Decomposition Scheme Research Articles

A decomposition scheme for continuous Level of Detail, streaming and lossy compression of unordered point clouds

Modern laser scanners, depth sensor devices and Dense Image Matching techniques allow for capturing of extensive point cloud datasets. While capturing has become more user-friendly, the size of registered point clouds results in large datasets which pose challenges for processing, storage and visualization. This paper presents a decomposition scheme using oriented KD trees and the wavelet transform for unordered point clouds. Taking inspiration from image pyramids, the decomposition scheme comes with a Level of Detail representation where higher-levels are progressively reconstructed from lower ones, thus making it suitable for streaming and continuous Level of Detail. Furthermore, the decomposed representation allows common compression techniques to achieve higher compression ratios by modifying the underlying frequency data at the cost of geometric accuracy and therefore allows for flexible lossy compression. After introducing this novel decomposition scheme, results are discussed to show how it deals with data captured from different sources.

Large-Scale Long-Term Prediction of Ship AIS Tracks via Linear Networks with a Look-Back Window Decomposition Scheme of Time Features

Approximating the positions of vessels near underwater devices, such as unmanned underwater vehicles and autonomous underwater vehicles, is crucial for many underwater operations. However, long-term monitoring of vessel trajectories is challenging due to limitations in underwater communications, posing challenges for the execution of underwater exploration missions. Therefore, trajectory prediction based on AIS data is vital in the fusion of underwater detection information. However, traditional models for underwater vessel trajectory prediction typically work well for only small-scale and short-term predictions. In this paper, a novel deep learning method is proposed that leverages a look-back window to decompose the temporal and motion features of ship movement trajectories, enabling long-term vessel prediction in broader sea areas. This research introduces an innovative model structure that enables trajectory features to be simultaneously learned for a larger range of vessels and facilitates long-term prediction. Through this innovative model design, the proposed model can more accurately predict vessel trajectories, providing reliable and comprehensive forecasting results. Our proposed model outperforms the Nlinear model by a 16% improvement in short-term prediction accuracy and an approximately 8% improvement in long-term prediction accuracy. The model also outperforms the Patch model by 5% in accuracy. In summary, the proposed method can produce competitive predictions for the long-term future trajectory trends of ships in large-scale sea areas.

The cumulative vehicle routing problem with arc time windows

In this paper, we introduce a new variant of the cumulative Vehicle Routing Problem (cum-VRP), where certain arcs of the undirected complete graph can only be utilized within specified time constraints. The problem is referred to as the Cumulative Vehicle Routing Problem with Arc Time Windows (Cum-VRPATW) and emerges in routing situations with flow disruptions across road segments, which generally emerges from military and civilian transportation. We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. To effectively address this problem, an effective algorithm is designed. It is a hybrid algorithm that combines principles of the Greedy Randomized Adaptive Search Procedure (GRASP) and decomposition strategies reducing computational complexity. Also, we propose two indexes, the RatioIn and the RatioTWL index that can identify difficult problems. Furthermore, we compare the CPLEX results vis-a-vis the new hybrid heuristic we have developed. Computational tests on converted Solomon (1987) data sets show that the new hybrid heuristic provides extremely good performance results for the cum-VRPATW large size test problems, justifying its effectiveness and robustness.

Adaptive task decomposition physics-informed neural networks

As a new approach for solving partial differential equations, physics-informed neural networks (PINNs) have received extensive attention in recent years and have made breakthroughs in various fields. Serving as a neural network-based universal solver, they possess advantages such as high continuity and being meshless. However, an increasing number of studies have pointed out that PINNs may fail to converge to accurate results when dealing with complex tasks. In this paper, we highlight the differences between training PINNs and regular neural network tasks, summarizing three key characteristics of training PINNs. Based on these findings, we propose a strategy of task decomposition and progressive learning, which successfully explains the effectiveness of existing methods for time-dependent problems and reveals their limitations. For time-dependent and time-independent problems, we partition the tasks into physically complete and progressively challenging sub-tasks. The division is based on the resolution requirements for time-independent problems and the coverage of the time domain for time-dependent problems. Through task parameters and the decomposition of the loss terms, we adaptively control the progressive increase in task complexity during the training process. The proposed method overcomes the limitations of existing approaches, incurs no additional computational cost, and is applicable to both time-dependent and time-independent problems, demonstrating higher generality. Furthermore, building upon the concepts of task decomposition and progressive learning, we introduce a stable and efficient minibatch training method for the first time. In a series of numerical experiments on baseline PDE problems, our approaches outperformed other state-of-the-art algorithms.

