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1

Modeling and Parameter Estimation of Radar Sea-Clutter with Trimodal Gamma Population

Terki Zakia, Mezache Amar, Chebbara Fouad

Journal of Telecommunications and Information Technology

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2022

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nr 2

82--90

EN

Real radar data often consist of a mixture of Gaussian and non-Gaussian clutter. Such a situation creates one or more inflexion points in the curve of the empirical cumulative distributed function (CDF). In order to obtain an accurate fit with sea reverberation data, we propose, in this paper, a trimodal gamma disturbance model and two parameter estimators. The non-linear least-squares (NLS) fit approach is used to avoid computational issues associated with the maximum likelihood estimator (MLE) and moments-based estimator for parameters of the mixture model. For this purpose, a combination of moment fit and complementary CDF (CCDF) NLS fit methods is proposed. The simplex minimization algorithm is used to simultaneously obtain all parameters of the model. In the case of a single gamma probability density function, a zlog(z) method is derived. Firstly, simulated life tests based on a gamma population with different shape parameter values are worked out. Then, numerical illustrations show that both MLE and zlog(z) methods produce closer results. The proposed trimodal gamma distribution with moments NLS fit and CCDF NLS fit estimators is validated to be in qualitative agreement with different cell resolutions of the available IPIX database.

2

A new elastic least-squares reverse time-migration method based on the new gradient equations

Zhong Yu, Liu Yangting, Gu Hanming, Mao Qinghui

Acta Geophysica

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2022

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Vol. 70, no 6

2733--2746

EN

Compared with single-component seismic data, multicomponent seismic data contain more P- and S-wave information. Making full use of multicomponent seismic data can improve the accuracy of seismic exploration. Elastic reverse-time migration (ERTM) is the most advanced migration technology for imaging multicomponent seismic data from complex subsurface structures. However, most conventional ERTM methods often use the adjoint operator of forward operator for approximation to the inverse operator. When the multicomponent seismic data suffer from a finite recording aperture, limited bandwidth, and imperfect illumination, the image quality of conventional ERTM is greatly reduced. In this study, we propose an elastic least-squares reverse-time migration (ELSRTM) scheme to improve the image quality of ERTM through multiple iterations. We first review the ERTM method; then, we derive the Born modeling equations, adjoint wave equations, and gradient equations of P- and S-wave images of ELSRTM. The new gradient equations, which use the time derivative of stress to replace the spatial derivative of particle velocity for improving the accuracy of gradients near the boundary, are also proposed. We compare the performance of ERTM with ELSRTM via synthetic experiments in numerical examples. Synthetic examples reveal that ELSRTM can generate high-quality images with higher resolution, fewer artifacts, and more balanced amplitude than ERTM.

3

Power spectrum optimization in the design of multisine manoeuvre for identification purposes

Lichota P., Szulczyk J., Noreña D. A., Vallejo Monsalve F. A.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 4

1193--1203

EN

In this paper, two sets of multisine signals are designed for system identification purposes. The first one is obtained without any information about system dynamics. In the second case, the a priori information is given in terms of dimensional stability and control derivatives. Magnitude Bode plots are obtained to design the multisine power spectrum that is optimized afterwards. A genetic algorithm with linear ranking, uniform crossover and mutation operator has been employed for that purpose. Both designed manoeuvres are used to excite the aircraft model, and then system identification is performed. The estimated parameters are obtained by applying two methods: Equation Error and Output Error. The comparison of both investigated cases in terms of accuracy and manoeuvre time is presented afterwards.

4

On the Properties of the Priority Deriving Procedure in the Pairwise Comparisons Method

Kułakowski K.

Fundamenta Informaticae

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2015

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Vol. 139, nr 4

403--419

EN

The pairwise comparisons method can be used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the Eigenvector Method, the Least Squares Method, the Chi Squares Method and others. Each of the above methods comes with one or more inconsistency indices that help to decide whether the consistency of input guarantees obtaining a reliable output, thus taking the optimal decision. This article explores the relationship between inconsistency of input and error of output. An error describes to what extent the obtained results correspond to the single expert’s assessments. On the basis of the inconsistency and the error, two properties of the weight deriving procedure are formulated. These properties are proven for eigenvector method and Koczkodaj’s inconsistency index. Several estimates using Koczkodaj’s inconsistency index for a principal eigenvalue, Saaty’s inconsistency index and the Condition of Order Preservation are also provided.

