Optimal Smoothing Research Articles

LiDAR DEM Smoothing and the Preservation of Drainage Features

Fine-resolution Light Detection and Ranging (LiDAR) data often exhibit excessive surface roughness that can hinder the characterization of topographic shape and the modeling of near-surface flow processes. Digital elevation model (DEM) smoothing methods, commonly low-pass filters, are sometimes applied to LiDAR data to subdue the roughness. These techniques can negatively impact the representation of topographic features, most notably drainage features, such as headwater streams. This paper presents the feature-preserving DEM smoothing (FPDEMS) method, which modifies surface normals to smooth the topographic surface in a similar manner to approaches that were originally designed for de-noising three-dimensional (3D) meshes. The FPDEMS method has been optimized for application with raster DEM data. The method was compared with several low-pass filters while using a 0.5-m resolution LiDAR DEM of an agricultural area in southwestern Ontario, Canada. The findings demonstrated that the technique was better at removing roughness, when compared with mean, median, and Gaussian filters, while also preserving sharp breaks-in-slope and retaining the topographic complexity at broader scales. Optimal smoothing occurred with kernel sizes of 11–21 grid cells, threshold angles of 10°–20°, and 3–15 elevation-update iterations. These parameter settings allowed for the effective reduction in roughness and DEM noise and the retention of terrace scarps, channel banks, gullies, and headwater streams.

Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems

On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many efforts would guarantee a solution of desired accuracy. In this paper, we pursue the opposite direction by deriving lower complexity bounds of first-order methods on large-scale SPPs. Our results apply to the methods whose iterates are in the linear span of past first-order information, as well as more general methods that produce their iterates in an arbitrary manner based on first-order information. We first work on the affinely constrained smooth convex optimization that is a special case of SPP. Different from gradient method on unconstrained problems, we show that first-order methods on affinely constrained problems generally cannot be accelerated from the known convergence rate $O(1/t)$ to $O(1/t^2)$, and in addition, $O(1/t)$ is optimal for convex problems. Moreover, we prove that for strongly convex problems, $O(1/t^2)$ is the best possible convergence rate, while it is known that gradient methods can have linear convergence on unconstrained problems. Then we extend these results to general SPPs. It turns out that our lower complexity bounds match with several established upper complexity bounds in the literature, and thus they are tight and indicate the optimality of several existing first-order methods.

Source characteristics of the March 16, 2014 Mw 6.7 earthquake and its implications for the Mw 8.2 Pisagua mainshock

The March 16, 2014 Mw 6.7 earthquake played an important role in the complex seismic sequence leading to the nucleation of the April 1st, 2014 Mw 8.2 Pisagua earthquake in northern Chile. The Mw 6.7, an upper plate reverse faulting event with nodal planes highly rotated counterclockwise with respect to the strike of the megathrust at its location, is analyzed. For each nodal plane of the regional W-phase centroid moment tensor solution, the spatiotemporal slip distribution is inverted using near-field records. The optimal space and time smoothing constraints are determined objectively based on the Akaike's Bayesian Information Criterion. We analyze seismicity on the region affected by the Mw 6.7 and Mw 8.2 Pisagua mainshock, with accurate hypocenter locations obtained using a 3D heterogeneous medium. We also performed regional moment tensor inversion of events (M≥4.0) occurred before the Mw 8.2. Our results suggest the sub-vertical fault plane dipping southward (dip∼70°) as being the causative fault of the March 16 Mw 6.7 earthquake. The rupture propagated to the northwest, lasted 15s, and yielded a total seismic moment of 1.36×1019Nm (Mw 6.7). Estimated slip is characterized by total rupture length of ∼22km, and suggest shallow slip distributed between ∼ 3km, down to 17km depth. A comparison between coastal tide gauge records and forward tsunami modeling show similarity of the time series, thus supporting the plausibility of our estimated slip models. Our interpretation suggests that the rupture of the Mw 6.7 intraplate could be explained by stress accommodation between two segments along-dip with different mechanical properties at the interplate boundary, and inside the upper plate.

