Proposed Decomposition Method Research Articles

Decomposition by Approximation With Pulse Waves Allowing Further Research on Sources of Voltage Fluctuations

Voltage fluctuations are common disturbances in power grids. Initially, it is necessary to selectively identify individual sources of voltage fluctuations to take actions to minimize the effects of voltage fluctuations. Selective identification of disturbing loads is possible using a signal chain consisting of demodulation, decomposition, and assessment of the propagation of component signals. The accuracy of such an approach is closely related to the applied decomposition method. The paper presents a new method for decomposition by approximation with pulse waves. The proposed method allows for a correct identification of selected parameters, that is, the frequency of changes in the operating state of individual sources of voltage fluctuations and the amplitude of voltage changes caused by them. The article presents results from numerical simulation studies and laboratory experimental studies, based on which the estimation errors of the indicated parameters were determined by the proposed decomposition method and other empirical decomposition methods available in the literature. The real states that occur in power grids were recreated in the research. The metrological interpretation of the results obtained from the numerical simulation and experimental research is discussed.

Forecasting Day-Ahead Electricity Prices for the Italian Electricity Market Using a New Decomposition—Combination Technique

Over the last 30 years, day-ahead electricity price forecasts have been critical to public and private decision-making. This importance has increased since the global wave of deregulation and liberalization in the energy sector at the end of the 1990s. Given these facts, this work presents a new decomposition–combination technique that employs several nonparametric regression methods and various time-series models to enhance the accuracy and efficiency of day-ahead electricity price forecasting. For this purpose, first, the time-series of the original electricity prices deals with the treatment of extreme values. Second, the filtered series of the electricity prices is decomposed into three new subseries, namely the long-term trend, a seasonal series, and a residual series, using two new proposed decomposition methods. Third, we forecast each subseries using different univariate and multivariate time-series models and all possible combinations. Finally, the individual forecasting models are combined directly to obtain the final one-day-ahead price forecast. The proposed decomposition–combination forecasting technique is applied to hourly spot electricity prices from the Italian electricity-market data from 1 January 2014 to 31 December 2019. Hence, four different accuracy mean errors—mean absolute error, mean squared absolute percent error, root mean squared error, and mean absolute percent error; a statistical test, the Diebold–Marino test; and graphical analysis—are determined to check the performance of the proposed decomposition–combination forecasting method. The experimental findings (mean errors, statistical test, and graphical analysis) show that the proposed forecasting method is effective and accurate in day-ahead electricity price forecasting. Additionally, our forecasting outcomes are comparable to those described in the literature and are regarded as standard benchmark models. Finally, the authors recommended that the proposed decomposition–combination forecasting technique in this research work be applied to other complicated energy market forecasting challenges.

Day-Ahead Electricity Demand Forecasting Using a Novel Decomposition Combination Method

In the present liberalized energy markets, electricity demand forecasting is critical for planning of generation capacity and required resources. An accurate and efficient electricity demand forecast can reduce the risk of power outages and excessive power generation. Avoiding blackouts is crucial for economic growth, and electricity is an essential energy source for industry. Considering these facts, this study presents a detailed analysis of the forecast of hourly electricity demand by comparing novel decomposition methods with several univariate and multivariate time series models. To that end, we use the three proposed decomposition methods to divide the electricity demand time series into the following subseries: a long-run linear trend, a seasonal trend, and a stochastic trend. Next, each subseries is forecast using all conceivable combinations of univariate and multivariate time series models. Finally, the multiple forecasting models are immediately integrated to provide a final one-day-ahead electricity demand forecast. The presented modeling and forecasting technique is implemented for the Nord Pool electricity market’s hourly electricity demand. Three accuracy indicators, a statistical test, and a graphical analysis are used to assess the performance of the proposed decomposition combination forecasting technique. Hence, the forecasting results demonstrate the efficiency and precision of the proposed decomposition combination forecasting technique. In addition, the final best combination model within the proposed forecasting framework is comparatively better than the best models proposed in the literature and standard benchmark models. Finally, we suggest that the decomposition combination forecasting approach developed in this study be employed to handle additional complicated power market forecasting challenges.

Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic

The COVID-19 virus’s high transmissibility has resulted in the virus’s rapid spread throughout the world, which has brought several repercussions, ranging from a lack of sanitary and medical products to the collapse of medical systems. Hence, governments attempt to re-plan the production of medical products and reallocate limited health resources to combat the pandemic. This paper addresses a multi-period production-inventory-sharing problem (PISP) to overcome such a circumstance, considering two consumable and reusable products. We introduce a new formulation to decide on production, inventory, delivery, and sharing quantities. The sharing will depend on net supply balance, allowable demand overload, unmet demand, and the reuse cycle of reusable products. Undeniably, the dynamic demand for products during pandemic situations must be reflected effectively in addressing the multi-period PISP. A bespoke compartmental susceptible-exposed-infectious-hospitalized-recovered-susceptible (SEIHRS) epidemiological model with a control policy is proposed, which also accounts for the influence of people’s behavioral response as a result of the knowledge of adequate precautions. An accelerated Benders decomposition-based algorithm with tailored valid inequalities is offered to solve the model. Finally, we consider a realistic case study – the COVID-19 pandemic in France – to examine the computational proficiency of the decomposition method. The computational results reveal that the proposed decomposition method coupled with effective valid inequalities can solve large-sized test problems in a reasonable computational time and 9.88 times faster than the commercial Gurobi solver. Moreover, the sharing mechanism reduces the total cost of the system and the unmet demand on the average up to 32.98% and 20.96%, respectively.

Internet of Vehicles Data-Oriented Arterial Travel Time Estimation Framework With Dynamic Multigraph Model

The rapid development of Internet of Vehicles (IoV) data powers various online intelligent transportation applications, such as network travel time reporting. However, the accuracy might be severely compromised due to limited probe vehicle sampling frequency. On that account, this article ­proposes a dynamic multigraph model-enabled framework to estimate reliable network travel time, even in low-IoV-frequency arterial corridors. The proposed framework first develops an improved sparse IoV travel time decomposition method. The segment travel time is further divided into the free-flow running time and static and dynamic delays. Second, a dynamic multigraph traffic network model (DMGTN) is developed to aid the proposed decomposition method. The model analyzes complicated spatiotemporal relevance between segments from multiple perspectives: the real-time travel time, congestion level, signal control (which is frequently neglected in previous research), and segment properties. Additionally, two distinct enhanced modules are designed for handing dense and sparse network graphs, respectively. This allows for a more efficient inspection over large-scale intricate arterial networks while maintaining precision. Field implementation is conducted in the downtown area of Zhangzhou, China. Compared to other high-performance baseline models, the designed DMGTN model as well as the proposed decomposition method demonstrate state-of-the-art accuracy and successfully capture travel time variability. The proposed framework better utilizes available IoV data to provide valuable traffic information for commuters and traffic management agencies.

On the exploration of regression dependence structures in multidimensional contingency tables with ordinal response variables

In this paper, we propose a new data-driven method to explore complex regression dependence structures in a multi-dimensional contingency table with an ordinal response variable and categorical (ordinal or nominal) explanatory variables. The proposed method is based on a sequential decomposition of the overall regression dependence for the data quantified by the checkerboard copula regression association measure (Wei and Kim, 2021) in an informative and interpretable fashion. It can measure the marginal and conditional contributions of any subset of all available explanatory variables to the overall regression association in a hierarchical manner taking into account the order of the explanatory variables. Thus, the proposed method enables a holistic description of various aspects of regression association in a multivariate contingency table, including marginal and conditional associations between an ordinal response variable and a subset of explanatory variables of interest. We investigate theoretical properties of the proposed decomposition method, and we further illustrate its performance through simulation and two real data examples, one from a randomized controlled trial and the other from a longitudinal epidemiological study.

