Decomposition Scheme Research Articles

A phase-field length scale insensitive mode-dependent fracture model for brittle failure

This article presents a consistent phase-field length scale insensitive mode-dependent fracture model for brittle failure by proposing mode-factor dependent degradation functions that incorporate the effect of two additional fracture parameters, namely the mode-II critical energy release rate and mode-II fracture strength, on the overall mechanical response. Using the proposed mode-factor dependent degradation functions and employing a recently proposed modified strain decomposition scheme, we provide analytical expressions for the mode-I and mode-II fracture strengths corresponding to the mode-dependent parts of the elastic energy. Adopting a modified Benzeggagh–Kenane (B–K) criteria, we propose mode-dependent driving forces by deriving expressions for the critical energy release rate corresponding to individual fracture modes. The proposed model provides a consistent coupling between the different fracture modes and can thus predict fracture for all possible mode-mixity ratios. A parametric study is carried out to unravel the effect of mixed-mode fracture parameters on the mechanical response of isotropic materials by considering a few representative numerical examples. The numerical results from the proposed model show an excellent agreement with experimental results reported in the literature.

Synthesis of flexible inter-plant heat exchanger networks: A decomposition method considering intermedium fluid circles

The traditional methods for synthesizing flexible heat exchanger networks (HENs) are not directly applicable to inter-plant HEN challenges, primarily due to the spread of system uncertainty across plants via intermedium fluid circles. This complicates the synthesis process significantly. To tackle this issue, this study proposes a decomposed stepwise methodology to facilitate the flexible synthesis of the inter-plant HENs performing indirect heat integration. A decomposition strategy is proposed to divide the overall network into manageable sub-networks by dissecting the intermedium fluid circles. To address the variability in intermedium fluid temperatures, a temperature fluctuation analysis approach is developed and a heuristic rule is introduced to maintain the temperature feasibility of the intermedium fluids. To ensure adequate flexibility and cost-effectiveness of the designed networks, flexibility analysis and network retrofit steps are conducted through model-based optimization techniques. The efficacy of the method is demonstrated through two case studies, showing its potential in achieving the desired operational flexibility for inter-plant HENs.

Influence mechanism of ZnCdS solid solution composition regulation on its energy band and photocatalytic hydrogen performance

The regulation of the band structure is crucial for the improvement of the photocatalytic performance, but the relationship between the composition of solid solution catalyst and their band structure is still unclear. Herein, the solid solution catalysts ZnxCd1-xS (1 > x > 0) were designed and synthesized using a handy solid-phase thermal decomposition strategy. It is interesting that the band structure and photocatalytic hydrogen production (PHP) performance of the obtained solid solution catalyst can be cleverly regulated by controlling the atomic ratio of the solid solution. Among the obtained series of ZnxCd1-xS solid solution catalysts, the optimal solid solution catalysts Zn0.5Cd0.5S exhibits the best PHP activity and favorable cycle stability: the corresponding PHP rate is 41211.2 μmol·h−1·g−1 and the QE value is 7.7 % at 400 nm. The outstanding photocatalytic hydrogen production performance is the result of significantly narrowing the band gap of sulfide solid solution. Additionally, the effective separation and transfer rate of photogenerated carrier has also been improved effectively. The construction of bimetallic sulfide solid solution photocatalyst via an ingenious solid-state thermal decomposition strategy in this work provided a new idea for improving the photocatalytic performance of bimetallic catalysts.

