Aleksey V. Nenarokomov

Optimal experiment design

Optimal experiment design is the definition of the conditions under which an experiment is to be conducted in order to maximize the accuracy with which the results are obtained. This paper summarizes a number of methods by which the parameters of the mathematical model of the system are estimated and describes the application of the Fisher information matrix. Examples are given for thermal property estimation in which the estimation is affected both by measurement noise, which is present during any experiment, but also by uncertainties in the parameters of the model used to describe the system.

Uncertainties in parameter estimation: the optimal experiment design

An extended maximum likelihood principle is described by which inverse solutions for problems with uncertainties in known model parameters can be treated. The method introduces the concept of an equivalent experimental noise which differs significantly from the measurement noise when the system response is sensitive to the uncertainties in the known parameters. When the equivalent noise varies smoothly and significantly over the range of uncertainty, the inverse solution tends to be independent of the uncertainties. By minimizing the equivalent noise through appropriate choice of a measurement protocol, an optimal experiment can be defined. Examples are given of designing an experiment for estimating conductivity and contact resistance when surface convective coefficients are uncertain.

Uncertainties in parameter estimation: the inverse problem

Abstract The procedure of parameter estimation and the parameter estimates are not only affected by the measurement noise, which is present during any experiment, but are also influenced by the known model parameters. The most commonly used functional, which is based on the maximum likelihood principle, only accounts for the experimental noise but not the effect of the uncertainties in the known parameters. A new functional for parameter estimation has been proposed, which will also take into account the uncertainties in the known model parameters. It is shown that, in the presence of uncertainties in the known model parameters, the proposed functional is superior to previous functionals.

Identification of thermal properties of materials with applications for spacecraft structures

This paper presents the results of computational and experimental studies of particular thermal processes in composite materials. The considered approach is based on the mathematical theory of ill-posed problems of mathematical physics. In the majority of cases this methodology is used for optimization, but in a number of practical situations it is the sole technique available, as, for example, in measuring the transient heat fluxes and heat transfer coefficients. Owing to the structural version and homogeneous surface heating in specimens a one-dimensional heat transfer process is realized. A complex of thermal properties of the composite material (thermal conductivity λ(T) and heat capacity coefficient C(T)) is estimated. The initial data for such problems are formed grounded on the results of measurements and include the boundary conditions and temperature–time values in several internal points of specimens. The type of boundary conditions and the number of points of temperature measurement should meet the conditions of uniqueness of the inverse problem solution under analysis.

Estimation of thermal properties of materials with application for inflatable spacecraft structure testing

The general method of iterative regularization is concerned with application to the estimation of material properties. The objective of this article is to estimate thermal and thermokinetic properties of advanced materials using the approach based on inverse methods. An experimental–computational system is presented for investigating the thermal and kinetics properties of composite materials by methods of inverse heat transfer problems and this is developed at the Thermal Laboratory of the Department of Space Systems Engineering, Moscow Aviation Institute. The system is aimed at investigating the materials in conditions of unsteady contact heating over a wide range of temperature changes and heating rates in vacuum, air and inert gas mediums.

IDENTIFICATION OF MATHEMATICAL MODEL OF MULTILAYER THERMAL INSULATION

The purpose of this paper is to introduce an iterative regularization method in the research of radiative and thermal properties of materials with further applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (heat capacity, emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the IHTP, based on sensitivity function approach, is presented too. The practical testing was performed for specimen of the real MLI. This paper consists of recent researches, which developed the approach suggested at [1].

Estimating thermal and radiative properties of insulating materials

In many practical situations, it is impossible to measure directly the characteristics, such as thermal and radiative properties, of analysed materials. The only way which can often be used to overcome these difficulties is indirect measurements. This type of measurement is usually formulated as the solution of inverse heat transfer problems. The experimental methods of identification of the mathematical models of heat transfer based on solving the inverse problems are one of the modern effective solving manners. The main purpose of this article is to estimate thermal and radiative properties of advanced materials (thermal conductivity , heat capacity and emissivity ) using the approach based on inverse methods. New metrology under development is the combination of accurate enough measurements, which can be experimentally observable under real conditions, and accurate data processing, which are based on the solutions of inverse heat transfer problems. In this article, the development of methods for estimating thermal and radiation characteristics is carried out for thermally stable, high-temperature insulating materials. Such problems are of great practical importance in the study of properties of materials used as non-destructive surface coating in objects of space engineering, power engineering, etc.

Radiative-conductive inverse problem for lumped parameter systems

The purpose of this paper is to introduce a iterative regularization method in the research of radiative and thermal properties of materials with applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented too. The practical testing were performed for specimen of the real MLI.

Parametric identification of a mathematical model of heat transfer in carbon–carbon (C–C) materials for aeronautical application

This paper is devoted to the development of heat transfer models that are adequate to the real processes by using the experimental and computational methodology based on the theory of inverse heat transfer problems.

Optimal design of multi-layer thermal protection of variable thickness

Purpose n n n n nThe presented paper aims to consider algorithm for optimal design of multilayer thermal insulation. n n n n nDesign/methodology/approach n n n n nDeveloped algorithm is based on a sequential quadratic programming method. n n n n nFindings n n n n n2D mathematical model of heat transfer in thermal protection was considered in frame of thermal design of spacecraft. The sensitivity functions were used to estimate the Jacobean of the object functions. n n n n nResearch limitations/implications n n n n nDesign of distributed parameter systems and shape optimization may be thought of as geometrical inverse problems, in which the positions of free boundaries are determined along with the spatial variables. In such problems, the missing data (i.e. the position of boundaries) are compensated for by the presence of the so-called inverse problem additional conditions. In the case under consideration, such conditions are constrains on the temperature values at the discrete points of the system. n n n n nPractical implications n n n n nResults are presented how to apply the algorithm suggested for solving a practical problem – thickness sampling for a thermal protection system of advanced solar probe. n n n n nOriginality/value n n n n nThe procedure proposed in the paper to solve a design problem is based on the method of quadratic approximation of the initial problem statement as a Lagrange formulation. This has allowed to construct a rather universal algorithm applicable without modification for solving a wide range of thermal design problems.