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1

Recursive identification of noisy autoregressive models via a noise-compensated overdetermined instrumental variable method

Barbieri Matteo, Diversi Roberto

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 1

65--79

EN

The aim of this paper is to develop a new recursive identification algorithm for autoregressive (AR) models corrupted by additive white noise. The proposed approach relies on a set of both low-order and high-order Yule-Walker equations and on a modified version of the overdetermined recursive instrumental variable method, leading to the estimation of both the AR coefficients and the additive noise variance. The main motivation behind our proposition is introducing model identification procedures suitable for implementation on edge-computing platforms and programmable logic controllers (PLCs), which are known to have limited capabilities and resources when dealing with complex mathematical computations (i.e., matrix inversion). Indeed, our development is focused on condition monitoring systems, with particular attention paid to their integration onboard industrial machinery. The performance of the recursive approach is tested using both numerical simulations and a laboratory case study. The obtained results are very promising.

2

ARMAX-based identification and diagnosis of vibration behavior of gas turbine bearings

Mahroug Youcef, Khaldi Belgacem Said, Guemana Mouloud, Hafaifa Ahmed, Iratni Abdelhamid, Colak Ilhami

Diagnostyka

|

2023

|

Vol. 24, No. 3

art. no. 2023310

EN

Parametric identification approaches play a crucial role in the control and monitoring of industrial systems. They facilitate the identification of system variables and enable the prediction of their evolution based on the input-output relationship. In this study, we employ the ARMAX approach to accurately predict the dynamic vibratory behavior of MS5002B gas turbine bearings. By utilizing real input-output data obtained from their operation, this approach effectively captures the vibration characteristics of the bearings. Additionally, the ARMAX technique serves as a valuable diagnostic tool for the bearings, enhancing the quality of identification of turbine variables. This enables continuous monitoring of the bearings and real-time prediction of their behavior. Furthermore, the ARMAX approach facilitates the detection of all potential vibration patterns that may occur in the bearings, with monitoring thresholds established by the methodology. Consequently, this enhances the availability of the bearings and reduces turbine downtime. The efficacy of the proposed ARMAX approach is demonstrated through comprehensive results obtained in this study. Robustness tests are conducted, comparing the real behavior observed through various probes with the reference model, thereby validating the approach.

3

Cascade tanks system identification for robust predictive control

Jakowluk Wiktor, Jaszczak Sławomir

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 6

art. no. e143646

EN

The main goal of estimating models for industrial applications is to guarantee the cheapest system identification. The requirements for the identification experiment should not be allowed to affect product quality under normal operating conditions. This paper deals with ensuring the required liquid levels of the cascade system tanks using the model predictive control (MPC) method. The MPC strategy was extended with the Kalman filter (KF) to predict the system’s succeeding states subject to a reference trajectory in the presence of both process and measurement noise covariances. The main contribution is to use the application-oriented input design to update the parameters of the model during system degradation. This framework delivers the least-costly identification experiment and guarantees high performance of the system with the updated model. The methods presented are evaluated both in the experiments on a real process and in the computer simulations. The results of the robust MPC application for cascade system water levels control are discussed.

4

Arriving air traffic separations generalized model identification

Pawełek Adrian, Lichota Piotr

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140694

EN

Quick development of computer techniques and increasing computational power allow for building high-fidelity models of various complex objects and processes using historical data. One of the processes of this kind is an air traffic, and there is a growing need for traffic mathematical models as air traffic is increasing and becoming more complex to manage. This study concerned the modelling of a part of the arrival process. The first part of the research was air separation modelling by using continuous probability distributions. Fisher information matrix was used for the best fit selection. The second part of the research consisted of applying regression models that best match the parameters of representative distributions. Over a dozen airports were analyzed in the study and that allowed to build a generalized model for aircraft air separation in function of traffic intensity. Results showed that building a generalized model which comprises traffic from various airports is possible. Moreover, aircraft air separation can be expressed by easy to use mathematical functions. Models of this kind can be used for various applications, e.g.: air separation management between aircraft, airports arrival capacity management, and higher-level air traffic simulation or optimization tasks.

