Basis Of Decomposition Research Articles

Prediction of proton stopping power ratios using dual-energy CT basis material decomposition.

Proton radiotherapy treatment plans are currently restricted by the range uncertainties originating from the stopping power ratio (SPR) prediction based on single-energy computed tomography (SECT). Various studies have shown that multi-energy CT (MECT) can reduce the range uncertainties due to medical implant materials and age-related variations in tissue composition. None of these has directly applied the basis material density (MD) images produced by projection-based MECT systems for SPR prediction. To present and evaluate a novel proton SPR prediction method based on MD images from dual-energy CT (DECT), which could reduce the range uncertainties currently associated with proton radiotherapy. A theoretical basis material decomposition into water and iodine material densities was performed for various pediatric and adult human reference tissues, as well as other non-tissue materials, by minimizing the root-mean-square relative attenuation error in the energy interval from 40 to 140keV. A model (here called MD-SPR) mapping predicted MDs to theoretically calculated reference SPRs was created with locally weighted scatterplot smoothing (LOWESS) data-fitting. The goodness of fit of the MD-SPR model was evaluated for the included reference tissues. MD images of two electron density phantoms, combined to form a head- and an abdomen-sized phantom setup, were acquired with a clinical projection-based fast-kV switching DECT scanner. The MD images were compared to the theoretically predicted MDs of the tissue surrogates and other non-tissue materials in the phantoms, as well as used for input to the MD-SPR model for generation of SPR images. The SPR images were subsequently compared to theoretical reference SPRs of the materials in the phantoms, as well as to SPR images from a commercial algorithm (DirectSPR, Siemens Healthineers, Forchheim, Germany) using image-based consecutive scan DECT for the same phantom setups. The predicted SPRs of the tissue surrogates were similar for MD-SPR and DirectSPR, where the adipose and bone tissue surrogates were within 1% difference to the reference SPRs, while other non-adipose soft tissue surrogates (breast, brain, liver, muscle) were all underestimated by between -0.7% and -1.8%. The SPRs of the non-tissue materials (polymethyl methacrylate (PMMA), polyether ether ketone (PEEK), graphite and Teflon) were within 2.8% for MD-SPR images, compared to 6.8% for DirectSPR. The MD-SPR model performed similar compared to other published methods for the human reference tissues. The SPR prediction for tissue surrogates was similar to DirectSPR and showed potential to improve SPR prediction for non-tissue materials.

Decompositions of the Kadomtsev–Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture, we carefully explain the basic decompositions for the Kadomtsev–Petviashvili (KP) equation as well as the necessary calculation procedures, and it is shown that the KP equation allows the Burgers–STO (BSTO) decomposition, two types of reducible coupled BSTO decompositions and the BSTO–KdV decomposition. Furthermore, we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions. Using the framework of standard Lie point symmetry theory, these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

Surrogate Modelling of Field Performance Analysis and Optimization via Hierarchical Proper Orthogonal Decomposition and Adaptive Sampling Radial Basis Function

Surrogate Modelling of Field Performance Analysis and Optimization via Hierarchical Proper Orthogonal Decomposition and Adaptive Sampling Radial Basis Function

Management model in the conditions of digitalization of business environment in the regional ecosystem

It is recognized that the role of business environment management in the regional ecosystem is paramount to ensure the balanced development of all ecosystem elements. This is made possible based on the prerequisites for digital transformation that have been created. There is a need for a management model that will bring the spontaneity of the region’s entrepreneurial environment into line, strengthen its vector momentum in increasing the activity of the ecosphere of the territory, and allow choosing the best solutions. The study aims to formation of a model for establishing interaction between the state and business in the framework of the Russian model of digitalization based on the study and development of scientific theories and ideas, best practices, research of the state and trends of entrepreneurial activity of the region and its ecosphere. Methods: fundamental theories of entrepreneurship and approaches to modern theoretical research on business environment management, knowledge within the framework of business environment management theory, concepts of regional ecosystem theory, digitalization models, and tools of meso-ecological models of the business environment. The model of establishing the interaction between the state and business in the region proposed is based on the study of theories, methods and analysis of the role and performance trends of the business environment. An adapted management model in the conditions of digitalization of the business environment is presented concerning the regional ecosystem based on the materials of the Strategy of Digital Transformation of Stavropol Territory. In the recommended model on a new technological basis decomposition of factors, agents of the mesoecological model of the business environment and factors of their assessment, the interaction of the business environment and its communication activity between all subjects are given.