POD–ANN as digital twins for surge line thermal stratification

This paper describes a hybrid proper orthogonal decomposition (POD) and artificial neural network (ANN) strategy to construct digital twins of a pressurizer surge line under thermal stratification conditions. The one-way coupled conjugate heat transfer and thermal stress analysis was conducted by use of parametric modeling and the introduction of the inverse distance weighted interpolation for the grid mapping, which allows for the mapped grids to have the same number of nodes regardless of variations of surge line geometries. A snapshot-based POD was utilized to obtain truncated lower-order modes and the full-order system response was projected onto these modes with reduced state coefficients. Then the ANN was employed to establish a surrogate model between the five chosen design variables of interest and the reduced state coefficients, resulting in a surrogate-assisted digital twin for a pressurizer surge line. Prediction of fluid–structure interface temperature and thermal stress distribution was thus achieved in an in-line real-time manner for a wide range of parameter variations. We publicly share all code implementations, and we believe that our efforts open a door for the digital twining of thermo–fluid–structure interaction problems

A dual-scale fused hypergraph convolution-based hyperedge prediction model for predicting missing reactions in genome-scale metabolic networks.

Genome-scale metabolic models (GEMs) are powerful tools for predicting cellular metabolic and physiological states. However, there are still missing reactions in GEMs due to incomplete knowledge. Recent gaps filling methods suggest directly predicting missing responses without relying on phenotypic data. However, they do not differentiate between substrates and products when constructing the prediction models, which affects the predictive performance of the models. In this paper, we propose a hyperedge prediction model that distinguishes substrates and products based on dual-scale fused hypergraph convolution, DSHCNet, for inferring the missing reactions to effectively fill gaps in the GEM. First, we model each hyperedge as a heterogeneous complete graph and then decompose it into three subgraphs at both homogeneous and heterogeneous scales. Then we design two graph convolution-based models to, respectively, extract features of the vertices in two scales, which are then fused via the attention mechanism. Finally, the features of all vertices are further pooled to generate the representative feature of the hyperedge. The strategy of graph decomposition in DSHCNet enables the vertices to engage in message passing independently at both scales, thereby enhancing the capability of information propagation and making the obtained product and substrate features more distinguishable. The experimental results show that the average recovery rate of missing reactions obtained by DSHCNet is at least 11.7% higher than that of the state-of-the-art methods, and that the gap-filled GEMs based on our DSHCNet model achieve the best prediction performance, demonstrating the superiority of our method.

MuDE: Multi-agent decomposed reward-based exploration

In cooperative multi-agent reinforcement learning, agents jointly optimize a centralized value function based on the rewards shared by all agents and learn decentralized policies through value function decomposition. Although such a learning framework is considered effective, estimating individual contribution from the rewards, which is essential for learning highly cooperative behaviors, is difficult. In addition, it becomes more challenging when reinforcement and punishment, help in increasing or decreasing the specific behaviors of agents, coexist because the processes of maximizing reinforcement and minimizing punishment can often conflict in practice. This study proposes a novel exploration scheme called multi-agent decomposed reward-based exploration (MuDE), which preferably explores the action spaces associated with positive sub-rewards based on a modified reward decomposition scheme, thus effectively exploring action spaces not reachable by existing exploration schemes. We evaluate MuDE with a challenging set of StarCraft II micromanagement and modified predator–prey tasks extended to include reinforcement and punishment. The results show that MuDE accurately estimates sub-rewards and outperforms state-of-the-art approaches in both convergence speed and win rates.

Optimal Allocation of Hybrid Energy Storage Capacity Based on ISSA-Optimized VMD Parameters

To address the issue where the grid integration of renewable energy field stations may exacerbate the power fluctuation in tie-line agreements and jeopardize safe grid operation, we propose a hybrid energy storage system (HESS) capacity allocation optimization method based on variational mode decomposition (VMD) and a multi-strategy improved salp swarm algorithm (ISSA). From typical wind load power and contact line agreement power, the HESS power is obtained. VMD decomposes this power into high- and low-frequency power, respectively, for the super capacitor and the Li-ion battery. Considering charging and discharging power and state of charge (SOC) constraints, an optimization model minimizing the system equivalent annual value cost is established. ISSA optimizes the best decomposition layer K and penalty coefficients α in VMD. The optimal cut-off point and corresponding energy storage allocation scheme are analyzed. A simulation and analysis on MATLAB show that the proposed ISSA-VMD HESS capacity allocation scheme saves 7.53% in costs compared to an empirical mode decomposition (EMD) scheme, proving the method’s effectiveness and superiority.

