Iterative Correction Algorithm Research Articles

A method of three-dimensional muon imaging using cosmic ray ground array

Cosmic ray muon imaging technology is an effective non-destructive imaging technique. It is currently used to survey the internal structure of large-scale objects such as active volcanoes, pyramids, and some buildings. Additionally, it is used to detect high-Z materials in scenarios such as border security, nuclear reactor monitoring, and container inspection. All applications of cosmic ray muons require a detector to reveal and measure the flux or angular variations of muons. However, detectors may have specific characteristics for each application depending on the detection requirements. Unlike single-point track detectors, we propose using ground array detectors to investigate how ground array detection technology can be used for 3D reconstruction of objects. We use ground array detection technology for simulation studies and apply the Iterative Correction Algorithm (ICA) to reconstruct two-dimensional projections and obtain three-dimensional images of density distribution. We have also addressed the convergence problem and analyzed and optimized some parameters that may affect the detection results. The advantages of using ground arrays include their ability to simultaneously measure the transmittance flux data of muons in different directions, achieve multi-angle detection, and have a large field of view, enabling the collection of sufficient data for more accurate detection results. To verify the feasibility of our new method, we conducted a simple experimental validation on a cylindrical cement building located in the Large High Altitude Air Shower Observatory (LHAASO). By comparing the experimental results with the cement building in the array, we found that their shape structure and density information are basically consistent, demonstrating the effectiveness of our method.

Dynamic iterative correction algorithm for designing diffractive optical elements

When utilizing the Gerchberg–Saxton (GS) algorithm to design diffractive optical elements, correction coefficients are introduced to improve the quality of the design results. The main design idea is to correct the target information dynamically during the iterative calculation process. The effectiveness of the proposed method is demonstrated through the verification of beam shaping and phase-type hologram designs. Compared to the traditional GS algorithm, the results of beam shaping show that the light intensity nonuniformity and the root-mean-square error (RMSE) of the shaped spot are reduced by an order of magnitude. The results of phase-type holograms show that the reconstructed image’s peak signal-to-noise ratio (PSNR) is improved by about 12 dB. Finally, the paper also discusses the selection of correction coefficients, providing insights into the selection of optimal design correction coefficients. The simulation and experimental results show that the improved algorithm proposed in this paper is not only simple in design but also highly efficient in obtaining a high-quality phase structure, which is of great help in designing high-quality diffractive optical elements.

Approximating First Hitting Point Distribution in Milestoning for Rare Event Kinetics.

Milestoning is an efficient method for rare event kinetics calculation using short trajectory parallelization. Mean first passage time (MFPT) is the key kinetic output of Milestoning, whose accuracy crucially depends on the initial distribution of the short trajectory ensemble. The true initial distribution, i.e., the first hitting point distribution (FHPD), has no analytic expression in the general case. Here, we introduce two algorithms, local passage time weighted Milestoning (LPT-M) and Bayesian inference Milestoning (BI-M), to accurately and efficiently approximate FHPD for systems at equilibrium condition. Starting from sampling the Boltzmann distribution on milestones, we calculate the proper weighting factor for the short trajectory ensemble. The methods are tested on two model examples for illustration purpose. Both methods improve significantly over the widely used classical Milestoning (CM) method in terms of the accuracy of MFPT. In particular, BI-M covers the directional Milestoning method as a special case in deterministic Hamiltonian dynamics. LPT-M is especially advantageous in terms of computational costs and robustness with respect to the increasing number of intermediate milestones. Furthermore, a locally iterative correction algorithm for nonequilibrium stationary FHPD is developed for exact MFPT calculation, which can be combined with LPT-M/BI-M and is much cheaper than the exact Milestoning (ExM) method.