5

Modelling of Dry-Low Emission Gas Turbine Fuel System using First Principle Data-Driven Method

Omar Mediah Binti, Ibrahim Rosdiazli, Abdullah Mohd Faris, Tarik Mohammad Haizad Mohd

Journal of Power Technologies

|

2020

|

Vol. 100, nr 1

1--13

EN

Achieving reliable power generation from Dry Low Emission gas turbines together with low CO2 and NOx discharge is a great challenge, as the rigorous control strategy is susceptible to frequent trips. Therefore, it is crucial to establish a dynamic model of the turbine (such as the one commonly attributed to Rowen) to ascertain the stability of the system. However, the major distinctive fuel system design in the DLE gas turbine is not constructed in the well-established model. With this issue in mind, this paper proposes a modelling approach to the DLE gas turbine fuel system which consists of integrating the main and pilot gas fuel valve into Rowen’s model, using the First Principle Data-Driven (FPDD) method. First, the structure of the fuel system is determined and generated in system identiﬁcation. Subsequently, the validated valve models are integrated into Rowen’s model as the actual setup of the DLE gas turbine system. Ultimately, the core of this modelling approach is fuel system integration based on the FPDD method to accurately represent the actual signals of the pilot and main gas fuel valves, gas fuel ﬂow and average turbine temperature. Then, the actual signals are used to validate the whole structure of the model using MAE and RMSE analysis. The results demonstrate the high accuracy of the DLE gas turbine model representation for future utilization in fault identiﬁcation and prediction study.

6

Aircraft system identification using simultaneous quantized harmonic input signals

Lichota P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 6

1351--1362

EN

In this paper, quanizted multisine inputs for a maneuver with simultaneous elevator, aileron and rudder deflections are presented. The inputs were designed for 9 quantization levels. A nonlinear aircraft model was exited with the designed inputs and its stability and control derivatives were identified. Time domain output error method with maximum likelihood principle and a linear aircraft model were used to perform parameter estimation. Visual match and relative standard deviations of the estimates were used to validate the results for each quantization level for clean signals and signals with measurement noise present in the data. The noise was included into both output and input signals. It was shown that it is possible to obtain accurate results when simultaneous flight controls deflections are quantized and noise is present in the data.

7

Parameter identification and estimation for stage-structured population models

Coll Carmen, Sánchez Elena

International Journal of Applied Mathematics and Computer Science

|

2019

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Vol. 29, no. 2

327--336

EN

A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.

8

An adaptive identification method based on the modulating functions technique and exact state observers for modeling and simulation of a nonlinear MISO glass melting process

Byrski Witold, Drapała Michał, Byrski Jędrzej

International Journal of Applied Mathematics and Computer Science

|

2019

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Vol. 29, no. 4

739--757

EN

The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.

9

System Identification and Model Predictive Control of the Chatter Phenomenon in Turning Process

Karimipour Atiyeh, Emami Mohsen

Advances in Science and Technology. Research Journal

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2019

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Vol. 13, no 3

217--228

EN

Chatter is a series of unwanted and extreme vibrations which frequently happens during different machining processes and impose variety of adverse effects on the machine-tool and surface finish. Chatter has two main types namely forced-chatter and self-existed chatter. The forced-chatter has an external cause; however, self-exited chatter has no external stimuli, rather it is created due to the phase difference between the previous and current waves on the surface of the workpiece. Due to the self-generative nature of this type of chatter, its recognition and prevention is much more difficult. For preventing self-exited chatter its model should be available first. The chatter is usually simulated as a one degree of freedom mass-spring-damper model with unknown parameters that they should be determined somehow. In this paper, the parameters of the tool equation of motion i.e. mass, damping, and stiffness coefficients of the system are predicted through a wavelet-based method online, and then based on the achieved parameters, the system is controlled via Model Predictive Control (MPC) approach. For the validation, the algorithm is applied to 25 different experimental tests in which the acceleration of the tool and cutting force are measured via an accelerometer and a dynamometer. By investigation of the SLDs generated by the predicted parameters, the presented system identification method is validated. Also, it is shown that the chatter vibration is completely restrained by means of MPC. For investigation of the MPC performance, MPC algorithm is compared with PID controller and simulations has indicated a much stronger performance of MPC rather than PID controller in terms of vibration attenuation and control effort.

