Anna Stankiewicz

University of Life Sciences in Lublin · Department of Technology Fundamentals

This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to non-integer order derivatives. To build a fractional Maxwell model when only the noise-corrupted discrete-time measurements of the relaxation modulus are accessible for identification is a basic concern. For fitting the...

The relaxation time and frequency spectra are vital for constitutive models and for insight into the viscoelastic properties of polymers, since, from the spectra, other material functions used to describe rheological properties of various polymers can be uniquely determined. In recent decades the non-integer order differential equations have attrac...

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modu...

Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model....

Recovering the relaxation spectrum, a fundamental rheological characteristic of polymers, from experiment data requires special identification methods since it is a difficult ill-posed inverse problem. Recently, a new approach relating the identification index directly with a completely unknown real relaxation spectrum has been proposed. The integr...

The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods...

Different viscoelastic models and characteristics are commonly used to describe, analyze, compare and improve the mechanical properties of polymers. A time-dependent linear relaxation modulus next to frequency-domain storage and loss moduli are the basic rheological material functions of polymers. The exponential Maxwell model and the exponential s...

The relaxation spectra, from which other material functions used to describe mechanical properties of materials can be uniquely determined, are important for modeling the rheological properties of polymers used in chemistry, food technology, medicine, cosmetics, and many other industries. The spectrum, being not directly accessible by measurement,...

The viscoelastic relaxation spectrum is vital for constitutive models and for insight into the mechanical properties of materials, since, from the relaxation spectrum, other material functions used to describe rheological properties can be uniquely determined. The spectrum is not directly accessible via measurement and must be recovered from relaxa...

The viscoelastic relaxation spectrum provides deep insights into the complex behavior of polymers. The spectrum is not directly measurable and must be recovered from oscillatory shear or relaxation stress data. The paper deals with the problem of recovery of the relaxation spectrum of linear viscoelastic materials from discrete-time noise-corrupted...

For the assumed bale volume, its dimensions (diameter, height), minimizing the consumption of the plastic film used for bale wrapping with the combined 3D method, depend on film and wrapping parameters. Incorrect selection of these parameters may result in an optimal bale diameter, which differs significantly from its height, while in agricultural...

The combined 3D method is used for wrapping cylindrical bales of agricultural materials based on biaxial rotation of the film applicators. The demand for minimization of plastic film consumption keeps increasing, with the goal to save the environment, reduce plastic costs, and minimize wrapping time. Consequently, methods have been reported to solv...

The technique of baled silage wrapped with plastic film is one of the core silage engineering and has been extensively developed over the past three decades. In this book, the model-based film coverage aspects like uniformity, reachability of arbitrary pre-assumed number of film layers and film usage minimisation have been grouped for the first tim...

Highlights A complete mathematical model describes stretch film consumption for wrapping round bales using IntelliWrap. An algorithm is presented for optimal, in the sense of minimal, film usage based on film width selection. A solution is presented for selecting the optimal width of commercially available film. Optimal film width guarantees up to...

A conventional method for wrapping round bales of agricultural materials by wrappers with a rotating table or with rotating arms is considered. In contemporary agriculture, the demand for minimal consumption of the film used to wrap bales is very high, in order to apply this method with lower cost and less damage to the environment. A combined mode...

The main objective of this article was to mathematically formulate the problem of the uniform coverage of round baled silage, solve this problem and propose a design approach. A mathematical model which describes the distribution and consumption of stretch film used for bale wrapping is derived. The model aims at capturing more features of a realis...

A combined method for wrapping round (i.e., cylindrical) bales of agricultural materials based on biaxial rotation of the film applicators is considered in this study. A complete mathematical model is derived describing the consumption of the film used to wrap the bales that can be applied for film consumption estimation and design purposes. The ba...

The identification of the linear relaxation modulus of viscoelastic materials on the basis of the stress data from non-ideal ramp tests where a time-variable strain rate is followed by a constant strain is considered. The loading phase strain is described by the third order polynomial of time. The aim of the paper is to develop a method to approxim...

A new fast scheme for approximate identification of linear relaxation modulus of viscoelastic materials on the basis of the discrete stress data from non-ideal ramp-tests, where a time-variable strain rate is followed by a constant strain, is proposed. The approximations of the relaxation modulus in successive time instants are determined on the ba...

The relaxation spectrum is a characteristic quantity describing the viscoelastic properties of many materials. Given the spectrum, it is very easy to convert one material function into another one. The paper deals with the problems of recovery of the spectrum of relaxation frequencies of linear viscoelastic materials from discrete-time noise corrup...