Equivalent Markov models for filtering and smoothing of mining vehicle positions

A linear state-space model is described whose second-order moments match that of a hidden Markov chain (HMC). This model enables a modified transition probability matrix to be employed within minimum-variance filters and smoothers. However, the ensuing filter/smoother designs can exhibit suboptimal performance because a previously reported transition-probability-matrix modification is conservative, and identified models can lack observability and reachability. This article describes a less-conservative transition-probability-matrix modification and a model-order-reduction procedure to enforce observability and reachability. An optimal minimum-variance predictor, filter, and smoother are derived to recover the Markov chain states from noisy measurements. The predictor is asymptotically stable provided that the problem assumptions are correct. It is shown that collapsing the model improves state-prediction performance. The filter and smoother recover the Markov states exactly when the measurement noise is negligible. A mining vehicle position tracking application is discussed in which performance benefits are demonstrated.

Extraction of grain boundary curvature from voxel-based representations of polycrystalline microstructures

Extracting the curvature of grain boundaries from 3D voxel-based representations of microstructure is challenging. Previous investigations have concluded that the accuracy of curvature estimation depends strongly on the degree of smoothing after a microstructure has been meshed. We find that best results are obtained when the degree of smoothing is determined on a boundary-by-boundary basis. Evaluating a voxelized representation of a Reuleaux tetrahedron of known boundary curvature, we establish that, for a given boundary, the optimal smoothing power minimizes the coefficient of variation (CV) of local curvature. We apply the minimum-CV criterion to the extraction of grain boundary curvatures from a measurement of polycrystalline Al-5 wt% Cu performed by 3D x-ray diffraction (3DXRD) microscopy. The results show that grain boundaries in this sample are surprisingly flat. Moreover, boundaries of larger area manifest lower curvature, while higher curvature values are observed solely for boundaries of smaller area.

A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization

Here, we propose a practical method for solving nonsmooth convex problems by using conjugate gradient type methods. We present a modified HS conjugate gradient method, as one of the most remarkable methods to solve smooth and large-scale optimization problems. In the case that we have a nonsmooth convex problem, by way of the Moreau-Yosida regularization, we convert the nonsmooth objective function to a smooth function and then we use our method, by making use of a nonmonotone line search, for solving a nonsmooth convex optimization problem. We prove that our algorithm converges to an optimal solution under standard condition. Our algorithm inherits the performance of HS conjugate gradient method.

Determination of Optimal Smoothing Constants for Holt - Winter’s Multiplicative Method

There are many trade time series parade having seasonality. This paper ponders on taking the appropriate smoothing constants of seasonal time series data using Holt-Winter’s exponential smoothing method in demand forecasting of toy production in a company. It is a quantitative technique in forecasting. This forecasting method is used three constants that assign weights to current demands and previous forecasts to decide on a new forecast. We have demonstrated the techniques how to choose these constants by presenting a real life example and calculated corresponding forecast value of this technique for the optimal smoothing constants.
 Dhaka Univ. J. Sci. 67(2): 99-104, 2019 (July)

Analytic approximation and differentiability of joint chance constraints

ABSTRACTAn inner–outer approximation approach was recently developed to solve single chance constrained optimization (SCCOPT) problems. In this paper, we extend this approach to address joint chance constrained optimization (JCCOPT) problems. Using an inner–outer approximation, two smooth parametric optimization problems are defined whose feasible sets converge to the feasible set of JCCOPT from inside and outside, respectively. Any optimal solution of the inner approximation problem is a priori feasible to the JCCOPT. As the approximation parameter tends to zero, a subsequence of the solutions of the inner and outer problems, respectively, converge asymptotically to an optimal solution of the JCCOPT. As a main result, the continuous differentiability of the probability function of a joint chance constraint is obtained by examining the uniform convergence of the gradients of the parametric approximations.

Commensal bacterial sharing does not predict host social associations in kangaroos.

Social network analysis has been postulated as a tool to study potential pathogen transmission in wildlife but is resource-intensive to quantify. Networks based on bacterial genotypes have been proposed as a cost-effective method for estimating social or transmission network based on the assumption that individuals in close contact will share commensal bacteria. However, the use of network analysis to study wild populations requires critical evaluation of the assumptions and parameters these models are founded on. We test (a) whether networks of commensal bacterial sharing are related to hosts' social associations and hence could act as a proxy for estimating transmission networks, (b) how the parameters chosen to define host associations and delineate bacterial genotypes impact inference and (c) whether these relationships change across time. We use stochastic simulations to evaluate how uncertainty in parameter choice affects network structure. We focused on a well-studied population of eastern grey kangaroos (Macropus giganteus), from Sundown National Park, Australia. Using natural markings, each individual was identified and its associations with other kangaroos recorded through direct field observations over 2years to construct social networks. Faecal samples were collected, Escherichia coli was cultured and genotyped using BOX-PCR, and bacterial networks were constructed. Two individuals were connected in the bacterial network if they shared at least one E.coli genotype. We determined the capacity of bacterial networks to predict the observed social network structure in each year. We found little support for a relationship between social association and dyadic commensal bacterial similarity. Thresholds to determine host associations and similarity cut-off values used to define E.coli genotypes had important ramifications for inferring links between individuals. In fact, we found that inferences can show opposite patterns based on the chosen thresholds. Moreover, no similarity in overall bacterial network structure was detected between years. Although empirical disease transmission data are often unavailable in wildlife populations, both bacterial networks and social networks have limitations in representing the mode of transmission of a pathogen. Our results suggest that caution is needed when designing such studies and interpreting results.

