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1

On some inverse problem for bi-parabolic equation with observed data in Lp spaces

Tuan Nguyen Huy

Opuscula Mathematica

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2022

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Vol. 42, no. 2

305--335

EN

The bi-parabolic equation has many practical significance in the field of heat transfer. The objective of the paper is to provide a regularized problem for bi-parabolic equation when the observed data are obtained in Lp. We are interested in looking at three types of inverse problems. Regularization results in the L2 space appears in many related papers, but the survey results are rare in Lp, p ̸= 2. The first problem related to the inverse source problem when the source function has split form. For this problem, we introduce the error between the Fourier regularized solution and the exact solution in Lp spaces. For the inverse initial problem for both linear and nonlinear cases, we applied the Fourier series truncation method. Under the terminal input data observed in Lp, we obtain the approximated solution also in the space Lp. Under some reasonable smoothness assumptions of the exact solution, the error between the the regularized solution and the exact solution are derived in the space Lp. This paper seems to generalize to previous results for bi-parabolic equation on this direction.

2

Two-step inversion of airborne geophysical data: a stable downward continuation approach for physical modelling

Azadi Majid, Abedi Maysam, Norouzi Gholam-Hossain

Acta Geophysica

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2022

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Vol. 70, no 1

121--139

EN

Airborne potential field geophysical survey is employed for a variety of purposes to cover in a cost-effective manner large prospect areas. Despite the many advantages of airborne data measurements, due to the height from the ground, the received response is weakened (signal attenuation) and causes inadequacies in data representation. Accordingly, it is expected that the inversion results are far from reality and there are shortcomings in the retrieved model. This study investigates the impact of airborne survey on small-sized magmatic units, where directly inverting airborne data suffer from signal attenuation and lead to the loss of the causative model. In this study we improved the airborne data inversion by mixing a two-step cooperative approach which enhances the potential field data by a stable downward continuation to the ground surface in the spectral domain, and subsequently running a physical property modelling. The efficiency of the method over one-step airborne data inversion is examined for a synthetic multi-source case (magnetic and gravity) and then is used to find out the close spatial link between magnetometry signatures and iron–phosphate sources in the Esfordi district in Iran. The results showed that the proposed method performed better than direct inversion of airborne data and could satisfactorily identify the sources of the anomaly.

3

Determinig of the sound power of the fan in in situ conditions using the virtual reference source method

Suder-Dębska Katarzyna, Czajka Ireneusz, Łojek Paweł

Vibrations in Physical Systems

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2021

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Vol. 32, nr 2

art. no. 2021206

EN

Sound power is one of the basic parameters characterizing the sound source and has a direct impact on the acoustic climate in its surroundings. Therefore, the determining of the sound power of machines is a practical problem. While there are many methods of determining the sound power, each of them has its own limitations. The authors presented the implementation of a comparative method of determining the sound power with the use of a virtual reference source. The method was used to test a high-efficiency flue gas exhaust fan installed on a laboratory stand. The sound source was placed in the geometric centre of the fan and the acoustic field distribution in the room was determined using geometrical methods. After determining the influence factors, the value of the source sound power of the source was calculated by means of the Moore-Penrose pseudo-inverse. Since the problem under study belongs to the inverse problems, the Tikhonov regularization was used, where the value of the parameter α was determined by the L-curve method.

4

Regularization based discriminative feature pattern selection for the classification of Parkinson cases using machine learning

Kaliyan Kamalakannan, Ganesan Anandharaj

Bio-Algorithms and Med-Systems

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2021

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Vol. 17, no. 3

181--189

EN

Objectives: This paper focuses on developing a regularization-based feature selection approach to select the most effective attributes from the Parkinson’s speech dataset. Parkinson’s disease is a medical condition that progresses as the dopamine-producing nerve cells are affected. Early diagnosis often reduces the effect on the individuals, minimizes the advancement over time. In recent times, intelligent computational models are used in many complex cases to diagnose a clinical condition with high precision. These models are intended to find meaningful representation from the data to diagnose the disease. Machine learning acts as a tool, gears up the model learning process through a mathematical baseline. But, not in all cases, machine learning will be demanded to perform optimally. It comes with a few constraints, mainly the representation of the data. The learning models expect a clean, noise-free input, which in-turns produces better discriminative patterns over different categories of classes. Methods: The proposed model identified five candidate features as predictors. This feature subset is trained with different varieties of supervised classifiers to trace out the best-performing model. Results: The results are validated through accuracy, precision, recall, and receiver’s operational characteristic curves. The proposed regularization- based feature selection model outperformed the benchmark algorithms by attaining 100% accuracy on most of the classifiers, other than linear discriminant analysis (99.90%) and naïve Bayes (99.51%). Conclusions: This paper exhibits the need for intelligent models to analyze complex data patterns to assist medical practitioners in better disease diagnosis. The results exhibit that the regularization methods find the best features based on their importance score, which improved the model performance over other feature selection methods.