PART I. PROBLEM AND EXAMPLE Summary. The two-part paper deals with the problem of recovery of continuous relaxation spectrum of linear viscoelastic materials from discrete-time noise corrupted measurements of relaxation modulus obtained in stress relaxation test. This problem is known to be severely Hadamard ill-posed. Thus even small changes in me...

The paper suggests a new fast scheme for approximate identification of linear relaxation modulus of viscoelastic materials on the basis of the stress data from ramp-tests where a time-variable strain rate is followed by a constant strain. Approximation of the relaxation modulus in successive time instants is determined on the basis of the stress an...

The problem of the linear relaxation modulus determination on the basis of the stress data from relaxation tests where a constant strain rate is followed by a constant strain is considered. The aim of the paper is to develop a method for approximate identification of relaxation modulus using relaxation data from such ramp test. Generalized three-po...

New algorithm of the least-squares approximation of the spectrum of relaxation frequencies by the finite series of Hermite functions using discrete-time noise corrupted measurements of relaxation modulus obtained in stress relaxation test has been proposed. Since the problem of relaxation spectrum identification is ill-posed, the inverse problem of...

The paper deals with the problem of recovery of continuous relaxation spectrum of linear viscoelastic materials from discrete-time noise corrupted measurements of relaxation modulus obtained in stress relaxation test. The leasts-quares problem of optimal approximation of the spectrum is solved based on the orthogonal series expansion. Hermite funct...

The problem of a weighted least-squares approximation of viscoelastic material by Maxwell model is discussed when the noise-corrupted time-measurements of the relaxation modulus obtained in relaxation test experiment are accessible for identifi cation. In the previous paper it has been shown that even when the true relaxation modulus description is...

The problem of a weighted least-squares approximation of viscoelastic material by generalized Maxwell model is discussed when only the noise-corrupted time-measurements of the relaxation modulus are accessible for identification. To build a Maxwell model, which does not depend on sampling instants is a basic concern. It is shown that even when the...

S t r e s z c z e n i e . W pracy zaakcentowano niebezpieczeństwa związane ze złym uwarunkowa-niem klasycznych problemów modelowania matematycznego materiałów lepkospręŜytych: zadań wyznaczania modeli Maxwella i Kelvina oraz zadań identyfikacji spektr relaksacji i retardacji tych materiałów. W problemach tych nawet niewielka zmiana danych zadania (...

S t r e s z c z e n i e . W pracy rozwaŜa się problem wyznaczania spektrum relaksacji materiałów lepkospręŜytych na podstawie dyskretnych zakłóconych pomiarów modułu relaksacji zgromadzo-nych w teście relaksacji napręŜeń. Zadanie to jest źle postawionym problemem odwrotnym. Celem pracy jest przedstawienie remedium, jakim jest ograniczenie zbioru ro...

The paper deals with the problem of Maxwell model determination from discretetime noise corrupted measurements of relaxation modulus obtained in stress relaxation test. This problem is known to be ill-posed. In this paper the Maxwell model is determined using nonlinear least squares method and Tikhonov regularization technique. The validity of the...

W pracy przedstawiono bazujący na metodzie Prony'ego algorytm identyfikacji modułu relaksacji liniowych materiałów lepkosprężystych opisanych modelem Maxwella. Udowodniono, że jeśli rzeczywisty moduł relaksacji dany jest czteroelementowym modelem Maxwella, a jego pomiary nie są obciążone zakłóceniami, to algorytm ten zapewnia identyfikowalność rzec...

An algorithm, based on Prony approach, for identification of the relaxation modulus of linear viscoelastic materials described by Maxwell model is presented. It is proved, that if the real relaxation modulus is four-element Maxwell and the measurements are not corrupted by noise, then the identifiability of the real parameters of the relaxation mod...

Celem pracy było opracowanie komputerowego algorytmu identyfikacji zmiennych w czasie modułów odkształcenia postaciowego i objętościowego materiałów liniowo lepkosprężystych na podstawie uzyskanych eksperymentalnie czasowych przebiegów funkcji relaksacji naprężeń w walcowych próbkach badanego materiału w stanie jednoosiowego odkształcenia i napręże...

The aim of the paper is to investigate a computer identification algorithm for determining the time-varying shear and bulk modulus of linear viscoelastic materials based on experimentally obtained stress and strain uniaxial relaxation functions of an cylindrical specimens of the tested material is proposed. On the first stage of the identification...

Celem pracy było opracowanie algorytmu wyznaczania ciągłego spektrum czasów relaksacji materiałów lepkosprężystych na podstawie uzyskanych eksperymentalnie czasowych przebiegów liniowych modułów relaksacji. Zaproponowano nowy algorytm identyfikacji spektrum relaksacji oparty na przybliżeniu modułu relaksacji skończonym szeregiem zmodyfikowanych fun...

