Inverse problems in measurement

Solopchenko, Gennadi N.

doi:10.1016/0263-2241(87)90023-6

Cited by 9 publications

(6 citation statements)

References 5 publications

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“…Such inverse problems are of general interest when monitoring critical infrastructure [1]. An introduction to inverse problems in measurement can be found in [2] II. PREVIOUS WORK Inclinometers are a standard method for monitoring deformations of structures [3] and geo-mechanical mon itoring.…”

Section: Motivationmentioning

confidence: 99%

Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

O’Leary

Harker

2014

2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

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This paper presents the theoretical back ground for a new measurement system for the monitoring of possible road subsidence and its verification with exper imental results. A combination of theodolite measurements and inclinometers are used to perform the monitoring of possible land subsidence. The aim is to detect ground motion near critical infrastructure during excavation is the vicinity. The required computation corresponds to an inverse boundary value problem with uncertain boundary values. The solution is formulated as a covariance weighted Hermite approximation problem. Additionally, a method of taking advantage of the properties of the over-constrained system to identify a defective sensor is presented. The correct functionality of the proposed method and its performance in terms of uncertainty is demonstrated with a Monte Carlo simulation. Additionally, tests were performed with a real monitoring system with reference measure ments. The correct functionality of the measurement system was verified.

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Section: Motivationmentioning

confidence: 99%

Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

O’Leary

Harker

2014

2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

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“…, t f is a given time moment. An operator G can be, for example, an integral operator of optical instrument in the image restoration problem [5], or a convolution operator of a measuring device in the metrological signal restoration problem [1].…”

Section: Ill-posed Problem Formulationmentioning

confidence: 99%

“…The problems of restoration of a system input and coefficients arise in various applications such as metrology [1][2][3][4], image processing [5,6], spectroscopy [7], geophysics [8,9], process control [10], engineering [11,12], medicine [13,14], and many others. The identification of the virus spread models, i.e., the restoration of the coefficients of the corresponding differential equations, became crucial in the period of coronavirus pandemic (see, e.g., [15,16]) for constructing reliable forecasts of the pandemic evolution.…”

Section: Introductionmentioning

confidence: 99%

Two Inverse Problems Solution by Feedback Tracking Control

Turetsky

2021

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Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

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“…В прошлом восстановление зашумленного сигнала в динамических измерениях осуществлялось при помощи обратного преобразования Фурье [1][2][3][4][5][6]. Но, к сожалению, такой подход дает только точечную оценку динамической погрешности и приводит к эффекту «накопления погрешности», для борьбы с этим эффектом требуется вносить изменения в параметры системы, путем добавления дополнительных фильтров.…”

Section: Introductionunclassified

Numerical Method for Processing the Results of Dynamic Measurements

Yaparov¹,

Shestakov²

2021

CTAC&R

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The problem of processing data obtained during dynamic measurements is one of the central problems in measuring technology. Purpose of the study. The article is devoted to the study of the stability of the method for solving the problem of processing the results of dynamic measurements with respect to the error in the initial data. Therefore, an urgent task is the development of algorithms for processing the results of dynamic measurements. Materials and methods. This article proposes an algorithm for processing the data obtained during dynamic measurements based on the finite-difference approach. The main prerequisites of the mathematical model of the problem of dynamic measurements associated with the processes of restoration of the input signal in conditions of incomplete and noisy initial data are as follows. Initially, the function of the noisy output signal is known. The restoration of the input signal is carried out using the transfer function of the sensor. The transfer function of the sensor is presented in the form of a differential equation. This equation describes the state of a dynamic system in real time. The proposed computational scheme of the method is based on finite-difference analogs of partial derivatives and the Tikhonov regularization method was used to construct a numerical model of the sensor. The problem of stability of the method for solving high-order differential equations is also one of the central problems of data processing in automatic control systems. Based on the approach of the generalized quasi-optimal choice of the regularization parameter in the Lavrent'ev method, the dependence of the regularization parameter, the parameters of the dynamic measuring system, the noise index and the required level of accuracy was found. Results. The main goal of the computational experiment was to construct a numerical solution to the problem under consideration. Standard test functions were considered as input signals. Test signals simulating various physical processes were used as an input signal. The function of the output signal was found using the proposed numerical method, the found function was noisy with an additive noise of 5 %. Conclusion. The input signal was restored from the noisy signal. The deviation of the reconstructed signal from the initial one in all experiments was no more than 0.05, which indicates the stability of this method with respect to noisy data.

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Inverse problems in measurement

Cited by 9 publications

References 5 publications

Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

Two Inverse Problems Solution by Feedback Tracking Control

Numerical Method for Processing the Results of Dynamic Measurements

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