The Splitting Characteristic Finite Difference Domain Decomposition Scheme for Solving Time-Fractional MIM Nonlinear Advection–Diffusion Equations

The Splitting Characteristic Finite Difference Domain Decomposition Scheme for Solving Time-Fractional MIM Nonlinear Advection–Diffusion Equations

Dual Domain Decomposition Method for High-Resolution 3D Simulation of Groundwater Flow and Transport

The high-resolution 3D groundwater flow and transport simulation problem requires massive discrete linear systems to be solved, leading to significant computational time and memory requirements. The domain decomposition method is a promising technique that facilitates the parallelization of problems with minimal communication overhead by dividing the computation domain into multiple subdomains. However, directly utilizing a domain decomposition scheme to solve massive linear systems becomes impractical due to the bottleneck in algebraic operations required to coordinate the results of subdomains. In this paper, we propose a two-level domain decomposition method, named dual-domain decomposition, to efficiently solve the massive discrete linear systems in high-resolution 3D groundwater simulations. The first level of domain decomposition partitions the linear system problem into independent linear sub-problems across multiple subdomains, enabling parallel solutions with significantly reduced complexity. The second level introduces a domain decomposition preconditioner to solve the linear system, known as the Schur system, used to coordinate results from subdomains across their boundaries. This additional level of decomposition parallelizes the preconditioning of the Schur system, addressing the bottleneck of the Schur system solution while improving its convergence rates. The dual-domain decomposition method facilitates the partition and distribution of the computation to be solved into independent finely grained computational subdomains, substantially reducing both computational and memory complexity. We demonstrate the scalability of our proposed method through its application to a high-resolution 3D simulation of chromium contaminant transport in groundwater. Our results indicate that our method outperforms both the vanilla domain decomposition method and the algebraic multigrid preconditioned method in terms of runtime, achieving up to 8.617× and 5.515× speedups, respectively, in solving massive problems with approximately 108 million degrees of freedom. Therefore, we recommend its effectiveness and reliability for high-resolution 3D simulations of groundwater flow and transport.

Computational decomposition and composition technique for approximate solution of nonstationary problems

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional equations can be reduced by additive decomposition of the problem operator(s) and composition of the approximate solution using particular explicit–implicit time approximations. Such a technique is currently applied in conditions where the decomposition step is uncomplicated. A general approach is proposed to construct decomposition–composition algorithms for evolution equations in finite-dimensional Hilbert spaces. It is based on two main variants of the decomposition of the unit operator in the corresponding spaces at the decomposition stage and the application of additive operator-difference schemes at the composition stage. The general results are illustrated on the boundary value problem for a second-order parabolic equation by constructing standard splitting schemes on spatial variables and region-additive schemes (domain decomposition schemes).

AC–DC security-constrained optimal power flow for the Australian National Electricity Market

This paper presents a new methodology to solve the integrated ac–dc security-constrained optimal power flow (SCOPF) problem for large-scale power systems, with a focus on the Australian National Electricity Market (NEM). The proposed SCOPF is based on a decomposition scheme that significantly reduces the dimensionality of the problem and thus improves the computational performance. It further supports a contingency ranking, evaluation, and non-dominated filtering algorithm, cyclic selection of filtered contingencies, careful choice of slack variables, and a tailored warm start to the nonlinear problem. The methodology is validated against the two-stage mathematical programming model that uses an explicit nonlinear model of both the base case and the contingency cases, at a slightly higher cost but significantly faster execution. Moreover, the NEM power system, is studied addressing different scenarios including load variations, renewable energy zone integration, and additional reinforcements like point-to-point and meshed HVDC. The proposed approaches provides preventive solutions in less than 5 min thus affirming the model’s effectiveness in real-time applications and planning studies.