Simulation of discrete control systems with parallelism of behavior

Objectives. The problem of functional verification of control devices with respect to their design specification is considered. When solving the problems of implementing and testing of discrete systems, one has to deal with the presence of parallelism in the behavior of interacting control objects, which is also displayed in the assignment for designing control systems. The aim of the work is to develop a method for simulating descriptions of such systems, which allows their behavior testing dynamically on the area limited by their possible functioning.Methods. The paper considers a class of control systems with parallelism of the processes occurring in them, which permits linearization of their execution. To specify the behavior of such control systems, it is proposed to use the PRALU language of parallel control algorithms, which is based on Petri nets and which allows to order events occurring during the device operation. An object-oriented approach to simulation of the description of the control algorithm at the transaction level is proposed. For this purpose, a TLM (Transaction-Level Modeling) model has been developed for describing the devices with behavior parallelism in PRALU language. The transaction level model describes a system as a set of interacting processes that run in parallel and determine the behavior of the system over time.Results. The key concepts of the TLM model for simulating the descriptions of control algorithms in the PRALU language are defined: data structure, transactions, processes, and a barrier mechanism for synchronization of parallel processes. A method is proposed for transforming the description of an algorithm in the language into a TLM model, which is based on the representation of language operations as compositions of elementary operations that are performed sequentially. The set of these operations forms the basis for the algorithmic decomposition of a parallel algorithm in PRALU language into intermediate language program that is executed strictly sequentially. Translators of this program into the Verilog and C languages have been developed, the results of their compilation are simulators of the behavior of control system.Conclusion. The proposed simulation method can be used to create a test bench for functional verification of the circuit implementation of control devices with behavior parallelism. In this case, test sequences for verifying the circuit implementation can be generated dynamically – in the process of simulating the description of the algorithm in the PRALU language directly the control device or system, which include the control algorithm and the algorithms of controlled objects behavior.

Coal structure identification based on geophysical logging data: Insights from Wavelet Transform (WT) and Particle Swarm Optimization Support Vector Machine (PSO-SVM) algorithms

Coal structure is closely related to microscopic and macroscopic properties of coal, and its accurate identification is of great significance to coalbed methane (CBM) reservoir evaluation, hydraulic fracturing performance and production efficiency prediction. The identification of coal structure based on geophysical logging data has become a popular topic as well as a challenge. The emerging Machine Learning (ML) provides convenience for this issue. Under this background, in the case of the Shanxi Formation No. 3 coal seam and the Taiyuan Formation No. 15 coal seam in Mabidong Block, Qinshui Basin, China, this paper proposed a new coal structure identification method based on geophysical logging data using Wavelet Transform (WT) and Particle Swarm Optimization Support Vector Machine (PSO-SVM) algorithms. Our results showed that the vertical resolution of logging data can be effectively improved when sym5 wavelet basis and third level decomposition were selected in wavelet decomposition, and 4.5 was selected as the weighting coefficient in wavelet reconstruction. The coal structure prediction model based on the logging data processed by WT was established by PSO-SVM algorithm, where PSO was used for parameter optimization (optimal penalty factor C and width parameter σ) and SVM with Radial Basis Function (RBF) kernel was used for model establishment. The Hold-out Cross Validation (HO CV) method was used to test the generalization ability of the prediction model, and the accuracy (ACC) of coal structure prediction in the training set and testing set was 94.26% and 88.46%, respectively. The prediction model was applied to identify the coal structure of two coring wells and the predicted coal structure class was consistent with the true coal structure class, confirming the validity of the model. The coal structure prediction results in the whole study area showed that the tectonic conditions control the coal structure. This work provides new insights for coal structure identification.

Quasidifferentiability and Uniform Observability of Linear Time-Varying Singularly Perturbed Systems

For linear time-varying singularly perturbed systems (LTVSPS) with quasidifferentiable coefficients and a small parameter multiplying some derivatives, the problem of uniform observability is considered. Necessary and sufficient conditions for the quasidifferentiability of the set of output functions independent of the small parameter are proved, observability matrices independent of the small parameter for the slow subsystem and the family of fast subsystems associated with the LTVSPS are constructed, and a connection is established between them and the observability matrix of the original system. On the basis of the complete decomposition of the original LTVSPS with respect to the action of the group of linear nonsingular transformations, we prove rank sufficient conditions for the uniform observability of the LTVSPS that are independent of the small parameter and valid for all sufficiently small values of it. The conditions are expressed in terms of the observability matrices of the slow subsystem and the family of fast subsystems of smaller dimensions than the original LTVSPS.

