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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.

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.

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.

T-shaped cavities occur by design in many technical applications. An example of such a stator cavity is the side space between the guide vane carriers and the outer casing of a steam turbine. Thermal conditions inside it have a significant impact on the deformation of the turbine casing. In order to improve its prediction, the purpose of this paper is to provide a methodology to gain better knowledge of the local heat transfer at the cavity boundaries based on experimental results.

To determine the heat transfer coefficient distribution inside a model cavity with the help of a scaled generic test rig, an inverse heat conduction problem is posed and a method for solving such type of problems in the form of linear combinations of Trefftz functions is presented.

The results of the calculations are compared with another inverse method using first-order gradient optimization technique as well as with estimated values obtained with an analytic two-dimensional thermal network model, and they show an excellent agreement. The calculation procedure is proved to be numerically stable for different degrees of complexity of the sought boundary conditions.

This paper provides a universal and robust methodology for the fast direct determination of an arbitrary distribution of heat transfer coefficients based on material temperature measurements spread over the confining wall.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

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 purpose of this paper is to demonstrate improvement of the accuracy of electrical tomography reconstruction by incorporation of a priori knowledge into the inverse problem solution.

The fusion of two different inversion algorithms capable of real‐time operation is discussed, namely a non‐iterative monotonicity‐based approach, determining the a priori knowledge and an iterative Gauss‐Newton (GN)‐based reconstruction algorithm. Furthermore, the method is compared with the unmodified algorithms themselves by means of reconstructions from simulated inclusions at different noise levels.

The accuracy of the inverse problem reconstructions, especially at the boundary regions of the unknown inclusions, benefit from the investigations of incorporating a priori knowledge about material values and can be considerable improved. The monotonicity method itself, which has low complexity, provides remarkable reconstruction results in electrical tomography.

The paper is applied to simulated discrete two‐phase scenarios, e.g. gas/oil mixtures. In a further step the method would be tested with measured data. Moreover, investigations have to be carried out in order to make the monotonicity‐based reconstruction principle more robust against disturbing artifacts.

The fusion of the non‐iterative monotonicity‐based method with the GN‐based algorithm demonstrates a novel approach of improving the reconstruction accuracy in electrical tomography.

A promising approach for the solution of the electrocardiographic inverse problem is the calculation of the cardiac activation sequence from body surface potential (BSP) mapping data. Here, a two‐fold regularization scheme is applied in order to stabilize the inverse solution of this intrinsically ill‐posed problem. The solution of the inverse problem is defined by the minimum of a non‐linear cost function. The L‐curve method can be applied for regularization parameter determination. Solving the optimization problem by a Newton‐like method, the L‐curve may be of pronged shape. Then a numerically unique determination of the optimal regularization parameter will become difficult. This problem can be avoided applying an iterative linearized algorithm. It is shown that activation time imaging due to temporal and spatial regularization is stable with respect to large model errors. Even neglecting cardiac anisotropy in activation time imaging results in an acceptable inverse solution.

The purpose of this paper is to demonstrate the applicability of swarm and evolutionary techniques for regularized machine learning. Generally, by defining a proper penalty function, regularization laws are embedded into the structure of common least square solutions to increase the numerical stability, sparsity, accuracy and robustness of regression weights. Several regularization techniques have been proposed so far which have their own advantages and disadvantages. Several efforts have been made to find fast and accurate deterministic solvers to handle those regularization techniques. However, the proposed numerical and deterministic approaches need certain knowledge of mathematical programming, and also do not guarantee the global optimality of the obtained solution. In this research, the authors propose the use of constraint swarm and evolutionary techniques to cope with demanding requirements of regularized extreme learning machine (ELM).

To implement the required tools for comparative numerical study, three steps are taken. The considered algorithms contain both classical and swarm and evolutionary approaches. For the classical regularization techniques, Lasso regularization, Tikhonov regularization, cascade Lasso-Tikhonov regularization, and elastic net are considered. For swarm and evolutionary-based regularization, an efficient constraint handling technique known as self-adaptive penalty function constraint handling is considered, and its algorithmic structure is modified so that it can efficiently perform the regularized learning. Several well-known metaheuristics are considered to check the generalization capability of the proposed scheme. To test the efficacy of the proposed constraint evolutionary-based regularization technique, a wide range of regression problems are used. Besides, the proposed framework is applied to a real-life identification problem, i.e. identifying the dominant factors affecting the hydrocarbon emissions of an automotive engine, for further assurance on the performance of the proposed scheme.

Through extensive numerical study, it is observed that the proposed scheme can be easily used for regularized machine learning. It is indicated that by defining a proper objective function and considering an appropriate penalty function, near global optimum values of regressors can be easily obtained. The results attest the high potentials of swarm and evolutionary techniques for fast, accurate and robust regularized machine learning.

The originality of the research paper lies behind the use of a novel constraint metaheuristic computing scheme which can be used for effective regularized optimally pruned extreme learning machine (OP-ELM). The self-adaption of the proposed method alleviates the user from the knowledge of the underlying system, and also increases the degree of the automation of OP-ELM. Besides, by using different types of metaheuristics, it is demonstrated that the proposed methodology is a general flexible scheme, and can be combined with different types of swarm and evolutionary-based optimization techniques to form a regularized machine learning approach.

The purpose of this paper is to develop a source reconstruction technique, applied to a case study in biomagnetism, using both evolutionary optimization and regularization techniques.

The magnetic field, produced by a current dipole in a spheroidal domain modeling the head, is calculated. Although the model is very simple, the magnetic effect of a brain source is appropriately simulated. In order to solve the source identification problem, the following approaches have been implemented: a single‐objective minimization of a residual function, based on an evolutionary algorithm, is applied first; then, the L‐curve criterion for regularization is implemented by means of an iterative search.

A variable number of unknown parameters, defining direction and magnitude of the current dipole, have been considered. As a consequence, several optimization problems are solved: a technique based on the use of the lead field matrix identifies the source with the smallest error. Eventually, an iterative procedure based on Tikhonov regularization is proposed. The algorithm is tested with and without noise affecting data. The results showed an accuracy comparable to that obtained independently with the optimization approach.

A model problem in inverse biomagnetism, which is both simple and significant, has been formulated and solved. The magnetic source of brain activity is reconstructed in a fast way and with small errors by means of two techniques of field inversion.