10

The variability of the Atlantic meridional circulation since 1980, as hindcast by a data-driven nonlinear systems model

Ayala-Solares J. R., Wei H.-L., Bigg G. R.

Acta Geophysica

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2018

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Vol. 66, no. 4

683--695

EN

The Atlantic meridional overturning circulation (AMOC), an important component of the climate system, has only been directly measured since the RAPID array’s installation across the Atlantic at 26N in 2004. This has shown that the AMOC strength is highly variable on monthly timescales; however, after an abrupt, short-lived, halving of the strength of the AMOC early in 2010, its mean has remained * 15% below its pre-2010 level. To attempt to understand the reasons for this variability, we use a control systems identification approach to model the AMOC, with the RAPID data of 2004–2017 providing a trial and test data set. After testing to find the environmental variables, and systems model, that allow us to best match the RAPID observations, we reconstruct AMOC variation back to 1980. Our reconstruction suggests that there is inter-decadal variability in the strength of the AMOC, with periods of both weaker flow than recently, and flow strengths similar to the late 2000s, since 1980. Recent signs of weakening may therefore not reflect the beginning of a sustained decline. It is also shown that there may be predictive power for AMOC variability of around 6 months, as ocean density contrasts between the source and sink regions for the North Atlantic Drift, with lags up to 6 months, are found to be important components of the systems model.

11

Output Error Method for Tiltrotor Unstable in Hover

Lichota P., Szulczyk J.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 1

23--36

EN

This article investigates unstable tiltrotor in hover system identification from flight test data. The aircraft dynamics was described by a linear model defined in Body-Fixed-Coordinate System. Output Error Method was selected in order to obtain stability and control derivatives in lateral motion. For estimating model parameters both time and frequency domain formulations were applied. To improve the system identification performed in the time domain, a stabilization matrix was included for evaluating the states. In the end, estimates obtained from various Output Error Method formulations were compared in terms of parameters accuracy and time histories. Evaluations were performed in MATLAB R2009b environment.

12

Helicity of Convective Flows from Localized Heat Source in a Rotating Layer

Sukhanovskii A., Evgrafova A., Popova E.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 2

177--188

EN

Experimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from observational data and numerical modelling including secondary flows in the boundary layer. Differential characteristics of the flow were studied by numerical simulation using CFD software Flow Vision. Helicity distribution in rotating fluid layer with localized heat source was analysed. Two mechanisms which play role in helicity generation are found. The first one is the strong correlation of cyclonic vortex and intensive upward motion in the central part of the vessel. The second one is due to large gradients of velocity on the periphery. The integral helicity in the considered case is substantial and its relative level is high.

13

Full-scale dynamic testing of the corrosion-damaged, steel-truss structure of Old Bridge over the Danube in Bratislava

Benčat J., Hadzima B.

Czasopismo Techniczne. Budownictwo

|

2015

|

Y. 112, iss. 2-B

217--227

EN

A large number of existing bridges need to be rehabilitated due to increasing traffic and/or loading requirements and also corrosion action. In this paper, a procedure is presented for estimating the ultimate capacity of a steel bridge over the Danube in Bratislava – Old Bridge (built in 1945). The development of a simplified Finite Element Model (FEM ) and basic modal parameter calculations preceded the experimental investigations of the bridge via static and dynamic in-situ loading tests, so that the main assumptions adopted in the FEM were assessed through comparison between measured and predicted dynamic and modal parameters of the bridge structure. The bridge structure computational model was then optimized by structure variables (primarily, steel structure joints mass and corrosion grade) to achieve the minimum differences between the experimental and theoretical results. The calibrated FEM with the optimal combinations of the mentioned variable values were defined and finally used for structure calculations and for strengthening the design of the real bridge structure.