Cost minimizing decisions on equipment and charging schedule for electric buses in a single depot

Combined decisions on equipment and charging schedule for electric buses (e-buses) are studied in this paper. The most representative day is considered, in which each e-bus fulfills a transfer task composed of a series of passenger transportation trips. Each trip starts and terminates at given times in the same single depot where e-buses re-charge their batteries. The problem is to determine battery variants for the e-buses, number of chargers of different types and daily cyclic charging schedule of e-buses such that a linear combination of (a) the total daily cost of the charging equipment, batteries wear and consumed energy, and (b) the total number of e-bus charging interruptions (switchings) is minimized. The constraints include an upper bound on the supplied electric power, restoration of the initial battery energy state before the next day transfer task for each e-bus and an upper bound on the maximal number of switchings for each e-bus in each depot visit over all e-buses and visits. A bi-level decomposition approach is proposed, in which decisions and constraints related to the detailed charging schedule and the number of switchings are moved to the lower-level problem. The lower level problem is formulated as Mixed Integer Linear Programming (MILP) problem. The upper-level problem is reduced to a MILP problem using linearization techniques. An exact decomposition scheme is developed for the upper-level MILP problem. A case study and comprehensive computer experiments are provided.

The dynamic factor particle swarm optimization (DFPSO) to inverse kinematics of CMOR based on pose decomposition strategy

The Chinese Fusion Engineering Testing Reactor (CFETR) is a superconducting Tokamak device, whose components would get gradually damaged by being susceptible to high temperature, strong magnetic field, radiation, and so on, and should be maintained regularly. The CFETR Multipurpose Overload Robot (CMOR) is a redundant robot designed as a macro-micro arm structure for a gigantic workspace in the blanket and diverter of CFETR's maintenance. Due to the macro-micro arm structure, the robot has a high degree of freedom, and its serial DOF is up to 16 so the traditional algorithm is low efficient for the robot's kinematics. Hence, in this paper, a kinematic decomposition strategy is proposed to allocate or decouple the position aim. Besides, a novel particle swarm optimization (PSO) with dynamic accuracy called dynamic factor particle swarm optimization (DFPSO) is designed to accelerate solving the high-dimensional nonlinear kinematic problem and to improve accuracy. The results of the research show the validation and efficiency of DFPSO in the CMOR system's kinematics. Moreover, it's also a universal kinematic algorithm for all high-DOF robots.

Iterative space-angle discontinuous Galerkin method for radiative transfer equation

The radiative transfer equation (RTE) is an integro-differential equation that describes the radiation energy absorbing, emitting, and scattering in both space and angle, which can be up to five-dimensional problems. It is difficult for a RTE solver to satisfy both accuracy and efficiency (less computational resources) for such high dimensional problems. In this paper, an iterative solver for one-dimensional cylindrical radiative transfer problems using the space-angle discontinuous Galerkin (DG) method is developed to achieve both accuracy and efficiency. The iterative solver is based on the angular decomposition (AD) scheme, which slices the spatial-angular domain into slabs and decouples the angular integration between slabs. Both Jacobi and successive over-relaxation (SOR) iterative schemes are investigated by numerical analysis and examples. The comparison of the two iterative schemes suggests that an appropriate relaxation factor for the SOR method may accelerate the convergence. Finally, the iterative scheme is more efficient than the direct solution of the system both in terms of memory usage and computational time, especially for finer meshes.

