to the smoothing application. In addition, for optimal smoothing, the appropriate number of smoothings according to the significant wave height range was calculated using a statistical technique, and the number of smoothings was found to increase due to the unstable spectral shape as the significant wave height decreased.

An Epipolar HS-NCC Flow Algorithm for DSM Generation Using GaoFen-3 Stereo SAR Images

Radargrammetry is a widely used methodology to generate the large-scale Digital Surface Model (DSM). Stereo matching is the most challenging step in radargrammetry due to the significant geometric differences and the inherent speckle noise. The speckle noise results in significant grayscale differences of the same feature points, which makes the traditional Horn–Schunck (HS) flow or multi-window zero-mean normalized cross-correlation (ZNCC) methods degrade. Therefore, this paper proposes an algorithm named Epipolar HS-NCC Flow (EHNF) for dense stereo matching, which is an improved HS flow method with normalized cross-correction constraint based on epipolar stereo images. First, the epipolar geometry is applied to resample the image to realize the coarse stereo matching. Subsequently, the EHNF method forms a global energy function to achieve fine stereo matching. The EHNF method constructs a local normalized cross-correlation constraint term to compensate for the grayscale invariance constraint, especially for the SAR stereo images. Additionally, two assessment methods are proposed to calculate the optimal cross-correlation parameter and smoothness parameter according to the refined matched point pairs. Two GaoFen-3 (GF-3) image pairs from ascending and descending orbits and the open Light Detection and Ranging (LiDAR) data are utilized to fully evaluate the proposed method. The results demonstrate that the EHNF algorithm improves the DSM elevation accuracy by 9.6% and 27.0% compared with the HS flow and multi-window ZNCC methods, respectively.

Theoretical and numerical comparison of first order algorithms for cocoercive equations and smooth convex optimization

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates of gradient descent, forward-backward, Peaceman-Rachford, and Douglas-Rachford algorithms for minimizing the sum of two smooth convex functions when one of them is strongly convex. A similar comparison is given in the more general cocoercive setting under the presence of strong monotonicity and we observe that the convergence rates in optimization are strictly better than the corresponding rates for cocoercive equations for some algorithms. We obtain improved rates with respect to the literature in several instances by exploiting the structure of our problems. Moreover, we indicate which algorithm has the smallest convergence rate depending on strong convexity and cocoercive parameters. From a numerical point of view, we verify our theoretical results by implementing and comparing previous algorithms in well established signal and image inverse problems involving sparsity. We replace the widely used ℓ1 norm with the Huber loss and we observe that fully proximal-based strategies have numerical and theoretical advantages with respect to methods using gradient steps.

Aerodynamic drag analysis and reduction strategy for satellites in Very Low Earth Orbit

Research interest in operating satellites in Very Low Earth Orbit (VLEO) is growing due to their potential applications for high quality Earth observation and telecommunication. In VLEO, atmospheric drag is not only a critical issue affecting the attitude control and orbit prediction of satellites, but also a key factor limiting the operational life of satellites. In this work, we first employ the direct simulation Monte Carlo (DSMC) method to calculate the aerodynamic drag of elementary shapes including flat plate, cylinder, and sphere in the VLEO region, which are validated and compared with the free molecular flow (FMF) theory. Then, we calculate the aerodynamic drag of a conceptual VLEO satellite model, and the effects of the orbital altitude, accommodation coefficient of surfaces, and the molecular speed ratio on the aerodynamic drag coefficient are analyzed. Two drag reduction strategies, referred to as lateral side smoothing and shape optimization, are investigated in detail by DSMC calculations. We propose that combining these two drag reduction strategies can achieve better drag reduction effect. In addition, we modify the optimum aspect ratio theory by considering the rarefied gas effect to give a better prediction of the optimum aspect ratio for aerodynamic drag at lower orbital altitudes.

