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Search results for: NUMERICAL ERRORS
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Balance errors in numerical solutions of shallow water equations
PublicationThe analysis of the conservative properties of the shallow water equations is presented in the paper. The work focuses on the consistency of numerical solution of these equations with the conservation laws of mass and momentum. The investigations involve two different conservative forms which are solved by an implicit box scheme. The theoretical analysis supported by numerical experiments is carried out for rectangular channel...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublicationThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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Balance error generated by numerical diffusion in the solution of Muskingum equation
PublicationIn the paper the conservative properties of the lumped hydrological models with variable parameters are discussed. It is shown that in the case of the non-linear Muskingum equation the mass balance is not satisfied. The study indicates that the mass balance errors are caused by the improper form of equation and by the numerical diffusion which is generated in the solution. It has been shown that the classical way of derivation...
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Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublicationThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
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Numerical solution of threshold problems in epidemics and population dynamics
PublicationA new algorithm is proposed for the numerical solution of threshold problems in epidemics and population dynamics. These problems are modeled by the delay-differential equations, where the delay function is unknown and has to be determined from the threshold conditions. The new algorithm is based on embedded pair of continuous Runge–Kutta method of order p = 4 and discrete Runge–Kutta method of order q = 3 which is used for the...
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Space-Time Conservation Method applied to numerical solution of water hammer equations
PublicationArtykuł poświęcony jest metodzie czasoprzestrzennych objętości skończonych (STC) zastosowanej do przypadku uderzenia hydraulicznego w stalowym przewodzie pracującym pod ciśnieniem. Metoda STC ze względu na swoje własności numeryczne - m.in. wysoką dokładność - może być interesującą alternatywą dla tradycyjnych metod numerycznych, szczególnie w przypadku, gdy efekty numeryczne mają bardzo silny wpływ na rozwiązanie, tym samym utrudniając...
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Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
PublicationTo find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and...
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Towards application of uncertainty quantification procedure combined with experimental procedure for assessment of the accuracy of the DEM approach dedicated for granular flow modeling
PublicationThere is a high demand for accurate and fast numerical models for dense granular flows found in many industrial applications. Nevertheless, before numerical model can be used its need to be always validated against experimental data. During the validation, it is important to consider how the measurement data sets, as well as the numerical models, are affected by errors and uncertainties. In this study, the uncertainty quantification...
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Towards Robust Identification of Nonstationary Systems
PublicationThe article proposes a fast, two-stage method for the identification of nonstationary systems. The method uses iterative reweighting to robustify the identification process against the outliers in the measurement noise and against the numerical errors that may occur at the first stage of identification. We also propose an adaptive algorithm to optimize the values of the hyperparameters that are crucial for this new method.
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An interval estimator for chlorine monitoring in drinking water distribution systems under uncertain system dynamics, inputs and chlorine concentration measurement errors
PublicationThe design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability...
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Robust estimation of deformation from observation differences for free control networks
PublicationDeformation measurements have a repeatable nature. This means that deformation measurements are performed often with the same equipment, methods, geometric conditions and in a similar environment in epochs 1 and 2 (e.g., a fully automated, continuous control measurements). It is, therefore, reasonable to assume that the results of deformation measurements can be distorted by both random errors and by some non-random errors, which...
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Solution of the dike-break problem using finite volume method and splitting technique
PublicationIn the paper the finite volume method (FVM) is presented for the solution of two-dimensional shallow water equations. These equations are frequently used to simulate the dam-break and dike-break induced flows. The applied numerical algorithm of FVM is based on the wave-propagation algorithm which ensures a stable solution and simultaneously minimizes the numerical errors. The dimensional decomposition according to the coordinate...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....
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Redundantly Actuated 3RRR Parallel Planar Manipulator - Numerical Analyses of its Dynamics Sensitivity on Modifications of its Platform’s Inertia Parameters
PublicationIn the paper, numerical analyses, as well as dynamics of a complex mechanism, are presented. Two objectives are crucial for the paper: inverse dynamic model is needed (dedicated to be use in the model predictive controller); an identification method is searched (some trajectory parameters are controlled, when specific trajectory is tracked under an open-loop model-based control), as selected parameters must be identified for the...
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A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law
PublicationPurpose – This paper aims to present a new one-variable first-order shear deformation theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets. Design/methodology/approach – The FSDT had errors in its assumptions owing to the assumption of constant shear stress distribution along the thickness of the plate, even though by using the shear correction factor (SCF), it has been slightly corrected, the errors...
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Rainscreen panels deformations mods
PublicationIn rainscreen panels designing simplified calculation models are used. For plate computation simply supported panels or panels with fixed edges are commonly used. Such approximations are subjected to large errors that lead to inefficient rainscreen panels design. In order to develop a method for determining the optimal geometry of the rainscreen panels, that would take into consideration the real stiffness of both continuous and...