Decomposition of <i>P</i><sub>6</sub>-Free Chordal Bipartite Graphs

Canonical decomposition for bipartite graphs, which was introduced by Fouquet, Giakoumakis, and Vanherpe (1999), is a decomposition scheme for bipartite graphs associated with modular decomposition. Weak-bisplit graphs are bipartite graphs totally decomposable (i.e., reducible to single vertices) by canonical decomposition. Canonical decomposition comprises series, parallel, and K + S decomposition. This paper studies a decomposition scheme comprising only parallel and K + S decomposition. We show that bipartite graphs totally decomposable by this decomposition are precisely P6-free chordal bipartite graphs. This characterization indicates that P6-free chordal bipartite graphs can be recognized in linear time using the recognition algorithm for weak-bisplit graphs presented by Giakoumakis and Vanherpe (2003).

Linear Time Electromigration Analysis Based on Physics-Informed Sparse Regression

In this work, we propose a novel physics-informed sparse regression (PISR) framework to solve stress evolution (described by Korhonen’s equations) in general multi-segment wires using an unsupervised learning scheme. Unlike the existing physics-informed neural network framework (PINN), the PISR method trains the trainable weights through the Moore-Penrose generalized inverse algorithm used in extreme learning machine (ELM), which is extremely faster than the back-propagation algorithm. To improve the accuracy of PISR for complex multi-segment interconnects, we employ domain decomposition schemes in both space and time. For each subdomain, we use different trainable weights but the same shared neural network to represent each subsolution, which leads to more efficient memory usage. Furthermore, we propose to use sparse matrix techniques to accelerate the training speed of the PISR method and prove that the resulting PISR has linear time complexity for analyzing tree-structured interconnects. Finally, we divide the time into many time internals and apply an autoregressive model to simulate each time interval in sequence to further improve scalability and reduce memory cost so that the PISR method can perform EM analysis for large-scale multi-segment interconnects. Experimental results on different kinds of interconnect structures show that the proposed PISR method has the same accuracy level as the numerical methods. The results on NT T-junctions interconnect trees show that the proposed PISR method indeed demonstrates true linear time complexity. Furthermore, PISR can deliver 8.9×, 20.6×, and 1284× speedups over the recently proposed semi-analytic method (ASOV), finite difference method accelerated with model order reduction (FDM-MOR), FDM for the interconnect with NT= 5000, respectively. Furthermore, we show that PISR also achieves an 818× speedup in training over the plain PINN method based on the traditional back-propagation algorithm.

A novel enterprise credit risk rating model with the perspective of multiple regulatory demands

With the number of market participants rising, the issue of contradiction between heavy supervision task and insufficient supervision resource have become increasingly urgent for regulatory authorities to consider. The credit risk rating of enterprises is therefore introduced to improve the efficiency of supervision. By analyzing the purposes of enterprise credit risk rating and the multiple demands for regulatory authorities, this paper offers a multi-classification ensemble model with hybrid decomposition strategy and two-stage multi-objective feature selection. First, an adaptive resampling technique is introduced into the hybrid decomposition strategy for multi-classification, so to appropriately allocate supervision resources in each credit risk class. Then, a two-stage multi-objective feature selection method is developed to combine the various demands of regulatory authorities for feature selection. In the first stage, results of multiple Filter feature selection methods are integrated as output to improve the performance of feature information; In the second stage, the feature information from the first stage is used as input to guide the Wrapper feature selection, which is based on the Improved Multi-objective Ant Colony Optimization. Finally, a real listed enterprise credit dataset of China is used to evaluate the performance of each module and the entire model. The empirical results show that the design of hybrid decomposition strategy and multi-objective feature selection can not only deal with the class-imbalanced problem during the decomposition process, but also take into account the balance of each demand well. More importantly, a desirable framework is set in this paper to simplify the process from imbalanced multi-classification to a balanced binary one.