Multiple Novel Decomposition Techniques for Time Series Forecasting: Application to Monthly Forecasting of Electricity Consumption in Pakistan

In today’s modern world, monthly forecasts of electricity consumption are vital in planning the generation and distribution of energy utilities. However, the properties of these time series are so complex that they are difficult to model directly. Thus, this study provides a comprehensive analysis of forecasting monthly electricity consumption by comparing several decomposition techniques followed by various time series models. To this end, first, we decompose the electricity consumption time series into three new subseries: the long-term trend series, the seasonal series, and the stochastic series, using the three different proposed decomposition methods. Second, to forecast each subseries with various popular time series models, all their possible combinations are considered. Finally, the forecast results of each subseries are summed up to obtain the final forecast results. The proposed modeling and forecasting framework is applied to data on Pakistan’s monthly electricity consumption from January 1990 to June 2020. The one-month-ahead out-of-sample forecast results (descriptive, statistical test, and graphical analysis) for the considered data suggest that the proposed methodology gives a highly accurate and efficient gain. It is also shown that the proposed decomposition methods outperform the benchmark ones and increase the performance of final model forecasts. In addition, the final forecasting models produce the lowest mean error, performing significantly better than those reported in the literature. Finally, we believe that the framework proposed for modeling and forecasting can also be used to solve other forecasting problems in the real world that have similar features.

Fully Distributed Energy and Reserve Scheduling for Hybrid AC/DC Systems

Preparing spin reserve power in advance is an efficient approach to address the intermittency of renewable energy. To promote renewables penetration levels and increase the cost-efficiency of bulk power system, a novel flexible HVDC model that allows both energy and reserve transmitted across regions is proposed. Based on this, a risk based dynamic reserve schedule (RBDRS) model is introduced for the investigating systems. In addition, renewable generation and load centers locate separately in an extensive spatial range and are usually managed by the different system operators in practice. Therefore, a fully distributed calculation method which is based on the alternating direction method of multipliers (ADMM) is proposed. The proposed decomposition method adaptively updates its parameters during the iteration process which guarantees calculation efficiency and convergence properties. Moreover, the dynamic updating strategy only requires limited information from the direct neighbor, therefore the privacy operational information of each regional AC grid is well protected while the fully distributed application is realized. The effectiveness and robustness of the proposed model and algorithm are validated through case studies based on a 2-area 6-bus system and a 3-area 354-bus system.

General Five-Component Scattering Power Decomposition with Unitary Transformation (G5U) of Coherency Matrix

The polarimetric synthetic aperture radar (PolSAR) provides us with a two-by-two scattering matrix data set. The ensemble averaged coherency matrix in an imaging window derived using a scattering matrix has all non-zero elements in its three-by-three matrix. It is a full 3 × 3 matrix that bears nine real-valued and independent polarimetric parameters inside. In the proposed decomposition method, G5U, we preprocess observed coherency matrix [T] by using two consecutive unitary transformations to become an ideal form for five-component decomposition. The transformation reduces nine parameters to seven, which is the best fit for five-component scattering model expansion. We can retrieve five powers corresponding to surface scattering, double bounce scattering, volume scattering, oriented dipole scattering, and compound dipole scattering, directly. These powers can be calculated easily and used to display superb polarimetric RBG images as never before, and are further applicable for polarimetric calibration, classification, validation, etc.

Distributed model predictive control‐oriented network decomposition based on full dynamic response

AbstractThis article addresses network decomposition for distributed model predictive control (DMPC), which includes two improvements. First, in the weighted input–output bipartite graph construction of a process network, a new measure called frequency affinity is proposed to characterize the input–output interaction considering the full dynamic response and structural information of a process. Then, in community detection, which is used to decompose the process network, the gap metric is added to quantify stability and the loss of control performance of each subsystem. Through the proposed decomposition, the obtained subsystems can be dynamically well‐decoupled since both transient and steady‐state responses are measured by the frequency affinity. As structural information is considered, the decomposition is consistent with the process physical topology. Furthermore, the utilization of gap metric can facilitate controller design for DMPC. Case studies on a reactor separator process and an air separation process demonstrate the effectiveness of the proposed decomposition method.

