Nonlinear Smoothing Research Articles

Sharp Local Well-Posedness and Nonlinear Smoothing for Dispersive Equations through Frequency-Restricted Estimates

Sharp Local Well-Posedness and Nonlinear Smoothing for Dispersive Equations through Frequency-Restricted Estimates

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

ℓ1${\ell }_1$ norm‐based recursive estimation for non‐linear systems with non‐Gaussian noises

AbstractThis study addresses the state estimation problem of discrete‐time non‐linear stochastic systems with non‐Gaussian noises, particularly impulsive noises. Instead of minimizing the mean square error of the state estimate, which tends to excessively focus on outliers caused by non‐Gaussian noises, the norm‐based non‐linear recursive filter (L1KF) is put forward in this paper. Here, minimizing the norm of model errors is actually to pursue the minimum sum of absolute values of all errors, which is equitable to all model errors rather than paying much attention on outliers. To further improve estimation accuracy, a recursive nonlinear smoother (L1KS) is proposed, based on minimizing the norm of model errors. The proposed norm‐based filter and smoother are implemented using unscented transformation for statistical linear regression applied to nonlinear models. Additionally, the computational complexity of the proposed method is analysed. Simulation results of tracking a radar target with impulsive noises demonstrate the effectiveness and robustness of the proposed estimator.

Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation

Abstract This paper is devoted to studying the pointwise convergence problem and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation. Firstly, we present an alternative proof of Theorem 1.5 of Linares and Ramos [Maximal function estimates and local well-posedness for the generalized Zakharov–Kuznetsov equation, SIAM J. Math. Anal. 53 (2021), 1, 914–936] and Theorem 1.8 of Linares and Ramos [The Cauchy problem for the L 2 L^{2} -critical generalized Zakharov–Kuznetsov equation in dimension 3, Comm. Partial Differential Equations 46 (2021), 9, 1601–1627]. Secondly, we give an alternative proof of Theorem 1.1 of Ribaud and Vento [A note on the Cauchy problem for the 2D generalized Zakharov–Kuznetsov equations, C. R. Math. Acad. Sci. Paris 350 (2012), 9–10, 499–503] and present the nonlinear smoothing and uniform convergence of two-dimensional generalized Zakharov–Kuznetsov equation. Thirdly, we give an alternative proof of Theorem 1.4 of Linares and Ramos [Maximal function estimates and local well-posedness for the generalized Zakharov–Kuznetsov equation, SIAM J. Math. Anal. 53 (2021), 1, 914–936]. Finally, we study the nonlinear smoothing and uniform convergence of 𝑛-dimensional generalized Zakharov–Kuznetsov equation with n ≥ 3 n\geq 3 .

Predictive Control Scheme for Fuel Cell Air Compressor Efficiency Enhancement with Surge‐ and Choke‐Constrained Awareness

AbstractThe efficiency and dynamic response of air compressors are crucial for stability and lifespan of hydrogen fuel cells. A predictive control scheme with surge‐ and choke‐constrained awareness is proposed to ensure safe and efficient operation of air compressors in this study. The proposed scheme consists of an efficiency enhancement model predictive control (EE‐MPC), and an improved active disturbance rejection control (IADRC). Surge‐ and choke‐constrained awareness is achieved by comparing predicted air flow with surge and choke limitations. Simultaneously, the EE‐MPC is constrained with oxygen excess ratio (OER) and obtains optimal solution by searching active set. The reference flow and supply manifold pressure trajectories for IADRC are generated by EE‐MPC. A designed piecewise differentiable nonlinear smoothing function is embedded in IADRC. The disturbances are estimated for coordinating flow and pressure control. Under China heavy‐duty commercial vehicle test cycle for bus conditions, root‐mean‐squared errors (RMSEs) of flow and pressure are 3.27 g s−1 and 1.88 × 103 Pa, respectively, and the mean efficiency can be enhanced by 13.4% compared to the MPC with fixed OER. Finally, a controller hardware‐in‐the‐loop test is conducted, with flow and pressure RMSEs of 2.48 g s−1 and 4.28 × 103 Pa between the test and simulation, respectively.