Intriguing type-II g-GeC/AlN bilayer heterostructure for photocatalytic water decomposition and hydrogen production

Adapting two-dimensional (2D) van der Walls bilayer heterostructure is an efficient technique for realizing fascinating properties and playing a key role in solar energy-driven water decomposition schemes. By means of first-principles calculations, this study reveals the intriguing potential of a novel 2D van der Walls hetero-bilayer consisting of GeC and AlN layer in the photocatalytic water splitting method to generate hydrogen. The GeC/AlN heterostructure has an appropriate band gap of 2.05 eV, wherein the band edges are in proper energetic positions to provoke the water redox reaction to generate hydrogen and oxygen. The type-II band alignment of the bilayer facilitates the real-space spontaneous separation of the photogenerated electrons and holes in the different layers, improving the photocatalytic activity significantly. Analysis of the electrostatic potential and the charge density difference unravels the build-up of an inherent electric field at the interface, preventing electron–hole recombination. The ample absorption spectrum of the bilayer from the ultra-violet to the near-infrared region, reaching up to 8.71 × 105/cm, combined with the resiliency to the biaxial strain, points out the excellent photocatalytic performance of the bilayer heterostructure. On top of rendering useful information on the key features of the GeC/AlN hetero-bilayer, the study offers informative details on the experimental design of the van der Walls bilayer heterostructure for solar-to-hydrogen conversion applications.

A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians

A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear-equality-constrained optimization problems in which the objective function is defined by an expectation. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, wherein each search direction is computed as the sum of a normal step (toward linearized feasibility) and a tangential step (toward objective decrease in the null space of the constraint Jacobian). However, the proposed method is unique from others in the literature in that it both allows the use of stochastic objective gradient estimates and possesses convergence guarantees even in the setting in which the constraint Jacobians may be rank-deficient. The results of numerical experiments demonstrate that the algorithm offers superior performance when compared with popular alternatives. Funding: This material is based upon work supported by the U.S. National Science Foundation’s Division of Computing and Communication Foundations under award [CF-1740796], by the Office of Naval Research under award [N00014-21-1-2532], and by the National Science Foundation under award [2030859] to the Computing Research Association for the CIFellows Project.

Decomposition strategy and attention-based long short-term memory network for multi-step ultra-short-term agricultural power load forecasting

Accurate forecasting of the agricultural power load is important for rural electricity networks’ safe and stable operation. But it is more uncertain and difficult to forecast than industrial, commercial, and residential loads. Multivariate time series prediction methods have problems such as poor refinement of weather services and difficulty in quantifying the influencing factors. Univariate time series prediction methods should be emphasized, and the characteristic information in the historical load data should be fully exploited. Therefore, this paper systematically investigates the decomposition strategy and attention-based recurrent neural network for univariate time-series multi-step prediction. The decomposition strategy is employed to generate derived variable sequences from the target sequence as inputs for the model, while the dual-stage attention mechanism is used for dynamically selecting features. A one-year real-world dataset of agricultural power loads in southern China is used for validation. The effectiveness of two different decomposition algorithms on dual-stage attention-based recurrent neural network (DARNN) is discussed, then the proposed ensemble empirical mode decomposition and dual-stage attention-based recurrent neural network (EEMD-DARNN) is compared with four univariate time series prediction models and three ablation models. The proposed model is optimal in four evaluation indicators, with R2, RMSE, MAPE, and MAE of 0.970, 12.298, 0.040, and 7.335 respectively in the shortest forecast horizon (15 min), and 0.941, 17.305, 0.065 and 11.347 respectively in the longest forecast horizon (1 h). It is a significant improvement over the existing models. In conclusion, EEMD-DARNN can achieve more accurate ultra-short-term agricultural power load forecasting.

