Basis Of Decomposition Research Articles

A rapid method to predict biaxial fatigue life of automotive wheels using proper orthogonal decomposition and radial basis function algorithm

This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests are being developed to evaluate wheel performance. However, these simulations are computationally expensive due to the need to simulate multiple discrete loading cases within a given biaxial spectrum. To address this issue, we propose a novel approach that utilizes proper orthogonal decomposition and radial basis function algorithm to improve computational efficiency. By leveraging high-fidelity simulation results from a small number of loading cases, a reduced order model is constructed to accurately predict the tire-rim interface force fields required for wheel strength calculations. The reduced order model significantly reduces the computational time by 65.4% for simulating all loading cases, while maintaining a maximum predicted error of less than 2% compared to the high-fidelity model. Subsequently, the predicted interface forces are mapped onto the rim surface for strength calculation, and the wheel fatigue life is determined using the Brown-Miller multiaxial damage criterion. Comparative analysis with experimental results demonstrates the desirable accuracy of our method in simulating the stress-strain history, crack initiation position, and minimum fatigue life of the wheel. Overall, the proposed method offers a powerful tool for the rapid fatigue analysis of spectrum-loaded wheels, providing an efficient and accurate means of predicting biaxial fatigue life.

Joint Reconstruction and Spectrum Refinement for Photon-Counting-Detector Spectral CT.

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

An Integrated Method for Tunnel Health Monitoring Data Analysis and Early Warning: Savitzky-Golay Smoothing and Wavelet Transform Denoising Processing.

A tunnel health monitoring (THM) system ensures safe operations and effective maintenance. However, how to effectively process and denoise several data collected by THM remains to be addressed, as well as safety early warning problems. Thus, an integrated method for Savitzky-Golay smoothing (SGS) and Wavelet Transform Denoising (WTD) was used to smooth data and filter noise, and the coefficient of the non-uniform variation method was proposed for early warning. The THM data, including four types of sensors, were attempted using the proposed method. Firstly, missing values, outliers, and detrend in the data were processed, and then the data were smoothed by SGS. Furthermore, data denoising was carried out by selecting wavelet basis functions, decomposition scales, and reconstruction. Finally, the coefficient of non-uniform variation was employed to calculate the yellow and red thresholds. In data smoothing, it was found that the Signal Noise Ratio (SNR) and Root Mean Square Error (RMSE) of SGS smoothing were superior to those of the moving average smoothing and five-point cubic smoothing by approximately 10% and 30%, respectively. An interesting phenomenon was discovered: the maximum and minimum values of the denoising effects with different wavelet basis functions after selection differed significantly, with the SNR differing by 14%, the RMSE by 8%, and the r by up to 80%. It was found that the wavelet basis functions vary, while the decomposition scales are consistently set at three layers. SGS and WTD can effectively reduce the complexity of the data while preserving its key characteristics, which has a good denoising effect. The yellow and red warning thresholds are categorized into conventional and critical controls, respectively. This early warning method dramatically improves the efficiency of tunnel safety control.

Material classification using basis material decomposition from spectral X-ray CT

Spectral X-ray Computed Tomography (CT) exploits advanced photon counting detectors (PCD) to measure a material’s spectrally resolved linear attenuation coefficient (LAC) with the simultaneous spectral acquisition at multiple energy thresholds. We present a method for material classification using spectral CT. The method employs a basis material decomposition model and estimates the effective atomic number (Zeff) from the spectral LAC measurements. Basis material decomposition builds on the fact that the LAC of any material can be well approximated by a linear combination of LACs of basis materials, with known Zeff values at the extremes of the relevant Zeff range. Spectral distortions of the energy spectrum due to the physical interactions between photons and the multi-energy-bin PCD such as charge sharing and photon pileup are corrected by a spectral correction algorithm. The validation of the method has been performed with experimental data acquired with a custom laboratory instrument for spectral CT, examining “real life” phantoms with materials in the range of 6≤Zeff≤15. The classification performance is estimated for different numbers of projections, energy bins and basis materials in LAC decomposition. When using just 12 projections, 15 energy bins and two basis materials, the method gives a relative deviation of 2.2% for Zeff, while this deviation is 5.9% when spectral correction is not used. The classification method is now ready for use in security screening where modern spectral CT systems are employed.

