Construction Of Dynamic Models Research Articles

Построение и исследование дискретных динамических окрестностных моделей в Mathcad

Построение и исследование дискретных динамических окрестностных моделей в Mathcad

Construction of dynamic factor models for forecasting of economic systems evolution

Construction of dynamic factor models for forecasting of economic systems evolution

Dynamic Model of Differential Closed Planetary Gearing and the Spectrum of its Eigenfrequencies

Problems that arise in the construction of dynamic models of differential closed planetary gearing used in drilling technology are considered. The influence of the parameters of the system on the eigenfrequencies of the oscillations of the dynamic model is estimated by serial variation with step 0.5 of all the elastic-inertial parameters in the range 0.5–2.0 from their computed values.

Toward a mechanistic understanding of trophic structure: inferences from simulating stable isotope ratios

Stable isotope ratios (SIR) are widely used to estimate food-web trophic levels (TLs). We built systems dynamic N-biomass-based models of different levels of complexity, containing explicit descriptions of isotope fractionation and of trophic level. The values of δ15N and TLs, as independent and emergent properties, were used to test the potential for the SIR of nutrients, primary producers, consumers, and detritus to align with food-web TLs. Our analysis shows that there is no universal relationship between TL and δ15N that permits a robust prognostic tool for configuration of food webs even if all system components can be reliably analysed. The predictive capability is confounded by prior dietary preference, intra-guild predation and recycling of biomass through detritus. These matters affect the dynamics of both the TLs and SIR. While SIR data alone have poor explanatory power, they would be valuable for validating the construction and functioning of dynamic models. This requires construction of coupled system dynamic models that describe bulk elemental distribution with an explicit description of isotope discriminations within and amongst functional groups and nutrient pools, as used here. Only adequately configured models would be able to explain both the bulk elemental distributions and the SIR data. Such an approach would provide a powerful test of the whole model, integrating changing abiotic and biotic events across time and space.

Nonlocal axial vibration of the multiple Bishop nanorod system

Construction of reliable dynamic models of nanostructures is an important task for design procedures of different nanoresonator devices. Such theoretical models allow as to perform different numerical experiments, which is the key point in the development of advanced nanodevices. This paper presents a new nanoresonator model based on the axial vibration of the elastic multi-nanorod system. It is assumed that the system of multiple nanorods is embedded in an elastic medium. The governing equations of motion of a coupled multi-nanorod system are derived using the Hamilton’s principle, the nonlocal elastic constitutive relation, and Bishop’s rod theory, where effects of inertia of the lateral motion and the shear stiffness are considered. Exact closed form solutions for natural frequencies are obtained for one and multiple nanorod systems with different boundary conditions. Then, results for natural frequencies obtained by the finite difference method are compared with the results obtained analytically. Effects of nonlocal parameter, different rod theories, number of nanorods and stiffness coefficient of an elastic medium on natural frequencies are examined through several numerical examples.

Dynamic Modeling of Labor Migration Between Scientific Organizations

In this article we examine the processes of academic potential reproduction, taking into account the main threats from scientific migration. Historically, since the 1990-s the amount of researchers in Russian Federation decreased by 58%. Under these conditions it is necessary to estimate the scale of further scientific migration and the outflow of researchers to other spheres of economy. For this purpose we developed a synthetic construction of dynamic models of labor migration and proportional economic growth with two-level optimization. The basis of this model is presented by the classical problem of optimal investments into capital management, expanded by the control unit of total costs directed to the labor resources. This model construction allows us to describe the migration movement between scientific organizations and institutes, taking into account the difference in working conditions. The pricing mechanism in this model is based on the assumption of organization’s output maximization at a fixed cost. As result we obtained a multi-level model for the prediction of scientific personnel migratory flows between organizations.

System equivalent model mixing

This paper introduces SEMM: a method based on Frequency Based Substructuring (FBS) techniques that enables the construction of hybrid dynamic models. With System Equivalent Model Mixing (SEMM) frequency based models, either of numerical or experimental nature, can be mixed to form a hybrid model. This model follows the dynamic behaviour of a predefined weighted master model. A large variety of applications can be thought of, such as the DoF-space expansion of relatively small experimental models using numerical models, or the blending of different models in the frequency spectrum. SEMM is outlined, both mathematically and conceptually, based on a notation commonly used in FBS. A critical physical interpretation of the theory is provided next, along with a comparison to similar techniques; namely DoF expansion techniques. SEMM's concept is further illustrated by means of a numerical example. It will become apparent that the basic method of SEMM has some shortcomings which warrant a few extensions to the method. One of the main applications is tested in a practical case, performed on a validated benchmark structure; it will emphasize the practicality of the method.

