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Search results for: POLYNOMIAL CHAOS EXPANSION
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Polynomial Chaos Expansion in Bio-and Structural Mechanics
PublicationThis monograph presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the...
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Polynomial Chaos Expansion in Bio- and Structural Mechanics
PublicationThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair...
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Regression points in non-intrusive polynomial chaos expansion method and D-optimal design
PublicationThe paper addresses selected issues of uncertainty quantification in the modelling of a system containing surgical mesh used in ventral hernia repair. Uncertainties in the models occur e.g. due to variability of abdominal wall properties among others. In order to include them, a non-intrusive regression-based polynomial chaos expansion method is employed. Its accuracy depends on the choice of regression points. In the study a relation...
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Sensitivity analysis based on non-intrusive regression-based polynomial chaos expansion for surgical mesh modelling
PublicationThe modelling of a system containing implants used in ventral hernia repair and human tissue suffers from many uncertainties. Thus, a probabilistic approach is needed. The goal of this study is to define an efficient numerical method to solve non-linear biomechanical models supporting the surgeon in decisions about ventral hernia repair. The model parameters are subject to substantial variability owing to, e.g., abdominal wall...
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Rapid Multi-band Patch Antenna Yield Estimation Using Polynomial Chaos-Kriging
PublicationYield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since the Monte Carlo sampling-based real physics simulation model evaluations are computationally intensive, this work proposes the polynomial chaos-Kriging (PC-Kriging) metamodeling technique for fast yield estimation. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel...
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Airfoil Design Under Uncertainty Using Non-Intrusive Polynomial Chaos Theory and Utility Functions
PublicationFast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated...
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Global sensitivity analysis of membrane model of abdominal wall with surgical mesh
PublicationThe paper addresses the issue of ventral hernia repair. Finite Element simulations can be helpful in the optimization of hernia parameters. A membrane abdominal wall model is proposed in two variants: a healthy one and including hernia defect repaired by implant. The models include many uncertainties, e.g. due to variability of abdominal wall, intraabdominal pressure value etc. Measuring mechanical properties with high accuracy...
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SENSITIVITY ANALYSIS IN THE REHABILITATION OF HISTORIC TIMBER STRUCTURES ON THE EXAMPLES OF GREEK CATHOLIC CHURCHES IN POLISH SUBCARPATHIA
PublicationThis work concerns structural and sensitivity analysis of carpentry joints used in historic wooden buildings in south-eastern Poland and western Ukraine. These are primarily sacred buildings and the types of joints characteristic for this region are saddle notch and dovetail joints. Thus, in the study the authors focus on these types of corner log joints. Numerical models of the joints are defined and finite element simulations...
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Portico Farmhouses of the Vistula Delta: Architecture, Current State and Finite Element Modelling of Timber Roof Truss under Material and Cross-section Uncertainty
PublicationThe article focuses on the oldest surviving I-type portico houses located in the Vistula Delta, which were built in the 17th and 18th centuries. The study describes the houses’ origins, structure, details of roof structures and technical condition, and it also includes numerical modelling of a roof truss and its mechanical analysis. Numerical models of the roof trusses are defined and analysed by means of the finite element method....
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Modelling of Abdominal Wall Under Uncertainty of Material Properties
PublicationThe paper concerns abdominal wall modelling. The accurate prediction and simulation of abdominal wall mechanics are important in the context of optimization of ventral hernia repair. The shell Finite Element model is considered, as the one which can be used in patient-specific approach due to relatively easy geometry generation. However, there are uncertainties in this issue, e.g. related to mechanical properties since the properties...
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Historical carpentry corner log joints—Numerical analysis within stochastic framework
PublicationThe paper presents the results of numerical analysis performed on historical, traditional carpentry corner logjoints of two basic topologies: the short-corner dovetail connection and the saddle notch connection. These types of carpentry joints are commonly used in currently preserved objects of wooden architecture. All connections have been modelled in pinewood, which has been defined in the Finite Element software MSC.Marc/Mentat...