Multiple discrete orthonormal S-transforms and its application in analyzing, modelling, and simulating random process and field

We examine the derivation and characteristics of the basis function employed in the discrete orthonormal S-transform (DOST). The examination is aimed at clarifying the interpretation of the power characteristics associated with the partitions and basis functions employed in DOST. Based on this examination, it is suggested that a one-half shift to the time index of the original DOST basis functions could be considered to facilitate the interpretation of the power distribution in the time–frequency domain. Although the non-redundant DOST is a highly efficient transform, its resolution in the time–frequency space is relatively coarse as compared to some of the continuous time–frequency decomposition techniques. To improve the resolution, and without significantly increasing the computational time, we propose the multiple DOSTs (MDOSTs) approach that uses M DOSTs, each associated with a different partition scheme in the time–frequency domain and a set of corresponding orthogonal basis functions. The redundancy factor of MDOSTs is simply equal to M. In addition, we show that the MDOSTs can be used to model and simulate nonstationary non-Gaussian processes and fields within the framework of the iterative power and amplitude correction algorithm. The use of MDOSTs for analyzing, modelling, and simulating seismic ground motion and corrosion surface is illustrated by numerical examples. The results show that using MDOSTs can effectively improve the time–frequency resolutions while maintaining high computational efficiency.

Application of wavelet transforms to the simulation of corrosion fields on buried pipelines

The present study presents a framework to analyze and simulate nonhomogeneous non-Gaussian corrosion fields on the external surface of buried in-service pipelines by using continuous and discrete wavelet transforms. The considered transforms are the two-dimensional continuous wavelet transform (CWT) using the complex Morlet wavelets, dual-tree complex discrete wavelet transform (DT-CDWT), and dual-tree complex discrete wavelet with hyperbolic wavelet transform scheme (DT-CHWT); the natural corrosion field is measured using a high-resolution laser scan. Scalograms and marginal distribution of the measured corrosion field are incorporated into the iterative power and amplitude correction (IPAC) algorithm to generate synthetic corrosion fields. The framework is explained and illustrated using a numerical example. The results indicate that the proposed framework can generate synthetic corrosion fields that effectively capture probabilistic characteristics of the measured corrosion field in terms of the scalogram, textural features, and burst capacity of the pipe segment containing the corrosion field. The results suggest that DT-CDWT and DT-CHWT combined with IPAC are efficient and viable options to simulate synthetic corrosion fields to facilitate the pipeline corrosion management practice, whereas the use of CWT in conjunction with IPAC is associated with high computational cost.

Use of transform pairs to represent and simulate nonstationary non-Gaussian process with applications

We extend the use of the iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary non-Gaussian processes by considering five transform pairs, including the redundant and non-redundant transform pairs that could provide time–frequency or time-scale decomposition. We compare the performance of the IPAC algorithm to that of the spectral representation method (SRM) in terms of matching the prescribed power spectral density function (PSDF) and the marginal probability distribution function. We also extend and examine the IPAC algorithm to simulate concatenated nonstationary non-Gaussian processes. It is emphasized that the IPAC algorithm can be used with a power or energy distribution defined in a transform domain corresponding to a selected transform pair and without directly relying on the definition of the evolutionary process. Unlike SRM, the use of the IPAC algorithm to simulate the nonstationary non-Gaussian process does not require evaluating the underlying Gaussian PSDF. This is especially advantageous for cases when one is interested in estimating the reliability or performance of a structural system during its design life that is subjected to a number of nonstationary non-Gaussian excitations, each defined by a different PSDF.

A framework for conditional simulation of nonstationary non-Gaussian random field and multivariate processes

We propose a conditional simulation framework for the nonstationary/nonhomogeneous non-Gaussian/Gaussian field and multivariate processes. There are three distinct stages within the proposed framework. The first one is to sample directly the unconditional nonstationary non-Gaussian field or multivariate processes without resorting to the underlying Gaussian characteristics. The second stage maps the unconditional samples and the conditions (i.e., observations) to the Gaussian space and uses them to find the conditional mean and covariance. In the final stage, the conditional samples by considering the effect of the conditioning are generated in Gaussian space and mapped back to the original non-Gaussian field. The efficiency of the framework relies on the efficient unconditional simulation algorithms (i.e., the iterative rank-dependent shuffling algorithm, and the iterative power and amplitude correction algorithm), and the reuse of the unconditional samples for the conditional simulation. The conditional samples match the conditional mean and conditional variance–covariance. The framework can directly apply to the random field and multivariate processes defined by the marginal probability distribution function and the covariance-variance information, or the time–frequency dependent PSD function. The framework is illustrated using several examples.

