Gaussian Basis Functions Research Articles

Real-Time Estimation of Lung Model Parameters and Breathing Effort During Assisted Ventilation

Abstract The estimation of lung mechanics’ parameters and the patient’s residual volitional breathing effort is a prerequisite to adjust the parameters of assisted ventilation in a patient-individual manner. A real-time capable approach is investigated that estimates the resistance and compliance of a first-order lung model in conjunction with the intrapleural pressure in real-time. Latter is a measure for the patient’s breathing effort. A signal generator model in the form of a Radial Basis Function (RBF) network is assumed for the intrapleural pressure. The Gaussian basis functions are periodic with the breathing cycle duration. This approach does not restrict the signal form of the patient-driven pressure curve. Recursive Least Squares (RLS) with selective forgetting is employed to consider the different dynamics of the estimated model parameters. A time-discrete version of the lung model is used for RLS. Computer simulations reveal that the approach is feasible and that selective forgetting is necessary to obtain satisfactory estimation results.

Reconstructed Gaussian basis to characterize flexural wave collimation in plates with periodic arrays of annular acoustic black holes

While embedding acoustic black holes (ABHs) in plates has proved to be a lightweight and useful solution for noise and vibration reduction, their potential for wave manipulation is only in its beginnings. Recent studies seem to indicate that amazing properties can be attained with them. A plate with ABH indentations can be viewed as a single-phase metamaterial that can alter wave propagation direction thanks to the ABH power-law thickness profile. Some typical unconventional dispersion properties of multi-phase metamaterials, like collimation or negative refraction, can be recovered in a simple way. This work focuses on the collimation of flexural waves in plates by means of ABH arrangements. The first goal of the paper is to propose a predictive semi-analytical method to describe such phenomenon in an efficient manner. The method is also expected to allow one to perform quick parametric analyses for different ABH configurations. To that purpose, the Gaussian expansion method (GEM) is extended to deal with ABH phononic crystals on infinite plates. The Lagrangian for a single cell is built and a new basis of Gaussian functions is constructed satisfying the periodic boundary conditions of the problem. The Rayleigh-Ritz method is then adopted to compute the displacement field of annular and circular ABH arrays. The accuracy of the reconstructed GEM approach is validated by comparing dispersion curves and modal shapes with those obtained from finite element simulations. Equi-frequency contours are then used to determine the frequency bands prone to collimation. The focus is placed on annular ABH configurations which allow one to achieve collimation at lower frequencies than the circular ones. The second main contribution of this work therefore consists of a thorough analysis to characterize the influence of geometric parameters on the performance of ABH arrays. Moreover, new designs of annular ABH arrangements on plates are proposed for wave conduction, including curvature, and energy focusing in the long wavelength limit.

Semi-analytical model of an acoustic black hole piezoelectric bimorph cantilever for energy harvesting

An acoustic black hole (ABH) beam termination can be achieved by decreasing its thickness according to a power-law profile. Waves entering the ABH slow down and vibrational energy strongly concentrates at the tip of the beam. This can be exploited for energy harvesting, as suggested in some recent works. The finite element method (FEM) is commonly used to carry out the simulations, which hampers long parametric analyzes. In this paper, we develop a semi-analytical approach to characterize the performance of a piezolectric bimorph cantilever with an ABH termination. The method can be easily extended to further configurations and allows one to determine ABH harvesting capabilities when varying system parameters, in a fast and efficient way. The Lagrangian of the ABH beam plus piezoelectric layers is constructed and the coupled equations for the flexural vibrations and voltage are derived from it. The flexural displacement field is expanded in terms of Gaussian basis functions. Vibration shapes and harvested power are computed with the proposed method and validated against FEM simulations. The ABH piezolectric bimorph cantilever is shown to substantially enhance the harvesting capabilities of a cantilever with uniform cross-section. The semi-analytical approach is then used to examine the influence of several ABH and piezoelectric layer parameters on energy harvesting efficiency. As regards the former, the effects of the tip truncation thickness and ABH order are explored. In what concerns the piezoelectric layer, we investigate the effects of its location, thickness, splitting it into several patches and varying the load resistors to enhance its performance in a broad frequency range. The proposed method constitutes a valuable tool for the design of ABH energy harvesting devices.

First Ionization Energy as the Asymptotic Limit of the Average Local Electron Energy.