Adaptive Doppler‐smoothed‐code bilateral kernel regression method for single‐frequency BeiDou receiver

AbstractCurrently, single‐frequency Global Navigation Satellite System (GNSS) receivers dominate maritime navigation units due to their simple structure and low cost but usually cannot meet the positioning requirements of Maritime Autonomous Surface Ship (MASS). Herein, a novel adaptive Doppler‐smoothed‐code Bilateral Kernel Regression (DBKR) method is proposed, which improves pseudorange accuracy in the range domain and then reconstructs observations in the position domain. In the range domain, the Doppler observable is utilised to smooth the pseudorange with an optimal window smoothing width for the BeiDou Navigation Satellite System (BDS) receiver to alleviate ionosphere delay. In the position domain, we elaborate a bilateral kernel regression model to further reduce the positioning drift. The on‐line regression process starts with mapping the observation space to Euclidean space and subsequently fusing all observations of the same epoch using the Gaussian Radial Basis Function (RBF). Finally, the experiments under static and dynamic scenarios are carried out, which verify the validity and efficiency of the proposed DBKR method.

OUTLIER IDENTIFICATION ON PENALIZED SPLINE REGRESSION MODELING FOR POVERTY GAP INDEX IN JAVA

Java is one of the islands in Indonesia which has good establishment acceleration. Even though economic growth was good, poverty is still a serious problem. Three of six provinces, including DI Yogyakarta, Central Java, and East Java still have poverty rates above national rates in March 2020. This problem indicates that an imbalance in poverty happens between those regions. Several regions have extreme conditions or known as outliers. Besides that, poverty gap data have a complex pattern so modeling using a non-parametric approach is suitable. This study aims to build an appropriate model to support the success of poverty alleviation in Java and the identification of outliers was carried out using an adjusted boxplot. The best-penalized regression spline model for Poverty Gap Index in Java Island was obtained by Generalized minimum Cross-Validation (GCV) using optimum smoothing parameter (λ) 0,12 and knot combination (1, 2, 4, 1, 5, 3, and 1) for seven predictor variables. The result shows that penalized spline regression model has a higher R2 than OLS regression. The R2 is obtained 69,10%, so the model is feasible to explain the variability of the poverty gap in Java. Moreover, based on the outliers’ identification shows a dependency between outlier in data and residual because some districts/cities are identified as outliers in both.

Near-Ground Delivery Drones Path Planning Design Based on BOA-TSAR Algorithm

With the advancement of technology and the rise of the unmanned aerial vehicle industry, the use of drones has grown tremendously. For drones performing near-ground delivery missions, the problem of 3D space-based path planning is particularly important in the autonomous navigation of drones in complex spaces. Therefore, an improved butterfly optimization (BOA-TSAR) algorithm is proposed in this paper to achieve the autonomous pathfinding of drones in 3D space. First, this paper improves the randomness strategy of the initial population generation in the butterfly optimization algorithm (BOA) via the Tent chaotic mapping method, by means of the removal of the short-period property, which balances the equilibrium of the initial solutions generated by the BOA algorithm in the solution space. Secondly, this paper improves the shortcomings of the BOA algorithm in terms of slower convergence, lower accuracy, and the existence of local optimal stagnation when dealing with high-dimensional complex functions via adaptive nonlinear inertia weights, a simulated annealing strategy, and stochasticity mutation with global adaptive features. Finally, this paper proposes an initial population generation strategy, based on the 3D line of sight (LOS) detection method, to further reduce the generation of path interruption points while ensuring the diversity of feasible solutions generated by the BOA algorithm for paths. In this paper, we verify the superior performance of BOA-TSAR by means of simulation experiments. The simulation results show that BOA-TSAR is very competitive among swarm intelligence (SI) algorithms of the same type. At the same time, the BOA-TSAR algorithm achieves the optimal path length measure and smoothness measure in the path-planning experiment.