PL

Wiele istniejących mostów musi zostać odnowionych w związku z rosnącym natężeniem ruchu i/lub z powodu wymagań obciążeniowych, a także w skutek działania korozji. W niniejszej pracy przedstawiono procedurę szacowania nośności granicznej stalowego mostu na Dunaju w Bratysławie - Old Bridge (zbudowanego w 1945 r.). Opracowanie uproszczonego modelu MES i podstawowe obliczenia parametrów modalnych poprzedzały badania statyczne i dynamiczne mostu w skali rzeczywistej. W związku z tym główne założenia modelowania MES zostały przyjęte na podstawie porównania między zmierzonymi i przewidywanymi dynamicznymi i modalnymi parametrami konstrukcji mostu. Model obliczeniowy konstrukcji mostu został następnie zoptymalizowany przez parametry konstrukcji (przede wszystkim przez uwzględnienie masy węzłów stalowych, stopnia korozji), aby osiągnąć minimalne różnice między wynikami badań doświadczalnych i teoretycznych. Skalibrowany model MES z optymalnymi kombinacjami wymienionych parametrów został zdefiniowany i wykorzystany do obliczeń i następnie wzmocnienia konstrukcji rzeczywistej mostu.

14

Nonparametric instrumental variables for identification of block-oriented systems

Mzyk G.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 3

521--537

EN

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

15

Semi-active suspension system modelling and parameters identification

Kogut K.

Automatyka / Automatics

|

2012

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Vol. 16, no. 1

25-44

EN

This paper presents a study of obtaining a model of the real quarter-car suspension device. The system is equipped with an automotive engineering magnetorheological (MR) rotary brake. Due to the complex mechanical structure of the apparatus the considered model contains several simplifications. In the parameter estimation process the grey-box method was used, while the process itself was split into two separate steps. In the first step, the parameters of the nonlinear model of suspension part are identified and the static profile of the MR damper is experimentally determined. The second step is to estimate the parameters of the model of the wheel-eccentricity part. Comparison of the modelled system trajectories and real-time experiments are presented. The identification results show that the obtained model is accurate and can be successfully applied to simulate the device.

PL

W artykule przedstawiono proces modelowania systemu zawieszenia ćwiartki pojazdu. Układ wyposażony jest w rotacyjny tłumik magnetoreologiczny (MR). Wykorzystany model dynamiczny urządzenia zawiera szereg uproszczeń, a w celu identyfikacji jego parametrów zastosowano metodologię szarych modeli. Estymacja parametrów modelu została podzielona na dwie fazy. W pierwszej fazie zidentyfikowano układ wahacza oraz wyznaczono statyczną charakterystykę tłumika MR. Druga faza polegała na identyfikacji parametrów układu wymuszenia kinematycznego koło-mimośród. W pracy przedstawiono porównanie eksperymentalnych i symulowanych trajektorii badanego systemu. Wyniki identyfikacji wskazują, że zaproponowany model wystarczająco wiernie przedstawia dynamikę obiektu rzeczywistego i może zostać użyty do jej symulacji.

16

Design of an optimal actuation signal for identification of a torsional spring system

Jakowluk W.

Przegląd Elektrotechniczny

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2011

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R. 87, nr 6

154-160

EN

The choice of an input signal used for perturbation of the system is critical in the task of model building and parameter identification. System identification, in practice is carried out by perturbing processes or plants in operation. In the paper the optimal excitation signal was generated for a torsional spring model. The objective of this kind of experiment design is to minimise the variance of the parameters to be estimated. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) in the form of a conventional integral criterion with amplitude constraints. It was shown that the optimal input signal used for system excitation minimises the volume of the ellipsoidal confidence region of parameters estimates.

PL

Dokładność uzyskiwanych estymat parametrów identyfikowanego modelu zależy przede wszystkim od doboru odpowiedniego sygnału wejściowego, który wzbudza wybrane wejście obiektu regulacji. W wielu praktycznych zastosowaniach identyfikacja jest przeprowadzana w czasie rzeczywistym, podczas normalnej pracy obiektu (procesu technologicznego). W pracy przedstawiono wyniki doboru optymalnego sygnału pobudzającego układem skrętnym. Celem takiego eksperymentu jest minimalizacja wariancji uzyskiwanych estymat parametrów. Maksymalizowano funkcjonał celu określony jako wyznacznik macierzy informacyjnej Fishera uwzględniając nałożone ograniczenia na amplitudę sygnału wejściowego. Stwierdzono, że optymalne pobudzenie identyfikowanego obiektu minimalizuje elipsoidalne obszary ufności estymowanych parametrów.

17

Identyfikacja i weryfikacja modelu obiektu dynamicznego na przykładzie procesu frezowania

Kulisz M.