5

An inverse backward problem for degenerate two-dimensional parabolic equation

Atifi Khalid, Essoufi El-Hassan, Khouiti Bouchra

Opuscula Mathematica

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2020

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Vol. 40, no. 4

427--449

EN

This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation [formula], where Ω is an open, bounded subset of R2, a [formula] with a ≥0 everywhere, and [formula], with initial and boundary conditions [formula] from final observations. This inverse problem is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. To show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of the Tikhonov functional. Also we present some numerical experiments to show the performance and stability of the proposed approach.

6

A Phase Field Approach to Limited-angle Tomographic Reconstruction

Turpin Léonard, Roux Stéphane, Caty Olivier, Denneulin Sébastien

Fundamenta Informaticae

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2020

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Vol. 172, nr 2

203--219

EN

The tomography of an object with limited angle can be addressed through Iterative Reconstruction Reprojection (IRR) procedure, where in a standard reconstruction procedure is used together with a "filtering" of the image at each iteration. It is here proposed to use as a filter a phase-field — or Cahn-Hilliard — regularization interlaced with a filtered back-projection reconstruction. This reconstruction procedure is tested on a cone-beam tomography of a 3D woven ceramic composite material, and is shown to retrieve a reconstructed volume with very low artifacts in spite of a large missing angle interval (up to 28%).

7

Simulations of concrete response to impact loading using two regularized models

Wosatko Adam, Winnicki Andrzej, Pamin Jerzy

Computer Assisted Methods in Engineering and Science

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2020

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Vol. 27, no. 1

27--60

EN

This paper focuses on a comparison of two regularized continuum models for concrete in the simulations of selected benchmarks of response to impact loading. Their overview is performed in the context of application in dynamics. The first one is the Hoffman viscoplastic consistency model, where the strain rate activates regularization. The second model is derived from the scalar damage theory enhanced by an averaging equation incorporating the Laplacian of an averaged strain measure. Both models are implemented in the FEAP package. The results of some standard wave propagation tests are discussed, considering discretization sensitivity and predicted failure modes. Three examples are pre- sented: the direct tension of a plain and reinforced concrete bar, the split test of a cylinder, and the four-point bending of a reinforced concrete beam. The ability of both models to simulate impact loading is assessed.

8

The regularization method in the classification task according to given examples

Kwiatkowski Włodzimierz

Przegląd Teleinformatyczny

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2019

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T. 7, Nr 3-4 (49)

3--13

EN

The article considers the problem of classification based on the given examples of classes. As a feature vector, a complete characteristic of object is assumed. The peculiarity of the problem being solved is that the number of examples of the class may be less than the dimension of the feature vector, and also most of the coordinates of the feature vector can be correlated. As a consequence, the feature covariance matrix calculated for the cluster of examples may be singular or ill-conditioned. This disenable a direct use of metrics based on this covariance matrix. The article presents a regularization method involving the additional use of statistical properties of the environment.

PL

W artykule rozpatrywany jest problem klasyfikacji na podstawie wskazanych przykładów klas. Jako wektor cech przyjmuje się kompletną charakterystykę obiektów. Osobliwość rozwiązywanego zadania wynika z tego, że liczba przykładów klasy może być mniejsza od wymiaru wektora cech, a także wektor cech może zawierać współrzędne skorelowane. W konsekwencji macierz kowariancji cech obliczana dla klastra przykładów może być osobliwa albo źle uwarunkowana. Uniemożliwia to bezpośrednie stosowanie metryk bazujących na tej macierzy kowariancji. W artykule została przedstawiona metoda regularyzacji polegająca na dodatkowym wykorzystaniu statystycznych właściwości środowiska.