Auxiliary two-filter particle smoothing for one generalized hidden Markov model

This paper develops two-filter particle smoothing (TFPS) algorithms for the nonlinear fixed-interval smoothing problem of one generalized hidden Markov model (GHMM), where the current observation depends not only on the current state, but also on one-step previous state. Firstly, by Bayesian approach, the two-filter smoothing (TFS) formula for GHMM is established to calculate smoothing densities. In this TFS formula, the backward information prediction density is generally not a density of the state. This results in a difficulty that the normal sequential Monte Carlo (SMC) sampling technique cannot be directly applied to design corresponding TFPS algorithms based on the TFS formula. To solve this difficulty, a generalized TFS formula for GHMM is then proposed by introducing a sequence of artificial densities. By combining this generalized TFS formula, SMC, and the auxiliary variable sampling technique, a basic auxiliary TFPS (ATFPS) algorithm with quadratic computational complexity is proposed, and a simplified ATFPS algorithm with linear computational complexity is further developed. Finally, the effectiveness and superiority of the two proposed ATFPS algorithms for GHMM are verified via simulation examples and real experimental data.

Lulu Filterized Lin’s correlative Theil-Sen regression-based fully connected deep multilayer perceptive neural network for eye gaze pattern recognition

Gaze estimation is process finding the point of gaze on observe axis of eye. Gaze tracking schemes are mainly employed in HCI and study of visual scanning samples. Traditional tracking schemes usually need accurate personal calibration procedure to evaluate the particular eye metrics. In order to improve the accurate gaze estimation, Lulu Filterized Lin?s Correlative Theil-Sen Regression-based Fully Connected Deep Multilayer Perceptive Neural Network (LFLCTR-FCDMPNN) is designed for accurate gaze pattern identification through lesser time consumption. Fully Connected Deep Multilayer Perceptive NN contains input layer, three hidden layers, output layer. In input layer, number of gaze images is collected. Then using Lulu nonlinear smoothing filtering method is applied in initial hidden layer for removing noise as well as enhancing image quality. In second hidden layer, Polar coordinate system-based eye-gaze point estimation is performed. Finally, the Gaze Pattern matching is carried out in third hidden layer using Lin?s Concordance Correlative Theil-Sen regression. The estimated gaze points are organized at gaze plane to identify gaze patterns. Then pattern matching performed by Lin?s Concordance Correlation. In this way, the eye gaze patterns are correctly recognized at the output layer. Experimental evaluation is conducted to demonstrate performance analysis of LFLCTR-FCDMPNN technique through different metrics like gaze pattern recognition accuracy, gaze pattern recognition time, and false-positive rate with different number of eye images. Explained result illustrates which LFLCTR-FCDMPNN method improves the accuracy of gaze pattern recognition and decreases the time consumption than the conventional prediction methods. Using the Synthes Eyes dataset, it turned out that the FPR of the suggested LFLCTR-FCDMPNN was 63% higher than existing.

Prediction method for the truck's fault time in open-pit mines based on exponential smoothing neural network

The transport truck is one of the important equipment for open-pit mines, and predicting the truck's fault time is of great significance in improving the economic benefits of open-pit mines. In this paper, we discuss the reason for the large prediction error of the exponential smoothing method. Then, we propose a novel nonlinear exponential smoothing method (ESNN) for predicting the truck's fault time, and demonstrate the equivalence between our approach and the neural network structure. Finally, based on the augmented Lagrange function, the solving method of ESNN is proposed. We conduct experiments on real-world datasets and our results demonstrate the effectiveness of ESNN in comparison to existing state-of-the-art methods. Our approach makes it easier for maintenance personnel to predict fault situations in advance and provides a basis for enterprises to develop preventive maintenance plans.

Inversion of VLF-R data using a non-linear rank order smoothing constraint and its implementation to image surface rupture of the North Anatolian Fault in Başiskele, Kocaeli, NW Turkey

Inversion of electromagnetic induction data is often realized using smoothing operators for regularizing the process. These operators are applied using derivative matrices, penalizing differences between neighboring mesh cells. The resulting smoothing effect is similar to that of low-pass Gaussian filters and may cause difficulties due to the smoothed boundaries between structures. To prevent such ambiguities, non-linear rank filters are applied widely in image processing applications to filter low frequency variations while keeping boundaries. Correspondingly, we have defined a non-linear rank order smoothing operator for regularization. The effects of the defined parameters are demonstrated on synthetic models and the operator is observed to be able to provide better defined boundaries. The implementation of the operator on field data is realized using single-frequency VLF-R data collected on profiles traversing the surface rupture of the North Anatolian Fault in Kocaeli, Turkey. In the study area, ERT data are also collected on a single profile, and its smooth inversions are realized individually and jointly with VLF-R data for comparisons. Inversions show that the recovered subsurface structure using the rank order smoothing is closer to that indicated by the ERT data and previous studies. According to the recovered models, the clayey fillings in the fault rupture are acting as a barrier affecting the horizontal fluid flow in the near-surface and the resulting water accumulations around the fault rupture may cause susceptibility for earthquake induced damages.