Analysis and calculation method for multiple faults in low-resistance grounded systems with inverter-interfaced distributed generators based on a PQ control strategy

The short-circuit characteristics of low-resistance grounded systems (LRGSs) under multiple faults have fundamentally changed because of the high penetration level of inverter-interfaced distributed generators (IIDGs). However, an analysis and calculation method for multiple faults (ACMMF) with IIDGs that is a standard basis for fault features, relay protection, safe evaluation and design of LRGSs is currently lacking. A novel systematic ACMMF is analytically proposed in this paper based on ideal transformer and multiport network theory. Based on the proposed ACMMF, composite networks under various fault conditions are established, which provides a straightforward presentation of fault current paths and equivalent impedance and simplifies the modelling procedure for fault analysis and calculation. Furthermore, to overcome the strong nonlinear inter-IIDG couplings, an iterative correction algorithm is proposed for accurate IIDG fault current calculations. Finally, the accuracy of the proposed method is verified by PSCAD/EMTDC simulation. The results show that the proposed methods have good adaptivity to different system structures, operation modes, fault types and flexible access of IIDGs.

Decomposing seismic accelerograms with optimized window and its application for generating artificial fully non-Gaussian and nonstationary ground motion time histories

In the present study, we propose a framework to simulate artificial seismic ground motion time histories for a given target record based on the time-frequency decomposition with an optimized window. The considered time-frequency decomposition technique is the S-transform (ST), where the optimized window is determined based on an energy concentration measure (ECM). For the evaluation of ECM for S-transform, we propose to use the time-frequency power spectral density function rather than the ST coefficients. Depending on the adopted assumption, the use of the iterative power and amplitude correction algorithm (IPAC) or the spectral represent method is suggested. The use of IPAC could also preserve the non-Gaussian characteristics of the target record. The proposed framework to simulate the artificial seismic ground motion time histories can capture the irregular pockets of power concentration in the time-frequency domain, and no assumptions on the functional forms of the spectra are required. The use of the proposed framework in simulating the time histories is illustrated by numerical examples, showing that the zero-upcrossing rate, the power distribution in time and in frequency, and the spectral acceleration of the simulated time histories match well their corresponding targets.

Restoration of Wintertime Ocean Color Remote Sensing Products for the High-Latitude Oceans of the Southern Hemisphere

Satellite ocean color products have been widely used to monitor spatiotemporal variations in marine ecological environments from regional to global oceans. However, current satellite ocean color products fail to provide effective records during the winter in high–latitude oceans, limiting understanding of the marine ecological environment during the winter season. In this study, we proposed an atmospheric correction model, namely, the Neural Network Atmospheric Correction algorithm for the Southern Hemisphere (NN–AC–SH), and recover winter satellite ocean color products for the high–latitude oceans of the Southern Hemisphere from 2003 to 2020. The accuracy of the NN–AC–SH model was verified based on the in situ data from the Aerosol Robotic Network–Ocean Color (AERONET–OC). The results indicate that the NN–AC–SH model performed better than the traditional near–infrared (NIR) iterative atmospheric correction algorithm, e.g., in the 443, 488 and 531 nm bands, the relative deviations of the NN–AC–SH model were 23.11%, 20.96% and 23.14%, respectively, while the values of the NIR model were 30.72%, 22.85%, and 24.81%, respectively. Under the observation condition of a high solar zenith angle (SZA), the NN–AC–SH model performed better than the NIR model in terms of the amount of effective data (94 vs. 78 data points) and model inversion accuracy (a relative deviation 32.83% vs. 43.60%). Moreover, in situ chlorophyll concentration data from the NASA bio–Optical Marine Algorithm Dataset (NOMAD) and Chinese Antarctic Research Expedition (CHINARE) were used to verify the accuracy of the restored chlorophyll concentration products, and the results reveal that the NN–AC–SH model resulted in more effective records of higher accuracy than those obtained with the NASA–distributed chlorophyll concentration products. Overall, for the first time, this study recovered long time–series (2003–2020) ocean color products for the high–latitude oceans of the Southern Hemisphere (≥50°S) in the winter, which could provide unique satellite products for investigating the marine ecological environment of the Antarctic and sub–Antarctic oceans in the winter.