Enhanced robust multimode process monitoring under dirty data via difference-based decomposition of matrix

Traditional data-driven methods generally suppose the training dataset is not corrupted by outliers. However, outliers are inevitable in the real industrial processes even with a relatively high ratio, which degrades the accuracy of data-based models. For multimode process monitoring, outliers may deteriorate the accuracy of both mode identification and fault detection. However, the existing robust methods can hardly deal with a large percentage of outliers, i.e., dirty data in neither single nor multimode processes. In this paper, a robust multimode process monitoring scheme is developed by alleviating the negative effect of dirty data. A difference-based decomposition of matrix (DDM) algorithm is first proposed to divide the data into a basic subpart and a non-basic subpart. The optimization function of the proposed DDM algorithm is solved by the alternating direction method of multipliers (ADMM). In the off-line procedure, an iterative decomposition strategy is designed based on the proposed DDM approach to identify dirty data and obtain the clean dataset of each mode. In the on-line procedure, an on-line sample identification strategy is developed by the type indicator derived from the DDM algorithm to determine whether the current sample belongs to a mode, the dirty data, or the fault. A numerical example and an industrial-scale multiphase flow facility indicate the proposed method can improve the accuracy of both mode identification and fault detection for multimode processes even under dirty data.

Fractional view analysis of the diffusion equations via a natural Atangana-Baleanu operator

In this article, the natural transform decomposition method (NTDM) is applied to evaluate the fractional-order diffusion equations utilizing the Atangana-Baleanu operator. The method offers an efficient analytical solution by combining the natural transform methodology with a decomposition strategy. The suggested method incorporates non-local effects and memory qualities introduced by the Atangana-Baleanu operator while demonstrating adaptability and applicability to various fractional-order diffusion equations. In comparison to previous analytical techniques, the NTDM has demonstrated the lowest calculation volume and the highest rate of convergence. The obtained results are presented illustratively by using graphical simulations. The suggested method is therefore easily adaptable to other non-linear issues. The NTDM includes comparative analysis capabilities, practicality, and accurate results for researchers and practitioners. In order to solve fractional-order phenomena, particularly diffusion equations, NTDM is regarded as the best analytical technique.

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

A hybrid efficient and highly accurate spectral matrix technique is adapted for numerical treatments of a class of two-pint boundary value problems (BVPs) with singularity and strong nonlinearity. The underlying model is a reaction-diffusion equation arising in the modeling of biomedical, chemical, and physical applications based on the assumptions of Michaelis–Menten kinetics for enzymatic reactions. The manuscript presents a highly computational spectral collocation algorithm for the model combined with the quasilinearization method (QLM) to make the proposed technique more efficient than the corresponding direct spectral collocation algorithm. A novel class of polynomials introduced by S.K. Chatterjea is used in the spectral method. A detailed proof of the convergence analysis of the Chatterjea polynomials (ChPs) is given in the L2 norm. Different numerical examples for substrate concentrations with all values of parameters are performed for the case of planar and spherical shapes of enzymes. For validation, these results are compared with those obtained via wavelet-based procedures and the Adomian decomposition scheme. To further improve the approximate solutions obtained by the QLM–ChPs method, the technique of error correction is introduced and applied based on the concept of residual error function. Overall, the presented results with exponential convergence indicate that the QLM–ChPs algorithm is simple and flexible enough to be applicable in solving many similar problems in science and engineering.

Combined wind speed forecasting model based on secondary decomposition and quantile regression closed-form continuous-time neural network

ABSTRACT Reliable interval forecasts can quantify the potential risk of wind speeds, which can help people make better use of wind energy. In this study, a new probabilistic prediction model, called Quantile Regression Closed-Form Continuous-time Neural Network (QRCfC), is proposed by combining quantile regression and closed-form continuous-time neural network. A new combined model combining QRCfC, secondary decomposition, multi-objective optimization, and dynamic weight combination strategy is proposed, which makes full use of the advantages of each single model to obtain accurate deterministic prediction and reliable probabilistic interval prediction of wind speed. First, the original wind speed series is divided into several subseries using a secondary decomposition technique built on variational mode decomposition and singular spectrum analysis. Then, four base models are used to predict these subseries separately. After that, the predicted values of the four base models are input into QRCfC for training, where the hyperparameters of QRCfC are dynamically adjusted by a multi-objective ant lion optimization algorithm. Finally, to verify the effectiveness of the proposed models, experiments are conducted using data sets from three wind farms in Gansu, China. Simulation results show that the proposed model achieves excellent prediction performance in both deterministic and probabilistic prediction. For example, compared with the unoptimized quantile regression time convolution network, quantile regression long-short time memory, quantile regression gated recurrent unit, and quantile regression neural network, the proposed model reduces the MAPE by 21.89% and the CRPS by 11.14% for 1-step prediction at site 1.