A simulation-based software to support the real-time operational parameters selection of tunnel boring machines

With the fact that the main operational parameters of the construction process in mechanized tunneling are currently selected based on monitoring data and engineering experience without exploiting the advantages of computer methods, the focus of this work is to develop a simulation-based real-time assistant system to support the selection of operational parameters. The choice of an appropriate set of these parameters (i.e., the face support pressure, the grouting pressure, and the advance speed) during the operation of tunnel boring machines (TBM) is determined by evaluating different tunneling-induced soil-structure interactions such as the surface settlement, the associated risks on existing structures and the tunnel lining behavior. To evaluate soil-structure behavior, an advanced process-oriented numerical simulation model based on the finite cell method is utilized. To enable the real-time prediction capability of the simulation model for a practical application during the advancement of TBMs, surrogate models based on the Proper Orthogonal Decomposition and Radial Basis Functions (POD-RBF) are adopted. The proposed approach is demonstrated through several synthetic numerical examples inspired by the data of real tunnel projects. The developed methods are integrated into a user-friendly application called SMART to serve as a support platform for tunnel engineers at construction sites. Corresponding to each user adjustment of the input parameters, i.e., each TBM driving scenario, approximately two million outputs of soil-structure interactions are quickly predicted and visualized in seconds, which can provide the site engineers with a rough estimation of the impacts of the chosen scenario on structural responses of the tunnel and above ground structures.

Time-varying nonlinear parameters identification of high-speed train suspension system based on WMA

The parameters identification of suspension components provides a foundation for health assessment of the high-speed train. Considering the time-varying nonlinearity of suspension parameters caused by changing temperature, this work identifies the time-varying nonlinear parameters based on the wavelet multiresolution analysis (WMA) combined with the proposed improved Akaike information criterion (AIC). Firstly, the parameters variation law against time-temperature are fitted based on test data and the vibration responses of a two-degree-of-freedom suspension model are obtained. Secondly, the time-varying nonlinear parameters are expanded into scale coefficients using WMA. Thus, the identification of time-varying nonlinear parameters is transformed into the identification of time-invariant wavelet scale coefficients. Then the improved AIC is utilized to select the optimal basis functions and decomposition scales in noisy environments. The identified parameters vectors are used by the improved AIC as evaluation index of identification model to reduce the effect of noise. Finally, the time-varying nonlinear parameters are reconstructed based on the optimal wavelet scale coefficients. The results show that the time-varying nonlinear stiffness and damping coefficients can be accurately identified based on the WMA combined with the proposed improved AIC.

The Leakage Identification and Location of Ship Pipeline System Based on Vibration Signal Processing

The leakage of the ship’s pipeline system will bring great risks to the engine equipment and seriously threaten the vitality of the ship. In this paper, the pipeline leakage detection and localization research are carried out based on the vibration signal generated by pipeline leakage. First, the finite element model of the pipeline is constructed to obtain the variation law of the vibration signal when the pipeline leaks are carried out. Second, the vibration signal is processed based on the variational mode decomposition (VMD) and radial basis function (RBF) neural networks. The wavelet packet threshold noise reduction is conducted before signal decomposition to improve the signal-to-noise ratio. Then, the denoised signal is decomposed by VMD. The effective component is identified by analyzing the correlation coefficient between the component and the denoised signal. The center frequency and energy of the effective component are used as feature vector to train the RBF neural network to identify and locate leakage. Finally, a pipeline leakage test platform is built under laboratory conditions. After processing the data samples collected from the test, the RBF neural network is trained to identify and locate leaks. The test sample identification results show that the leak identification and localization method based on VMD-RBF has a high accuracy.

An automatic workflow for risk analysis on spatial output properties using kriging‐based surrogate models—Application to stratigraphic forward modelling

AbstractStratigraphic numerical forward process‐based models represent the formation and evolution of sedimentary basins through time. Their main deliverable is a 3D digital grid which can help to better understand the sedimentary basin infill. These models depend on several input parameters that need to be characterized for the studied basin. However, available data such as well logs and seismic data may not provide enough information to identify a unique possible value for these parameters. It is then crucial to take the uncertainty induced by this non‐uniqueness into account in the decision‐making process. As a single numerical stratigraphic forward simulation can be very time consuming, solutions are needed to limit the computational cost required to estimate such uncertainties. In particular, machine learning techniques can be used to build meta‐models that mimic the simulator and provide fast estimations of its outputs for any values of the input parameters. The key step for the efficiency of such an approach stands in the choice of the set of simulations (or training set) used to build the meta‐models: it should be informative enough to obtain accurate predictions for the output properties of interest, but also of reasonable size to limit simulation time. Then, meta‐models can be used to investigate a large number of models and make uncertainty quantification easier. Here, we focus on the prediction of spatial outputs of interest approximated from the joint use of several kriging‐based meta‐models combined to reduced basis decomposition. Sequential approaches have been proposed in the literature to identify training sets iteratively for a kriging‐based meta‐model, building upon the specific structure of such surrogates. We propose here to extend these approaches to the context of spatial output predictors. The results obtained on two synthetic test cases, representing a carbonate platform and a clastic environment, highlight the potential of the proposed approach for risk analysis to iteratively build training sets with a satisfactory efficiency in terms of simulation time and prediction accuracy.

Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)

Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process of obtaining MSCT data can be modeled as a nonlinear system and the basis material decomposition comes down to the inverse problem of the nonlinear system. For different spectra data, geometric inconsistent parameters cause geometrical inconsistent rays, which will lead to the mismatched nonlinear system. How to solve the mismatched nonlinear equations accurately and quickly is a hot issue. This paper proposes a general iterative method (SOMA) to invert the mismatched nonlinear equations. The SOMA method gives different equations different confidence and searches along the more accurate hyperplane by Schmidt orthogonalization, which can get the optimal solution quickly. The validity of the SOMA method is verified by MSCT basis material decomposition experiments. The results show that the SOMA method can decompose the basis material images accurately and improve the convergence speed greatly.

An adaptive decomposition algorithm for quantitative spectral CT imaging

AbstractWith the development of photon counting detectors (PCDs), spectral CT achieves higher performance than in the past, thus has better application prospects. In this paper, an adaptive dual effect decomposition (ADED) algorithm is proposed to perform the quantitative estimation of effective atomic number and electron density. The algorithm is an empirical material identification algorithm that achieves calibration by combining polynomials on the projection data and constraining in the image domain. In addition, we also propose an innovative effective atomic number estimation model with an accurate physical model that adaptively adjusts the parameters according to the x‐ray energy and material type. The performance of the algorithm was verified by experiment and simulation in this paper. Compared to the conventional basis material decomposition algorithm, the proposed ADED algorithm reduces the relative error in the quantification of the effective atomic number from 4.5%–12.0% to 0.3%–4.5%. Overall, the results demonstrate that the proposed algorithm significantly improves the accuracy of quantifying the effective atomic number.

The role of synoptic eddies on remote response of Eurasian atmosphere to the tropical forcing associated with 2021/2022 winter

AbstractIn this paper, the role of eddy feedback in the formation and excitation of stream function anomaly pattern over Eurasian atmosphere (SFA) during 2021/2022 December–February (DJF) season is examined in terms of a low‐order linear model with a synoptic eddy and low frequency (SELF) feedback empirical closure onto the empirical orthogonal function decomposition bases (EOF‐bases). The results show that the SFA can be produced roughly and the SELF feedback plays important role in shaping the SFA during 2021/2022 DJF over Eurasian atmosphere. The SFA can be produced roughly owing to the internal action of the linear dynamical system. However, the importance of the external forcing on the formation of SFA depends on the role of the eddy feedback to a different degree. For the North Atlantic oscillation (NAO)‐like pattern with the wave train at high latitudes, the external forcing in the tropical Atlantic contributes greater with eddy feedback. While for the wave train at lower latitudes, the forcing will have little influence with the increase of the SELF feedback. A set of experiments with isolated forcing show that the forcing over tropical Atlantic Ocean can induce the wave train patterns alike the SFA, but the forcing to the east over South Asian to western Indian Ocean also contributes for shaping the SFA, especially the anomalous cyclone over Tibetan Plateau (TP). The combined effects of the response to both the tropical Atlantic Ocean and the eastern forcing over South Asian to western Indian Ocean contributes much to the formation of the two wave trains over Eurasia, thereby a negative stream function centre over TP, which might be the main cause for the excessive DJF rainfall over South China during 2021/2022. The diagnosis of the role of synoptic eddy on the atmospheric response to the external forcing for specific events can be helpful for understanding the causes for the formation of extreme climate events deeply.

Uncertainty qualification in evaluating dynamic and static stress intensity factors using SBFEM based on model order reduction

This paper presents a novel framework for Monte Carlo simulation (MCs) of dynamic and static fracture problems. The stress intensity factors can be directly extracted by using polygon scaled boundary finite element method (SBFEM) to analyze dynamic and static fracture problems. Uncertainty qualification analysis focuses on the output uncertainty caused by the uncertainty of system input. MCs is considered as a general tool to solve complex multi-dimensional uncertainty problems because of its simplicity and directness. However, its applicability is hindered due to the huge calculating cost. The use of singular value decomposition (SVD) and radial basis function (RBF) can reduce the computational cost, improve the computational efficiency, and realize the rapid uncertainty qualification analysis based on MCs. Considering the influence of uncertainty of structural material property parameters and structural shape parameters on the calculation results, MCs is used to analyze the statistical characteristics of structural response under random variables. Finally, several examples are given to verify the correctness and effectiveness of the algorithm.