Variational Identification of Linearly Parameterized Nonlinear State-Space Systems

A variational Bayesian (VB) approach to the identification of linearly parameterized nonlinear state-space models (LP-NSSMs) is developed in this article. Conjugate priors over the unknown parameters are introduced, and the posterior distributions are approximated under the VB framework. In order to estimate the hidden states of the LP-NSSMs with random parameters, the augmented LP-NSSMs are established such that nonlinear smoothing methods can be applied. An extension to comprehensively tackling data anomalies, such as outliers and missing observations, is also considered to further improve the robustness of the presented method. Finally, a numerical example and the practical benchmarks are adopted to validate the efficacy of the proposed algorithm.

The mean reversion/persistence of financial cycles: Empirical evidence for 24 countries worldwide

Research background: The globalization trend has inevitably enhanced the connectivity of global financial markets, making the cyclicality of financial activities and the spread of market imbalances have received widespread attention, especially after the global financial crisis. Purpose of the article: To reduce the negative effects of the contagiousness of the financial cycles, it is necessary to study the persistence of financial cycles and carve out the total connectedness, spillover paths, and sources of risks on a global scale. In addition, understanding the relationship between the financial cycle and economic development is an important way to prevent financial crises. Methods: This paper adopts the nonlinear smoothing transition autoregressive (STAR) model to extract cyclical and phase characteristics of financial cycles based on 24 countries during 1971Q1?2015Q4, covering developed and developing countries, the Americas, Europe, and Asia regions. In addition, the frequency connectedness approach is used to measure the connectedness of financial cycles and the relationship between the global financial cycle and the global economy. Findings & value added: The analysis reveals that aggregate financial cycles persist for 13.3 years for smoothed and 8.7 years for unsmoothed on average. The national financial cycles are asynchronous and exhibit more prolonged expansions and faster contractions. The connectedness of financial cycles is highly correlated with systemic crises and contributes to the persistence and harmfulness of shocks. It is mainly driven by short-term components and exhibits more pronounced interconnectedness within regions than across regions. During the financial crisis, the global financial cycle movements precede and are longer than the business fluctuations. Based on the study, some policy implications are presented. This paper emphasizes the impact of systemic crises on the persistence of financial cycles and their connectedness, which contributes to refining research related to the coping mechanisms of financial crises.

Feature Sampling based on Multilayer Perceptive Neural Network for image quality assessment

Image quality assessment (IQA) has a vital issue in image processing to measure the perceptual quality of the image. This aims at the human visual system (HVS) by viewing for distorted images from reference images. HVS is the ultimate receiver of visual data in major applications. But, quality assessment is generally a time-consuming and luxurious method. In our work, the novel Bilateral Smoothing Filtered Feature Sampling-Based Tanimoto Index’ve Multilayer Perceptive Neural Network (BSFFS-TIMPNN) technique is developed. The main contribution of the designed BSFFS-TIMPNN technique is for enhancing the quality of the assessment performance with full reference and no reference images with multiple layers. At first, the original and reference image is taken to the input layer and sent to the first hidden layer. Followed by, image preprocessing is performed in the first hidden layer by using the novelty of a nonlinear bilateral smoothing filtering technique for eradicating noisy pixels with a higher-quality image. Next, patch extraction is executed in the second hidden layer with the novelty of the nearest neighbor sampling approach to split images into various patches. Then, the different features of the image such as shape, color, and texture are extracted in the third hidden layer. Finally, classification is carried out output layer by applying the innovation of the Tanimoto similarity index to examine the extracted features for IQA. We estimate the proposed BSFFS-TIMPNN technique on the Tampere Image Database (TID2013) dataset with qualitative and quantitative results analysis. The proposed BSFFS-TIMPNN technique is employed to compute image quality with maximum accuracy and minimum time and memory consumption when compared to other related methods by MATLAB simulator. The observed quantitative result demonstrates the better performance of the proposed BSFFS-TIMPNN technique by full reference and no reference with higher PSNR by 8%, accuracy by 15%, 17%, lesser memory consumption by 15%, 17, and faster prediction time by 9%, 9% than the state of art methods respectively.