5

Stretching the Least Squares to Embed Loss Function Tables

Yoneda K., Moretti A. C., Poker J. Jr.

Decision Making in Manufacturing and Services

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2015

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Vol. 9, no. 2

105--116

EN

The method of least squares is extended to accommodate a class of loss functions specified in the form of function tables. The function tables are embedded into the standard quadratic loss function so that nonlinear least squares algorithms can be adopted for loss minimization. This is an alternative to a more straightforward approach which interpolates the function tables and minimizes the resulting loss function by some generic optimization algorithm. The alternative approach has advantages over the straightforward, such as the wider availability of the least squares programs compared to the generic optimization programs and reduction in computational complexity. Examples are given for its application to multiplicative utility function maximization problems.

6

Acoustic Reverse-time Migration using Optimal Staggered-grid Finite-difference Operator Based on Least Squares

Yan H., Yang L., Liu H.

Acta Geophysica

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2015

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Vol. 63, no. 3

715--734

EN

Reverse-time migration (RTM) directly solves the two-way wave equation for wavefield propagation; therefore, how to solve the wave equation accurately and quickly is very important for RTM. The conventional staggered-grid finite-difference (SFD) operators are usually based on the Taylor-series expansion theory. If they are used to solve wave equation on a larger frequency content, a strong dispersion will occur, which directly affects the seismic image quality. In this paper, we propose an optimal SFD operator based on least squares to solve acoustic wave equation for prestack RTM, and obtain a new antidispersion RTM algorithm that can use short spatial difference operators. The synthetic and real data tests demonstrate that the least squares SFD (LSSFD) operator can mitigate the numerical dispersion, and the acoustic RTM using the LSSFD operator can effectively improve image quality comparing with that using the Taylor-series expansion SFD (TESFD) operator. Moreover, the LSSFD method can adopt a shorter spatial difference operator to reduce the computing cost.

7

The analysis of synchronous blade vibration using linear sine fitting

Przysowa R.

Journal of KONBiN

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2014

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No. 2 (30)

5--20

EN

In Blade Tip Timing several sensors installed circumferentially in the casing are used to record times of arrival (TOA) and observe deflections of blade tips. This paper aims to demonstrate methodology of model-based processing of aliased data. It focuses on the blade vibration excited by the forces synchronous with engine rotation, which are called integral responses. The driven harmonic oscillator with single degree of freedom (SDOF) is used to analyze blade vibration measured by tip-timing sensors during engine deceleration. When integral engine order EO is known, the linear sine fitting techniques can be used to process data from sensors to estimate amplitude, phase and frequency of blade vibration in each rotation. The oscillator model is implemented in MATLAB and used to generate resonance curves and simulate blade responses observed with tip sensors, installed in the axial compressor. Generated TOA data are fitted to the sine function to estimate vibration parameters. The validated procedure is then employed to analyze real test data.

PL

W metodzie dyskretno-fazowej (ang. tip-timing) kilka czujników zamocowanych na obwodzie w korpusie maszyny wirnikowej jest używanych do pomiaru czasów przyjścia i obserwacji odkształceń wierzchołków łopatek wirnika. W artykule przedstawiono metodyki przetwarzania rzadko próbkowanych danych pomiarowych z wykorzystaniem modelu matematycznego. Skoncentrowano się na drganiach łopatek wymuszanych przez siły synchroniczne z obrotami wirnika. Wymuszony oscylator harmoniczny, o jednym stopniu swobody, został wykorzystany do analizy drgań łopatek mierzonych przez czujniki podczas deceleracji silnika. Jeśli znana jest rzędowość wymuszenia, liniowe techniki dopasowania funkcji sinus mogą być używane do przetwarzania danych w celu estymacji amplitudy, fazy i częstotliwości drgań łopatek w kolejnych obrotach wirnika. Generowane czasy przyjścia dopasowywane są do funkcji sinus w celu estymacji parametrów drgań. Zweryfikowana w ten sposób procedura jest następnie wykorzystana do analizy danych z rzeczywistych testów silnika.