PauliComposer: compute tensor products of Pauli matrices efficiently

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is benchmarked against state-of-the-art techniques, showing a remarkable acceleration. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians.

Adaptive detection of tool-workpiece contact for nanoscale tool setting based on multi-scale decomposition of force signal

Due to tool wear under long-time and long-distance cutting, it is inevitable to change the tool to achieve relay machining. However, the existing tool setting methods based on visual inspection and trial cutting have the problems of low precision and complicated process, resulting in low precision and poor consistency of surface quality in relay machining. In order to solve the above problems, this paper proposes a method to detect the contact status between the tool and the workpiece with the discrete wavelet transform (DWT) of force signal to realize the nanoscale tool setting. Firstly, a weighted smoothness evaluation metric is proposed to guide the selection of wavelet basis function and decomposition scale of DWT to achieve noise suppression and impact signal enhancement. Then, the force signal processed by DWT under the optimal parameters is input to density-based spatial clustering of applications with noise (DBSCAN) to detect the contact status between the tool and the workpiece. The parameters selection of DBSCAN is adaptively realized by differential evolution (DE) algorithm so as to improve the accuracy of the contact detection. Finally, ultra-precision tool setting experiments were carried out on the single-point diamond turning tools with a radius of 10um and workpieces with various materials such as brass, copper and red copper. The results show that the wavelet basis function and decomposition scale with the minimum value of the proposed metric are optimal for the task. In analysis of force signals with different signal-to-noise ratios (1 dB, 5 dB, 12.5 dB, 20 dB), the proposed metric all works well. In terms of the contact detection between the tool and workpiece, the proposed method achieves 0 % false positive rate compared to other detection methods, and the corresponding tool setting accuracy is about 3 nm, which is much higher than the traditional tool setting method.

An Improved Ensemble-Strategy-Assisted Wind Speed Prediction Method for Railway Strong Wind Warnings

Reliable short-term wind speed prediction is one of the core technologies in the strong wind warning system for railway applications, which is of great significance for ensuring the safety of high-speed train operations and ancillary railway facilities. To improve forecasting accuracy, decomposition-based methods have attracted extensive attention due to their superior ability to address complex data characteristics (e.g., nonstationarity and nonlinearity). Currently, there are two pre-processing schemes for decomposition-based methods, i.e., one-time decomposition and real-time decomposition. In order to apply them better, this paper first expounds the difference between them, based on a combination of DWT (discrete wavelet transform) and CKDE (conditional kernel density estimation). The results show that although the one-time decomposition-based method has an unexceptionable accuracy, it only can provide offline prediction and thus may not be practical. The real-time decomposition-based method possesses stronger practicability and is able to provide online prediction, but it has limited accuracy. Then, an improved ensemble strategy is developed by optimizing the selection of appropriate decomposed components to conduct the prediction on the basis of real-time decomposition. This improved ensemble strategy provides an effective guidance for this selective combination, including taking historical information into consideration in the data. Finally, numerical examples and practicality analysis using two groups of measured wind speed data demonstrate that the proposed method is effective in providing high-precision online wind speed prediction. For example, compared with CKDE, the average degrees of improvement achieved by the proposed method in terms of MAE, RMSE, and MRPE, are 16.25%, 17.66%, and 16.93, respectively, while those compared with the traditional real-time decomposition method are 17.11%, 18.54%, and 16.84, respectively.