Learning Smooth Motion Planning for Intelligent Aerial Transportation Vehicles by Stable Auxiliary Gradient

Deep Reinforcement Learning (DRL) has been widely attempted for solving real-time intelligent aerial transportation vehicle motion planning tasks recently. When interacting with environment, DRL-driven aerial vehicles inevitably switch the steering actions in high frequency during both exploration and execution phase, resulting in the well known flight trajectory oscillation issue, which makes flight dynamics unstable, and even endangers flight safety in serious cases. Unfortunately, there is hardly any literature about achieving flight trajectory smoothness in DRL-based motion planning. In view of this, we originally formalize the practical flight trajectory smoothen problem as a three-level Nested pArameterized Smooth Trajectory Optimization (NASTO) form. On this basis, a novel Stable Auxiliary Gradient (SAG) algorithm is proposed, which significantly smoothens the DRL-generated flight motions by constructing two independent optimization aspects: the major gradient, and the stable auxiliary gradient. Experimental result reveals that the proposed SAG algorithm outperforms baseline DRL-based intelligent aerial transportation vehicle motion planning algorithms in terms of both learning efficiency and flight motion smoothness.

Compensation-Based Output Feedback Control for Fuzzy Markov Jump Systems With Random Packet Losses.

This article is concerned with the problem of compensation-based output feedback control for Takagi-Sugeno fuzzy Markov jump systems subject to packet losses. The phenomenon of packet losses is assumed to randomly occur in the feedback channel, which is modeled by a Bernoulli process. Employing the single exponential smoothing method as a compensation scheme, the missing measurements are predicted to help offset the impact of packet losses on system performance. Then, an asynchronous output feedback controller is designed by the hidden Markov model. Based on the mode-dependent Lyapunov function, some novel sufficient conditions on the controller existence are derived such that the closed-loop system is stochastically stable with strict dissipativity. Besides, an algorithm for determining the optimal smoothing parameter is proposed. Finally, the validity and advantages of the design approach are manifested by some simulation results.

Novel mass-based multigrid relaxation schemes for the Stokes equations

In this work, we propose three novel block-structured multigrid relaxation schemes based on distributive relaxation, Braess–Sarazin relaxation, and Uzawa relaxation, for solving the Stokes equations discretized by the marker-and-cell scheme. The mass matrix obtained from the bilinear finite element method is directly used to approximate the inverse of scalar Laplacian operator in the relaxation schemes. Using local Fourier analysis, we theoretically derive optimal smoothing factors for the resulting three relaxation schemes. Specifically, mass-based distributive relaxation, mass-based Braess–Sarazin relaxation, and mass-based σ-Uzawa relaxation have optimal smoothing factor 13, 13 and 13, respectively. These smoothing factors are smaller than those in our earlier work [1], where weighted Jacobi iteration is used for inventing Laplacian involved in the Stokes equations. The mass-based relaxation schemes do not cost more than the original ones using the Jacobi iteration. Another superiority of mass-based relaxation is that there is no need to compute the inverse of a matrix. These new relaxation schemes are appealing.

A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity

In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are presented to illustrate the performance of the proposed stochastic approximations in the PDE-constrained optimization setting.

Calibration-free pH long-time measurement method based on electrode potential drift dynamic compensation-applying self-adaptive dynamic optimization exponential smoothing method

The long-term in-situ accurate measurement of pH value is an urgent need for environmental water quality monitoring without calibration of pH electrodes. The nonlinearity and potential drift of pH electrode is the main problem which restricts long-term continuous monitoring. The characteristic rules including electrode potential, zero value, electrode slope coefficient, and electrode potential drift for pH electrode are analyzed in detail under the condition of long-term continuous use. The exponential smoothing potential drift prediction model with self-adaptive dynamic optimization smoothing order and smoothing coefficient is established. Combining electrode potential drift threshold judgment and Nernst equation, calibration-free dynamic calculation mathematical model of pH long-term monitoring is established. Indoor simulation and field test indicate that the measurement absolute error caused by electrode drift is within 0.01 pH and the specified measurement error for pH monitoring instrument is always within 0.1 pH. The proposed method is very suitable for the terminal of pH detector with the advantages of good portability for the MCU chip, small samples, high-precision and fast running speed. Furthermore, the life of pH electrode can be prolonged significantly. It is also proved that the proposed method has a good application prospect.