Homotopy method for solving mathematical programs with bounded box-constrained variational inequalities

ABSTRACTOn the basis of Robinson's normal equation and smoothing projection operator, a homotopy method for solving mathematical programs with box-constrained variational inequalities (MPBVI) is presented. In which, the Chen–Harker–Kanzow–Smale smooth function is used to transform MPBVI into a smooth optimization problem. Under some mild assumptions, the existence and global convergence of a smooth path from almost any initial point to the GKKT point of the approximate problems is proven. And, the convergence of the GKKT point to a strong C-stationary point of the original problems is proved. Finally, some numerical results are given to show the effectiveness and feasibility of the homotopy method.

Unscented Rauch–Tung–Streibel smoother‐based power system forecasting‐aided state estimator using hybrid measurements

A hybrid estimator to track the power system states considering fast-rate PMUs and slow-rate supervisory control and data acquisition (SCADA) system is proposed in this article. SCADA measurements arrive at the control centre with various time delays. The estimates obtained using these delayed measurements significantly differs from the actual power system states and is known as the time skew problem. The missing SCADA measurements, owing to their time skewness, are replaced by their predicted values which lead to reduced estimation accuracy. Optimal smoothing algorithms can be utilised to include dynamics in the future measurements to reduce the errors introduced by the time skew problem. Unscented Rauch–Tung–Streibel smoother is used in this study to handle the time skew problem. The performance of the proposed techniques in handling anomalous situations is also studied. The proposed estimator is validated under real-time environment using RTDS, a real-time simulation tool, to assess its applicability in the control centre.

Optimal Filtering and a Smoothing Algorithm for a Singular System With a Complex Stochastic Uncertain Parameter Matrix

This brief considers estimation algorithms for linear singular systems with random uncertain parameter matrices. We propose an optimal filtering algorithm and an optimal fixed-interval smoothing algorithm to filter out artifacts, such as noise, from the parameter matrix by using the projection theorem and an equivalent transformation. A performance analysis and simulation results verify the proposed algorithms.

Recovery of a Compressed Sensing CT Image Using a Smooth Re-weighted Function- Regularized Least-Squares Algorithm

It is challenging to recover the required compressed CT (Computed Tomography, CT) image, which is got by transferred through the internet or is stored in a signal library after being compressed. We present a recovery method for compressed sensing CT images. At present, minimizing 0-norm, 1-norm and p-norm is used to recover compressed sensing signals. However, sometimes 0-norm is an NP problem, 1-norm has no solution in theory and p-norm is not a convex function. We introduce a recovery method of compressed sensing signal based on regularized smooth convex optimization. In order to avoid solving the non-convex optimization problems and no solution condition, a convex function is designed as the objective function of optimization to fit 0-norm of signal and a fast iterative shrinkage-thresholding algorithm is proposed to find solution with the convergence speed is quadratic convergence. Experimental results show that our method has a sound recovery effect and is well suitable for processing big data of compressed CT images.

Using 3D robust smoothing to fill land surface temperature gaps at the continental scale

Land surface temperature (LST) data derived from Moderate Resolution Imaging Spectroradiometer (MODIS) products has been widely applied in environmental studies, and natural disaster management. However missing data in space and time due to cloud contamination, cloud shadows and atmospheric conditions has hindered its application. Accurate gap filling algorithms for a large spatiotemporal scale of LST data are necessary to enhance the utility of this product. This study applied a three-dimensional (3-D) gap-filling method to fill gaps in 9 years of LST data over Australia (2002–2011). As the gap-filling method relies on a smoothing parameter that controls the accuracy of the reconstruction algorithm, we estimated optimal smoothing parameters to separately reconstruct daytime and nighttime LST products. The reconstructed LST were validated against ground-based LST obtained from the OzFlux network and recommendations made on appropriate smoothing parameters. The results demonstrate that the gap-filling algorithm provides an accurate approach to generating reconstructed LST products for a long period over large spatial scales.