Basic Principles for the Construction of Dynamic Models of the Planetary Gears Used in Drilling Rigs

Questions regarding the construction of discrete dynamical models are considered, using as an example 2K-N planetary gears with different types of stop couplings and their analytic dynamic models are presented. The principal assumption adopted in the creation of dynamic models of the types of simple planetary gears used in drilling rigs involves the supposition that the motion of the planetary wheel may be decomposed into two types of rotation, first, about the natural axis and, second, about the common axis of the reducing gear (carrier). An evaluation of the assumption is given.

New statistical models of nonergodic cognitive systems and their pathologies

Cognition most singularly involves choice that reduces uncertainty. Reduction of uncertainty implies the existence of an information source ‘dual’ to the cognitive process under study. However, information source uncertainty for path-dependent nonergodic systems cannot be described as a conventional Shannon ‘entropy’ since time averages are not ensemble averages. Nonetheless, the essential nature of information as a form of free energy allows study of nonergodic cognitive systems having complex dynamic topologies whose algebraic expression is in terms of directed homotopy groupoids rather than groups. This permits a significant extension of the Data Rate Theorem linking control and information theories via an analog to the spontaneous symmetry breaking arguments fundamental to modern physics. In addition, the identification of information as a form of free energy enables construction of dynamic empirical Onsager models in the gradient of a classic entropy that can be built from the Legendre transform of even path-dependent information source uncertainties. The methodology provides new analytic tools that should prove useful in understanding failure modes and their dynamics across a broad spectrum of cognitive phenomena, ranging from physiological processes at different scales and levels of organization to critical system automata and institutional economics.

Dynamic force matching: Construction of dynamic coarse-grained models with realistic short time dynamics and accurate long time dynamics.

We recently developed a dynamic force matching technique for converting a coarse-grained (CG) model of a molecular system, with a CG potential energy function, into a dynamic CG model with realistic dynamics [A. Davtyan et al., J. Chem. Phys. 142, 154104 (2015)]. This is done by supplementing the model with additional degrees of freedom, called "fictitious particles." In that paper, we tested the method on CG models in which each molecule is coarse-grained into one CG point particle, with very satisfactory results. When the method was applied to a CG model of methanol that has two CG point particles per molecule, the results were encouraging but clearly required improvement. In this paper, we introduce a new type (called type-3) of fictitious particle that exerts forces on the center of mass of two CG sites. A CG model constructed using type-3 fictitious particles (as well as type-2 particles previously used) gives a much more satisfactory dynamic model for liquid methanol. In particular, we were able to construct a CG model that has the same self-diffusion coefficient and the same rotational relaxation time as an all-atom model of liquid methanol. Type-3 particles and generalizations of it are likely to be useful in converting more complicated CG models into dynamic CG models.

Bayesian Modelling of Induced Responses and Neuronal Rhythms

Neural rhythms or oscillations are ubiquitous in neuroimaging data. These spectral responses have been linked to several cognitive processes; including working memory, attention, perceptual binding and neuronal coordination. In this paper, we show how Bayesian methods can be used to finesse the ill-posed problem of reconstructing—and explaining—oscillatory responses. We offer an overview of recent developments in this field, focusing on (i) the use of MEG data and Empirical Bayes to build hierarchical models for group analyses—and the identification of important sources of inter-subject variability and (ii) the construction of novel dynamic causal models of intralaminar recordings to explain layer-specific activity. We hope to show that electrophysiological measurements contain much more spatial information than is often thought: on the one hand, the dynamic causal modelling of non-invasive (low spatial resolution) electrophysiology can afford sub-millimetre (hyper-acute) resolution that is limited only by the (spatial) complexity of the underlying (dynamic causal) forward model. On the other hand, invasive microelectrode recordings (that penetrate different cortical layers) can reveal laminar-specific responses and elucidate hierarchical message passing and information processing within and between cortical regions at a macroscopic scale. In short, the careful and biophysically grounded modelling of sparse data enables one to characterise the neuronal architectures generating oscillations in a remarkable detail.

Computer realization of research into the dynamics of mechanical systems

The article considers the application of methods of component modeling and of object-oriented technologies in automated construction of dynamic models of mechanisms in their program realization.

Simulation of Discrete-Continuous Process via E-Network

This paper denotes approaches to discrete-continuous process simulation via E-network. It covers principals of discrete-continuous process simulation via E-networks using the scheme of the interaction of static and dynamic components modeling. The construction of discrete-continuous process dynamic models is based on the state space method and is implemented by using E-network.