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Multi-fidelity robust aerodynamic design optimization under mixed uncertainty
PublicationThe objective of this paper is to present a robust optimization algorithm for computationally efficient airfoil design under mixed (inherent and epistemic) uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions derived from the Non-Intrusive Polynomial Chaos (NIPC) technique to create surrogate models utilized in the optimization process. A combined NIPC expansion approach is used, where both...
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Rapid Design Centering of Multi-Band Antennas Using Knowledge-Based Inverse Models and Response Features
PublicationAccounting for manufacturing tolerances as well as uncertainties concerning operating conditions and material parameters is one of the important yet often neglected aspects of antenna development. Appropriate quantification of uncertainties allows for estimating the fabrication yield but also to carry out robust design (e.g., yield maximization). For reliability reasons, statistical analysis should be executed at the accuracy level...
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublicationModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation
PublicationThis paper presents a new approach for variability analysis of microwave devices with a high dimension of uncertain parameters. The proposed technique is based on modeling an approximation of system by its poles and residues using several modeling methods, including ordinary kriging, Adaptive Polynomial Chaos (APCE), and Support Vector Machine Regression (SVM). The computational cost is compared with the traditional Monte-Carlo...
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Thermodynamic study of binary mixtures of toluene with ionic liquids, 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, 1-hexyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide and 1-butylpyridinium bis(trifluoromethylsulfonyl)imide
PublicationDensities, refractive indices and viscosities at 293.15, 298.15, 303.15, 308.15 and 313.15 K of binary mixtures of toluene with 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, 1-hexyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide and 1-butylpyridinium bis(trifluoromethylsulfonyl)imide have been measured over the miscible region at p = 0.1 MPa. From the experimental data, values of excess molar volume,...
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Fundamentals of Data-Driven Surrogate Modeling
PublicationThe primary topic of the book is surrogate modeling and surrogate-based design of high-frequency structures. The purpose of the first two chapters is to provide the reader with an overview of the two most important classes of modeling methods, data-driven (or approx-imation), as well as physics-based ones. These are covered in Chap-ters 1 and 2, respectively. The remaining parts of the book give an exposition of the specific aspects...
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CHAOS
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Nilpotent singularities and chaos: Tritrophic food chains
PublicationLocal bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...
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CHAOS
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Discrete convolution based on polynomial residue representation
PublicationThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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Structure and thermal expansion of liquid bismuth
PublicationExperimental structural data for liquid Bi were used for estimation of the main structure parameters as well as the thermal expansion coefficient both in supercooled and superheated temperature ranges. It was shown that the equilibrium melt had a positive thermal expansion coefficient within a temperature range upon melting and a negative one at higher temperatures. The former was related to structure changes upon melting, whereas...
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Implementation of discrete convolution using polynomial residue representation
PublicationConvolution is one of the main algorithms performed in the digital signal processing. The algorithm is similar to polynomial multiplication and very intensive computationally. This paper presents a new convolution algorithm based on the Polynomial Residue Number System (PRNS). The use of the PRNS allows to decompose the computation problem and thereby reduce the number of multiplications. The algorithm has been implemented in Xilinx...
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Polynomial triset metric for unrooted phylogenetic trees
Publicationthe following paper presents a polynomial triset metric for unrooted phylogenetic trees (based on weighted bipartite graphs and the method of determining a minimum edge cover) and its basic characteristics. also a list of further directions of research and examples of the wider use of this metric is presented.
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Parameter values for topological chaos in the reduced Chialvo model
Open Research DataThe following dataset is connected with a map-based neuron model introduced by D. Chialvo (Chaos, Solitons & Fractals, 5 (3-4) 1995). The reduced version of this model is a one dimensional discrete system which describes the evolution of the membrane voltage when the value of the second variable, the recovery variable, is fixed. We have recently...
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Ship Evolutionary Trajectory Planning Method with Application of Polynomial Interpolation
PublicationPaper presents the application of evolutionary algorithms and polynomial interpolation in ship evolutionary trajectory planning method. Evolutionary algorithms allows to find a coIlision free trajectory in real time, while polynomial interpolation allows to model smooth trajectory which keeps continuity of velocity and acceleration values along path. Combination of this two methods allows to find trajectory, which under some assumptions,...
