Метод определения параметров утечек в трубопроводах на основе гидродинамических моделей

It is known that on the basis of the pipeline non-stationary hydrodynamic model after identification of parameters included in it, it is possible to adequately reproduce the full-scale hydraulic characteristics of transported medium flow by resolving the primal problem of hydraulics, in particular, the primal problem of identifying leakage parameters. The numerical solution of the inverse problem, in contrast to the analytical solution, is usually reduced to a multiple solution of the primal problem. In the present work, the hydrodynamic mathematical model of a pipeline with two parameters that have been identified and fluid withdrawal in the set section is confined to differential equations of evolutionary type for medium cross-section pressure and mass flow. Based on the built partial analytical solutions of these equations, dependences have been obtained for calculation of pressure values in the oil pipeline operated in stationary mode with existing liquid withdrawal (leakage). Results of application of analytical solutions to the method of sensitivity functions in the inverse problem of identifying leakage parameters have been reviewed. Exact analytical solution (in implicit form) of the inverse problem has been obtained to make it possible to relate the location of the leak to readings of pressure sensors, to the pipeline and the transported fluid parameters. Известно, что на основе нестационарной гидродинамической модели трубопровода после идентификации входящих в нее параметров можно адекватно воспроизводить натурные гидравлические характеристики потока транспортируемой среды путем решения прямой задачи гидравлики, в частности, прямой задачи об утечке, когда местоположение и расход отбора заданы. Численное решение обратной задачи, в отличие от аналитического обычно сводится к многократному решению прямой задачи. В предлагаемой работе гидродинамическая математическая модель трубопровода с двумя параметрами, прошедшими идентификацию, и отбором жидкости в заданном сечении сведена к дифференциальным уравнениям эволюционного типа для среднего по сечению давления и массового расхода. На основе частных аналитических решений данных уравнений получены зависимости для определения давления в работающем в стационарном режиме нефтепроводе при наличии отбора (утечки). Рассмотрены результаты применения аналитических решений к методу функций чувствительности в обратной задаче утечки. Получено точное аналитическое решение (в неявной форме) обратной задачи, позволяющее связать местоположение утечки с показаниями датчиков давления, характеристиками трубопровода и транспортируемой среды.

RESEARCH SENSITIVITY OF THE ROTOR FLUX LINKAGE OBSERVER TO CHANGE PARAMETERS OF THE ASYNCHRONOUS MACHINE

When changing the parameters of the control object to ensure the required quality of control, the tuning parameters of the control system must be changed. Investigation of the sensitivity of mathematical models helps to choose the right technical parameters of the regulators. Therefore, there is an urgent scientific task, which consists in the development of mathematical models for calculating the steady-state values ​​of the sensitivity functions of the coordinates of non-linear systems to changes in their parameters. When synthesizing observers of the rotor flux linkage, it is indicated that the signal for evaluating the rotor flux linkage is most sensitive to a change in the active resistance of the rotor of an induction machine. However, the numerical values ​​of the transmission coefficients between the coordinates of the observer and the increments of the parameters of the asynchronous machine during its operation are not given, which does not allow a comparative analysis of the degree of influence of changes in certain parameters of the asynchronous machine on the signals of the observer of the flux linkage. The task is to find and compare the numerical values ​​of the functions of the sensitivity of the coordinates of the observer of the rotor flux linkage to the change in the parameters of the asynchronous machine by joint analytical solution of the static equations of the observer's sensitivity model and the state model of the asynchronous machine. In this work, analytical expressions are obtained for the steady-state values ​​of the sensitivity functions of the coordinates of such a nonlinear object as an observer of the rotor flux linkage to a change in the parameters of an asynchronous machine. A comparative analysis of the values ​​of the transmission coefficients between the parameters and coordinates in the system asynchronous machine — observer of the rotor flux linkage for its various rotation speeds is carried out. The proposed technique makes it possible to find the numerical values ​​of the transmission coefficients and to compare the degree of influence of various parameters of the asynchronous machine on the coordinates of the flux linkage observer. Transient processes obtained in the course of solving the equations of the dynamics of an asynchronous electric drive with an observer of flux linkage complement the results of analytical calculations. The performed calculations are aimed at increasing the depth of analysis of the properties of the flux link observer, which helps to reasonably choose the structure of feedbacks when synthesizing a closed observer.