Managing power balance and reserve feasibility in the AC unit commitment problem

Incorporating the AC power flow equations into unit commitment models has the potential to avoid costly corrective actions required by less accurate power flow approximations. However, research on unit commitment with AC power flow constraints has been limited to a few relatively small test networks. This work investigates large-scale AC unit commitment problems for the day-ahead market and develops decomposition algorithms capable of obtaining high-quality solutions at industry-relevant scales. The results illustrate that a simple algorithm that only seeks to satisfy unit commitment, reserve, and AC power balance constraints can obtain surprisingly high-quality solutions to this AC unit commitment problem. However, a naive strategy that prioritizes reserve feasibility leads to AC infeasibility, motivating the need to design heuristics that can effectively balance reserve and AC feasibility. Finally, this work explores a parallel decomposition strategy that allows the proposed algorithm to obtain feasible solutions on large cases within the two hour time limit required by typical day-ahead market operations.

A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation

This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot’s coefficient not only with the phase-field variable (damage) but also with the energy decomposition scheme. Furthermore, we propose a new approach to update porosity solely determined by the strain change rather than damage evolution as in the existing models. As such, these poroelastic behaviors of Biot’s coefficient and the porosity dictate Biot’s modulus and the thermal expansion coefficient. For numerical implementation, we employ an isotropic diffusion method to stabilize the advection-dominated heat flux and adapt the fixed stress split method to account for the thermal stress. We verify our model against a series of analytical solutions such as Terzaghi’s consolidation, thermal consolidation, and the plane strain hydraulic fracture propagation, known as the KGD fracture. Finally, numerical experiments demonstrate the effectiveness of the stabilization method and intricate thermo-hydro-mechanical interactions during hydraulic fracturing with and without a pre-existing weak interface.

A long-term multivariate time series prediction model for dissolved oxygen

Accurate and efficient long-term prediction of marine dissolved oxygen (DO) is crucial for the sustainable development of aquaculture. However, the multidimensional time dependency and lag effects of marine chemical variables present significant challenges when handling multiple inputs in univariate long-term prediction tasks. To address these issues, we designed a multivariate time-series long-term prediction model (LMFormer) based on the Transformer architecture. The proposed multivariate time-series decomposition strategy effectively leverages the feature information of prediction variables at different scales, thereby reducing the loss of critical information. Additionally, a dynamic variable selection strategy based on a gating mechanism was designed to optimize the collinearity problem in the multivariate data feature extraction process. Finally, an efficient two-stage attention architecture is proposed to effectively capture the long-range dependencies between dynamic features. This study conducted high-precision 7-day advance DO long-term predictions in two case studies, the environmentally stable Shandong Peninsula in China and the San Juan Islands in the United States, which are affected by extreme conditions such as ocean currents. The experimental results demonstrate the superior prediction performance and generalizability of the designed model. In the Shandong Peninsula case, the mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and Kling–Gupta efficiency (KGE) reached 0.0159, 0.126, 0.9743, and 0.9625, respectively. In the San Juan Islands case, the MAE was reduced by an average of 42.34% compared to that of the baseline model, the RMSE was reduced by an average of 24.57%, the R2 increased by 22.54%, and the KGE improved by an average of 12.04%. Overall, the proposed prediction model effectively achieves long-term prediction of multivariate marine chemical data, providing valuable references for sustainable management and decision-making in aquaculture.