9

Implications of Pooling Strategies in Convolutional Neural Networks: A Deep Insight

Sharma Shallu, Mehra Rejesh

Foundations of Computing and Decision Sciences

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2019

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Vol. 44, No. 3

303--330

EN

Convolutional neural networks (CNN) is a contemporary technique for computer vision applications, where pooling implies as an integral part of the deep CNN. Besides, pooling provides the ability to learn invariant features and also acts as a regularizer to further reduce the problem of overfitting. Additionally, the pooling techniques significantly reduce the computational cost and training time of networks which are equally important to consider. Here, the performances of pooling strategies on different datasets are analyzed and discussed qualitatively. This study presents a detailed review of the conventional and the latest strategies which would help in appraising the readers with the upsides and downsides of each strategy. Also, we have identified four fundamental factors namely network architecture, activation function, overlapping and regularization approaches which immensely affect the performance of pooling operations. It is believed that this work would help in extending the scope of understanding the significance of CNN along with pooling regimes for solving computer vision problems.

10

On regularization properties of artificial datasets for deep learning

Antczak Karol

Computer Science and Mathematical Modelling

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2019

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No. 9

13--18

EN

The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process, described as injecting noise to high-level features, bears several similarities to existing regularization methods for deep neural networks. One can treat this property of artificial data as a kind of “deep” regularization. It is thus possible to regularize hidden layers of the network by generating the training data in a certain way.

PL

W artykule omówiono własności regularyzacyjne sztucznych danych używanych w uczeniu głębokim. Dane te pozwalają na uczenie sieci neuronowych w sytuacji niedoboru danych rzeczywistych. Okazuje się, że proces generacji danych sztucznych, opisany jako zaszumianie wysokopoziomowych cech, wykazuje wiele podobieństw do istniejących metod regularyzacyjnych dla głębokich sieci neuronowych. Dzięki temu możliwa jest regularyzacja warstw ukrytych sieci poprzez generowanie sztucznych danych uczących w odpowiedni sposób.

11

Reflected wave least squares reverse time migration with angle illumination compensation

Zhou Huamin, Chen Shengchang, Zhou Liming, Ren Haoran, Wu Rushan, Xiao Guoqiang

Acta Geophysica

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2019

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Vol. 67, no. 6

1551--1561

EN

High-quality seismic data imaging plays an important role in the lithological interpretation of subsurface structures. However, high-quality imaging remains a challenging task. Based on the linear inversion theory of reflected wave equations, this paper proposes reflected wave least squares reverse time migration with angle illumination compensation to better balance the amplitude of seismic imaging. We use the reflected wave migration equation to unify forward and backward propagation, which helps to obtain an image with correct phase and symmetric waveform. Under the assumption that the spectrum of seismic wavefield remains unchanged, the Poynting vector method is used to efficiently calculate the propagation direction of seismic waveform and seismic illumination in the angle domain. During iteration, angle-domain illumination is used as a preconditioner to compensate for the amplitude of the iterated gradient terms based on the angle value. In this manner, we can enhance the imaging energy of steeply inclined structures. To improve the stability of linear inversion, the spatial derivative of the image is used as a regularized constraint term. Numerical tests show that the proposed method can suppress imaging noise as well as improve resolution and amplitude fidelity of the images. Furthermore, the inversed result can be used to estimate underground reflectivity, which is important for the further development of seismic inversion technology.

12

Multichannel antileakage least squares spectral analysis for seismic data regularization beyond aliasing

Ghaderpour Ebrahim

Acta Geophysica

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2019

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Vol. 67, no. 5

1349--1363

EN

The antileakage least-squares spectral analysis is a new method of regularizing irregularly spaced data series. This method mitigates the spectral leakages in the least-squares spectrum caused by non-orthogonality of the sinusoidal basis functions on irregularly spaced series, and it is robust when data series are wide-sense stationary. An appropriate windowing technique can be applied to adapt this method to non-stationary data series. When data series present mild aliasing, this method can efectively regularize the data series; however, additional information or assumption is needed when the data series is coarsely sampled. In this paper, we show how to incorporate the spatial gradients of the data series into the method to regularize data series presenting severe aliasing and show its robust performance on synthetic and marine seismic data examples.