The first vertical ionization energy of an atom or molecule is encoded in the rate of exponential decay of the exact natural orbitals. For natural orbitals represented in terms of Gaussian basis functions, this property does not hold even approximately. We show that it is nevertheless possible to deduce the first ionization energy from the long-range behavior of Gaussian-basis-set wave functions by evaluating the asymptotic limit of a quantity called the average local electron energy (ALEE), provided that the most diffuse functions of the basis set have a suitable shape and location. The ALEE method exposes subtle qualitative differences between seemingly analogous Gaussian basis sets and complements the extended Koopmans theorem by being robust in situations where the one-electron reduced density matrix is ill-conditioned.

Power balance and efficiency of metasurface antennas

This paper presents two methods for the efficient evaluation of the power balance in circular metasurface (MTS) antennas implementing arbitrary modulated surface impedances on a grounded dielectric slab. Both methods assume the surface current in the homogenized MTS to be known. The first technique relies on the surface current expansion with Fourier-Bessel basis functions (FBBF) and proceeds by integration of the Poynting vector on a closed surface. The second method is based on the evaluation of the residue of the electric field spectrum at the surface-wave (SW) pole, and is demonstrated by using a current expansion in Gaussian ring basis functions (GRBF). The surface current expansions can be directly obtained either by analyzing the antenna with a Method of Moments (MoM) tool for homogenized MTSs based on FBBF or GRBF, or derived by a projection process. From there, the power contributions, namely the total power delivered by the feed, the radiated power, the SW power, and the Ohmic power losses in the dielectric are computed. Several efficiency metrics are presented and discussed: tapering efficiency, conversion efficiency, loss factor, and diffraction factor. Since the MTS apertures at hand are leaky-wave (LW) antennas, the designer must find a compromise between the aperture efficiency and the conversion efficiency. This requires accurate and fast computational techniques for the efficiency. The present paper demonstrates for the first time that the efficiency of MTS antenna devices can be accurately evaluated in a few minutes. The compromise that should be made during the design process between the tapering efficiency and the conversion efficiency is highlighted. The impact on the efficiency of isotropic versus anisotropic MTS, uniform versus non-uniform modulation index, is analyzed. An excellent agreement is obtained between both approaches, commercial software, and experimental data.

Auto-regressive modeling with dynamic weighted canonical correlation analysis

Multivariate statistical analytical methods, such as principal component analysis (PCA) and canonical correlation analysis (CCA), are widely used to extract useful information from data collected in modern industrial processes. Their dynamic extensions are also designed intensively in the literature to exploit dynamic variations in the processes. However, none of these algorithms consider the inevitably strong dependence in adjacent samples caused by high sampling frequencies or relatively slow continuous process changes, and the dependence may lead to unnecessarily large time lags and sub-optimal prediction performance. In this paper, a dynamic weighted CCA (DWCCA) algorithm is proposed to address this issue with the aid of basis functions. DWCCA constructs its latent space by maximizing the correlation between current data and a weighted representation of past data. To remove the negative effect caused by strongly collinear successive samples, it is assumed that the weights of past data rely only on a limited number of basis functions, and in this work, polynomial basis, Fourier basis, and Gaussian basis functions are considered and compared. Comprehensive modeling scheme is also designed for DWCCA with subsequent PCA decomposition to exploit static and dynamic variations concurrently. Case studies on the Tennessee Eastman process and the boiler process are presented to illustrate the effectiveness of the proposed dynamic models over other existing dynamic methods.

Computing integrals for electron molecule scattering on heterogeneous accelerator systems

SummaryUsing heterogeneous accelerators to obtain high performance for mathematical kernels remains an active research frontier in computational science. The accelerators have compute architectures that are different from the CPUs and in addition have memory spaces independent of the CPU systems to which they are connected. It follows that accelerators require a different approach to writing optimal code than that needed on a multi‐CPU system. Taken together these issues have represented a significant barrier to widespread adoption of accelerators for execution with large legacy code bases. OpenCL has emerged as a common programming language with which to implement code that runs across a range of parallel architectures, including multi‐core CPUs. This article is a case study on how the instruction‐level parallelism offered by field programmable gate arrays (FPGAs) and GPUs through OpenCL can be exploited in molecular physics. The algorithm which we study is the evaluation of tail integrals between Gaussian type basis functions for the R‐matrix method, a task that arises in the study of scattering of low energy electrons by molecular targets. The results of our productivity study, which is the first application of OpenCL in this problem domain, show that significant performance can be obtained from both FPGA and graphics processing unit (GPU) accelerators for this application. We discuss suitable transformations unique to each accelerator architecture for the integrals studied and present performance results comparing the FPGA and GPU with execution on Intel multi‐core systems.

Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because of the very thin thickness attained at the ABH central area. Semi-analytical approaches relying on the Rayleigh-Ritz method with wavelet or Gaussian basis functions have thus revealed as an accurate and fast alternative to determine the ABH vibration field in parametric studies. To date however, the vast majority of works on ABHs have only dealt with ABH indentations on straight beams and flat plates. It would be also worth exploring the feasibility of ABHs to control the vibrations of curved shells, typically found in aerospace and naval structures. In this work, we address this issue and extend the Gaussian expansion method (GEM) to characterize annular ABHs embedded on cylindrical shells. First, we show how the GEM can be modified to make Gaussian shape functions satisfy periodic boundary conditions in the circumferential direction of the cylinder. The GEM is then used to determine the vibration field of the ABH cylindrical shell and gets validated by comparison with finite element simulations. A thorough analysis of the performance of the annular ABH follows, which stresses the differences with the behavior of ABHs on flat surfaces. In particular, we show the influence that waves propagating in the circumferential direction have on the operational frequency range of the ABH. The effects of the viscoelastic layer and the inclusion of longitudinal stiffeners to strengthen the cylinder rigidity are also analyzed by means of the proposed GEM approach. This work broadens previous semi-analytical methods to start investigating the ABH effect on curved structures.

New algorithm using L1 regularization for measuring electron energy spectra.

Retrieving the spectrum of physical radiation from experimental measurements typically involves using a mathematical algorithm to deconvolve the instrument response function from the measured signal. However, in the field of signal processing known as "Source Separation" (SS), which refers to the process of computationally retrieving the separate source components that generate an overlapping signal on the detector, the deconvolution process can become an ill-posed problem and crosstalk complicates the separation of the individual sources. To overcome this problem, we have designed a magnetic spectrometer for inline electron energy spectrum diagnosis and developed an analysis algorithm using techniques applicable to the problem of SS. An unknown polychromatic electron spectrum is calculated by sparse coding using a Gaussian basis function and an L1 regularization algorithm with a sparsity constraint. This technique is verified by using a specially designed magnetic field electron spectrometer. We use Monte Carlo simulations of the detector response to Maxwellian input energy distributions with electron temperatures of 5.0 MeV, 10.0 MeV, and 15.0 MeV to show that the calculated sparse spectrum can reproduce the input spectrum with an optimum energy bin width automatically selected by the L1 regularization. The spectra are reproduced with a high accuracy of less than 4.0% error, without an initial value. The technique is then applied to experimental measurements of intense laser accelerated electron beams from solid targets. Our analysis concept of spectral retrieval and automatic optimization of energy bin width by sparse coding could form the basis of a novel diagnostic method for spectroscopy.

Numerical Approach to a Nonlocal Advection-Reaction-Diffusion Model of Cartilage Pattern Formation

We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme.

Numerical methods for solving Schrödinger equations in complex reproducing kernel Hilbert spaces

In this paper, complex reproducing kernel Hilbert spaces and their reproducing kernels are introduced. The reproducing kernel is constructed by combining Gaussian radical basis function kernel and spline kernel. In the spaces, using the related theory, a novel numerical method is developed to solve Schroinger equations. The present method is a meshless method and does not require connection between nodes of the simulation domain. The results of numerical experiments show our method is simple and has high accuracy.

Hybrid Gaussian–discrete-variable representation for describing molecular double-ionization events

A hybrid method that combines Gaussian basis functions typically used in bound-state molecular electronic structure calculations with a grid-based discrete-variable representation with finite elements suitable for a general electronic continuum representation is used to fully describe the double ionization of molecular ${\mathrm{H}}_{2}$ by a single photoabsorption. This work expands the hybrid method, previously applied to single-ionization events, to double photoionization. Constructing the full two-electron operator encoding the electron correlation necessary to doubly ionize the target via the action of a single photon requires all classes of mixed integrals between combinations of the different basis-function types. Comparison of the present results with benchmark theoretical calculations and experimental results shows excellent agreement for both molecular ${\mathrm{H}}_{2}$ and its united-atom limit, atomic helium; the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the frame of the molecule are compared. The two-electron results computed using this hybrid basis hint at application of this general descriptive scheme beyond this simplest molecular target towards describing double ionization in more complicated and experimentally relevant molecules.

