Regularization Coefficient Research Articles

Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation

In this paper, a non-modal parametric method to identify structural damage using a regularized autoregressive moving average time series model under environmental excitation is proposed in combination with the virtual impulse response function. This method can use the structural vibration response to determine the damage caused to the structure during environmental excitation. Firstly, the virtual impulse response function is obtained by using the structural vibration response. Then, a regularized ARMA time series model is used to fit the virtual impulse response function. Based on the change of auto-regression coefficients in the regularization model under different damage cases, the structural damage is identified. The authors derive the regularization equation of an ARMA time series model to solve the problems in a time series model and obtain the regularization coefficient. Finally, this method is applied to a three-degrees-of-freedom chain structure and a three-floor shear structure of the Los Alamos National Laboratory (LANL). The experimental results show that the method based on the regularized ARMA time series model under environmental excitation can effectively identify the structural damage, which is a reliable method for damage identification. The regularized ARMA time series model can accurately extract signal features and has invaluable application prospects in the field of structural health monitoring.

Robustness of Extreme Learning Machine in the prediction of hydrological flow series

Prediction of hydrological flow series generated from a catchment is an important aspect of water resources management and decision making. The underlying process underpinning catchment flow generation is complex and depends on many parameters. Determination of these parameters using a trial and error method or optimization algorithm is time consuming. Application of Artificial Intelligence (AI) based machine learning techniques including Artificial Neural Network, Genetic Programming (GP) and Support Vector Machine (SVM) replaced the complex modeling process and at the same time improved the prediction accuracy of hydrological time-series. However, they still require numerous iterations and computational time to generate optimum solutions. This study applies the Extreme Learning Machine (ELM) to hydrological flow series modeling and compares its performance with GP and Evolutionary Computation based SVM (EC-SVM). The robustness and performance of ELM were studied using the data from two different catchments located in two different climatic conditions. The robustness of ELM was evaluated by varying number of lagged input variables the number of hidden nodes and input parameter (regularization coefficient). Higher lead days prediction and extrapolation capability were also investigated. The results show that (1) ELM yields reasonable results with two or higher lagged input variables (flows) for 1-day lead prediction; (2) ELM produced satisfactory results very rapidly when the number of hidden nodes was greater than or equal to 1000; (3) ELM showed improved results when regularization coefficient was fine-tuned; (4) ELM was able to extrapolate extreme values well; (5) ELM generated reasonable results for higher number of lead days (second and third) predictions; (6) ELM was computationally much faster and capable of producing better results compared to other leading AI methods for prediction of flow series from the same catchment. ELM has the potential for forecasting real-time hydrological flow series.

Description of relations between regularity coefficients of time‐varying linear systems

AbstractIn this paper we consider regularity coefficients of a discrete linear time‐varying systems. The main result presents a complete description of the relations between Lyapunov, Perron and Grobman regularity coefficients of mutually adjoint systems.

Inertial Forward–Backward Algorithms with Perturbations: Application to Tikhonov Regularization

In a Hilbert space, we analyze the convergence properties of a general class of inertial forward–backward algorithms in the presence of perturbations, approximations, errors. These splitting algorithms aim to solve, by rapid methods, structured convex minimization problems. The function to be minimized is the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper lower semicontinuous convex function. The algorithms involve a general sequence of positive extrapolation coefficients that reflect the inertial effect and a sequence in the Hilbert space that takes into account the presence of perturbations. We obtain convergence rates for values and convergence of the iterates under conditions involving the extrapolation and perturbation sequences jointly. This extends the recent work of Attouch–Cabot which was devoted to the unperturbed case. Next, we consider the introduction into the algorithms of a Tikhonov regularization term with vanishing coefficient. In this case, when the regularization coefficient does not tend too rapidly to zero, we obtain strong ergodic convergence of the iterates to the minimum norm solution. Taking a general sequence of extrapolation coefficients makes it possible to cover a wide range of accelerated methods. In this way, we show in a unifying way the robustness of these algorithms.