Research on power allocation strategy and capacity configuration of hybrid energy storage system based on double-layer variational modal decomposition and energy entropy

This paper deals with the study of the power allocation and capacity configuration problems of Hybrid Energy Storage Systems (HESS) and their potential use to handle wind and solar power fluctuation. A double-layer Variable Modal Decomposition (VMD) strategy is proposed. Firstly, using the Sparrow Search Algorithm with Sine-cosine and Cauchy mutation (SCSSA) to optimize the parameters in VMD. Considering the different characteristics of batteries and supercapacitors and the richness of information that may be contained in the high frequency residuals obtained from the primary VMD, the secondary VMD is carried out to decomposition. In response to the modal aliasing phenomenon of the secondary VMD, the high and low frequency demarcation points of the secondary VMD are discriminated by combining the energy entropy (eN) to enable the more accurate power allocation strategy. Secondly, a mathematical model for cost analysis of the HESS is established by considering the daily integrated operating cost of the HESS and the relevant constraints of the renewable generation system. Finally, HESS capacity configuration and validation are based on the power allocation strategy proposed in this paper. The simulation results show that the power allocation strategy proposed in this paper is more accurate and has a better economy for the capacity configuration of HESS.

Toward accurate extraction of bearing fault modulation characteristics with novel time–frequency modulation bispectrum and modulation Gini index analysis

Rolling bearings are extremely critical rotating mechanical components, and when they fail, they can damage the equipment, causing safety threats or economic losses. Collecting and analyzing vibration signals of faulty bearings is a common fault diagnosis method. Modulation signal bispectrum (MSB) can utilize the inherent modulation characteristics of the signal to achieve fault feature recognition, but it is easily affected by strong background noise and other modulation signals, making it difficult to detect the fault feature frequency in the end. Based on this, a time–frequency modulation bispectrum (TFMB) method is proposed in this paper. The signal is first transformed into the time–frequency domain through short-time Fourier transform, retaining both time and frequency information. It reduces the amplitude of bispectral noise, highlights spectral lines related to fault information, and displays modulation information more clearly, making the demodulation results more accurate. Based on the characteristics of bispectrum, a two-dimensional singular value decomposition (2D SVD) strategy is designed to reduce the amplitude of the noise components in the bispectrum, and the relative change rate is proposed to automatically determine the number of effective singular values. At the same time, considering that the Gini index has good sparse property, the modulation Gini index (MGI) is proposed based on the Gini index, which can identify the repetitive pulses in the signal, suppress the random pulses and noise interference, and extract the modulation component. MGI can be used to evaluate the proportion of fault information contained in TFMB slices and select the optimal frequency slice. The simulation signal verifies the effectiveness of the method in fault diagnosis of rolling bearing, and the proposed method is applied to the diagnosis of rolling bearing outer ring fault, inner ring fault, and compound fault respectively. The experimental results show that the method can effectively reduce noise amplitude, enhance fault information in the bispectrum, and extract the optimal frequency slice to accurately detect bearing fault characteristic frequencies. The proposed method is compared with MSB detector, Fast Kurtogram and Autogram, which proves the superiority of TFMB method in extraction of rolling bearing fault characteristics.

Understanding the coupling of non-metallic heteroatoms to CO2 from a Conceptual DFT perspective

ContextA Conceptual DFT (CDFT) study has been carry out to analyse the coupling reactions of the simplest amine (CH3NH2), alcohol (CH3OH), and thiol (CH3SH) compounds with CO2 to form the corresponding adducts CH3NHCO2H, CH3OCO2H, and CH3SCO2H. The reaction mechanism takes place in a single step comprising two chemical events: nucleophilic attack of the non-metallic heteroatoms to CO2 followed by hydrogen atom transfer (HAT). According to our calculations, the participation of an additional nucleophilic molecule as HAT assistant entails important decreases in activation electronic energies. In such cases, the formation of a six-membered ring in the transition state (TS) reduces the angular stress with respect to the non-assisted paths, characterised by four-membered ring TSs. Through the analysis of the energy and reaction force profiles along the intrinsic reaction coordinate (IRC), the ratio of structural reorganisation and electronic rearrangement for both activation and relaxation energies has been computed. In addition, the analysis of the electronic chemical potential and reaction electronic flux profiles confirms that the highest electronic activity as well as their changes take place in the TS region. Finally, the distortion/interaction model using an energy decomposition scheme based on the electron density along the reaction coordinate has been carried out and the relative energy gradient (REG) method has been applied to identify the most important components associated to the barriers.MethodsThe theoretical calculation were performed with Gaussian-16 scientific program. The B3LYP-D3(BJ)/aug-cc-pVDZ level was used for optimization of the minima and TSs. IRC calculations has also been carried out connecting the TS with the associated minima. Conceptual-DFT (CDFT) calculations have been carried out with the Eyringpy program and in-house code. The distortion/interaction model along the reaction coordinate have used the decomposition scheme of Mandado et al. and the analysis of the importance of each components have been done with the relative energy gradient (REG) method.

