Sparse Plane Wave Approximation of Acoustic Modes to Address Basis Mismatch

Low-frequency sound field reconstruction in an enclosed space has many applications where the plane wave approximation of acoustic modes plays a crucial role. However, the basis mismatch of the plane wave directions degrades the approximation accuracy. In this study, a two-stage method combining ℓ1-norm relaxation and parametric sparse Bayesian learning is proposed to address this problem. This method involves selecting sparse dominant plane wave directions from pre-discretized directions and constructing a parameterized dictionary of low dimensionality. This dictionary is used to re-estimate the plane wave complex amplitudes and directions based on the sparse Bayesian framework using the variational Bayesian expectation and maximization method. Numerical simulations show that the proposed method can efficiently optimize the plane wave directions to reduce the basis mismatch and improve acoustic mode approximation accuracy. The proposed method involves slightly increased computational cost but obtains a higher reconstruction accuracy at extrapolated field points and is more robust under low signal-to-noise ratios compared with conventional methods.

Multi-label feature selection based on fuzzy neighborhood rough sets

Multi-label feature selection, a crucial preprocessing step for multi-label classification, has been widely applied to data mining, artificial intelligence and other fields. However, most of the existing multi-label feature selection methods for dealing with mixed data have the following problems: (1) These methods rarely consider the importance of features from multiple perspectives, which analyzes features not comprehensive enough. (2) These methods select feature subsets according to the positive region, while ignoring the uncertainty implied by the upper approximation. To address these problems, a multi-label feature selection method based on fuzzy neighborhood rough set is developed in this article. First, the fuzzy neighborhood approximation accuracy and fuzzy decision are defined in the fuzzy neighborhood rough set model, and a new multi-label fuzzy neighborhood conditional entropy is designed. Second, a mixed measure is proposed by combining the fuzzy neighborhood conditional entropy from information view with the approximate accuracy of fuzzy neighborhood from algebra view, to evaluate the importance of features from different views. Finally, a forward multi-label feature selection algorithm is proposed for removing redundant features and decrease the complexity of multi-label classification. The experimental results illustrate the validity and stability of the proposed algorithm in multi-label fuzzy neighborhood decision systems, when compared with related methods on ten multi-label datasets.

Large-Scale Truss Topology and Sizing Optimization by an Improved Genetic Algorithm with Multipoint Approximation

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.

Modelling of the reflectance profile of axisymmetrical radiolocation objects using the integral equation method

Based on the first-kind integral equation method for the electric field, the procedure and software for calculating the radar cross-section of axisymmetrical objects, bodies of revolution, are developed. Algorithms are proposed for computation of the matrix of mutual impedances and Green's function of a ring source providing the computation accuracy required for obtaining a stable solution. The method of solution approximation accuracy evaluation by azimuthal harmonics is proposed. Comparison with test examples is carried out and the applicability for solving real-world problems is shown.

Flow Balancing in Modeling of Multi-Phase Flow using Non-Conformal Finite Element Meshes

The method of balancing numerical finite element flows in modeling a process of multiphase flow using non-conformal hexagonal meshes is considered. Studies have been carried out for a simple reservoir configuration and on a more complex model of a real field of high-viscosity oil in the Tatarstan. The research results showed that the balancing method allows one to obtain a conservative solution when using non-conformal finite element meshes with sufficiently large cells. At the same time, this method is completely free of problems associated with grid orientation, even for complex models containing zones with highly variable permeability. The proposed algorithm for the adaptive choice of parameters allows to do the factorization of the SLAE matrix at sufficiently small number of time steps; therefore, the computational costs of the flow balancing procedure are an order of magnitude less than the costs associated with calculating the pressure field and phase transfer. The used non-conformal finite element meshes with an arbitrary number of docked hexagons can significantly reduce the number of degrees of freedom when modeling multiphase flows in reservoirs with much small local heterogeneity and in the presence of several perforated zones. As a result, computational costs are reduced by almost an order of magnitude, and, at the same time, the required approximation accuracy is maintained. With an increase in the scale of the model and the number of operating wells, this advantage increases even more.

Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

ON APPROXIMATION OF PERIODIC ATEB-FUNCTIONS

Two versions of approximation formulae for periodic Ateb-sine and Ateb-cosine in the first quarter of their common period are proposed. The first version is a Pade type approximation derived when constructing analytical solution of corresponding integral equation by iteration method with transforming the power series into a closed sum by Shanks’ formula. Two iteration approximations are considered. The first one is more concise but of worse approximation accuracy which deteriorates with increasing the argument value. To improve the approximation accuracy a hybrid approximation is proposed when the values of the Ateb-functions in the beginning (for the cosine) and in the end (for the sine) of the quarter period are computed by a separate formula obtained a priory by the asymptotic method. The comparison analysis of the approximate and exact values of the special functions indicates the error of the approximation proposed to be less than one per cent. The second variant of approximation is by replacing the periodic Ateb-functions by trigonometric functions of specific argument. The arguments are chosen so that the values of the special functions are exact at specific points of the quarter period. Five such collocation points are introduced in the paper. To implement this version of approximation a separate table of the values of the periodic Ateb-functions at the collocation points is compiled. The computational examples presented in the paper show the approximate values of the special functions obtained by the second version of approximation to have a good accuracy.

A Generative Model for Correlated Graph Signals

A graph signal is a random vector with a partially known statistical description. The observations are usually sufficient to determine marginal distributions of graph node variables and their pairwise correlations representing the graph edges. However, the curse of dimensionality often prevents estimating a full joint distribution of all variables from the available observations. This paper introduces a computationally effective generative model to sample from arbitrary but known marginal distributions with defined pairwise correlations. Numerical experiments show that the proposed generative model is generally accurate for correlation coefficients with magnitudes up to about 0.3, whilst larger correlations can be obtained at the cost of distribution approximation accuracy. The generative models of graph signals can also be used to sample multivariate distributions for which closed-form mathematical expressions are not known or are too complex.

Modeling the age distribution of retinoblastomas

In this work, based on real data on the size of the eyeball (in a fetus, in a child, and in young people under 20), we constructed a model function of the growth of the retinal cell tissue. We used this function to construct a theoretical age distribution of retinoblastomas. We constructed theoretical age distributions for four different models of retinoblastoma: a complex mutational model, a third mutational model, a model with a sequence of key events, and a model of a single oncogenic event with two different latencies (hereditary and non-hereditary retinoblastoma). We compared the theoretical age distribution of retinoblastomas with the real age distribution based on SEER data (Surveillance Epidemiology and End Results; program of the American National Cancer Institute). In total, we examined 843 cases in women and 908 cases in men. For all models (separately for women and men), we obtained estimates of the following cancer parameters: the specific frequency of key events (events that trigger cancer); the duration of the latency period of cancer; the number of key events required for cancer to occur. For the composite age distributions, we calculated the theoretical mean age at diagnosis for hereditary and non-hereditary retinoblastomas. The best approximation accuracy (for male and female forms of retinoblastoma) is shown by a model with a sequence of key events.

Nonlinear approximation of wildfire front temperature on MODIS data for sub-pixel analysis of burning

An improved approach to evaluate thermal anomalies characteristics using the pixel-based analysis of the MODIS imagery was proposed. The approach allows us to improve the accuracy in estimating characteristics of active combustion zones comparing to the standard Dozier method. We used the imagery of active wildfires in Siberian forests from the MODIS radiometer acquired in the spectral ranges of 3.930–3.990 and 10.780–11.280 mm (bands 21 and 31, respectively). Nonlinear exponential function was used to describe the approximation of the temperature of combustion zones. Available data of field and numerical experiments were used for validating of the approximation accuracy. Nonlinear approximation of wildfire front temperature allows to determine the portion of the active pixel of the MODIS image with the given temperature excess comparing to the temperature of background cover. This improves the accuracy in extracting of active burning zones as well as in classifying the heat release rate at the sub-pixel level of analysis.