Effects of manipulating the number of targets in U9, U11, U15 and U17 futsal players’ tactical behaviour

This study identified how the manipulation in the number of goal targets affects the tactical behaviour of players from different age groups (U9, U11, U15 and U17). Forty youth futsal players performed two small-sided games based on Gk + 4vs4 + Gk situation with one regular and two small targets. TACTO software was used to capture players and ball displacements. The following variables were computed and presented as absolute values, coefficient of variation and regularity (approximate entropy): (i) distance from each player to the team centre (DtC); (ii) distance from each player to the ball (DtB); (iii) distance between team centres (DbTC); and (iv) distance from team centre to the ball (DCtB). The team dispersion increased with two goal targets (mainly the DbTC, U9 and U17, large effects; U11 and U15, very large effects). Also, the use of two goal targets condition increased the variability in the DbTC (U9, small effects; U11 and U15 moderate effects; U17, very large effects) and DCtB (U9 and U17 moderate effects and U11 and U15 small effects). Overall, the approximate entropy values showed higher regularity in the condition with two targets. All age groups were sensitive to the manipulation of goal targets, however, the U9 were the most sensitive to the changes, as seen by the dispersion of players in the field. Thus, coaches can use one target to promote movement irregularity of players and two targets to increase the team dispersion, mainly in younger age groups that tend to be agglomerated around the ball.

Adaptive Image Mismatch Removal With Vector Field Interpolation Based on Improved Regularization and Gaussian Kernel Function

When the regularized kernel methods are utilized in the mismatch removal problem, the regularization coefficient and the choice of kernel function will seriously affect the performance of the methods. In this paper, we propose a method that combines an improved regularization and an adaptive Gaussian kernel function to interpolate the vector fields so as to overcome the issue. We formulated the problem as a modified maximum a posterior estimation of a Bayesian model. In this model, a two-order term of the regularization coefficient is introduced into the regularized risk function in order that the coefficient can be adaptively estimated in the expectation–maximization algorithm. In addition, an adaptive Gaussian kernel function also is imposed to construct the regularization, in which the width of the kernel function is adaptively determined by the diagonal length of the maximum enveloping rectangle of the sample set. Our experimental results verified that our method was robust to large outlier percentages and was slightly superior to some state-of-the-art methods in precision-recall tradeoff and efficiency. The evidence that the performance of our method was insensitive to the remaining inner parameters verified its good self-adaptability. Finally, airborne image pairs were used to demonstrate that our method can establish the feature correspondences even under a discontinuous vector field scene. In addition, we found that our method can obtain higher precision given a residual threshold for special applications such as robust epipolar geometry estimation in computer vision and photogrammetry.

Image Deformation With Vector-Field Interpolation Based on MRLS-TPS

Image deformation has been successfully applied in many different kinds of fields. However, how to get an approach with high efficiency and perfect visual effect remains a challenging task. In this paper, we present a vector-field interpolation method for non-rigid image deformation, which is based on moving regularized least squares (MRLS) optimization with a thin-plate spline (TPS). The proposed approach takes user-controlled points as input data and estimates the spatial transformation for each pixel by the control points. In order to achieve a realistic deformation, we formulate the deformation as a novel closed-form transformation estimation problem by MRLS. Unlike moving least squares (MLS), we model the mapping function by a non-rigid TPS function with a regularization coefficient. Therefore, the deformation not only satisfies the global linear affine transformation but also adapts to local non-rigid deformation. In terms of the transformation, we derive a closed-form solution and achieve a fast implementation. Furthermore, the approach can show us a wonderful user experience and can give us a fast and convenient manipulating. Extensive experiments on 2D images and 3D surfaces demonstrated that the proposed method performs better than other state-of-the-art methods like MLS and the commercial software as Adobe PhotoShop CS 6, especially in the case of flexible object motion.

A robust learning approach for regression models based on distributionally robust optimization

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our approach mitigates the impact of outliers by hedging against a family of probability distributions on the observed data, some of which assign very low probabilities to the outliers. The set of distributions under consideration are close to the empirical distribution in the sense of the Wasserstein metric. We show that this DRO formulation can be relaxed to a convex optimization problem which encompasses a class of models. By selecting proper norm spaces for the Wasserstein metric, we are able to recover several commonly used regularized regression models. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior (prediction bias), and the other concerns the discrepancy between the estimated and true regression planes (estimation bias). Extensive numerical results demonstrate the superiority of our approach to a host of regression models, in terms of the prediction and estimation accuracies. We also consider the application of our robust learning procedure to outlier detection, and show that our approach achieves a much higher AUC (Area Under the ROC Curve) than M-estimation (Huber, 1964, 1973).

Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator possesses higher regularity coefficients, we show that higher powers are essentially self-adjoint if and only if this condition is satisfied. In the case that the low-regularity Riemannian metric induces a complete length space, we demonstrate essential self-adjointness of the operator and its higher powers up to the regularity of its coefficients. We also present applications to Dirac operators on Dirac bundles when the metric is non-smooth.

Weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with non-regular drift

We consider an Euler–Maruyama type approximation method for a stochastic differential equation (SDE) with a non-regular drift and regular diffusion coefficient. The method regularizes the drift coefficient within a certain class of functions and then the Euler–Maruyama scheme for the regularized scheme is used as an approximation. This methodology gives two errors. The first one is the error of regularization of the drift coefficient within a given class of parametrized functions. The second one is the error of the regularized Euler–Maruyama scheme. After an optimization procedure with respect to the parameters we obtain various rates, which improve other known results.

Multivariate Calibration Transfer between two Potentiometric Multisensor Systems

AbstractA multivariate calibration of multisensor systems is a very important stage in their application. Construction of reliable calibration model requires significant investment of time and money. Once established, calibration model can be applied normally only together with that particular multisensor system, which was employed for its’ construction – this can be a serious limitation for a wide adoption of multisensor systems in common laboratory practice. In order to address this issue we have studied the applicability of several calibration transfer techniques, such as direct standardization, single wavelength standardization and standardization with regularization coefficient for the data obtained from two potentiometric multisensor systems in analysis of complex lanthanide mixtures. It was found that mathematical correction of sensor array response using standardization with regularization coefficient allows for using the regression model derived for one sensor array together with the data obtained from another sensor array. The value of root mean squared error of prediction for total lanthanide concentration increased insignificantly (0.10 instead of 0.07 in log scale) compared with that provided by the first multisensor system.

The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

The state-of-the-art in realization of the method of distribution of relaxation times (DRT) as applied to the analysis of data of electrochemical impedance spectroscopy is briefly surveyed. The theoretical fundamentals of the DRT method are described, the methods of solving the Fredholm equation of the 1st order with respect to the unknown DRT function are considered as an ill-defined problem. The Tikhonov regularization method presently considered as the most suitable for solving this equation is discussed. For several numerical experiments, the high resolution of the DRT method and its stability with respect to noise in impedance spectra are demonstrated. Among the problems and limitations of the DRT methods, the choice of the optimal regularization coefficient is considered as the most significant. Particularly, it is shown that in those cases where several relaxation processes with the constant phase angle appear in the response of objects under study to ac disturbances, different regularization coefficients should be selected for each of these elements in order to obtain adequate results.

3-5 正則化係数と画像に依存しない安定なシーンフロー計算(第3部門コンピュータビジョン)

3-5 正則化係数と画像に依存しない安定なシーンフロー計算(第3部門コンピュータビジョン)

Pointwise convergence in probability of general smoothing splines

Establishing the convergence of splines can be cast as a variational problem which is amenable to a $$\Gamma $$ -convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, n, as $$\lambda _n=n^{-p}$$ . Using standard theorems from the $$\Gamma $$ -convergence literature, we prove that the general spline model is consistent in that estimators converge in a sense slightly weaker than weak convergence in probability for $$p\le \frac{1}{2}$$ . Without further assumptions, we show this rate is sharp. This differs from rates for strong convergence using Hilbert scales where one can often choose $$p>\frac{1}{2}$$ .

Short-term Wind Power Prediction Using GA-ELM

Focusing on short-term wind power forecast, a method based on the combination of Genetic Algorithm (GA) and Extreme Learning Machine (ELM) has been proposed. Firstly, the GA was used to prepossess the data and effectively extract the input of model in feature space. Basis on this, the ELM was used to establish the forecast model for short-term wind power. Then, the GA was used to optimize the activation function of hidden layer nodes, the offset, the input weights, and the regularization coefficient of extreme learning, thus obtaining the GA-ELM algorithm. Finally, the GA-ELM was applied to the short-term wind power forecast for a certain area. Compared with single ELM, Elman algorithms, the experimental results show that the GA-ELM algorithm has higher prediction accuracy and better ability for generalization.