13

Algorithms of Sustainable Estimation of Unknown Input Signals in Control Systems

Yusupbekov Nadirbek, Igamberdiev Husan, Mamirov Uktam

Journal of Automation Mobile Robotics and Intelligent Systems

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2018

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Vol. 12, No. 4

83--86

EN

The problem of estimating unknown input effects in control systems based on the methods of the theory of optimal dynamic filtering and the principle of expansion of mathematical models is considered. Equations of dynamics and observations of an extended dynamical system are obtained. Algorithms for estimating input signals based on regularization and singular expansion methods are given. The above estimation algorithms provide a certain roughness of the filter parameters to various violations of the conditions of model problems, i.e. are not very sensitive to changes in the a priori data.

14

Regularized inversion of amplitude‑versus‑incidence angle (AVA) based on a piecewise‑smooth model

Li Z., Wang M., Xu F.

Acta Geophysica

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2018

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Vol. 66, no. 6

1383--1396

EN

Different from the stacked seismic data, pre-stack data includes abundant information about shear wave and density. Through inversing the shear wave and density information from the pre-stack data, we can determine oil-bearing properties from different incident angles. The state-of-the-art inversion methods obtain either low vertical resolution or lateral discontinuities. However, the practical reservoir generally has sharp discontinuities between different layers in vertically direction and is horizontally smooth. Towards obtaining the practical model, we present an inversion method based on the regularized amplitude-versus-incidence angle (AVA) data to estimate the piecewise-smooth model from pre-stack seismic data. This method considers subsurface stratum as a combination of two parts: a piecewise smooth part and a constant part. To fix the ill-posedness in the inversion, we adopt four terms to define the AVA inversion misfit function: the data misfit itself, a total variation regularization term acting as a sparsing operator for the piecewise constant part, a Tikhonov regularization term acting as a smoothing operator for the smooth part, and the last term to smoothly incorporate a priori information for constraining the magnitude of the estimated model. The proposed method not only can incorporate structure information and a priori model constraint, but also is able to derive into a convex objective function that can be easily minimized using iterative approach. Compared with inversion results of TV and Tikhonov regularization methods, the inverted P-wave velocity, S-wave velocity and density of the proposed method can better delineate the piecewise-smooth characteristic of strata.

15

Regularization of Coulomb potential for calculating electron density in quantum mechanical systems

Kshevetskty S., Shapilov A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2017

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Vol. 21, No 2

177--184

EN

In this paper we show a simple and effective method for regularizing the Coulomb potential for numerical calculations of quantum mechanical problems, such as, for example, the solution of the Schrödinger equation, the expansion of charge density and others. The introduction explains why the regularization of the Coulomb potential is important. In the second part, the regularization method itself as well as its advantages and disadvantages will be described in detail. The third part demonstrates some numerical calculations for the Sulfur + Hydrogen system using the proposed method. In the final part, the obtained results are summed up.

16

On problem of Rossby and Pointcare atmospheric waves separation and spectra

Karpov I., Leble S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2017

|

Vol. 21, No 2

97--108

EN

We propose a new inverse problem formulation based on the hydrodynamics consideration of a gas/water fluid that results in planetary waves diagnostics. We analyze such a possibility beginning from a simplest version of geophysical hydrodynamics, written in the b-plane model. The problem of diagnostics is solved approximately after expansion with respect to the transverse basis functions applying projecting to Rossby and Poincare waves in each transverse subspace that contains its superposition. The corresponding discrete version of the operators is built to be applied to the observation data.

17

Leak Detection in Waterworks: Comparison Between STFT and FFT with an Overcoming of Limitations

Lay-Ekuakille A., Griffo G., Visconti P., Primiceri P., Velazquez R.

