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The purpose of this paper is to study the feasibility on the use of alternative parameters for representing acoustic emission (AE) and acousto-ultrasonic (AU) signals, using a wavelet-based approach and the computation of Chebyshev moments.

Two tests were performed, one on AE artificial signals generated on a CFRP plate and one on an AU setup used for actively detecting impact damage. The waveforms were represented using a data reduction technique based on the Daubechies wavelet and an image processing technique using Chebyshev moments approximation, to get 32 descriptors for each waveform.

The use of such descriptors allowed in the AE case to verify that the moments are similar when the waveforms are similar; in the AU setup the correlation coefficient of the descriptors with respect to a reference data set was found to be linked to the delimitation size.

Such a data reduction while retaining all the useful information will be positive for wireless sensor networks, where power consumption during data transmission is key. With having to send only a reliable set of descriptors and not an entire waveform, the power consumption is believed to be reduced.

This paper is a preliminary study that fulfils a need for a more reliable data reduction for ultrasonic transient signals, such as those used in AE and AU.

This paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.

Under the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.

In this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

One‐dimensional radiative heat transfer is considered in a plane‐parallel geometry for an absorbing, emitting, and linearly anisotropic scattering medium subjected to azimuthally symmetric incident radiation at the boundaries. The integral form of the transport equation is used throughout the analysis. This formulation leads to a system of weakly‐singular Fredholm integral equations of the second kind. The resulting unknown functions are then formally expanded in Chebyshev series. These series representations are truncated at a specified number of terms, leaving residual functions as a result of the approximation. The collocation and the Ritz‐Galerkin methods are formulated, and are expressed in terms of general orthogonality conditions applied to the residual functions. The major contribution of the present work lies in developing quantitative error estimates. Error bounds are obtained for the approximating functions by developing equations relating the residuals to the errors and applying functional norms to the resulting set of equations. The collocation and Ritz‐Galerkin methods are each applied in turn to determine the expansion coefficients of the approximating functions. The effectiveness of each method is interpreted by analyzing the errors which result from the approximations.

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

This paper aims to present a new method for the approximate solution of two-dimensional nonlinear Volterra–Fredholm partial integro-differential equations with boundary conditions using two-dimensional Chebyshev wavelets.

For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of Chebyshev wavelets. The use of these operational matrices simplifies considerably the structure of the computation used for a set of the algebraic system has been obtained by using the collocation points and solved.

Theorem for convergence analysis and some illustrative examples of using the presented method to show the validity, efficiency, high accuracy and applicability of the proposed technique. Some figures are plotted to demonstrate the error analysis of the proposed scheme.

This paper uses operational matrices of two-dimensional Chebyshev wavelets and helps to obtain high accuracy of the method.

Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform temperature or heat flux, assuming that the rest of the cavity is completely adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity.

The problem is written with non-homogeneous boundary conditions. Momentum and energy equations are numerically solved in space by a spectral collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the resolution in time.

The results clearly show the evolution of multicellular regime during the process of fusion and the kinetics of phase change depends on the boundary condition imposed on the bottom cell wall. Thus the charge and discharge processes in energy storage cells can be controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal convective heat and mass transfer are highlighted during the transient regime. This model is particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in the process of storage/release energy.

The time-dependent physical properties that induce non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in the present model. The present model is actually extended to these coupled situations. This problem requires smoother geometries. One can try to palliate this disadvantage by constructing smoother approximations of non-smooth geometries. The augmentation of polynomials developments orders increases strongly the computing time. When the external heat flux or temperature imposed at the PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to assume the algorithms convergence.

Among the areas where this work can be used, are: buildings where the PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical, to minimize temperature variations of food, drug or sensitive materials; and the textile industry, PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM intervene to regulate heat transfer between the body and the outside.

The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions.

This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.

Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.

CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.

The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

The purpose of this paper is to illustrate three types of basis functions and their asymptotic forms defined over the patch to model the unknown currents.

A rigorous calculation of a microstrip structure that contains isotropic and anisotropic substrates via Galerkin's method is presented. The dyadic Green's functions of the problem are efficiently determined by the (TM, TE) representation.

The resonant frequency of a rectangular microstrip patch antenna using these different asymptotic basis functions is investigated. The effect of uniaxial anisotropy in the resonant frequency is presented for these asymptotic currents.

Comparisons are made, and show that the utilization of the asymptotic basis function provides a significant improvement in the computation time over the exact form in the evaluation of the resonant frequency of a microstrip patch antenna. Convergent solutions are in good agreement with the exact sinusoid basis function without edge condition and with those obtained from literature.

Community detection of dynamic networks provides more effective information than static network community detection in the real world. The mainstream method for community detection in dynamic networks is evolutionary clustering, which uses temporal smoothness of community structures to connect snapshots of networks in adjacent time intervals. However, the error accumulation issues limit the effectiveness of evolutionary clustering. While the multi-objective evolutionary approach can solve the issue of fixed settings of the two objective function weight parameters in the evolutionary clustering framework, the traditional multi-objective evolutionary approach lacks self-adaptability.

This paper proposes a community detection algorithm that integrates evolutionary clustering and decomposition-based multi-objective optimization methods. In this approach, a benchmark correction procedure is added to the evolutionary clustering framework to prevent the division results from drifting.

Experimental results demonstrate the superior accuracy of this method compared to similar algorithms in both real and synthetic dynamic datasets.

To enhance the clustering results, adaptive variances and crossover probabilities are designed based on the relative change amounts of the subproblems decomposed by MOEA/D (A Multiobjective Optimization Evolutionary Algorithm based on Decomposition) to dynamically adjust the focus of different evolutionary stages.