Low regularity well–posedness for dispersive equations on semi–infinite intervals

We summarize and report recent advancements in the theory of dispersive equations posed on semi–infinite intervals. By employing modern Fourier analysis techniques we show how these initial-boundary value problems can be resolved for initial data in Sobolev spaces of low regularity. In almost all the cases, we obtain sharp results that match the regularity of their full line analogues. We especially address the issues of local well–posedness, nonlinear smoothing, and uniqueness of solutions. In the second part of the paper we apply some of the tools we discussed in the first part, to prove existence and uniqueness of $ L^2 $ solutions for the biharmonic equation, extending the result in [10].

Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation

A polynomial-in-time growth bound is established for global Sobolev \(H^s({\mathbb {T}})\) solutions to the derivative nonlinear Schrödinger equation on the circle with \(s>1\). These bounds are derived as a consequence of a nonlinear smoothing effect for an appropriate gauge-transformed version of the periodic Cauchy problem, according to which a solution with its linear part removed possesses higher spatial regularity than the initial datum associated with that solution.

A reliable method of wind power fluctuation smoothing strategy based on multidimensional non‐linear exponential smoothing short‐term forecasting

This paper investigates the multi-dimensional non-linear exponential smoothing prediction method under different weight coefficients, so as to realize the short-term prediction of the original wind power output. Based on the current research on wind power fluctuation prediction, this paper firstly proposes a new multi-dimensional nonlinear exponential smoothing prediction method. Based on different weight coefficients, the corresponding short-term forecast volatility is obtained. Then, the wavelet packet decomposition method is used to further realize the secondary smoothing of the prediction wind power fluctuations. Hybrid energy storage system (HESS) plays an important role in wind power fluctuation suppression from different frequency bands. However, the traditional fixed frequency power allocation method significantly degrades the performance of the accuracy of the algorithm. Therefore, this paper proposes a frequency conversion entropy strategy, which combines energy value with wavelet packet decomposition. By calculating the energy components of different frequency bands, the fluctuation can be divided effectively. Finally, simulation and experiment discussions show that the proposed algorithm in this paper can realize the power allocation effectively compared to the traditional one. And it further verifies the feasibility and reliability of the strategy proposed in this work.

Nonlinear smoothing for the periodic generalized nonlinear Schrödinger equation

We consider the periodic nonlinear Schrödinger equation with nonlinearity given by |u|p−1u for odd p>1 in dimension 1. We first establish that the difference between the nonlinear evolution and a phase rotation of the linear evolution is in a smoother space. We then study forced and damped defocusing nonlinear Schrödinger equations of the above type and establish an analogous smoothing statement that extends globally in time. As a corollary we establish both existence and smoothness for global attractors in the energy space.

Convergence of a finite volume scheme for a parabolic system applied to image processing

Abstract We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to the finite volume scheme. Then, based on the derivation of a series of a priori estimates and the use of Kolmogorov’s compactness criterion, we prove that the solution to the finite volume scheme converges to the weak solution. In the numerical experiments, we show the effectiveness of the proposed model with respect to the modified (in the sense of Catté, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoothing equation in terms of preserving small details, texture, and fine structures.

Anatomical mining method of cervical nerve root syndrome under visual sensing technology

INTRODUCTION: The gray resolution of anatomical image of cervical nerve root syndrome is low, that can not be mined accurately. OBJECTIVES: Aiming at the defect of low gray resolution of anatomical images, an image mining method using visual perception technology was studied. METHODS: According to the visual perception technology, the internal parameter matrix and external parameter matrix of binocular visual camera were determined by coordinate transformation, and the anatomical images of cervical nerve root syndrome were collected. The collected images are smoothed and enhanced by nonlinear smoothing algorithm and multi-scale nonlinear contrast enhancement method. The directional binary simple descriptor method is selected to extract the features of the enhanced image; Using K-means clustering algorithm, the anatomical image mining of cervical nerve root syndrome is completed by obtaining the initial clustering center and image mining. RESULTS: Experimental results show that the information entropy of the images mined by the proposed method is higher than 5, the average gradient is greater than 7, the edge information retention is greater than 0.7, the peak signal-to-noise ratio is higher than 30 dB, and the similarity of the same category of images is greater than 0.9. CONCLUSIONS: This method can effectively mine the anatomical images of cervical nerve root syndrome and provide an important basis for the diagnosis and treatment of cervical nerve root syndrome.