Metrology and Measurement Systems

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2017

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Vol. 24, nr 4

631--644

EN

Detection of leakages in pipelines is a matter of continuous research because of the basic importance for a waterworks system is finding the point of the pipeline where a leak is located and - in some cases - a nature of the leak. There are specific difficulties in finding leaks by using spectral analysis techniques like FFT (Fast Fourier Transform), STFT (Short Term Fourier Transform), etc. These difficulties arise especially in complicated pipeline configurations, e.g. a zigzag one. This research focuses on the results of a new algorithm based on FFT and comparing them with a developed STFT technique. Even if other techniques are used, they are costly and difficult to be managed. Moreover, a constraint in the leak detection is the pipeline diameter because it influences accuracy of the adopted algorithm. FFT and STFT are not fully adequate for complex configurations dealt with in this paper, since they produce ill-posed problems with an increasing uncertainty. Therefore, an improved Tikhonov technique has been implemented to reinforce FFT and STFT for complex configurations of pipelines. Hence, the proposed algorithm overcomes the aforementioned difficulties due to applying a linear algebraic approach.

18

Entropy-based regularization of AdaBoost

Bereta M.

Computer Assisted Methods in Engineering and Science

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2017

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Vol. 24, no. 2

89--100

EN

In this study, we introduce an entropy-based method to regularize the AdaBoost algorithm. The AdaBoost algorithm is a well-known algorithm used to create aggregated classifiers. In many real-world classification problems in addition to paying special attention classification accuracy of the final classifier, great focus is placed on tuning the number of the so-called weak learners, which are aggregated by the final (strong)classifier. The proposed method is able to improve the AdaBoost algorithm in terms of both criteria. While many approaches to the regularization of boosting algorithms can be complicated, the proposed method is straightforward and easy to implement. We compare the results of the proposed method (EntropyAdaBoost) with the original AdaBoost and also with its regularized version, є-AdaBoost on several classification problems. It is shown that the proposed methods of EntropyAdaBoost and є-AdaBoost are strongly complementary when the improvement of AdaBoost is considered.

19

Interpolacja i regularyzacja 5D z uwzględnieniem antyaliasingu przestrzennego

Gieras J.

Prace Naukowe Instytutu Nafty i Gazu

|

2016

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nr 209 wyd. konferencyjne

237--240

PL

Nowoczesne algorytmy regularyzacji i interpolacji danych sejsmicznych wykorzystując idee interpolacji 5D odtwarzają trasy poprzez iteracyjną rekonstrukcję w domenie Fouriera. Na odtworzenie trasy sejsmicznej składa się wygenerowanie parametrów zawartych w nagłówkach tras oraz samego sygnału z rozróżnieniem na kierunki i częstotliwości. W zależności od potrzeb dane mogą zostać odtworzone w żądanej domenie. Przykłady z różnych projektów demonstrują skuteczność metody.

EN

Modern algorithms of interpolation and regularization harnessing idea of 5D reconstruct traces by iterative steps in Fourier domain. To generate new seismic trace headers and seismic signal must be taken into account. This processes can be made for any domain depending on what we need. Below pictures demonstrate how algorithms works.

20

Maxent Modelling for Distribution of Plant Species Habitats of Rangelands (Iran)

Chahouki M. A. Z., Sahragard H. P.

Polish Journal of Ecology

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2016

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Vol. 64, nr 4

453--467

EN

Quantifying the pattern of habitat distribution for range plant species can assist sustainable planning of rangeland use and management. However, data of plant species distribution are often scarce and modeling of habitat distribution using commonly used models is difficult. In this study, the Maximum Entropy Method (MaxEnt) was used to model the distribution of plant habitat to find the effective variables in plant species occurrence in the Poshtkouh rangelands on Yazd province, central Iran. Maps of the environmental variables were generated using GIS and Geostatistics facilities. Accuracy of model output was assessed using area under the curve (AUC) of the receiver operating characteristic and keeping 30 percent of the data. Evaluation of model accuracy by AUC indicated good and acceptable predictive accuracy for all plant species habitats, except Artemisia sieberi which had high frequency. The predictive maps of Artemisia aucheri, Scariola orientalis — Astragalus albispinus, A. sieberi2 and A. sieberi — Zygophyllum eurypterum had fair agreement with their corresponding observed maps. In addition, the accuracy of S. orientalis — A. sieberi and Tamarix ramosissima predictive maps was low and the estimated conformity rate of prediction and observed maps was poor. In fact, due to differences in the optimal ecological range, level of agreement of predictive and observed maps at each site was different. MaxEnt was substantially excellent to predict distributions of plant species habitat with narrow ecological niches e.g. Rheum ribes — A. sieberi, Seidlitzia rosmarinus and Cornulaca monacantha. It can also perform well with fairly few samples due to employing regularization.