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Thermal and Chemical Expansion in Proton Ceramic Electrolytes and Compatible Electrodes
PublicationThis review paper focuses on the phenomenon of thermochemical expansion of two specific categories of conducting ceramics: Proton Conducting Ceramics (PCC) and Mixed Ionic-Electronic Conductors (MIEC). The theory of thermal expansion of ceramics is underlined from microscopic to macroscopic points of view while the chemical expansion is explained based on crystallography and defect chemistry. Modelling methods are used to predict...
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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublicationDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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Polynomial description of dynamic impedance spectrogram—introduction to a new impedance analysis method
PublicationThis paper presents a polynomial description of spectrograms obtained using Dynamic Electrochemical Impedance Spectroscopy. A method to fit the polynomial degree correctly is discussed. A simple electrical system of a diode connected in parallel with a capacitor was used for testing. Dynamic impedance measurements during potentiodynamic polarization were conducted. This paper presents an alternative analysis method that allows...
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Cavity-expansion approximation for projectile impact and penetration into sand
PublicationA one-dimensional problem of a spherical cavity expanding at a constant velocity from zero initial radius in an infinite granular medium, which has the first-kind self-similar solution, is considered. We are solving this dynamic spherical cavity-expansion problem to model rigid spheres penetrating into a granular media. Elastic–plastic deformation of the granular media is described in a barotropic approximation, using the high-pressure...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Subcritical Thermodynamic Cycles with Organic Medium and Isothermal Expansion
PublicationThe efffciencies of the Organic Rankine Cycle (ORC) are not very high and only very seldom do they exceed 20%. The increase and optimization of initial parameters and certain modifications of the thermodynamic cycle make it possible to overcome these drawbacks. A new modified cycle has been described and analyzed in detail in the paper. Similarly to the Ericsson cycle for gas turbines, isothermal expansion in the turbine is suggested...
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Finding small-width connected path decompositions in polynomial time
PublicationA connected path decomposition of a simple graph $G$ is a path decomposition $(X_1,\ldots,X_l)$ such that the subgraph of $G$ induced by $X_1\cup\cdots\cup X_i$ is connected for each $i\in\{1,\ldots,l\}$. The connected pathwidth of $G$ is then the minimum width over all connected path decompositions of $G$. We prove that for each fixed $k$, the connected pathwidth of any input graph can be computed in polynomial-time. This answers...
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CHAOS SOLITONS & FRACTALS
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A Formal Approach to Model the Expansion of Natural Events: The Case of Infectious Diseases
PublicationA formal approach to modeling the expansion of natural events is presented in this paper. Since the mathematical, statistical or computational methods used are not relevant for development, a modular framework is carried out that guides from the external observation down to the innermost level of the variables that have to appear in the future mathematical-computational formalization. As an example we analyze the expansion of Covid-19....
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Experimental Comparison of Straight Lines and Polynomial Interpolation Modeling Methods in Ship Evolutionary Trajectory Planning Problem
PublicationPaper presents the application of evolutionary algorithms and polynomial interpolation in ship evolutionary trajectory planning method and its comparison to classic approach, where trajectory is modeled by straight lines. Evolutionary algorithms are group of methods that allows\ to find a collision free trajectory in real time, while polynomial interpolation allows to model smooth trajectory, which keeps continuity of velocity...
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Experiences from operation of various expansion devices in small scale ORC
PublicationThe main aim of this paper was to present various expansion devices for an application in the small scale ORC system. The investigations were carried out in two parallel directions. One direction was to design and construct a device dedicated to the analyzed ORC system. The second direction was to adapt existing expansion devices for the needs of the analyzed ORC system. Four various devices were described and presented together...
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Interactive Query Expansion with the Use of Clustering by Directions Algorithm
PublicationThis paper concerns Clustering by Directions algorithm. The algorithm introduces a novel approach to interactive query expansion. It is designed to support users of search engines in forming web search queries. When a user executes a query, the algorithm shows potential directions in which the search can be continued. This paper describes the algorithm and it presents an enhancement which reduces the computational complexity of...