Pariser–Parr–Pople Model Based Configuration-Interaction Study of Linear Optical Absorption in Lower-Symmetry Polycyclic Aromatic Hydrocarbon Molecules

The electronic and optical properties of various polycyclic aromatic hydrocarbons (PAHs) with lower symmetry, namely, benzo[ghi]perylene (C22H12), benzo[a]coronene (C28H14), naphtho[2,3a]coronene (C32H16), anthra[2,3a]coronene (C36H18), and naphtho[8,1,2-abc]coronene (C30H14), were investigated. We performed electron-correlated calculations using screened and standard parameters in the π-electron Pariser–Parr–Pople (PPP) Hamiltonian, and the correlation effects were included, both for ground and excited states, using multireference singles–doubles configuration-interaction (MRSDCI) methodology. The PPP model Hamiltonian includes long-range Coulomb interactions, which increase the accuracy of our calculations. The results of our calculations predict that, with the increasing sizes of the coronene derivatives, optical spectra are red-shifted, and the optical gaps decrease. In each spectrum, the first peak representing the optical gap is of moderate intensity, while the more intense peaks appear at higher energies. Our computed spectra are in good agreement with the available experimental data. For the purpose of comparison, we also performed first-principles time-dependent density-functional theory (TDDFT) calculations of the optical gaps of these molecules using Gaussian basis functions and found that they yielded values lower than our configuration-interaction (CI) results.

Retrieval of Cloud Liquid Water Using Microwave Signals from LEO Satellites: A Feasibility Study through Simulations

A novel approach, using low Earth orbit (LEO) satellite microwave communication links for cloud liquid water measurements, is proposed in this paper. The feasibility of this approach is studied through simulations of the retrieval system including a LEO satellite communicating with a group of ground receivers equipped with signal-to-noise ratio (SNR) estimators, a synthetic cloud attenuation field and a tomographic retrieval algorithm. Rectangular and Gaussian basis functions are considered to define the targeted field. Simulation results suggest that the proposed least-squares based retrieval algorithm produces satisfactory outcomes for both types of basis functions. The root-mean-square error of the retrieved field is around 0.2 dB/km, with the range of the reference field as 0 to 2.35 dB/km. It is also confirmed that the partial retrieval of the cloud field is achievable when a limited number of receivers with restricted locations are available. The retrieval outcomes exhibit properties of high resolution and low error, indicating that the proposed approach has great potential for cloud observations.

Speech emotion recognition using hybrid spectral-prosodic features of speech signal/glottal waveform, metaheuristic-based dimensionality reduction, and Gaussian elliptical basis function network classifier

In this paper, a hybrid system consisting of three stages of feature extraction, dimensionality reduction, and feature classification is proposed for speech emotion recognition (SER). At feature extraction stage, an informationally-rich spectral-prosodic hybrid feature vector comprised of perceptual-spectral features; that is, mel-frequency cepstral coefficient (MFCC), perceptual linear prediction coefficient (PLPC), and perceptual minimum variance distortionless response (PMVDR) coefficient along with the prosodic feature of pitch (i.e. F0) are extracted for each frame. This feature vector is extracted from both speech signal and its glottal-waveform. The first and the second-order derivatives are then added to the above-mentioned vector to form a high-dimensional hybrid feature vector characterized by a large number of dimensions. At the next stage, i.e. dimensionality reduction, the dimensionality of this feature vector is reduced using a new proposed quantum-behaved particle swarm optimization (QPSO)-based approach. In this paper, a new QPSO algorithm (so-called, pQPSO) is presented that makes use of a truncated Laplace distribution (TLD) to generate new particles and thus to produce solutions (i.e. particles) that are all within a valid range of a problem (contrary to the standard QPSO). The contraction-expansion (CE) factor of the proposed pQPSO is also selected adaptively. Using the proposed QPSO algorithm, an optimal discriminative dimensionality reduction matrix (i.e. projection matrix) is estimated with emotion classification accuracy as a class-discriminative criterion. At the subsequent stage, vectors with reduced feature dimensionality are fed into a Gaussian elliptical basis function (GEBF)-type neural network classifier to detect their speech emotion. To accelerate the training phase of the GEBF classifier, a fast-scaled conjugate gradient (SCG) algorithm is correspondingly employed that does not need to adjust the learning rate. Finally, the proposed method is evaluated on three standard emotional speech databases of Berlin Database of Emotional Speech (EMODB), Surrey Audio-Visual Expressed Emotion (SAVEE), and Interactive Emotional Dyadic Motion Capture (IEMOCAP). The experimental results showed that the proposed method was more accurate than state-of-the-art ones in terms of detecting speech emotions.