Prediction and explanation of debris flow velocity based on multi-strategy fusion Stacking ensemble learning model

The debris flow velocity fundamentally determines its intensity, thereby rendering its prediction a crucial aspect of disaster prevention and control strategies. However, accurate velocity prediction has consistently posed significant challenges due to the intricate interplay of various influential factors. To address the limitations of existing models, an explainable multi-strategy fusion of Stacking ensemble learning is proposed. Initially, an improved snake optimization (ISO) algorithm is employed to adjust parameters within the model’s learners. Benchmark function comparison tests are then conducted to validate the reliability of the ISO algorithm. Subsequently, a learner selection method based on predictive performance and degree of difference is established to facilitate the selection of basic learners and meta-learners. This leads to the construction of the Stacking ensemble learning model, achieved through the integration of parameter optimization strategies from the improved swarm intelligence algorithm strategy, the error weighting strategy, and the decomposition strategy. To assess the model, a case study of the Jiangjiagou Gulley debris flow is undertaken, focusing on the prediction of the debris flow velocity. The results demonstrate high predictive accuracy, with RMSE, MAE, and MAPE values of 0.19, 0.17, and 2.46% respectively. Furthermore, under the SHAP framework, global and local explanations of the predictions are provided. Through feature importance analysis, the bed slope gradient is identified as the most crucial feature in the velocity prediction of the Jiangjiagou Gulley debris flow. Coupling effects and contributions of input features to the debris flow velocity prediction are further analyzed and explained through feature interaction analysis and single sample analysis. This study not only provides a new method for debris flow velocity prediction but also provides guiding suggestions for debris flow monitoring and control.

Exchange-correlation effects in interatomic energies for pure density functionals and their application to the molecular energy prediction.

In this proof-of-concept paper, we show how exchange-correlation effects can be simply recovered for interatomic energies within the interacting quantum atoms decomposition when local, gradient generalized, or meta-gradient generalized approximations are used in density functional theory (DFT) calculations. We also demonstrate how inhomogeneity and non-local effects can be introduced even from a pure local scheme, without resorting to any orbital information. Finally, we provide numerical evidence on a database of selected energetic molecules that this decomposition scheme can be efficiently used to build accurate models for the prediction of molecular energies from an initial "cheap" DFT calculation.

Decomposition strategy for surface EMG with few channels: a simulation study

Objective. In the specific use of electromyogram (EMG) driven prosthetics, the user’s disability reduces the space available for the electrode array. We propose a framework for EMG decomposition adapted to the condition of a few channels (less than 30 observations), which can elevate the potential of prosthetics in terms of cost and applicability. Approach. The new framework contains a peel-off approach, a refining strategy for motor unit (MU) spike train and MU action potential and a re-subtracting strategy to adapt the framework to few channels environments. Simulated EMG signals were generated to test the framework. In addition, we quantify and analyze the effect of strategies used in the framework. Main results. The results show that the new algorithm has an average improvement of 19.97% in the number of MUs identified compared to the control algorithm. Quantitative analysis of the usage strategies shows that the re-subtracting and refining strategies can effectively improve the performance of the framework under the condition of few channels. Significance. These prove that the new framework can be applied to few channel conditions, providing a optimization space for neural interface design in cost and user adaptation.