Benefit evaluation analysis of new energy power consumption information collection with basic steady-state harmonic characteristics

Abstract In this paper, firstly, the load monitoring characteristics of new energy power consumption are studied and analyzed in terms of both steady-state and transient characteristics, and suitable characteristic values are selected for different types as the basis of load decomposition. A comparative analysis of various types of load imprints is conducted to highlight the advantages of steady-state harmonic features as load monitoring feature data. Then, an evaluation model of the demand response potential of electricity information collection is established based on a multi-objective optimization algorithm, and technical and economic analysis of electricity information collection is carried out to evaluate the response potential of power companies collecting customer data. Finally, the situation and benefits of collecting electricity consumption information for new energy power are analyzed. The daily maximum load moments of typical users are all cut by more than 10%, the peak load portion cut by more than 97% is also more obvious, and the maximum moments of valley filling response are all more than 11%. D Power saved a total of 3.759 billion yuan in labor costs by reducing labor costs by 400 million yuan after adopting electricity consumption information collection. The indices of excellent and qualified management benefit and social benefit evaluation of electricity consumption information collection are above 0.8. Overall, the benefits of electricity consumption information collection for new energy power with basic steady-state harmonic characteristics are significant and effective.

A multi-modal multi-objective evolutionary algorithm based on dual decomposition and subset selection

Multi-modal multi-objective problems (MMOPs) arise frequently in real world applications, in which multiple Pareto-optimal solution sets (PSs) correspond to the same point on the Pareto front (PF). Diversity preservation is a crucial issue in multi-modal multi-objective evolutionary algorithms (MMOEAs), which aims at evolving the population toward the PF and equivalent PSs with a uniform distribution and good spread. In spite of many diversity preservation approaches in MMOEAs, most of them guarantee the diversity in decision space with a degraded performance in objective space. To address the above issues, this article proposes a MMEA based on dual decomposition and subset selection, which employes the weight vectors and grids to decompose both the objective and decision spaces. On the basis of dual decomposition, the mating selection are adaptively performed based on estimated optimization stages of current subproblem. Moreover, a subset with good diversity in both the objective and decision spaces are selected from the promising solutions ever collected during the evolution process. Experimental results on 22 benchmark problems demonstrate our advantages to maintain a more balanced diversity in both objective and decision spaces.© 2017 Elsevier Inc. All rights reserved.

Accurate expression of neck motion signal by piezoelectric sensor data analysis

The development of high-precision sensors using flexible piezoelectric materials has the advantages of high sensitivity, high stability, good durability, and lightweight. The main problem with sensing equipment is low sensitivity, which is due to the mismatch between materials and analysis methods, resulting in the inability to effectively eliminate noise. To address this issue, we developed the denoising analysis method to motion signals captured by a flexible piezoelectric sensor fabricated from poly(l-lactic acid) (PLLA) and polydimethylsiloxane (PDMS) materials. Experimental results demonstrate that this improved denoising method effectively removes noise components from neck muscle motion signals, thus obtaining high-quality, low-noise motion signal waveforms. Wavelet decomposition and reconstruction is a signal processing technique that involves decomposing a signal into different scales and frequency components using wavelets and then selectively reconstructing the signal to emphasize specific features or eliminate noise. The study employed the sym8 wavelet basis for wavelet decomposition and reconstruction. In the denoised signals, a high degree of stability and periodic peaks are distinctly manifested, while amplitude and frequency differences among different types of movements also become noticeably visible. As a result of this study, we are enabled to accurately analyze subtle variations in neck muscle motion signals, such as nodding, shaking the head, neck lateral flexion, and neck circles. Through temporal and frequency domain analysis of denoised motion signals, differentiation among various motion states can be achieved. Overall, this improved analytical approach holds broad application prospects across various types of piezoelectric sensors, such as healthcare monitoring, sports biomechanics.

Deformation decomposition method of discrete element for irregular structures

In order to satisfy the demand of quantitative analysis of deformation properties of arbitrary irregular structures, a deformation decomposition method for arbitrary triangular element and arbitrary tetrahedral element is proposed based on mechanical equilibrium and mathematical orthogonality. The projection coefficients of various basic deformations of the structure can be obtained by applying the deformation decomposition method to the model divided by triangular or tetrahedral element. The quantitative and visual analysis of the structural deformation performance are realized. The work can provide theoretical basis for the orthonormal decomposition of arbitrary irregular elements and greatly improve the orthonormal deformation decomposition method.

Deep learning methods for blood flow reconstruction in a vessel with contrast enhanced x-ray computed tomography.

The reconstruction of blood velocity in a vessel from contrast enhanced x-ray computed tomography projections is a complex inverse problem. It can be formulated as reconstruction problem with a partial differential equation constraint. A solution can be estimated with the a variational adjoint method and proper orthogonal decomposition (POD) basis. In this work, we investigate new inversion approaches based on PODs coupled with deep learning methods. The effectiveness of the reconstruction methods is shown with simulated realistic stationary blood flows in a vessel. The methods outperform the reduced adjoint method and show large speed-up at the online stage.

