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The linear regression technique is widely used to determine empirical parameters of fatigue life profile while the results may not continuously depend on experimental data. Thus Tikhonov-Morozov method is utilized here to regularize the linear regression results and consequently reduces the influence of measurement noise without notably distorting the fatigue life distribution. The paper aims to discuss these issues.

Tikhonov-Morozov regularization method would be shown to effectively reduce the influences of measurement noise without distorting the fatigue life distribution. Moreover since iterative regularization methods are known to be an attractive alternative to Tikhonov regularization, four gradient iterative methods called as simple iteration, minimum error, steepest descent and conjugate gradient methods are examined with an appropriate initial guess of regularized coefficients.

It has been shown that in case of sparse fatigue life measurements, linear regression results may not have continuous dependence on experimental data and measurement error could lead to misinterpretations of the solution. Therefore from engineering safety point of view, utilizing regularization method could successfully reduce the influence of measurement noise without significantly distorting the fatigue life distribution.

An excellent initial guess for mixed iterative-direct algorithm is introduced and it has been shown that the combination of Newton iterative approach and Morozov discrepancy principle is one of the interesting strategies for determination of regularization parameter having an excellent rate of convergence. Moreover since iterative methods are known to be an attractive alternative to Tikhonov regularization, four gradient descend methods are examined here for regularization of the linear regression problem. It has been found that all of gradient decent methods with an appropriate initial guess of regularized coefficients have an excellent convergence to Tikhonov-Morozov regularization results.

This paper deals with the problem of magnetization identification. We consider a ferromagnetic body placed in an inductor field. The goal of this work is, from static magnetic field measurements taken around the device, to obtain an accurate model of its magnetization. This inverse problem is usually ill‐posed and its solution is non‐unique. It is then necessary to use mathematical regularization. However, we prefer to transform it to a better posed one by incorporating our physical knowledge of the problem. Our approach is tested on the magnetization's identification of a real ferromagnetic sheet.

This study aims to reveal the essential characteristics of nonstationary signals and explore the high-concentration representation in the joint time–frequency (TF) plane.

In this paper, the authors consider the effective TF analysis for nonstationary signals consisting of multiple components.

To make it, the authors propose the combined multi-window Gabor transform (CMGT) under the scheme of multi-window Gabor transform by introducing the combination operator. The authors establish the completeness utilizing the discrete piecewise Zak transform and provide the perfect-reconstruction conditions with respect to combined TF coefficients. The high-concentration is achieved by optimization. The authors establish the optimization function with considerations of TF concentration and computational complexity. Based on Bergman formulation, the iteration process is further analyzed to obtain the optimal solution.

With numerical experiments, it is verified that the proposed CMGT performs better in TF analysis for multi-component nonstationary signals.

In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady‐state heat conduction problem in an anisotropic medium. The convergence and the stability of the numerical methods are investigated and compared. The numerical results obtained confirm that stable numerical results can be obtained by various regularization methods, but if high accuracy is required for the temperature, or if the heat flux is also required, then care must be taken when choosing the regularization method since the numerical results are substantially improved by choosing the appropriate method.

The paper aims to identify both the location and severity of damage in complex framed buildings using limited noisy vibration measurements. The study aims to directly adopt incomplete measured mode shapes in structural damage identification and effectively reduce the influence of measurement errors on predictions of structural damage.

Damage indicators are properly chosen to reflect both the location and severity of damage in framed buildings at element level for braces and at critical point level for beams and columns. Basic equations for an iterative solution procedure are provided to be solved for the chosen damage indicators. The Tikhonov regularisation method incorporating the L‐curve criterion for determining the regularisation parameter is employed to produce stable and robust solutions for damage indicators.

The proposed method can correctly assess the quantification of structural damage at specific locations in complex framed buildings using only limited information on modal data measurements with errors, without requiring mode shape expansion techniques or model reduction processes.

Further work may be needed to improve the accuracy of inverse predictions for very small structural damage from noisy measurements.

The paper includes implications for the development of reliable techniques for rapid and on‐line damage assessment and health monitoring of framed buildings.

The paper offers a practical approach and procedure for correctly detecting structural damage and assessing structural condition from limited noisy vibration measurements.