Integrability and continuity of solutions to double divergence form equations

We obtain sharp conditions for higher integrability and continuity of solutions to double divergence form second-order elliptic equations with coefficients of low regularity. In addition, we prove Harnack’s inequality in this case.

ОЦЕНКА СРЕДНЕСТАТИСТИЧЕСКИХ ХАРАКТЕРИСТИК КЕРНОВОГО МАТЕРИАЛА С ПОЗИЦИИ МОДЕЛЕЙ СЛУЧАЙНЫХ ПОЛЕЙ

Background The spatial heterogeneity of productive porous media of oil and gas fields is described by the parameters of the theory of random fields, among which the most frequently used are the space-correlation characteristics, spatial two-dimensional spectral characteristics and a number of quantitative indicators, for example, determining the periodicity and chaotic structure of porous media. In statistics, the autocorrelation of a random process describes the correlation between process values at different instants of time. Autocorrelation function is a statistical relationship between random values from one series, but taken with a shift, for example, for a random process - with a time shift or pore location on the core surface. The autocorrelation function of the profile of the selected row makes it possible to detect explicit and hidden periodicity of the change in the investigated parameter, for example, the brightness of the surface profile, and also the regularity coefficient. Aims and Objectives Based on the models of random fields, the development of the technique of digital microscopy for the study of the porosity of rock samples and the estimation of the average statistical characteristics of the core material. Rezults As a result of the analysis, from the point of view of the used mathematical approximations, the existing methods for determining the inhomogeneities of porous media it is shown that different variations of the phenomenological level are mainly used to describe the petrophysical parameters of porous media. As a result of the study of productive rocks from the position of statistical physics, a technique is proposed for estimating the average statistical characteristics of a core material on the basis of the theory of random fields, taking into account the characteristics of the structure of the productive rock of oil and gas fields.

NON‐UNIFORM TRICHOTOMIES AND ARBITRARY GROWTH RATES

For a non-autonomous dynamics defined by a sequence of matrices, we consider the notion of a non-uniform exponential trichotomy for an arbitrary growth rate (this means that there may exist contracting, expanding and neutral directions with an arbitrary fixed growth rate). The purpose of our work is two-fold: to use a regularity coefficient in order to show that these trichotomies occur naturally and to provide several alternative characterizations of those for which the non-uniform part is arbitrarily small. This includes characterizations in terms of the growth rate of volumes and of the Lyapunov exponents of the dynamics and its adjoint. We also obtain sharp lower and upper bounds for the regularity coefficient.

Firefly-Algorithm-Inspired Framework With Band Selection and Extreme Learning Machine for Hyperspectral Image Classification

A firefly algorithm (FA) inspired band selection and optimized extreme learning machine (ELM) for hyperspectral image classification is proposed. In this framework, FA is to select a subset of original bands to reduce the complexity of the ELM network. It is also adapted to optimize the parameters in ELM (i.e., regularization coefficient C , Gaussian kernel σ, and hidden number of neurons L ). Due to very low complexity of ELM, its classification accuracy can be used as the objective function of FA during band selection and parameter optimization. In the experiments, two hyperspectral image datasets acquired by HYDICE and HYMAP are used, and the experiment results indicate that the proposed method can offer better performance, compared with particle swarm optimization and other related band selection algorithms.

An error analysis of the finite element method overcoming corner singularities for the stationary Stokes problem

In this paper, we introduce a mixed finite element method to overcome corner singularities of the stationary Stokes system on a non-convex polygon. The reference Choi and Kweon (2013) says that the velocity field and the pressure function are composed of singular parts and regular remainders near a non-convex vertex, and furthermore the regular parts are sufficiently smooth on the polygon. We use the corner singularity expansion and propose new extraction formulae for coefficients of singularities. For the proposed numerical method, we first try to find finite element solutions for the regular parts and then calculate approximations of the coefficients by the derived formulae expressed by the remainders and given functions. We show error estimates of the approximations for the regular parts and coefficients, and give some numerical experiments to confirm the efficiency and reliability of the proposed method.