Iterative Data-Driven Control for Closed Loop with Two Unknown Controllers

Iterative idea is combined with data-driven control and is used to design the feedforward controller and feedback controller simultaneously. Consider one closed loop system with two controllers, the classical model-based control holds on the condition of known plant. To alleviate the modeling process for plant, data-driven control is applied to design the two controllers. After these two controllers are parametrized by two unknown parameter vectors, the iterative idea is introduced to identify these two parameter vectors. Furthermore, for more general case of controllers, the closed relations between controllers and expected transfer functions are derived. Then, the iterative idea is also introduced to achieve the controller design. To be of benefit for latter stability analysis, some equities are derived for output-input sensitivity functions with three kinds of disturbances. Generally, after formulating the problem of the controller design as one model-matching problem, the purpose of this paper is threefold. First, we derive that, in case of two parametrized controllers, the iterative idea is performed to identify these two unknown parameter vectors, even when parameters converge to their true values. Second, we show how to design the two controllers iteratively for more general forms and find the closed relations between these controllers and expected closed loop transfer functions. Third, we provide some heuristic considerations on output-input sensitivity functions, which are of benefit for our stability analysis on data-driven control. Finally, one example is given to show the feasibility of our proposed theories.

Measurement and Estimation of Spectral Sensitivity Functions for Mobile Phone Cameras

Mobile phone cameras are often significantly more useful than professional digital single-lens reflex (DSLR) cameras. Knowledge of the camera spectral sensitivity function is important in many fields that make use of images. In this study, methods for measuring and estimating spectral sensitivity functions for mobile phone cameras are developed. In the direct measurement method, the spectral sensitivity at each wavelength is measured using monochromatic light. Although accurate, this method is time-consuming and expensive. The indirect estimation method is based on color samples, in which the spectral sensitivities are estimated from the input data of color samples and the corresponding output RGB values from the camera. We first present an imaging system for direct measurements. A variety of mobile phone cameras are measured using the system to create a database of spectral sensitivity functions. The features of the measured spectral sensitivity functions are then studied using principal component analysis (PCA) and the statistical features of the spectral functions extracted. We next describe a normal method to estimate the spectral sensitivity functions using color samples and point out some drawbacks of the method. A method to solve the estimation problem using the spectral features of the sensitivity functions in addition to the color samples is then proposed. The estimation is stable even when only a small number of spectral features are selected. Finally, the results of the experiments to confirm the feasibility of the proposed method are presented. We establish that our method is excellent in terms of both the data volume of color samples required and the estimation accuracy of the spectral sensitivity functions.

Rapid modeling of borehole measurements of nuclear magnetic resonance via spatial sensitivity functions

Borehole measurements of nuclear magnetic resonance (NMR) are routinely used to estimate in situ rock and fluid properties. Conventional NMR interpretation methods often neglect bed-boundary and layer-thickness effects in the calculation of fluid volumetric concentrations and NMR relaxation-diffusion correlations. Such effects introduce notable spatial averaging of intrinsic rock and fluid properties across thinly bedded formations or in the vicinity of boundaries between layers exhibiting large property contrasts. Forward modeling and inversion methods can mitigate the aforementioned effects and improve the accuracy of true layer properties in the presence of mud-filtrate invasion and borehole environmental effects across spatially complex formations. We have developed a fast and accurate algorithm to simulate borehole NMR measurements using the concept of spatial sensitivity functions (SSFs) that honor NMR physics and incorporate tool, borehole, and formation geometry. Tool sensitivity maps are derived from a 3D multiphysics forward model that couples NMR tool properties, magnetization evolution, and electromagnetic propagation. In addition, a multifluid relaxation model based on Brownstein-Tarr’s equation is introduced to estimate layer NMR porosity decays and relaxation-diffusion correlations from pore-size-dependent rock and fluid properties. The latter model is convolved with the SSFs to reproduce borehole NMR measurements. The results indicate that NMR spatial sensitivity is controlled by porosity, electrical conductivity, excitation pulse duration, and tool geometry. We benchmark and verify the SSF-derived forward approximation against 3D multiphysics simulations for a series of synthetic cases with variable bed thickness and petrophysical properties, and in the presence of mud-filtrate invasion in a vertical well. Results indicate that the approximation can be executed in a few seconds in a central processing unit, by a factor of 1000 times faster than rigorous multiphysics calculations, with maximum root-mean-square errors of 1%.