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Accuracy of the Discrete Green's Function Formulation of the FDTD Method
PublicationThis paper reports an evaluation of the accuracy of the discrete Greens function (DGF) formulation of the finite-difference time-domain (FDTD) method. Recently, the closed-form expression for the DGF and its efficient numerical implementation were presented, which facilitates applications of the DGF in FDTD simulations of radiation and scattering problems. So far, the accuracy of the DGF formulation of the FDTD method has been...
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A Goal-Oriented Error Estimator for Reduced Basis Method Modeling of Microwave Devices
PublicationThis letter proposes a novel a-posteriori error estimator suitable for the reduced order modeling of microwave circuits. Unlike the existing error estimators based on impedance function residuals, the new one exploits the residual error associated with the computation of the scattering matrix. The estimator can be effectively used in the Reduced Basis Method (RBM) to automatically generate reduced-order models. The results of numerical...
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On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis
PublicationHybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches are employed to derive behaviors that approximate the analytic solution. An important part of this is the approximation of differential equation behavior by numerical integration. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially...
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Modeling and control of a redundantly actuated variable mass 3RRR planar manipulator controlled by a model-based feedforward and a model-based-proportional-derivative feedforward–feedback controller
PublicationIn the paper, dynamics of a complex mechatronics system is considered. A redundantly actuated planar manipulator is the base of the mechanical part of it. It is a 3RRR 1 platform based parallel manipulator. To control its trajectory, a model-based feedforward controller is employed. Three aspects are fundamental in the presented investigations. The first focus is on development of an accurate numerical model used to solve the inverse...
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Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow
PublicationThe paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. Thi smakes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a...
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A Review: Applications of the Spectral Finite Element Method
PublicationThe Spectral Finite Element Technique (SFEM) has Several Applications in the Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The Spectral Finite Element Method (SFEM) is a Variant of the Traditional Finite Element Method FEM that Makes use of Higher Order Basis Functions (FEM). One of the most Fundamental Numerical Techniques Employed in the Numerical Simulation is the SFEM, which Outperforms...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Smooth least absolute deviation estimators for outlier-proof identification
PublicationThe paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes...
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Identification of models and signals robust to occasional outliers
PublicationIn this paper estimation algorithms derived in the sense of the least sum of absolute errors are considered for the purpose of identification of models and signals. In particular, off-line and approximate on-line estimation schemes discussed in the work are aimed at both assessing the coefficients of discrete-time stationary models and tracking the evolution of time-variant characteristics of monitored signals. What is interesting,...
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Identification of models and signals robust to occasional outliers
PublicationIn this paper estimation algorithms derived in the sense of the least sum of absolute errors are considered for the purpose of identification of models and signals. In particular, off-line and approximate on-line estimation schemes discussed in the work are aimed at both assessing the coefficients of discrete-time stationary models and tracking the evolution of time-variant characteristics of monitored signals. What is interesting,...
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Hybridization of the FDTD method with use of the discrete Green's function
PublicationIn this contribution, a hybrid technique is presented which combines the finite-difference time-domain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many free-space cells. Therefore, the hybrid method was developed which is applicable to complex...
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Alternative Approach to Convolution Term of Viscoelasticity in Equations of Unsteady Pipe Flow
PublicationIn the paper the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function
PublicationIn this letter, a technique combining the finite-difference time-domain (FDTD) method and its formulation based on the discrete Green's function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method...
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Safety at railway level crossings and Vision Zero
PublicationIn this work, safety analysis at the railway level crossings is presented using advanced mathematical modelling. Resistivity of track subgrade panels is taken into account. The analysis does not refer to the assessment of the current regulations. Specific cases of generalized dynamic system are considered by introducing operations S=Δ, S=P defined in space C(N) of real sequences. In this model, generalized discrete exponential...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublicationThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Direction-of-Arrival Estimation Using an ESPAR Antenna with Simplified Beam Steering
PublicationIn this paper, it has been shown, how electronically steerable parasitic array radiator (ESPAR) antenna, in which beam steering is done in a simple way, can be used for directionof- arrival (DoA) estimation of an unknown signal impinging the antenna. The concept is based on an ESPAR antenna having twelve parasitic elements, in which beam switching is realized by RF switches providing required loads to its parasitic elements. Numerical...
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The effects of vehicle restraint systems on road safety
PublicationKey to understanding the needs and tools of road infrastructure management for preventing run-off-road crashes or minimising their consequences, is to identify the hazads and sources of hazards caused by wrong or improper use of road safety devices and identify errors in the desifn, structure, construction and operation of road safety devices. Studying such an extended scope of the problem required fieldwork and surveys with road...
