scholarly journals Inverse problems of the dynamics of observation interpretation systems

2021 ◽  
Vol 2131 (3) ◽  
pp. 032109
Author(s):  
A Verlan ◽  
M Sagatov

Abstract Based on the analysis and systematization of the inverse problems of dynamics, the study of the properties and features of the types of dynamic models under consideration, an approach is proposed for the development of appropriate methods of mathematical modeling based on the use and implementation of integral models in the form of Volterra equations of the I and II kind, their functional capabilities are determined in the study of various classes of problems, and also formulated the features that affect the choice of methods for their numerical solution. Methods for obtaining integral models are proposed, which are the basis for constructing algorithms for solving inverse problems of dynamics for a fairly wide class of dynamic objects. Integral methods for the identification of dynamic objects have been developed, which make it possible to obtain stable non-optimization algorithms for calculating the parameters of mathematical models. Recurrent methods of parametric identification of transfer functions of dynamic objects with an arbitrary input action are proposed (the obtained parameters of the transfer functions are also coefficients of the corresponding differential equations, which makes it possible to obtain equivalent mathematical models in the form of integral equations). The study of algorithms that implement the proposed identification methods allows us to conclude about their efficiency in terms of the amount of computation and ease of implementation, as well as the high accuracy of calculating the model parameters.

2021 ◽  
pp. 12-22
Author(s):  
Serhii Kochuk ◽  
Dinh Dong Nguyen ◽  
Artem Nikitin ◽  
Rafael Trujillo Torres

The object of research in the article is various well-known approaches and methods of structural and parametric identification of dynamic controlled objects - unmanned aerial vehicles (UAVs). The subject of the research is the parameters of linear and nonlinear mathematical models of spatial and isolated movements, describing the dynamics and aerodynamic properties of the UAV and obtained both from the results of flight experiments and using computer object-oriented programs for 3-D UAV models. The goal is to obtain mathematical models of UAV flight dynamics in the form of differential equations or transfer functions, check them for reliability and the possibility of using them in problems of synthesis of algorithms for automatic control systems of UAVs. Tasks to be solved: evaluation of the analytical (parametric), direct (transient), as well as the identification method using the 3-D model of the control object. Methods used structural and parametric identification of dynamic objects; the determination of static and dynamic characteristics of mathematical models by the type of their transient process; the System Identification Toolbox package of the MatLab environment, the Flow Simulation subsystem of the SolidWorks software and the X-Plane software environment. The experimental parameters of UAV flights, as well as the results of modeling in three-dimensional environments, are the initial data for the identification of mathematical models. The following results were obtained: the possibility of analytical and computer identification of mathematical models by highly noisy parameters of the UAV flight was shown; the mathematical models of UAVs obtained after identification is reliable and adequately reproduce the dynamics of a real object. A comparative analysis of the considered UAV identification methods is conducted, their performance and efficiency are confirmed. Conclusions. The scientific novelty of the result obtained is as follows: good convergence, reliability and the possibility of using the considered identification methods for obtaining mathematical models of dynamic objects to synthesize algorithms for automatic control systems of UAVs is shown.


Author(s):  
С.А. Мамаев ◽  
В.М. Дорофеев ◽  
А.С. Мамаев

Представлены результаты исследований, направленных на создание динамических моделей сооружений, пригодных для расчета на сейсмостойкость. Рассмотрен метод определения параметров моделей на основе инженерно-сейсмометрической информации. Приведены примеры определения динамических параметров одномассовой модели для детерминированного и статистического случаев. Динамические нагрузки на сооружения характеризуются изменением динамических характеристик сооружения, возникающие колебаниями при землетрясениях и взрывах, при ударах массивных тел и т.д. Колебательный характер имеют не только перемещения точек сооружения, но и внутренние усилия и напряжения в его элементах. Определение ожидаемых амплитуд перемещений, внутренних усилий и напряжений в сооружении при его колебаниях под действием динамической нагрузки, т.е. при вынужденных колебаниях и сравнение их с допустимыми значениями составляют основное содержание динамического расчёта сооружения. Допустимые значения амплитуд внутренних усилий обусловлены требованиями прочности и долговечности строительных конструкций, а значения амплитуд скоростей и ускорений колебаний зданий и сооружений, в которых находятся люди или помещение производства с точной технологией, требованиями безвредного влияния колебаний на здоровье людей и на качество выпускаемой продукции Савович, 2005. По записям сейсмометрических приборов, установленных на покрытии здания, приблизительно определяются собственные периоды колебаний сооружений. В основном эти измерения соответствуют действительному периоду собственного колебания сооружения (основному тону собственных колебаний) лишь при небольших сейсмических воздействиях, микросейсмах или специально возбуждаемых для подобных исследований искусственных колебаний, т.к. при достаточно сильных сейсмических воздействиях выделение видимого периода значительно осложнено. Для определения динамических параметров зданий и возможности использования методов расчета сооружений с применением импульсных передаточных функций разработаны статистические методы решения обратных задач по восстановлению подобных передаточных функций на базе инженерно-сейсмометрической информации. Анализ зарегистрированных на инженерно-сейсмометрических станциях процессов входа и (основание, фундамент) и выхода (покрытие, перекрытия) позволяет определять импульсные передаточные функции, после чего решить приведенные интегральные уравнения Дейч, 1979 Denisov et al., 1986. The results of studies aimed at creating dynamic models of structures suitable for calculating earthquake resistance are presented. A method for determining model parameters based on engineering-seismometric information is considered. Examples of determining the dynamic parameters of a single-mass model for deterministic and statistical cases are given. Dynamic loads on structures are characterized by a change in the dynamic characteristics of the structure, arising from vibrations during earthquakes and explosions, when massive bodies are struck, etc. Not only the movement of the points of the structure, but also the internal forces and stresses in its elements are oscillatory. Determination of the expected amplitudes of displacements, internal forces and stresses in the structure during its oscillations under the action of dynamic load, i.e. in case of forced vibrations and their comparison with acceptable values are the main content of the dynamic calculation of the structure. The permissible values of the amplitudes of internal forces are determined by the requirements of strength and durability of building structures, and the amplitudes of the velocities and accelerations of vibrations of buildings and structures in which people or a production room with precise technology are located, by the requirements of the harmless effect of fluctuations on peoples health and on the quality of products Savovich, 2005. According to the records of seismometric instruments installed on the buildings cover, their own periods of oscillation of the structures are approximately determined. Basically, these measurements correspond to the actual period of the buildings own vibration (the fundamental tone of natural vibrations) only with small seismic effects, microseisms or artificial vibrations specially excited for such studies, because with sufficiently strong seismic effects, the selection of the visible period is significantly complicated. To determine the dynamic parameters of buildings and the possibility of using methods for calculating structures using pulsed transfer functions, statistical methods have been developed for solving inverse problems to restore such transfer functions on the basis of engineering-seismometric information. An analysis of the input and (base, foundation) and output (cover, overlap) processes recorded at the engineering-seismometric stations allows determining the impulse transfer functions, and then solving the given integral equations Deutsch, 1979 Denisov et al., 1986.