Postępy Nauki i Techniki

|

2011

|

nr 8

76-82

PL

Przedstawiony w pracy proces jest obiektem dynamicznym, którego proces identyfikacji przeprowadzono za pomocą modelu "czarnej skrzynki". W tym celu użyto narzędzia System Identyfication Toolbox w środowisku Matlab. Przeprowadzono identyfikację modelu poprzez estymację struktury i parametrów modelu. Porównano zgodność różnych postaci modeli.

EN

The object discussed in the present paper is dynamic. Its identification process was conducted with the use of a "black box" model. For this purpose The System Identification Toolbox in the Matlab environment has been used. The model identification was carried out due to the model structure and parameters' estimation. As a result, various models' forms was compared.

18

Estimation of feedwater heater parameters based on a grey-box approach

Barszcz T., Czop P.

International Journal of Applied Mathematics and Computer Science

|

2011

|

Vol. 21, no 4

703-715

EN

The first-principle modeling of a feedwater heater operating in a coal-fired power unit is presented, along with a theoretical discussion concerning its structural simplifications, parameter estimation, and dynamical validation. The model is a part of the component library of modeling environments, called the Virtual Power Plant (VPP). The main purpose of the VPP is simulation of power generation installations intended for early warning diagnostic applications. The model was developed in the Matlab/Simulink package. There are two common problems associated with the modeling of dynamic systems. If an analytical model is chosen, it is very costly to determine all model parameters and that often prevents this approach from being used. If a data model is chosen, one does not have a clear interpretation of the model parameters. The paper uses the so-called grey-box approach, which combines first-principle and data-driven models. The model is represented by nonlinear state-space equations with geometrical and physical parameters deduced from the available documentation of a feedwater heater, as well as adjustable phenomenological parameters (i.e., heat transfer coefficients) that are estimated from measurement data. The paper presents the background of the method, its implementation in the Matlab/Simulink environment, the results of parameter estimation, and a discussion concerning the accuracy of the method.

19

Design of an optimal excitation signal for identification of inertial systems in time domain

Jakowluk W.

Przegląd Elektrotechniczny

|

2009

|

R. 85, nr 6

125-129

EN

The choice of an input signal used for actuation of the system is critical in the task of model building and parameter identification. In the paper the optimal excitation signal was generated for an inertial model. The objective of this kind of experiment design is to minimise the variance of the parameters to be estimated. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant in the form of a conventional integral criterion with amplitude constraints. It was shown that the optimal input signal used for system excitation minimises the volume of the ellipsoidal confidence region of parameters estimates.

PL

Dokładność uzyskiwanych estymat parametrów identyfikowanego modelu zależy przede wszystkim od doboru odpowiedniego sygnału wejściowego, który wzbudza wybrane wejście obiektu regulacji. W pracy przedstawiono wyniki doboru optymalnego sygnału pobudzającego układem jednoinercyjnym. Celem takiego eksperymentu jest minimalizacja wariancji uzyskiwanych estymat parametrów. Maksymalizowano funkcjonał celu określony jako wyznacznik macierzy informacyjnej Fishera uwzględniając nałożone ograniczenia na amplitudę sygnału wejściowego. Stwierdzono, że optymalne pobudzenie identyfikowanego obiektu minimalizuje elipsoidalne obszary ufności estymowanych parametrów.

20

Computer-aided evaluation of a new interrupter algorithm in respiratory mechanics measurement

Jabłoński I., Mroczka J.

Biocybernetics and Biomedical Engineering

|

2006

|

Vol. 26, no. 3

33-47

EN

The fIow interrupter technique is an attractive method of respiratory mechanics measurement. Lack of reliable algorithms for processing of the data measured as well as a low level of the routine informativity schemes disqualify the method as a useful tool in clinical and diagnostic practice. The theoretical basis of the enhanced interrupter technique (EIT) prepared by the authors is a chance to change the role of the technique in the set of available measurement methods. In the report, computer investigations showing an advantage of EIT over the most popular methods of the postocclusional data analysis, characterised in literature, are presented. Beside the evidence of an improvement of the basic algorithm informativity, also an increased accuracy of the results in the simulation experiment organised by the authors has been shown.