Distributionally robust economic scheduling of a hybrid hydro/solar/pumped-storage system considering the bilateral contract flexible decomposition and day-ahead market bidding

A hybrid renewable energy system (HRES) utilizes the coaction of diverse energy to enhance energy efficiency while improving economic benefit. Under the paradigm of the electricity market, the HRES decomposes bilateral contract (BC) signed in the medium to long-term market and bids in the spot market are a promising way to get more revenue while ensuring basic profits by exploiting the synergy of different markets. However, the scheme of BC decomposition and the uncertainties of renewable energy affect the revenue of HRES scheduling. This paper proposes an optimal scheduling model for HRES to perform the BC flexible decomposition while bidding in the day-ahead energy market to maximize total revenue. The HRES is a real system located in Southwest China, and its constituent units are a pumped storage, two hydropower, and two solar stations. The Wasserstein metric ambiguity set is adopted to portray the uncertainty of available solar power and the forecasted market price error. Then, the proposed model is formulated as a distributionally robust chance-constrained scheduling model. Finally, the conditional value-at-risk approximation and strong duality are employed to reformulate this model into a tractable problem. The numerical results show that the proposed model can increase the total profit of HRES by 2.26 % (i.e., 2.56 × 104 DKK) compared to the case of fixed BC decomposition and bidding. Moreover, the impact analysis related to the ambiguity set and risk tolerance of uncertainty on total revenue of the proposed model is also presented, which provides the measure for the HRES to trade-off the robustness and economy of the solution.

Bus-Passenger-Flow Prediction Model Based on WPD, Attention Mechanism, and Bi-LSTM

The prediction of the bus passenger flow is crucial for efficient resource allocation, frequency setting, and route optimization in bus transit systems. However, it remains challenging for a single model to simultaneously capture the time-series data of the bus passenger flow with periodicity, correlation, and nonlinearity. Aiming at the complex volatility possessed by the time-series data of the bus passenger flow, a new hybrid-strategy bus-passenger-flow prediction model based on wavelet packet decomposition, an attention mechanism, and bidirectional long–short-term memory is proposed to improve the accuracy of bus-passenger-flow prediction. The differences between this study and the existing studies are as follows: Firstly, this model combines decomposition strategies and deep learning. Wavelet packet decomposition can decompose the original data into a series of smoother data components, allowing the model to be more adequate in capturing the temporal characteristics of passenger-flow data. And the model can consider the information after the predicted moment via backward computation. In addition, the model is equipped with the ability to focus on important features by incorporating an attention mechanism to minimize the interference of irrelevant information. Bus-passenger-flow prediction experiments are conducted using the Harbin bus-passenger-flow dataset as an example. The experimental results show that the model proposed in this paper can obtain more accurate bus-passenger-flow prediction results than the five baseline models can obtain.

A novel efficient method for transient heat analysis of cylindrical periodic structure based on the physical features and group theory

In this paper, a novel efficient and accurate numerical method is developed for analyzing the transient temperature responses of cylindrical periodic structures. By exploiting the structure’s circumferential cyclic periodic property and leveraging group theory, a circumferential decomposition strategy is presented to transform the temperature response analysis of the cylindrical periodic structure into the analyses of a series of one-dimensional periodic structures. Then, based on the physical nature of the transient heat conduction, an axial decomposition strategy is developed to convert the computations of the temperatures of these one-dimensional periodic structures into the calculations of the temperatures of a series of small-scale structures. The computational cost of these small-scale structures is further reduced by using the group theory. Several numerical examples demonstrate that the proposed method has higher accuracy and computational efficiency in comparison with the Crank-Nicolson method. When the Crank-Nicolson method attains the acceptable results, the proposed method is about 10 and 20 times faster than the Crank-Nicolson method with direct and preconditioning conjugate gradient solvers, respectively.