Inverse heat conduction problems occur in many theoretical and practical applications where it is difficult or practically impossible to measure the heat flux generated and the temperature of the layer conducting the heat flux to the body. Thus it becomes imperative to devise some means to cater for such a problem and estimate the heat flux inversely. Adaptive state estimator is one such technique which works by incorporating the semi-Markovian concept into a Bayesian estimation technique thereby developing an inverse input and state estimator consisting of a bank of
parallel adaptively weighted Kalman filters. The problem presented in this study deals with a three dimensional system of a cube with one end conducting heat flux and all the other sides are insulated while the temperatures are measured on the accessible faces of the cube. The measurements taken on these accessible faces are fed into the estimation algorithm and the input heat flux and the temperature distribution at each point in the system is calculated.
A variety of input heat flux scenarios have been examined to underwrite the robustness of the estimation algorithm and hence insure its usability in practical applications. These include sinusoidal input flux, a combination of rectangular,
linearly changing and sinusoidal input flux and finally a step changing input flux. The estimator’s performance limitations have been examined in these input set-ups and error associated with each set-up is compared to conclude the realistic application of
the estimation algorithm in such scenarios. Different sensor arrangements, that is different sensor numbers and their locations are also examined to impress upon the importance of number of measurements and their location i.e. close or farther from
the input area. Since practically it is both economically and physically tedious to install more number of measurement sensors, hence optimized number and location is very important to determine for making the study more application oriented.
Before the inverse estimation, a comprehensive mesh sensitivity analysis is given for the system’s governing equation finite difference calculations to get an optimized mesh size for the forward and inverse analysis to be correct and within the
tolerable error limits and computationally undemanding at the same time.
Inhaltsverzeichnis (Table of Contents)
- I. INTRODUCTION.
- 1. Background - Inverse Problems
- 2. Related Work...
- 3. Kalman Filtering and Present Problem
- II. Forward Problem......
- 1. Problem Description and Finite Difference Solution.....
- 2. Sensitivity Analysis..........\li>
- III. INVERSE ESTIMATION.
- 1. Kalman Filtering.
- 2. Adaptive State Estimation - ASE.
- IV. RESULTS.
- V. CONCLUSION.
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This thesis presents an inverse estimation method for determining heat flux and temperature distribution within a 3D finite domain. The research utilizes the Kalman filtering technique and its adaptive state estimation variant to address the challenges inherent in inverse problems.
- Inverse estimation of heat flux and temperature distribution in 3D finite domain
- Application of Kalman filtering and adaptive state estimation techniques
- Analysis of the forward problem using finite difference methods
- Exploration of sensitivity analysis for understanding parameter influence
- Presentation of results and concluding remarks
Zusammenfassung der Kapitel (Chapter Summaries)
- I. INTRODUCTION: This chapter provides an overview of the concept of inverse problems, examines related research, and introduces the Kalman filtering technique as it applies to the specific problem of heat flux and temperature estimation.
- II. Forward Problem: This chapter delves into the forward problem, outlining the specific problem description and its solution using finite difference methods. It also includes a comprehensive analysis of the sensitivity of the problem to different parameters.
- III. INVERSE ESTIMATION: This chapter focuses on the core of the research, presenting two methods for inverse estimation: Kalman filtering and its adaptive state estimation variant.
- IV. RESULTS: This chapter presents the results obtained from the application of the inverse estimation methods, showcasing the effectiveness of the proposed solutions.
Schlüsselwörter (Keywords)
The research focuses on inverse problems, heat flux, temperature distribution, 3D finite domain, Kalman filtering, adaptive state estimation, finite difference methods, sensitivity analysis.
Frequently Asked Questions
What is an inverse heat conduction problem?
It is a problem where the internal heat flux or temperature distribution must be estimated from measurements taken on accessible surfaces, because direct measurement is impossible.
How does the Adaptive State Estimator (ASE) work?
The ASE incorporates semi-Markovian concepts into Bayesian estimation, using a bank of parallel Kalman filters to adaptively estimate input and state changes.
What types of heat flux scenarios were examined in this study?
The study tested sinusoidal input flux, step changes, and combinations of rectangular and linearly changing fluxes to prove the algorithm's robustness.
Why is sensor placement important in 3D heat estimation?
The number and location of sensors (close or far from the heat source) significantly affect the accuracy and economic feasibility of the inverse estimation.
What is mesh sensitivity analysis in this context?
It is a process to determine the optimal mesh size for finite difference calculations to ensure results are accurate within tolerable error limits while remaining computationally efficient.
- Arbeit zitieren
- Nauman Malik Muhamad (Autor:in), 2009, Inverse Estimation of Heat Flux and Temperature in 3D Finite Domain, München, GRIN Verlag, https://www.grin.com/document/176816