A sequence of k projects of independent activities, each project composed of activities available for realization at the same time, is considered. It is assumed that the activities are continuous dynamical systems with dynamics that depend continuously on the alloted amounts of the resource and that the initial and terminal states are fixed. The pr...

A two-stage scheme is introduced to find the large-scale globally optimal model of an interconnected steady-state system having a structure described by an interconnection matrix. Numerical realization of the scheme by using the standard optimization techniques is discussed, and an analysis of the identification accuracy is conducted.

A decentralized two-level identification scheme using the interaction balance as a coordination principle is proposed to find the model of a large-scale interconnected steady-state system with the structure described by an interconnection matrix. The applicability conditions of the interaction balance method (IBM) to determine the best, in the leas...

A decentralizsd two-level identification scheme using the interaction balance as coordination principle is proposed to find the model of a large-scale interconnected steady-state system with the structure described by an interconnection matrix. The applicability conditions of interaction balance method (IBM) to determine the best, in the least squa...

The contribution deals with the problem of time-optimal resource allocation (control) in a sequence of projects of independent activities, when the maximum level of total usage of renewable, continuously divisible, resource is time-variable and piece-wise constant. The solution concept, based on the notion of the set of reachable states and convex...

The problem of a weighted least-squares approximation of a memoryless system within a given class of models is discussed, and an identification algorithm leading to the best model when only input-output data are accessible is derived using a concept of random choice of inputs.

The paper deals with the problem of the optimal reduction of linear constant system description. The idea consists in determining a simplified model for which the open-loop model-based control is the best for the real system in the least-squares sense. The necessary conditions for optimal reduced model parameters are derived.

The paper deals with the parametric problem of multiple-input multiple-output (MIMO) system identification under deterministic conditions. Two different identification procedures: two-stage [12] and a direct one are discussed and the equivalence conditions of these algorithms — in the sense of the obtained identification result — are investigated w...

In this paper an attempt is made to combine the problems of the control and modelling of large-scale systems. Starting from the idea of the model-based (open-loop) solution of the two-layer steady-state optimization problem for the noiseless large-scale system, or one corrupted by slow-varying disturbances, an appropriate two-level identification s...

It is shown that the Anderson—Moore iterative algorithm can be eliminated in the approach used by Eitelberg and Rode (1982) to the optimal output feedback design by the appropriate choice of the reduced model.

The paper deals with time-optimal control of a complex of independent operations having concave models, when the maximum level of total usage of renewable continuously divisible resource is time-variable and piece-wise constant. In the case considered, neither the moments of a step change of the maximum level of resource, nor their amounts in the c...

Abstract. The purpose of the paper is to investigate an algorithm for recovery of the continuous relaxation time spectrum of viscoelastic materials from time-measurements of linear relaxation modulus. A new identification scheme based on the least-squares approximation of relaxation modulus by finite serious of modified Bessel functions is proposed...

Streszczenie. W pracy [Stankiewicz 2009] przedstawiono metodę wyznaczania spektrum re-laksacji na podstawie dyskretnych, zakłóconych pomiarów modułu relaksacji zgromadzonych w standardowym teście relaksacji naprężeń, w której model spektrum dobierany jest tak, aby zapewnić najlepsze jego wygładzenie przy równoczesnym odtworzeniu pomiarów modułu rel...

Streszczenie. Systemy sterowania klimatem we współczesnych szklarniach to złożone struktury wykorzystujące model matematyczny sterowanego procesu i nowoczesne koncepcje sterowania. W pracy rozważa się zadanie równoczesnej stabilizacji temperatury powietrza i stężenie dwutlenku węgla wewnątrz szklarni przy odcinkami stałych wartościach zadanych. Zap...

Streszczenie. W pracy rozważa się zadanie równoczesnego sterowania temperaturą powietrza i stężeniem dwutlenku węgla wewnątrz szklarni dla wybranego, znanego w literaturze, systemu klimatycznego szklarni. Sterowanie realizowane jest w systemie sterowania typu feedback-feedforward, który pozwala w torze sprzężenia "wprzód" skutecznie i szybko kompen...

Streszczenie. W pracy zaproponowano metodę identyfikacji spektrum relaksacji na podsta-wie dyskretnych, zakłóconych pomiarów modułu relaksacji zgromadzonych w teście relaksa-cji naprężeń, w której model spektrum dobierany jest tak, aby zapewnić najlepsze jego wy-gładzenie przy równoczesnym odtworzeniu pomiarów modułu relaksacji. W obliczeniach nume...