Newly exposed conflicting news based network opinion reversal

Studying the process of network public opinion reversal is of great significance for guiding public opinion toward a positive direction. Currently, the research on opinion reversal mainly focuses on the construction of dynamic models and analysis of simulations and the results of which have a certain theory value. However, whether these models are applicable to the real social network environment has not been tested. For studying the process of public opinion reversal, we build a model according with the realities, and make an in-depth analysis of the typical case of opinion reversal. Some rules are found from the observation and statistics: the fundamental reason of public opinion reversal is the conflicting news. Spreading of news affects the opinions of the group. The news properties, including transmission rate, credibility, opinion polarity, publication date and the degree of message source determine the extent to reverse. Based on these rules, parameters of news properties are set, and a model of opinion reversal is proposed by combing the information dissemination with opinion evolution. Simulation results show that the transmission rate of news, the credibility of news, and the degree of message source have a positive influence on the margin of reversal. The influence of credibility is more dramatic than that of transmission rate. Moreover, the public opinion would be reversed more quickly and completely if the conflicting news is released more easily. The proposed model can fit the actual data, which is helpful for understanding and explaining the process of network public opinion reversal, and provides theoretical basis for guiding the network public opinion.

RESERVOIR MODELING OF A BV8FORMATION, SEVERO-POKURSKY FIELD

One of the main directions of improving the quality of design, management and monitoring of the development of oil and gas field is the use of filtration models. Digital hydrodynamic models of reservoirs and fields make it possible to monitor the dynamics of the production of residual hydrocarbon reserves, more precisely predict the oil and gas production, to model the geological and technical measures to improve oil recovery and performance of the enterprise, more reasonably expect the most rational and cost-effective options for the development of productive reservoirs. In the present paper we describe the construction of digital geological and dynamic models of the object BV 8 1-3 , Severo-Pokursky field. As a source of information for constructing a three-dimensional geological model were used parameters of the counting inventory. There also was made a unified digital database of geological and geophysical data on the previously drilled and new wells, which include: data directional survey of wells, the curves of geophysical research, the results of the interpretation of geophysical research, data perforation and testing, the correlation of wells, the mark of water-oil contact in wells. Created on basis of geological model, the hydrodynamic model takes into account basic geophysical and technological factors, and with the required accuracy describes the real hydrodynamic processes occurring in the formations of the field. Comparison of calculated and historical development indicators, such as oil production and water cut, suggests high-quality adaptation of a model and them according to the actual data. The digital filtration model of a BV 8 1-3 formation can be used as a tool for the prediction and analysis of the existing system of reservoir development.

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

The focus of this work is on economic model predictive control (EMPC) that utilizes well‐conditioned polynomial nonlinear state‐space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well‐conditioned over a broad region of process operation in the sense that they can be correctly integrated in real‐time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state‐space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well‐conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov‐based EMPC (LEMPC) systems for nonlinear processes using the well‐conditioned nonlinear models that can be readily implemented in real‐time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed‐loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3353–3373, 2015

Organization of Continuous Process Simulation via E-Network

In this article, the proposed approaches to continuous process simulation via E-network are considered in order to construct analytical and simulation models using unified methodology. Principals of continuous process simulation via E-networks using Block Function Diagram programming technology are presented. The construction of continuous process dynamic models is based on the state space method and is implemented using E-network algorithmic simulation scheme.

Time windowed comparisons between models and measurements

The present work proposes and demonstrates a method for improving the accuracy of large finite element models using measurements. Finite element analysis routinely allows for the construction of dynamic models with millions of degrees of freedom. The models often involve a large number of parameters, such as material properties and dimensions, that are not precisely known. For example, one may measure the material properties of a homogeneous sample but those properties will vary from sample to sample. Moreover, material properties may change considerably during construction as the material is prestressed, bonded, or welded. Therefore, it is often the case that the finite element model does not agree with measurements and one is faced with the task of modifying model parameters to yield agreement. This is made difficult by the large number of parameters as well as the computational cost of evaluating the model for each set of parameter choices. The present work proposes a time windowing method that localizes the spatial volume of response in the model and experiment and therefore isolates a small number of model parameters that may be varied to bring agreement. Numerical examples are presented to illustrate the method.

Instantaneous Modelling and Reverse Engineering of Data-Consistent Prime Models in Seconds!

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute.

Fostering and supporting the coordinated use of digital technologies in mathematics learning

The wide use of different digital technologies in social and daily activities has been transforming ways in which people interact and communicate. To what extent can the coordinated use of several digital technologies foster and enhance students' development of mathematical knowledge? What kind of reasoning do problem solvers construct as a result of using several digital technologies to represent, explore and solve a mathematical problem? Addressing these questions led us to outline a framework that aims to characterise ways in which multiple purpose technologies and ad hoc technologies can be used in problem solving approaches. In particular the construction of dynamic models of tasks or problems plays a crucial role in looking for mathematical relationships and novel approaches to solve those problems.