A Hörmander–Fock space

ABSTRACT In a recent paper, we used a basic decomposition property of polyanalytic functions of order 2 in one complex variable to characterize solutions of the classical ∂ ¯ -problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander–Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by η = ( η n ) n ≥ 0 leading to a special entire function E ( z ) that is used to express the kernel function of the Hörmander–Fock space. We present also an example of a special function belonging to the class Mittag-Leffler (ML) introduced recently by Alpay et al. and apply a Bochner–Minlos type theorem to this function, thus motivating further connections with the theory of stochastic processes.

Spectral response between particle and fluid kinetic energy in decaying homogeneous isotropic turbulence

In particle-laden turbulence, the Fourier Lagrangian spectrum of each phase is regularly computed, and analytically derived response functions relate the Lagrangian spectrum of the fluid and the particle phase. However, due to the periodic nature of the Fourier basis, the analysis is restricted to statistically stationary flows. In the present work, utilizing the bases of time-focalized proper orthogonal decomposition (POD), this analysis is extended to temporally non-stationary turbulence. Studying two-way coupled particle-laden decaying homogeneous isotropic turbulence for various Stokes numbers, it is demonstrated that the temporal POD modes extracted from the dispersed phase may be used for the expansion of both fluid and particle velocities. The POD Lagrangian spectrum of each phase may thus be computed from the same set of modal building blocks, allowing the evaluation of response functions in a POD frame of reference. Based on empirical evaluations, a model for response functions in non-stationary flows is proposed. The related energies of the two phases is well approximated by simple analytical expressions dependent on the particle Stokes number. It is found that the analytical expressions closely resemble those derived through the Fourier analysis of statistically stationary flows. These results suggest the existence of an inherent spectral symmetry underlying the dynamical systems consisting of particle-laden turbulence, a symmetry which spans across stationary/non-stationary particle-laden flow states.

The Transient Performance-Evaluation Model for Desalination of Seawater Based on Matrix Algorithm – a Requirement for a Ported Arabic Smart City

Abstract Based on the transient performance model for desalination of seawater based on the matrix algorithm, the desalination device is designed according to the evaporation condensation mechanism of falling film in horizontal tube, and its structure operation and operation principle are analyzed. Then, the differential equation of the transient heat-conduction problem of the seawater desalination device is constructed. On the basis of experimental data or numerical calculation results, the temperature field of structure at some time is selected to form the snapshots matrix, and a set of optimal eigenorthogonal decomposition bases is obtained by eigenorthogonal decomposition of the snapshots matrix. Finally, the finite-element discrete scheme of the nonlinear transient heat-conduction problem is reduced by using eigenorthogonal decomposition bases of the linear problem, and the lower-order ordinary differential equations of the reduced-order model for the nonlinear transient heat-conduction problem of the seawater desalination device are obtained. The ordinary differential equations of the reduced-order model are solved by solving the ordinary differential equations of the reduced-order model. The distribution of the temperature field at each time of the structure is obtained. The performance of the model is verified by numerical examples under the conditions of two-stage temperature-difference heating and only the top-level heating. The results show that the model has good accuracy and efficiency.

A data-driven model reduction method for parabolic inverse source problems and its convergence analysis

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems with uncertain data efficiently. Our method consists of offline and online stages. In the offline stage, we explore the low-dimensional structures in the solution space of parabolic partial differential equations (PDEs) in the forward problems with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension reduction. Equipped with the POD basis functions, we can solve the forward problems extremely fast in the online stage. Thus, we develop a fast algorithm to solve the optimization problem in parabolic inverse source problems, which is referred to as the POD method. Moreover, we design an a posteriori algorithm to find the optimal regularization parameter in the optimization problem using the proposed POD method without knowing the noise level. Under a weak regularity assumption on the solution of the parabolic PDEs, we prove the convergence of the POD method in solving the forward parabolic PDEs. In addition, we obtain the error estimate of the POD method for parabolic inverse source problems. Finally, we present numerical examples to demonstrate the accuracy and efficiency of the proposed method. Numerical results show that the POD method provides considerable computational savings over the finite element method while maintaining the same accuracy.