8

Standard sine fitting algorithms applied to Blade Tip Timing data

Kaźmierczak K., Przysowa R.

Journal of KONBiN

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2014

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No. 2 (30)

21--30

EN

Blade Tip Timing (BTT) is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA) is recorded when a blade is passing a stationary sensor. The measurement data, in form of under sampled (aliased) tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.

PL

Metoda dyskretno-fazowa (ang. tip-timing) jest nieinwazyjnym sposobem pomiaru drgań łopatek w przepływowych maszynach wirnikowych. Czas przyjścia zapisywany jest w momencie, kiedy łopatka mija stacjonarny czujnik. Do analizy danych pomiarowych w formie rzadko próbkowanego sygnału odkształcenia wierzchołka (aliasing) wykorzystano standardowe metody dopasowania funkcji sinus dostarczone przez normę IEEE-STD-1057 w celu estymacji parametrów drgań łopatek. Przemieszczenia wierzchołków łopatki w dziedzinie czasu zasymulowano wykorzystując model oscylatora o jednym stopniu swobody. Wyniki liniowego dopasowania, wykonanego ze znaną a priori częstotliwością, porównano z wynikami dopasowania nieliniowego. Uzyskane algorytmy i wyniki testowania mają być wykorzystane do analizy drgań asynchronicznych łopatek.

9

Using the Total Least Square Method by Deformation Strain Analyses of the Eastern Edge Eastern Tatras

Weiss G., Gasinec J., Zeliznakova V., Gasincova S.

Inżynieria Mineralna

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2014

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R. 15, nr 1

213--226

EN

This contribution discusses the course of deformation analysis of the eastern edge of the High Tatras - for this purpose, a static method with three hours of observations using each point designed appropriately chosen points of the State spatial network in the locality. It was used a three-dimensional Helmert transformation using two methods - the ordinary least squares and total least squares method - to transform of coordinates between the different epochs of deformation of the investigation. Due to the better visualization of the displacements, co-ordinates of the points of both epochs of deformation investigation are transformed from the European Terrestrial Reference System 1989 (ETRS89) to the Uniform Trigonometric Cadastral Network (JTSK 03). The final section of that article is devoted to the analysis of strain and consequently draw up the illustrated maps with horizontal and vertical displacements.

PL

W artykule przedstawiono wyniki badań nad możliwością wykorzystania popiołów lotnych w technologiach zawiesinowych stosowanych w górnictwie podziemnym. Zawiesiny sporządzono z dwóch popiołów pochodzących z różnych instalacji, spalających komunalne osady ściekowe w kotłach fluidalnych. Właściwości zawiesin jak i kierunek ich zastosowania określono zgodnie z Polską Normą PN-G-11011 1998. Sporządzone zawiesiny nie spełniały wymagań dotyczących zastosowania w podsadzce zestalanej, natomiast w zależności od ich składu mogą być stosowane do izolacji i doszczelniania zrobów zawałowych.

10

Subset selection for improved parameter identification in a bio-ethanol production process

López D., Barz T., Arellano-Garcia H., Wozny G., Villegas A., Ochoa S.

Czasopismo Techniczne. Mechanika

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2012

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R. 109, z. 1-M

137--147

EN

A systematic approach for system identification is applied to experimental data of ethanol production from cellulose. Special attention is given to the identification of model parameters, which can be reliably estimated from available measurements. For this purpose, an identifiable parameter subset selection algorithm for nonlinear least squares parameter estimation is used. The procedure determines the parameters whose effects are unique and have a strong effect on the predicted (measurement variables) output variables. The system is described by a generic process model for the simultaneous saccharification and fermentation including three enzyme-catalyzed reactions. The process model is clearly over-parameterized. By applying the subset selection approach the parameter space is reduced to a reasonable subset, whose estimated parameters are still able to predict the experimental data accurately.