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Zastosowanie metody galwanostatycznej do wyznaczania błędu fazy elektrod woltamperometrycznych
PublicationW pracy przeanalizowano właściwości metrologiczne elektrod woltamperometrycznych w dziedzinie częstotliwości. Wykazano, że w przypadku, gdy reakcja elektrochemiczna kontrolowana jest procesem transportu jonów, elektroda woltamperometryczna zachowuje się tak jak przetwornik pomiarowy I rzędu. Jej właściwości metrologiczne opisane są przez czułość, częstotliwość graniczną, błąd amplitudy i błąd fazy. Przeprowadzona analiza pokazała,...
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublicationThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Open Research DataThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Open Research DataPresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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A Method of Fast and Simultaneous Calibration of Many Mobile FMCW Radars Operating in a Network Anti-Drone System
PublicationA market for small drones is developing very fast. They are used for leisure activities and exploited in commercial applications. However, there is a growing concern for accidental or even criminal misuses of these platforms. Dangerous incidents with drones are appearing more often, and have caused many institutions to start thinking about anti-drone solutions. There are many cases when building stationary systems seems to be aimless...
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Lateral forces determine dimensional accuracy of the narrow‑kerf sawing of wood
PublicationThe shrinking global forest area limits the supply of industrially usable raw resources. This, in combination with the ever‑increasing consumption of timber due to population growth can lead to the lack of a positive balance between the annual volumetric growth and consumption of wood. An important innovation toward increasing environmental and economic sustainability of timber production is to reduce the volume of wood residues...
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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On the influence of shell element properties on the response of car model in crash test
PublicationIt goes without saying that numerical simulations play important role in the modern engineering practice. Contemporary CAD environments combined with FEM solvers, along with computer power of modern processors, give the engineer fast and efficient tool. Ultimately, however it is the user alone who is responsible for the correctness of the results. As long as the FEM calculations remain in the sphere of academic exercise, the inevitable...
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Modeling and simulation of blood flow under the influence of radioactive materials having slip with MHD and nonlinear mixed convection
PublicationRadioactive materials are widely in industry, nuclear plants and medical treatments. Scientists and workers in these fields are mostly exposed to such materials, and adverse effects on blood and temperature profiles are observed. In this regard, objective of the current study is to model and simulate blood based nanofluid with three very important radioactive materials, named as Uranium dioxide (UO2), Thorium dioxide (ThO2) and...
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Proportional-Derivative and Model-based Controllers used for a Serial Type Manipulator in case of a Variable Mass Payload
PublicationIn the paper, numerical analysis of dynamics of a variable mass system is considered. Its reference example is a serial-like manipulator composed of revolute joints and rigid bodies. Payload of its gripper is considered as its variable mass element (mass and inertia irregularly between subsequent payloads). For the rest of the system, inertia parameters are considered as known (precisely identified during the assembling process)....
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Nondestructive methods complemented by FEM calculations in diagnostics of cracks in bridge approach pavement
PublicationNondestructive methods of road pavement diagnostics are an alternative to traditional approach to pavement failure investigation. The article presents a detailed multidisciplinary inspection carried out using ground-penetrating radar (GPR), laser scanning technology and finite element method (FEM) calculations. It was done in order to assess the factors that contributed to occurrence of premature cracks of a bridge approach pavement....
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Near-Field Wireless Sensing of Plastics and Papers Using Frugal Peel-Off Passive Tag
PublicationThis article presents a novel frugal approach of testing plastics and papers using a near-field microwave sensing technique with a peel-off tag. The proposed sensing technique involves two electrical entities: the sensor, which may be regarded as a reader, and a disposable tag. The reader is a modified design of a gap-coupled microstrip line (GCML) sensor, while the passive tag is a standard double-ring complementary split-ring...
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Shaping of the workpiece surface in single-disc lapping
PublicationShape errors of the tool exert a dominant influence on the shape accuracy of the workpiece. The correlation between flatness errors of the lap and flatness errors of the workpieces was checked experimentally and determined analytically. Computer model of the workpiece shaping by lapping was developed. Evaluation method of the workpiece orientation as well as some simulation results for a lap with shape errors of convexity and cincavity...
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Bridge Non-Destructive Measurements Using a Laser Scanning during Acceptance Testing: Case Study
PublicationOwing to the recent proliferation of inventory works on roads and railways, bridge acceptance tests have increased exponentially. These tests’ results are often misinterpreted owing to the use of various measuring equipment types, rendering integrated interpretation problematic. It is also problematic that adjusting the measurement method is difficult when the structure’s response to load is uncertain. Therefore, it is important...