Prescribed performance adaptive DSC for a class of time-delayed switched nonlinear systems in nonstrict-feedback form: Application to a two-stage chemical reactor

This study deals with the tracking problem for a class of nonstrict-feedback switched nonlinear systems (SNSs) with unknown time-delay and unknown functions under arbitrary switching. To achieve this goal, an adaptive neural network-based dynamic surface control (DSC) based on backstepping approach is proposed. A neural network (NN) approximator based on radial basis functions (RBFs) is utilized to approximate unknown functions. Considering properties of Gaussian basis function in RBFNNs, an adaptive neural network DSC for nonstrict-feedback structure has been developed. A Lyapunov-krasovskii functional is applied to compensate the effect of unknown delay terms. Furthermore, a prescribed performance bound (PPB) control strategy is utilized to retain the tracking error within a predefined bound. Finally, a practical example is provided to prove the effectiveness of the proposed method.

Analysis, Design, and Generalization of Electrochemical Impedance Spectroscopy (EIS) Inversion Algorithms

We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown distributions, (2) the minimization of a metric of error to estimate parameters arising from the chosen representation, subject to constraints on (3) the complexity control parameters, and (4) a means for choosing optimal control parameter values. These features must be present to overcome the ill-posed nature of EIS inversion problems. We review three established EIS inversion algorithms to illustrate the pervasiveness of these features, and show the utility of the framework by resolving ambiguities concerning three more algorithms. Our framework is then used to design the generalized EIS inversion (gEISi) algorithm, which uses Gaussian basis function representation, modality control parameter, and cross-validation for choosing the optimal control parameter value. The gEISi algorithm is applicable to the generalized EIS inversion problem, which allows for a wider range of underlying models. We also considered the construction of credible intervals for distributions arising from the algorithm. The algorithm is able to accurately reproduce distributions which have been difficult to obtain using existing algorithms. It is provided gratis on the repository https://github.com/suryaeff/gEISi.git.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy.

The emergence of X-ray free electron lasers (X-FELs) has made it possible to probe structural dynamics on the femtosecond timescale. This extension of experimental capabilities also calls for a simultaneous development in theory to help interpret the underlying structure and dynamics encoded within the experimental observable. In the ultrafast regime this often requires a time-dependent theoretical treatment that describes nuclear dynamics beyond the Born-Oppenheimer approximation. In this work, we perform quantum dynamics simulations based upon time-evolving Gaussian basis functions (GBFs) and simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom. Two methods to simulate the excited state XANES spectra are applied, the first is based upon the multi-configurational second order perturbation theory restricted active space (RASPT2) method and the second uses a combination of the maximum overlap method (MOM) and time-dependent density functional theory (TDDFT). We demonstrate that despite the simplicity of the MOM/TDDFT method, it captures several qualitative features of the RASPT2 simulations at much reduced computational effort. However, features such as the conical intersection are a particular exception as they require a multi-configurational treatment. For the nuclear dynamics, we demonstrate that even a small number of GBFs can provide reasonable description of the spectroscopic observable. This work provides perspectives for computationally efficient approaches important for addressing larger systems.

Adaptive Electrical Impedance Tomography Resolution Enhancement Using Statistically Quantized Projected Image Sub-Bands

This paper proposes an adaptive image enhancement method for electrical impedance tomography (EIT). The images are enhanced based on a steerable and multi-scale resolution enhancement algorithm. It is initiated by capturing the spatial variations in decomposition orientations, and decomposition scales of the EIT image. The interpretation of projected image sub-bands is translated into resolution through statistical processes. A steerable filter containing Gaussian basis function derivatives captures the statistical information. Using the regional quantization method (RQM) proposed in this paper, projection weights are computed through spatial statistics of the image sub-bands and tuned adaptively. RQM assigns more resolution to those directional edges which have higher standard deviation and embeds high-order curvatures into the EIT images while suppressing noise. Comparison with conventional image enhancement methods demonstrates the superior performance of RQM. Using RQM it is shown that for 16, 32 and 64 electrode configurations with noise-free recording of 32 × 32 EIT images the number of electrodes can be reduced by 5, 7 and 12 respectively without loss of detail.

3-D Topology Optimization of Claw-Pole Alternator Using Gaussian-Basis Function With Global and Local Searches

This article proposes a two-step topology optimization method based on the normalized Gaussian functions. The proposed method is shown to be effective for design of a claw-pole alternator. In this method, the global search using the micro-genetic algorithm ( $\boldsymbol {\mu }$ GA) is followed by the local search using the sensitivity analysis based on the adjoint variable method. The 3-D structure of the rotor is optimized using the proposed method under low- and high-speed conditions.