PL

Systematyczne podejście do identyfikacji systemu stosowane jest wraz z doświadczalnymi danymi dotyczącymi wytwarzania etanolu z celulozy. Szczególną uwagę zwraca się na określanie parametrów modelu, które można wiarygodnie oszacować na podstawie ogólnodostępnych pomiarów. W tym celu zastosowano algorytm podzbioru parametru identyfikowalnego służący do nieliniowego szacowania parametrów metodą najmniejszych kwadratów. Procedura ta określa parametry, które dają niepowtarzalne efekty i wywierają silny wpływ na przewidywane zmienne zdolności produkcyjnej (zmienne pomiarów). System ten opisywany jest przez rodzajowy model procesu jednoczesnego scukrzania i fermentacji, wliczając w to trzy reakcje katalizowane enzymowo. Model procesowy jest nadmiernie sparametryzowany. Przy zastosowaniu opisywanego podejścia dana przestrzeń zostaje ograniczona do uzasadnionego podzbioru, którego szacowane parametry pozwalają nadal celnie przewidywać dane doświadczalne.

11

Unbiased estimates for linear regression with roundoff error

Withers C. S., Nadarajah S.

Probability and Mathematical Statistics

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2011

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Vol. 31, Fasc. 2

177--182

EN

We consider the linear regression model, where the residuals have zero mean and an otherwise unspecified distribution F. Suppose that least squares estimates are formed by using rounded values of the dependent variables.We show that these are still unbiased, and that unbiased estimates for the moments and cumulants of F are given by applying Sheppard’s corrections to their estimates.

12

Estimation of an equivalent short solenoid model using different numerical methods

Miron O., Desideri D., Micu D.D., Maschio A., Ceclan A., Czumbil L.

Archives of Electrical Engineering

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2011

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Vol. 60, nr 4

433-444

EN

This paper deals with an inverse magnetostatic problem related to the reconstruction of a permanent magnet encapsulated inside the cathode of a magnetron sputtering device. The numerical analysis is aimed to obtain the estimation of a short solenoid equivalent to the unknown magnet. Least squares approach has been used to solve the functional defined as squared sum of the residuals. A comparison of the results obtained with Genetic Algorithm approach and nonlinear system of equations is performed. A regularized solution, which is in good agreement with the experimental data, was found by applying a Newton adapted regularization technique.

13

Generalized inverses of cracovians - a question of paternity Jean Dommanaget

Dommanaget J.

Geodezja i Kartografia

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2008

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Vol. 57, no 1

41-44

EN

Half a century ago two papers were published, related to generalized inverses of cracovians by two different authors, in chronological order, respectively by Jean Dommanget and by Helmut Moritz. Both independently developed papers demonstrated new theorems, however, certa in similarity between them appeared. Helmut Moritz having recognized that situation, promised to mention it later in one of his published papers. This has never been done, so the author of the present paper gives some details about the situation and claims his paternity.

PL

Pół wieku temu zostały opublikowane dwa artykuły dotyczące uogólnionych odwrotności krakowianów przez dwóch różnych autorów: Jean Dommangeta i Helmuta Moritza, wymienionych w kolejności chronologicznej. W obu artykułach przedstawiono niezależnie nowe teorie, które jednak zawierają pewne wspólne cechy. Helmut Moritz, po uświadomieniu sobie zaistniałej sytuacji, obiecał udzielić wyjaśnień w tej sprawie w jednej ze swoich kolejnych publikacji. Obietnica ta nigdy nie została spełniona, toteż autor niniejszej pracy podaje w niej pewne szczegóły dotyczące zaistniałej sytuacji i domaga się uznania, iż on jako pierwszy sformułował teorię uogólnionej odwrotności krakowianów.

14

Structured total least norm for MISO ARX system identification

Larkowski T., Vinsonneau B., Burnham K. J.

Systems Science

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2007

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Vol. 33, no 4

73-83

EN

The errors-in-variables (EIV) identification framework concerns the identification of dynamic models of systems where all the variables are corrupted by noise. The total least squares (TLS) is one of the most prominent techniques that has proven to be both robust and reliable. The structured total least norm (STLN) can be seen as a natural extension to TLS that preserves any affine structure of the joint data matrix, which is mostly the case in identification schemes. In contrast to the least squares (LS), TLS or mixed LS-TLS problems, the STLN solution cannot be expressed in a closed form, therefore, an optimization procedure is required. Note that STLN allows different norms to be considered other than the usual square norm (or 2 norm). This paper describes a direct application of the STLN approach for systems that can be represented by auto-regressive with exogenous input (ARX) multi-input single-output (MISO) models. The performance of the proposed STLN algorithm (in the case of the square norm) is compared to the LS, the bias-eliminating LS (BELS), the extended matrix LS (EMLS), the instrumental variables (IV), TLS and the compensated TLS (CTLS) methods when applied to a simulated MISO ARX system. Results, obtained from Monte Carlo simulation, show that, under the conditions considered here, STLN surpasses all other investigated techniques, attaining the best estimates of the true system parameters.