A New Cyclic Iterative Correction Algorithm for Retrieving Sea Surface Wind Speed Based on a Multilayer-Medium Model

At high sea conditions, e.g., typhoons and hurricanes, the sea surface waves break and produce foams, spray droplets, and bubbles, which are collectively known as whitecaps. Whitecaps covering the rough sea surface greatly absorb the electromagnetic pulses emitted by satellite remote sensors, such as altimeters, scatter-meters, and the Surface Waves Investigation and Monitoring (SWIM). Thus, the whitecaps reduce the sea surface backscattering, which results in the sea surface wind speed being overestimated, an error that is particularly prevalent at high wind speeds. Many algorithms of retrieving wind speeds can retrieve effectively sea surface wind speed when the wind speed is less than 15m/s, but the bias of retrieving wind speed is become bigger and bigger when wind speed is more than 20m/s. In order to eliminate the effect of whitecaps on retrieving the sea surface wind speed at high wind speeds(>15m/s), we propose a Cyclic Iterative Correction Algorithm(CICA). Firstly, a four-layer medium with including whitecaps is established. Secondly, the effect of whitecaps is calculated. Finally, the retrieving and correcting wind speed is continuously repeated. The ultimate goal is to remove the whitecaps’ influence on the backscattering coefficient and re-correct the overestimated wind speed until it reaches a constant value. The wind speeds measured by SWIM were corrected by using CICA, and then were compared with buoy measurements. Those comparisons show that using CICA can improve the wind speed inversion accuracy to 1.5 m/s, an improvement that is particularly evident in high sea conditions.

NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

Input–output‐driven gain‐adaptive iterative learning control for linear discrete‐time‐invariant systems

AbstractFor a class of linear discrete‐time‐invariant systems repetitively operated in a finite time length, an iterative correction algorithm is exploited to identify the system Markov parameters with multi‐operation inputs and outputs in obeying a criterion, of which the time order of the corrector is adaptive to the time order of the controller. Interactively, an adaptive iterative learning control is architected which composes the compensator with the approximated Markov parameters and the tracking error in sequentially minimizing a quadratic objective function of the tracking error and the compensation. Algebraic manipulation achieves that the Markov parameters correction error is monotonically declining without any step parameter selection. Further, a rigorous derivation clarifies that the time order of the learning compensator must agree to the relative degree of the system and the tracking error is linearly monotonously convergent if the Markov parameters correction error falls into an allowable range. Inspiringly, the methods and results release the confinement to both the correction and the learning ratios. In addition, a smaller learning ratio factor tolerates a larger Markov parameters correction error. Numerical experiments support the significance and the validity.

Correcting photodetector nonlinearity in dual-comb interferometry.

Photodetector nonlinearity, the main limiting factor in terms of optical power in the detection chain, is corrected to improve the signal-to-noise ratio of a short-time measurement in dual-comb spectroscopy. An iterative correction algorithm minimizing out-of-band spectral artifacts based on nonlinearity correction methods used in classical Fourier-transform spectrometers is presented. The exactitude of the nonlinearity correction is validated using a low power linear measurement. Spectroscopic lines of H12CN are provided and the increase in absorption depth of 24% caused by the saturation of the detector is corrected yielding residuals limited by the measurement noise.

An algorithm to simulate nonstationary and non-Gaussian stochastic processes

We proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Wavefront correction algorithm based on a complete second-order DM-SHWS model for free-space optical communications.