State-Space Realizations and Optimal Smoothing for Gaussian Generalized Reciprocal Processes

This technical note derives stochastic realization and optimal smoothing algorithms for a class of Gaussian generalized reciprocal processes (GGRP). The note exploits the interplay between reciprocal processes and Markov bridges which underpin the GGRP model. A forward–backward algorithm for stochastic realization of GGRP is described. The form on the inverse covariance matrix for the GGRP is used, via Cholesky factorization, to derive a procedure for optimal (MMSE) smoothing of GGRP observed in noise. The note demonstrates that the associated smoothing error is also a GGRP with known covariance which may be used to assess the performance of smoothing as a function of the model parameters. A numerical example is provided to illustrate the performance of the MMSE smoother compared to those derived from compatible Markov and reciprocal model-based algorithms.

Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates

Allowing for the existence of irrelevant covariates, we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data. We estimate the conditional quantile regression function using the check-function-based kernel method and suggest a data-driven cross-validation (CV) approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates. When the number of covariates is large, we first use a screening method to remove the irrelevant covariates and then apply the CV criterion to those that survive the screening procedure. Simulations and an empirical application demonstrate the usefulness of the proposed methods.

Reachability of optimal convergence rate estimates for high-order numerical convex optimization methods

The Monteiro-Svaiter accelerated hybrid proximal extragradient method (2013) with one step of Newton’s method used at every iteration for the approximate solution of an auxiliary problem is considered. The Monteiro-Svaiter method is optimal (with respect to the number of gradient and Hessian evaluations for the optimized function) for sufficiently smooth convex optimization problems in the class of methods using only the gradient and Hessian of the optimized function. An optimal tensor method involving higher derivatives is proposed by replacing Newton’s step with a step of Yu.E. Nesterov’s recently proposed tensor method (2018) and by using a special generalization of the step size selection condition in the outer accelerated proximal extragradient method. This tensor method with derivatives up to the third order inclusive is found fairly practical, since the complexity of its iteration is comparable with that of Newton’s one. Thus, a constructive solution is obtained for Nesterov’s problem (2018) of closing the gap between tight lower and overstated upper bounds for the convergence rate of existing tensor methods of order p ≥ 3.

Distributed Smooth Convex Optimization With Coupled Constraints

This note develops a distributed algorithm to solve a convex optimization problem with coupled constraints. Both coupled equality and inequality constraints are considered, where functions in the equality constraints are affine and functions in the inequality constraints are convex. Different from primal-dual subgradient methods with decreasing stepsizes for nonsmooth optimizations, our algorithm focuses on smooth problems and uses a fixed stepsize to find the exact optimal solution. Convergence analysis is derived with rigorous proofs. Our result is also illustrated by simulations.

Two families of scaled three-term conjugate gradient methods with sufficient descent property for nonconvex optimization

In this paper, we present two families of modified three-term conjugate gradient methods for solving unconstrained large-scale smooth optimization problems. We show that our new families satisfy the Dai-Liao conjugacy condition and the sufficient descent condition under any line search technique which guarantees the positiveness of ${y_{k}^{T}} s_{k}$. For uniformly convex functions, we indicate that our families are globally convergent under weak-Wolfe-Powell line search technique and standard conditions on the objective function. We also establish a weaker global convergence theorem for general smooth functions under similar assumptions. Our numerical experiments for 260 standard problems and seven other recently developed conjugate gradient methods illustrate that the members of our families are numerically efficient and effective.

Optimization of Process Conditions for Styrene Epoxidation Based on the Artificial Intelligence Method

AbstractA novel prediction and optimization method based on improved generalized regression neural network (GRNN) and particle swarm optimization (PSO) algorithm is proposed to optimize the process conditions for styrene epoxidation to achieve higher yields. This model was designed to optimize the five input parameters reaction temperature and time as well as catalyst, solvent, and oxidant dosage. The output of the improved GRNN was given to the PSO algorithm to optimize the process conditions. The optimal smoothing parameter σ of GRNN was chosen from the training sample with a minimum cross validation error. Under the five optimized process conditions the maximum yield reached 95.76 %. This innovative model of improved GRNN hybrid PSO algorithm proved to be a useful tool for optimization of process conditions for styrene epoxidation.