The Method of Relaxed Causality in the Bond Graph Analysis of Nonlinear Systems

1974 ◽  
Vol 96 (1) ◽  
pp. 95-99 ◽  
Author(s):  
B. J. Joseph ◽  
H. R. Martens
Keyword(s):  
Nonlinear Systems ◽  
Mathematical Models ◽  
Bond Graph ◽  
Graph Analysis ◽  
Algebraic Equations ◽  
Underlying Principle ◽  
Systematic Derivation

A method is presented for the formulation of mathematical models of nonlinear systems. The method employs as the underlying principle the relaxation of the requirement of explicit causality at 0- and 1-junctions. Instead, causal assignments are made which are consistent with the computing causality of the nonlinear elements, thus leading to causal violations in the conventional sense. A classification of causal violations is identified which provides information useful in the systematic derivation of algebraic equations. A most attractive aspect of the method is the fact that causal relaxation is required only when needed, and only to the extent needed.

scholarly journals A comprehensive review of sucker rod pumps’ components, diagnostics, mathematical models, and common failures and mitigations

2021 ◽  
Author(s):  
Sherif Fakher ◽  
Abdelaziz Khlaifat ◽  
M. Enamul Hossain ◽  
Hashim Nameer
Keyword(s):  
Mathematical Models ◽  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Gas Industry ◽  
Holistic View ◽  
Comprehensive Review ◽  
Artificial Lift ◽  
Sucker Rod ◽  
Sucker Rod Pump

AbstractIn many oil reservoirs worldwide, the downhole pressure does not have the ability to lift the produced fluids to the surface. In order to produce these fluids, pumps are used to artificially lift the fluids; this method is referred to as artificial lift. More than seventy percent of all currently producing oil wells are being produced by artificial lift methods. One of the most applied artificial lift methods is sucker rod pump. Sucker rod pumps are considered a well-established technology in the oil and gas industry and thus are easy to apply, very common worldwide, and low in capital and operational costs. Many advancements in technology have been applied to improve sucker rod pumps performance, applicability range, and diagnostics. With these advancements, it is important to be able to constantly provide an updated review and guide to the utilization of the sucker rod pumps. This research provides an updated comprehensive review of sucker rod pumps components, diagnostics methods, mathematical models, and common failures experienced in the field and how to prevent and mitigate these failures. Based on the review conducted, a new classification of all the methods that can fall under the sucker rod pump technology based on newly introduced sucker rod pump methods in the industry has been introduced. Several field cases studies from wells worldwide are also discussed in this research to highlight some of the main features of sucker rod pumps. Finally, the advantages and limitations of sucker rod pumps are mentioned based on the updated review. The findings of this study can help increase the understanding of the different sucker rod pumps and provide a holistic view of the beam rod pump and its properties and modeling.

scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

Classification of Mathematical Models for Process Design

2021 ◽  
Vol 41 (11) ◽  
pp. 1045-1048
Author(s):  
S. Yu. Kalyakulin ◽  
E. V. Mitin ◽  
S. P. Sul’din
Keyword(s):  
Mathematical Models ◽  
Process Design

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals Mathematical Modeling of Main Classes of Stochastic Productive Systems

2019 ◽  
Vol 29 (4) ◽  
pp. 496-509
Author(s):  
Alexander A. Butov ◽  
Maxim A. Volkov ◽  
Viktor N. Golovanov ◽  
Anatoly A. Kovalenko ◽  
Boris M. Kostishko ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Time Distribution ◽  
Just In Time ◽  
Birth And Death Processes ◽  
Multistage System ◽  
Martingale Methods ◽  
Time Class ◽  
Productive Systems ◽  
Time Systems

Introduction. The article deals with mathematical models of two main classes of processes in stochastic productive systems. For a multistage system, conditions of belonging to a “just-in-time” class or a class with infinite support of the time distribution function for productive operations are determined. Materials and Methods. Descriptions and investigations of models are carried out by trajectory (martingale) methods. For “just-in-time” systems and multistage stochastic productive systems, terms and methods of random walks in a random environment and birth and death processes are used. The results are formulated as descriptions of intensity characteristics of equalizers of point counting processes. Results. Two theorems are given and proved; they justify the proposed classification of the mathematical models of productive systems. The criteria of the belonging of the stochastic productive system to the class “just-in-time” are given. A theorem on the incompatibility of groups of “just-in-time” systems and systems infinite support of the time distribution for operations is proved. Discussion and Conclusion. The results show the feasibility of analyzing stochastic productive systems by martingale methods. The descriptions of terms of intensities of the equalizers time of productive processes admit generalization.

scholarly journals Analysing and simulating energy-based models in biology using BondGraphTools

2021 ◽  
Author(s):  
Peter Cudmore ◽  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Systems Biology ◽  
Mathematical Models ◽  
Bond Graph ◽  
Experimental Measurements ◽  
Bond Graphs ◽  
Graph Models ◽  
Conservation Of Energy ◽  
Conservation Of Mass ◽  
Physical Systems ◽  
Complex Interactions

AbstractLike all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

scholarly journals HARMONIC BALANCE THEORY FOR SCHEME TECHNICAL DESIGN

T-Comm ◽  
2020 ◽  
Vol 14 (11) ◽  
pp. 21-32
Author(s):  
Svetlana F. Gorgadze ◽  
◽  
Anton A. Maximov ◽  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Projection Methods ◽  
Algebraic Equations ◽  
Electronic Circuits ◽  
Large Signal ◽  
Linear Algebraic Equations ◽  
Methods Of Synthesis ◽  
Signal Mode

The analysis and generalization of the main publications on the methods of synthesis and analysis of non-linear active microwave circuits based on the use of the harmonic balance method are presented. As a result of some classification of mathematical approaches and techniques used in the context of this method, a selection and review of basic algorithms was made, the sequential application of which makes it possible to obtain the final result for a scheme of any complexity. The principles of drawing up the initial system of differential equations for electronic circuits and reducing it to a system of linear algebraic equations are considered. A detailed and, at the same time, simplified interpretation of the approaches involving the use of projection methods and Krylov subspaces is given in order to make them easier to understand. Both the complete and the restart generalized method of minimal residuals are considered, in which the desired solution is obtained in the course of an iterative process, at each stage of which subspaces of lower dimension are constructed. The possibilities of simulators and application packages intended for circuit design of electronic circuits are considered. The problem of matching a power amplifier in large signal mode using the APLAC simulator, which is NI AWR technology for designing high-frequency circuits, is discussed.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Classification of mathematical models of technological design

2021 ◽  
pp. 68-71
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Technological Process ◽  
Process Design ◽  
Geometric Parameters ◽  
Technological Design ◽  
Technological Processes ◽  
Technological Preparation

The use of mathematical models is of great importance for the automation of the design of technological processes. Representation of the geometric parameters of the part in the form of mathematical models allows automating the development of the structure and calculation of the parameters of the technological process, which is important for the complete digitalization of the technological preparation of production. Keywords: technological process, design, mathematical model, digitalization. [email protected]

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