15

Revisiting least squares: A discussion on the leading estimation principle in geodesy

Kotsakis C., Sideris M. G.

Geodezja i Kartografia

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2006

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Vol. 55, no 1

3-22

EN

Least squares (LS) estimation is one of the most important tools in geodetic data analysis, However, its prevailing use is not often complemented by an objective view of its rudiments, Within the standard formalism of LS estimation theory there are actually several paradoxical and curious issues which are seldom explicitly formulated. The aim of this expository paper is to present some of these issues and to discuss their implications for geodetic data analysis and parameter estimation problems, In the first part of the paper, an alternative view of the statistical principles that are traditionally linked to LS estimation is given. Particularly, we show that the property of unbiasedness for the ordinary LS estimators can be replaced with a different, yet equivalent, constraint which implies that the numerical range of the unknown parameters is boundless. In the second part of the paper, the shortcomings of the LS method are exposed from a purely algebraic perspective, without employing any concepts from the probabilistic/statistical framework of estimation theory, In particular, it is explained that what is 'least' in least squares is certainly not the errors in the estimated model parameters, and that in every LS-based inversion of a linear model there exists a critical trade-off between the Euclidean norms of the parameter estimation errors and the adjusted residuals

PL

Estymacja metodą najmniejszych kwadratów (LS) jest jednym z najważniejszych narzędzi w analizowaniu danych geodezyjnych. Jednakże powszechne korzystanie z tej metody nie zawsze idzie w parze z pelnym uświadomieniem sobie jej podstaw. W standardowym formalizmie teorii estymacji LS w rzeczywistości istnieje kilka paradoksalnych i osobliwych zagadnień rzadko formułowanych wprost. Celem niniejszej pracy jest przedstawienie niektórych z tych zagadnień i przedyskutowanie ich konsekwencji w analizie danych geodezyjnych oraz problematyce estymacji parametrów. W pierwszej części pracy przedstawiony jest alternatywny pogląd na podstawy statystyczne, które są tradycyjnie łączone z estymacją LS. W szczególności pokazano, że właściwość nieobciążoności dla zwykłych estymatorów LS może być zastąpiona przez inne, równoważne jej uwarunkowanie, które powoduje, że zakres numeryczny nieznanych parametrów jest nieograniczony. W drugiej części pracy przedstawiono wady metody LS z czysto algebraicznego punktu widzenia, bez uwzględnienia pojęć z zakresu probabilistycznego/statystycznego teorii estymacji. W szczególności wyjaśnione zostało, do czego odnosi się 'najmniejszy' (Ieast) w metodzie najmniej szych kwadratów. Z pewnością nie odnosi się do błędów wyznaczanych parametrów modelu. Ponadto stwierdzono, że w kazdej inwersji modelu liniowego opartej na metodzie LS istnieje krytyczna zamiana pomiędzy normami euklidesowymi blędów wyznaczanych parametrów i wyrównanych residuów.

16

Models of relative abundance distributions. 1, Model fitting by stochastic models

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 2

145-147

EN

The present paper studies possibilities to discriminate between 9 stochastic models of relative abundance distributions (RADs). It develops a new test statistic for fitting based on least square distances and tests the applicability of methods described so far. The paper identifies three basic shapes of RADs termed power fraction, random assortment and Zipf-Mandelbrot type shape. It is shown that even a correct identification of the shape of a given data set requires that this data set is replicated more than 10 times. Estimates of necessary sample sizes for real animal or plant communities revealed that for communities with 20 to 100 species at least 200 to 500 times the species number is necessary for a correct model identification. The implications of these findings for the applicability of models of relative abundance distributions are discussed.