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1
Content available remote

Adaptive modeling of reliability properties for control and supervision purposes

100%
Dettmann K.-U., Söffker D.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 3
479-486
EN
Modeling of reliability characteristics typically assumes that components and systems fail if a certain individual damage level is exceeded. Every (mechanical) system damage increases irreversibly due to employed loading and (mechanical) stress, respectively. The main issue of damage estimation is adequate determination of the actual state-of-damage. Several mathematical modeling approaches are known in the literature, focusing on the task of how loading effects damage progression (e.g., Wöhler, 1870) for wear processes. Those models are only valid for specific loading conditions, a priori assumptions, set points, etc. This contribution proposes a general model, covering adequately the deterioration of a set of comparable systems under comparable loading. The main goal of this contribution is to derive the loading-damage connection directly from observation without assuming any damage models at the outset. Moreover, the connection is not investigated in detail (e.g., to examine the changes in material, etc.) but only approximated with a probabilistic approach. The idea is subdivided into two phases: A problem-specific relation between loading applied (to a structure, which contributes to the stress) and failure is derived from simulation, where a probabilistic approach only assumes a distribution function. Subsequently, an adequate general model is set up to describe deterioration progression. The scheme will be shown through simulation-based results and can be used for estimation of the remaining useful life and predictive maintenance/control.
2
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Planning identification experiments for cell signaling pathways: An NFκB case study

100%
Fujarewicz K.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 4
773-780
EN
Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear ordinary differential equations (ODEs). It is very difficult to obtain a proper model. There are many hypotheses about the structure of the model (sets of variables and phenomena) that should be verified. The next step, fitting the parameters of the model, is also very complicated because of the nature of measurements. The blotting technique usually gives only semi-quantitative observations, which are very noisy and collected only at a limited number of time moments. The accuracy of parameter estimation may be significantly improved by a proper experiment design. Recently, we have proposed a gradient-based algorithm for the optimization of a sampling schedule. In this paper we use the algorithm in order to optimize a sampling schedule for the identification of the mathematical model of the NFκB regulatory module, known from the literature. We propose a two-stage optimization approach: a gradient-based procedure to find all stationary points and then pair-wise replacement for finding optimal numbers of replicates of measurements. Convergence properties of the presented algorithm are examined.
3
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Identification of a quasilinear parabolic equation from final data

100%
Fernández L. A., Pola C.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 4
859-879
EN
We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization problem that allows for the reconstruction of the nonlinearities. Some numerical results in the one-dimensional case are presented, even in the case of noisy data.
4
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Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

100%
Verdiere N., Denis-Vidal L., Joly-Blanchard G., Domurado D.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 4
517-526
EN
The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it a priori parameter values. Then the resulting parameter estimate is improved by using the classical least-squares method.
5
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Sensor network design for the estimation of spatially distributed processes

100%
Uciński D., Patan M.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 3
459-481
EN
In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum-likelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.
6
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Iterative estimators of parameters in linear models with partially variant coefficients

100%
Hu S., Meinke K., Chen R., Huajiang O.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 2
179-187
EN
A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and applicable in practical fields.
7
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Distributed scheduling of sensor networks for identification of spatio-temporal processes

88%
Patan M.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 2
299-311
EN
An approach to determine a scheduling policy for a sensor network monitoring some spatial domain in order to identify unknown parameters of a distributed system is discussed. Given a finite number of possible sites at which sensors are located, the activation schedule for scanning sensors is provided so as to maximize a criterion defined on the Fisher information matrix associated with the estimated parameters. The related combinatorial problem is relaxed through operating on the density of sensors in lieu of individual sensor positions. Then, based on the adaptation of pairwise communication algorithms and the idea of running consensus, a numerical scheme is developed which distributes the computational burden between the network nodes. As a result, a simple exchange algorithm is outlined to solve the design problem in a decentralized fashion.
8
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Nonlinear state observers and extended Kalman filters for battery systems

88%
Rauh A., Butt S., Aschemann H.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 3
539-556
EN
The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.
9
Content available remote

Sensor network scheduling for identification of spatially distributed processes

88%
Uciński D.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 1
25-40
EN
The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the Dₛ-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.
10
Content available remote

Configuring a sensor network for fault detection in distributed parameter systems

75%
Patan M., Uciński D.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 4
513-524
EN
The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.
11
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On-line parameter and delay estimation of continuous-time dynamic systems

75%
Kozłowski J., Kowalczuk Z.
International Journal of Applied Mathematics and Computer Science
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2015
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tom 25
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nr 2
223-232
EN
The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.
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