The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author and his colleagues to the solution to ill-posed inverse heat transfer problems (IHTPs) with their possible extension to a wider class of inverse problems of mathematical physics and, most importantly, to show the wide possibilities of this methodology by examples of aerospace applications. In this regard, this study can be seen as a continuation of those applications that were discussed in the lecture.

The application of the inverse method was pre-tested with experimental investigations on a special test equipment in laboratory conditions. In these studies, the author used the solution to the nonlinear inverse problem in the conjugate (conductive and convective) statement. The corresponding iterative algorithm has been developed and tested by a numerical and experimental way.

It can be stated that the theory and methodology of solving IHTPs combined with experimental simulation of thermal conditions is an effective tool for various fundamental and applied research and development in the field of heat and mass transfer.

With the help of the developed methods of inverse problems, the investigation was conducted for a porous cooling with a gaseous coolant for heat protection of the re-entry vehicle in the natural environment of hypersonic flight. Moreover, the analysis showed that the inverse methods can make a useful contribution to the study of heat transfer at the surface of a solid body under the influence of the hypersonic heterogeneous (dusty) gas stream and in many other aerospace applications.

The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing the wavelets.

For noise reduction, sensor data were treated as input to the filter bank used for signal decomposition and implementation of discrete wavelet transform. This is followed by the application of wavelet denoising algorithm that is applied on the wavelet coefficients of signal components at different resolution levels. Both noisy and de‐noised measurement temperatures are then used as input data to a numerical experiment of IHCP. The inverse problem deals with an estimation of unknown surface heat flux in a 2D slab and is solved by the variable metric method.

Comparison of estimated heat fluxes obtained using denoised data with those using original sensor data indicates that noise reduction by wavelet has a potential to be a powerful tool for improvement of IHCP results.

Noise reduction using wavelets, while it can be implemented very easily, may also significantly relegate (or even eliminate) conventional regularization schemes commonly used in IHCP.

To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.

An inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.

A hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.

Parametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.

Magnetic induction tomography (MIT) is a tomographic imaging technique with a wide range of potential industrial applications. Planar array MIT is a convenient setup but unable to access freely from the entire periphery as it only collects measurements from one surface, so it remains challenging given the limited data. This study aims to assess the use of sparse regularization methods for accurate position and depth detection in planar array MIT.

The most difficult challenges in MIT are to solve the inverse and forward problems. The inversion of planar MIT is severely ill-posed due to limited access data. Thus, this paper posed a total variation (TV) problem and solved it efficiently with the Split Bregman formulation to overcome this difficulty. Both isotropic and anisotropic TV formulations are compared to Tikhonov regularization with experimental MIT data.

The results show that Tikhonov method failed or underestimated the object position and depth. Both isotropic and anisotropic TV led to accurate recovery of depth and position.

There are numerous potential applications for planar array MIT where access to the materials under testing is restrict. Sparse regularization methods are a promising approach to improving depth detection for limited MIT data.

The purpose of this paper is to present an efficient algorithm based on a multi‐level adaptive mesh refinement strategy for the solution of ill‐posed inverse heat conduction problems arising in pool boiling using few temperature observations.

The stable solution of the inverse problem is obtained by applying the conjugate gradient method for the normal equation method together with a discrepancy stopping rule. The resulting three‐dimensional direct, adjoin and sensitivity problems are solved numerically by a space‐time finite element method. A multi‐level computational approach, which uses an a posteriori error estimator to adaptively refine the meshes on different levels, is proposed to speed up the entire inverse solution procedure.

This systematic approach can efficiently solve the large‐scale inverse problem considered without losing necessary detail in the estimated quantities. It is shown that the choice of different termination parameters in the discrepancy stopping conditions for each level is crucial for obtaining a good overall estimation quality. The proposed algorithm has also been applied to real experimental data in pool boiling. It shows high computational efficiency and good estimation quality.

The high efficiency of the approach presented in the paper allows the fast processing of experimental data at many operating conditions along the entire boiling curve, which has been considered previously as computationally intractable. The present study is the authors' first step towards a systematic approach to consider an adaptive mesh refinement for the solution of large‐scale inverse boiling problems.