Quantifying and characterizing the impacts of PM2.5 and humidity on atmospheric visibility in 182 Chinese cities: A nationwide time-series study

Ambient particulate matter less than 2.5 μm (PM2.5) and humidity have been considered as two leading determinants of atmospheric visibility. However, quantitative evidence of their independent and interactive effects on visibility is rare at multi-city level. Based on the data of 190 monitoring stations from 182 Chinese cities, the generalized linear model combined with nonlinear smoother was constructed to estimate the station-specific effects of PM2.5 and relative humidity on visibility. Then, multivariate meta-analysis was used to pool the station-specific estimates. Finally, attributable visibility loss respectively due to PM2.5 and humidity were calculated. In general, both PM2.5 and relative humidity were detected to have a significant non-linear negative influence on visibility. Per 1 μg/m3 increase in PM2.5 was associated with a visibility reduction of 0.232 km and 0.030 km under the level of PM2.5 below or above 68 μg/m3, respectively. The visibility declined by 0.105 km, 0.254 km, and 0.569 km per 1% increase in relative humidity under low (<58%), middle (58%–85%), and high (>85%) humidity, respectively. Significant interactive effects of PM2.5 and humidity were observed. The impacts of PM2.5 on visibility were significantly amplified in days with moderate humidity. However, extremely high humidity could largely attenuate the PM2.5-visibility association. The influence of extremely high humidity (like 99%) also consistently declined as the PM2.5 concentration elevated. From the national perspective, PM2.5 accounted for a higher proportion of average daily visibility loss than humidity [9.75 km (95%CI: 7.94, 11.57) vs. 7.23 km (95%CI: 5.02, 9.45)]. The relatively mild polluted southern China suffered from similar PM2.5-attributable visibility loss with northern China. The findings could provide important information for the prediction and improvement of atmospheric visibility.

O-133 Association between normal-range paternal serum free thyroxine concentrations and outcomes of assisted reproductive technologies

Abstract Study question Are paternal serum free thyroxine (FT4) concentrations within the reference range associated with outcomes of assisted reproductive technologies (ART)? Summary answer Men of older reproductive age (≥ 35 years old) with low FT4 concentrations within the reference range are associated with a decreased live birth rate. What is known already The impact of maternal thyroid dysfunction on ART outcomes has been widely elucidated. However, few studies have investigated the impact of paternal thyroid dysfunction on ART outcomes. Our previous study showed a detrimental impact of paternal subclinical hypothyroidism (SCH) on the clinical outcomes of ART. Patients with SCH had relatively lower concentrations of FT4 compared to those with euthyroidism. Therefore, it remains to be determined whether the detrimental impacts of paternal SCH on ART outcomes arise from low concentrations of FT4. Study design, size, duration This retrospective cohort study included 4,066 couples who received 4,894 ART treatment cycles in our clinic between 1 April 2016 and 31 August 2021. Participants/materials, setting, methods The differences in sperm parameters and ART outcomes across the paternal FT4 tertiles were compared using generalised linear models or generalised estimation equation models. The primary outcomes were the clinical pregnancy rate (CPR) and live birth rate (LBR), and the secondary outcomes were sperm parameters, fertilisation rate, good-quality embryo rate, blastocyst formation rate, and implantation rate. Main results and the role of chance The mean ages of the males and their female partners were 33.0 and 31.0 years, respectively. No significant differences are observed in the sperm parameters and ART outcomes across the paternal FT4 tertiles in the overall population. However, stratified analysis of men aged ≥ 35 shows a non-significantly lower CPR in the lower paternal FT4 tertile (adjusted rate: 0.36, 95% CI: 0.27–0.45) relative to the middle (adjusted rate: 0.45, 95% CI: 0.38–0.53) and upper (adjusted rate: 0.43, 95% CI: 0.36–0.51) tertiles. The adjusted LBR is 0.21 (95% CI: 0.15–0.30) for men aged ≥ 35 in the lower FT4 tertile (p = 0.024, with reference to the upper tertile), 0.27 (95% CI: 0.21–0.35) for those in the middle tertile and 0.30 (95% CI: 0.23–0.38) for those in the upper tertile. No differences in these outcomes are seen among men aged &amp;lt; 35. The nonlinear smoothing curve obtained by using FT4 as a continuous variable further supports these findings. Limitations, reasons for caution Due to the retrospective design of the study, a causal relationship between paternal FT4 concentrations and ART outcomes could not be established. In addition, the study participants were patients who sought fertility treatment, which may have biased the results when we analysed the associations between FT4 concentrations and sperm parameters. Wider implications of the findings These results suggest that in older men, low paternal FT4 concentrations, although within the reference range, are associated with worse ART outcomes, especially LBR. Future prospective studies are warranted to confirm the detrimental effects of low paternal FT4 concentrations on ART outcomes. Trial registration number Not applicable