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3D POINT-CLOUD SPATIAL EXPANSION BY TOTAL LEAST-SQUARES LINE FITTING
PublicationPoint-cloud spatial expansion (PCSE) allows the creation of a new pointcloud form that presents an alternative geometry of an entire object in a single spatial view. Spatial expansion facilitates the analysis process and introduces an additional spatial parameter describing the point cloud. An important element of the PCSE method is determining the position of the axis of symmetry of a symmetrical object: the procedure for determining...
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Spike patterns and chaos in a map-based neuron model
PublicationThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
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Application of Illuminating Modes concept in modal expansion of elliptical resonator
PublicationIn the paper an IlluminatingModes (IM) approach as an extension of Spectral Domain Approach (SDA) is presented. IM concept is applied to the case of open microstrip planar elliptical resonator. A modal expansion of currents induced in the structures during illuminating them by a single plane wave is the novelty of the method. As an example of application of the method, we present the results obtained by an examination of two resonators...
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Transcriptional activity of epigenetic remodeling genes declines in keratinocytes after in vitro expansion
PublicationPURPOSE: In vitro expansion is an invaluable method to obtain keratinocytes in amounts necessary for effective transplantation therapies. In vitro cell culturing provokes questions concerning potential epigenetic alterations occurring in expanded cells in the context of usefulness for transplantation and safety. The purpose of this study was to investigate as to whether keratinocyte expansion is associated with changes in the activity...
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Container port expansion towards the sea in the context of maritime spatial planning
PublicationThe growth of ships causes a significant increase in demand for new port surfaces and demands for the depths of water bodies in the ports. Due to technological changes in the transshipment and development pressure ports lacks space and they move towards the sea with their activities. The paper discusses the reasons for the phenomenon of expansion of ports towards the sea and its effects on maritime spatial planning.
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Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models
PublicationTernary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).
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Hybrid analysis of microwave components in cylindrical coordinates with function expansion in subdomains.
PublicationW artykule zaproponowano wydajną metodę przyspieszenia analizy FDTD, poprzez podział dziedziny obliczeniowej i zastosowanie różnych algorytmów w różnych elementach dziedziny. Zaproponowano uniwersalną metodę łączenia techniki PEE (Partial Eigenfunction Expansion)i niezmodyfikowanej FDTD w jednej analizie. Uzyskano redukcję liczby zmiennych oraz wydłużenie kroku czasowego.
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TreeCmp: Comparison of Trees in Polynomial Time
PublicationMetryki filogenetyczne umożliwiają ocenę jakości wyników analizy filogenetycznej oraz wiarygodności algorytmów przeprowadzających taką analizę. Aplikacja TreeCmp oferuje efektywne, wielomianowe implementacje ośmiu takich metryk (dla drzew nieukorzenionych i zawierających korzeń) zdefiniowanych dla dowolnych filogenez (nie koniecznie binarnych). Program ten jako pierwszy umożliwia wyznaczanie nowych metryk, definiowanych w oparciu...
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TESTING CONTRACTION AND THERMAL EXPANSION COEFFICIENT OF CONSTRUCTION AND MOULDING POLYMER COMPOSITES
PublicationThe paper presents results of systematic tests of contraction and thermal expansion coefficients of materials based on polymer composites. The information on the above material properties is essential both at the design stage and during the use of finished products. Components for the samples were selected in such a way as to represent typical materials used for production of construction and moulding elements. The performed tests...
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Chaos Theory and Applications
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Employees’ self-expansion as a mediator between perceived work conditions and work engagement and productive behaviors
PublicationThere has been increasing scientific interest in the relationships between self-perception and group identity development processes as well as the behavioural implications of these processes in organizational contexts. Recently, the concept of workplace self-expansion has been introduced to work and organizational psychology. That is, the self-expanding characteristics of work and the workplace have been related to job satisfaction...
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ANYTIME POLYNOMIAL HEURISTIC ALGORITHM FOR PARTITIONING GROUPS OF DATA WITH PRESERVING CLASS PROPORTIONS FOR CROSS-VALIDATION
PublicationThe article describes a problem of splitting data for k-fold cross-validation, where class proportions must be preserved, with additional constraint that data is divided into groups that cannot be split into different cross-validation sets. This problem often occurs in e.g. medical data processing, where data samples from one patient must be included in the same cross-validation set. As this problem is NP-complete, a heuristic...