A novel memory stabilization controller design for descriptor Markovian jump systems with time-varying delays

This paper is focused on the stochastic stability and controller design of descriptor Markovian jump systems with time-varying delays. For achieving this goal, systems are decomposed into differential-algebraic equations firstly. A modified mode-dependent Lyapunov-Krasovskii functional (LKF) and a memory state feedback controller are constructed on the basis of the state decomposition. Then, combining the auxiliary functions integral inequality and the extended reciprocally convex matrix inequality (ERCMI), an ameliorative stochastic stability criterion is obtained. Based on this novel stability condition, the designed controller is used to make sure the closed-loop systems are stochastically stable. Finally, the effectiveness of presented results is confirmed with some numerical examples.

SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.

Nonlinear and chaos features over EMD/VMD decomposition methods for ictal EEG signals detection

The detection and identification of epileptic seizures attracted considerable relevance for the neurophysiologists. In order to accomplish the detection of epileptic seizures or equivalently ictal EEG states, this paper proposes the use of nonlinear and chaos features not computed over the raw EEG signals as it was commonly experienced, but instead over intrinsic mode functions (IMFs) extracted subsequently to the application of newly time-frequency signal decomposition methods on the basis of empirical mode decomposition (EMD) and variational mode decomposition (VMD) methods. The first step within the proposed methodology is to excerpt the various components of the IMFs by EMD and VMD decomposition methods on time EEG segments. The Hjorth parameters, the Hurst exponent, the Recurrence Quantification Analysis (RQA), the detrended fluctuation analysis (DFA), the Largest Lyapunov Exponent (LLE), The Higuchi and Katz fractal dimensions (HFD and KFD), seven nonlinear and chaos features computed over the IMFs were investigated and their classification performances evaluated using the k-nearest neighbor (KNN) and the multilayer perceptron neural network (MLPNN) classifiers. Furthermore, the combination of the best nonlinear features has also been examined in terms of sensitivity, specificity and overall classification accuracy. The publicly available Bonn EEG dataset has been has been employed to validate the efficiency of the proposed method for detecting ictal EEG signals from normal or interictal EEG segments. Among the several experiments involved in the current study, the ultimate results establish that the overall classification accuracy can achieve 100%, 99.45%, 99.8%, 99.8%, 98.6% and 99.1% for six different epileptic seizure detection case problems studied, confirming the ability of the proposed methodology in helping the clinic practitioners in the epilepsy detection care units to classify seizure events with a great confidence.

Design of Discrete and Hybrid Nonlinear Control Systems

In this article the new method of discrete control systems design for nonlinear plants with differentiable nonlinearities is suggested. The increasing demands on the quality of control processes and the widespread use of computer technology provide ample opportunities for the design and implementation of digital control systems. However, discrete models of control plants are needed to solve this problem. In the case of linear plants, such models are created on the basis of z-transformation, Euler or Tustin formulas. In the case of nonlinear plants, these transformations are not applicable, so a large number of approximate discretization methods have been developed to date. Euler and Runge-Kutt transformations are used for these purposes most often, but they lead to satisfactory results only with very small period of discretization. In the case of automatic control systems, this requires the use of digital automation tools with very high speed, which is often economically impractical. Methods of discretization with a long period were most often developed on the basis of decomposition into series of the right-hand sides of the differential equations, transformed on Euler. Here, firstly, the problem of selecting the number of the series members, which to be retained arises, and secondly, already in the third or fourth order of the plant, the calculating ratios turn out to be extremely complex. The discretization method suggested below differs in that it is not the equations of nonlinear plants in the Cauchy form that are discretized, but the corresponding quasilinear model. In this case, a modified trapezoid method is used, and the discretization purpose is not the most accurate approximation of the original equations of the plant, but the stability of a closed nonlinear control system with rather big period. This system is designed using the algebraic polynomial-matrix method for designing of the nonlinear control systems. As a result, a hybrid nonlinear system with fairly simple algebraic calculation expressions is formed. The suggested approach makes it possible to create the control systems for nonlinear controlled plants using conventional computational automation tools.

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.