Free-space optical communication brings large-capacity communication with excellent confidentiality, though fatal obstacles are set by atmospheric turbulence that causes phase shifting in laser links. Therefore, we derived a novel, to the best of our knowledge, iterative wavefront correction algorithm based on a complete second-order deformable mirror (DM) Shack-Hartmann wavefront sensor model as a solution to it. For correcting static wavefront aberration, the proposed algorithm possesses a converging speed faster than the traditional one. In terms of correcting dynamic atmospheric turbulence, it can achieve convergence within two iterations with a residual wavefront root mean square value of less than 1/8 wavelength. The input wavefront under 1.5 wavelength can be corrected on our testbed due to the deformability of the micromachined membrane DM. The research result offers a solution for atmospheric turbulence in the adaptive optics field and may contribute to the development of free-space optical communication.

Simulating nonstationary and non‐Gaussian vector ground motions with time‐ and frequency‐dependent lagged coherence

AbstractSeismic ground motions at multiple sites are nonstationary and non‐Gaussian with potentially time‐ and frequency‐dependent coherence, although the nonstationarity or non‐Gaussian or time‐dependent coherence aspects are often neglected because of lack of algorithm or method to take all these aspects into account to simulate synthetic ground motion records at multiple sites. In the present study, an iterative power and amplitude correction algorithm is proposed to simulate the nonstationary and non‐Gaussian vector process and takes into account time‐ and frequency‐dependent coherence. The algorithm usually converges within 10 iterations. It can be viewed as the extension of the well‐known iterative amplitude adjust Fourier transform algorithm for generating a vector of surrogates. The proposed algorithm uses the S‐transform and discrete orthonormal S‐transform rather than the ordinary Fourier transform. The adequacy of the proposed algorithm is validated numerically by using simulated ground motions.

Simulation of complex free surface flows

We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].

Iterative baseline correction algorithm for dead time truncated one-dimensional solid-state MAS NMR spectra

We present an algorithm suitable for automatically correcting rolling baseline coming from time-domain truncation induced by the dead time in pulse-acquire one-dimensional MAS NMR spectra. It relies on an iterative estimation of the baseline restricted in the time-domain by the dead time duration combined with a histogram filter allowing adaptive selection of the baseline points. This method does not make any assumption regarding the NMR resonances line shapes or widths and does not modify the acquired free induction decay points. This makes it suitable for accurate deconvolution and quantification of single-pulse MAS NMR spectra. The baseline correction accuracy is evaluated on synthetic solid-state spectra of 19F, 71Ga, and 23Na by comparing the fitted baseline to the theoretical one. The versatility of the algorithm is also exemplified on three additional solid-state spectra of 23Na and 71Ga. The algorithm is made available to the community through a user-friendly standalone Matlab® application.

Projection-based improvement of 3D reconstructions from motion-impaired dental cone beam CT data.

Computed tomography (CT) and, in particular, cone beam CT (CBCT) have been increasingly used as a diagnostic tool in recent years. Patient motion during acquisition is common in CBCT due to long scan times. This results in degraded image quality and may potentially increase the number of retakes. Our aim was to develop a marker-free iterative motion correction algorithm that works on the projection images and is suitable for local tomography. We present an iterative motion correction algorithm that allows the patient's motion to be detected and taken into account during reconstruction. The core of our method is a fast GPU-accelerated three-dimensional reconstruction algorithm. Assuming rigid motion, motion correction is performed by minimizing a pixel-wise cost function between all captured x-ray images and parameterized projections of the reconstructed volume. Our method is marker-free and requires only projection images. Furthermore, it can deal with local tomography data. We demonstrate the effectiveness of our approach on both simulated and real motion-beset patient images. The results show that our new motion correction algorithm leads to accurate reconstructions with sharper edges, better contrasts and more detail. The presented method allows for correction of patient motion with observable improvements in image quality compared to uncorrected reconstructions. Potentially, this may reduce the number of retakes caused by corrupted reconstructions due to patient movements.