Damage location diagnosis of frame structure based on wavelet denoising and convolution neural network implanted with Inception module and LSTM

Accurate diagnosis of the damage location of the frame structure is very important for the overall damage assessment and subsequent maintenance of the frame structure. However, the frame structure generally works in the noise environment, which increases the difficulty of health monitoring and fault diagnosis of frame structure based on vibration data. In order to realize the accurate damage location diagnosis of structural frame under noise environment, this paper proposes a fault diagnosis method based on wavelet denoising, convolutional neural network, Inception module, and long short-term memory (LSTM) on the basis of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In order to verify the effectiveness and superiority of the method proposed in this paper, the 4-story steel frame model of the University of British Columbia is taken as the research object, and the experiments are carried out with the method proposed in this paper, and under the same conditions, the comparative experiments are carried out with other similar methods. The experimental results show that the method proposed in this paper not only has high accuracy, but also has strong anti-noise ability, and its performance is better than other similar methods. Therefore, the fault diagnosis method proposed in this paper can effectively perform the accurate diagnosis of damage location of frame structure under noise environment.

Statistical inference for high-dimensional panel functional time series

AbstractIn this paper, we develop statistical inference tools for high-dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high-dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the panel dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data.

Mineral quantitative characterization method based on basis material decomposition model by dual-energy computed tomography.

Dual-energy computed tomography (DECT) can reconstruct electron density ρe and effective atomic number Zeff distribution for material discrimination. Image-domain basis material decomposition (IBMD) method is a widely used DECT method. However, IBMD method cannot be used for mineral identification directly due to limitations of complex basis material determination, beam hardening artifacts, and inherent errors caused by approximate empirical formulas. This study proposes an improved IBMD (IIBMD) method to overcome the above limitations. In IIBMD method, the composition of basis material is optimized to obtain accurate decomposition coefficients, which enables accurate ρe and Zeff distribution. Moreover, the thickness of basis material is optimized to reduce the effect of beam hardening. Furthermore, two formulas in place of empirical formulas are proposed to calculate ρe and Zeff. Finally, a threshold technique is applied to separate different mineral phases. Numerical simulations and practical experiments using a photon-counting detector CT system are implemented to verify IIBMD method. Results show that the relative errors of ρe and Zeff for seven common minerals are down to 5%, lower than most of the existing DECT methods for rocks. Reasonable volume fraction results of mineral phases are thus obtained through threshold segmentation. This study demonstrates that the proposed IIBMD method has high practical value in mineralogical identification.

Comparison of the Effect of NaOH Pretreatment and Microbial Agents on Rice Straw Decomposition

Rice straw contains a large amount of lignocellulose which is difficult to be decomposed. The objective of this study was to determine the effect of alkaline pretreatment (sodium hydroxide, NaOH) and microbial agents on the decomposition of rice straw. The experimental detail consisted of NaOH (control and NaOH solution pretreatment) and microbial agent (Bacillus licheniformis agent, Bacillus subtilis agent, Trichoderma viride agent, and no microbial agent) treatments. Compared with no NaOH pretreatment, the pH of NaOH pretreatment increased by 6.30–18.28%, while the electrical conductivity decreased by 49.18%, but the change in total nutrient content was not obvious. Under no NaOH pretreatment, Bacillus subtilis agent improved the temperature of the rice straw decomposition. Compared with Bacillus licheniformis agent and Trichoderma viride agent, Bacillus subtilis agent increased the alkali-hydrolyzable nitrogen, available phosphorus, and available potassium in rice straw by 1.39–10.30%. The organic carbon content was reduced by 3.50% and 17.15%. The germination index was greater than 80%. Under NaOH pretreatment, the pile with Bacillus subtilis agent reached the maximum temperature (39.5 °C) on the 12th day. Compared with Bacillus licheniformis agent and Trichoderma viride agent, Bacillus subtilis agent increased the content of alkali-hydrolyzable nitrogen and available phosphorus in rice straw by 1.64–11.87%. The humus polymerization, organic carbon, and carbon/nitrogen ratio were reduced by 6.40–44.06%. In addition, gray analysis, principal component analysis, and comprehensive evaluation were used to comprehensively evaluate the effect of straw decomposition. The results showed that Bacillus subtilis agent under NaOH pretreatment and no NaOH pretreatment had the most obvious effect on rice straw composting. This study provides a scientific basis for efficient decomposition of rice straw.