2001 ◽  
Vol 29 (1) ◽  
pp. 23-43 ◽  
Author(s):  
D. Tsihlas ◽  
T. Lacroix ◽  
B. Clayton

Abstract Different numerical sub-structuring techniques for the representation of tire modal behavior have been developed in the past 20 years. By using these numerical techniques reduced dynamic models are obtained which can not only be used for internal studies but also be provided to the automobile industry and linked to reduced dynamic vehicle models in order to optimize the coupled vehicle-tire response for noise vibration and harshness purposes. Two techniques that have been developed in a custom-made finite element code are presented: 1) the component mode synthesis type models for which the wheel center interface is free and 2) the Craig and Bampton type models for which the wheel center interface is fixed. For both techniques the interface between the tire and the ground is fixed. The choice of fixed or free wheel center boundary condition is arbitrary. In this paper we will compare the formulation of these two numerical methods, and we will show the equivalency of both methods by showing the results obtained in terms of frequency and transfer functions. We will show that the two methods are equivalent in principle and the reduced dynamic models can be converted from one to the other. The advantages-disadvantages of each method will be discussed along with a comparison with experimentally obtained results.


1982 ◽  
Vol 47 (10) ◽  
pp. 2639-2653 ◽  
Author(s):  
Pavel Moravec ◽  
Vladimír Staněk

Expressions have been derived for four possible transfer functions of a model of physical absorption of a poorly soluble gas in a packed bed column. The model has been based on axially dispersed flow of gas, plug flow of liquid through stagnant and dynamic regions and interfacial transport of the absorbed component. The obtained transfer functions have been transformed into the frequency domain and their amplitude ratios and phase lags have been evaluated using the complex arithmetic feature of the EC-1033 computer. Two of the derived transfer functions have been found directly applicable for processing of experimental data. Of the remaining two one is useable with the limitations to absorption on a shallow layer of packing, the other is entirely worthless for the case of poorly soluble gases.


Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1516
Author(s):  
Daniel Gratz ◽  
Alexander J Winkle ◽  
Seth H Weinberg ◽  
Thomas J Hund

The voltage-gated Na+ channel Nav1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Nav1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Nav1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Nav1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.


Author(s):  
Hamed Moradi ◽  
Firooz Bakhtiari-Nejad ◽  
Majid Saffar-Avval ◽  
Aria Alasty

Stable control of water level of drum is of great importance for economic operation of power plant steam generator systems. In this paper, a linear model of the boiler unit with time varying parameters is used for simulation. Two transfer functions between drum water level (output variable) and feed-water and steam mass rates (input variables) are considered. Variation of model parameters may be arisen from disturbances affecting water level of drum, model uncertainties and parameter mismatch due to the variant operating conditions. To achieve a perfect tracking of the desired drum water level, two sliding mode controllers are designed separately. Results show that the designed controllers result in bounded values of control signals, satisfying the actuators constraints.


Author(s):  
Kaitlyn Johnson ◽  
Grant R. Howard ◽  
Daylin Morgan ◽  
Eric A. Brenner ◽  
Andrea L. Gardner ◽  
...  

SummaryA significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other data types. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic mechanistic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal population-size data. We demonstrate that the explicit inclusion of the transcriptomic information in the parameter estimation is critical for identification of the model parameters and enables accurate prediction of new treatment regimens. Inclusion of the transcriptomic data improves predictive accuracy in new treatment response dynamics with a concordance correlation coefficient (CCC) of 0.89 compared to a prediction accuracy of CCC = 0.79 without integration of the single cell RNA sequencing (scRNA-seq) data directly into the model calibration. To the best our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with longitudinal treatment response data into a mechanistic mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multimodal data sets into identifiable mathematical models to develop optimized treatment regimens from data.


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