On multivariate randomized classification trees: [formula omitted]-based sparsity, VC dimension and decomposition methods

Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (2020) for training sparse optimal randomized classification trees. Sparsity is important not only for feature selection but also to improve interpretability. We first consider alternative methods to sparsify such trees based on concave approximations of the l0 “norm”. Promising results are obtained on 24 datasets in comparison with the original l1 and l∞ regularizations. Then, we derive bounds on the VC dimension of multivariate randomized classification trees. Finally, since training is computationally challenging for large datasets, we propose a general node-based decomposition scheme and a practical version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the testing accuracy.

Soil moisture retrieval over crop fields based on two-component polarimetric decomposition: a comparison of generalized volume scattering models

Model-based polarimetric decomposition can separate to some extent the backscattered radar signals from the vegetation canopy and the underlying ground, hence enabling a strategy for soil moisture retrieval in vegetated agricultural fields. However, the volume scattering models used in previous studies are only applicable to specific cases, making it difficult to completely remove the volume component induced by the vegetation layer. In this paper, three generalized volume scattering models (i.e., generalized volume scattering model (GVSM), simplified adaptive volume scattering model (SAVSM), and simplified Neumann volume scattering model (SNVSM)) are incorporated in the decomposition and evaluated for soil moisture retrieval. Considering the complexity and descriptive ability of the available physical models, a modified two-component model-based decomposition is proposed as the basic decomposition framework. This decomposition is also based on the physical constraint of the dielectric constants included in the model. The employed models combine an X-Bragg surface scattering model with three continuous generalized volume scattering models. The analytic solution of the parameters is obtained, and the minimum residual power criterion is used to determine the optimal solution to fit the model. By using the proposed model-based decomposition framework, the performance of the three models to simulate the canopy scattering and, as a result, to later estimate soil moisture under agricultural vegetation is evaluated. Fully polarimetric RADARSAT-2 C-band images acquired on eight dates in 2013 and 2015 over fields covered by two crops (wheat and soybean) were employed for validation. Results show that the proposed decomposition method, using any of the three volume scattering models, can provide promising inversion results of soil moisture, with RMSEs ranging from 2.89 to 7.43 [vol.%]. Compared with the other two models, the SNVSM simulates the vegetation contribution more accurately in this framework, and it provides a stable soil moisture inversion performance at different crop phenological stages, with an optimal overall accuracy of RMSE = 4.99 [vol.%] and a correlation coefficient of R = 0.78.

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm.

Hydrogen-Based Networked Microgrids Planning Through Two-Stage Stochastic Programming With Mixed-Integer Conic Recourse

Networked microgrids that integrate the hydrogen fueling stations (HFSs) with the on-site renewable energy sources (RES), power-to-hydrogen (P2H) facilities, and hydrogen storage could help decarbonize the energy and transportation sectors. In this paper, to support the hydrogen-based networked microgrids planning subject to multiple uncertainties (e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles), we propose a two-stage stochastic formulation with mixed integer conic program (MICP) recourse decisions. Our formulation involves the holistic investment and operation modeling to optimally site and configure the microgrids with HFSs. The MICP problems appearing in the second-stage capture the nonlinear power flow of networked microgrids system with binary decisions on storage charging/discharging status and energy transactions (including the trading of electricity, hydrogen, and carbon credits to recover the capital expenditures). To handle the computational challenges associated with the stochastic program with MICP recourse, an augmented Benders decomposition algorithm (ABD) is developed. Numerical studies on 33- and 47-bus exemplary networks demonstrate the economics viability of electricity-hydrogen coordination on microgrids level, as well as the benefits of stochastic modeling. Also, our augmented algorithm significantly outperforms existing methods, e.g., the progressive hedging algorithm (PHA) and the direct use of a professional MIP solver, which has largely improved the solution quality and reduced the computation time by orders of magnitude. Note to Practitioners—This paper proposes an optimal planning model for electricity-hydrogen microgrids with the renewable hydrogen production, storage, and refueling infrastructures. Our planning model is extended under a two-stage stochastic framework to address the multi-energy-sector uncertainties, e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles. The first-stage problem is to optimize the siting and sizing plan of microgrids. Then, in the second-stage problem, the coordinated scheduling of electricity and hydrogen supply systems is modeled as second-order conic programs (SOCPs) to accurately capture the power flow representation under stochastic scenarios. Also, the logical constraints with binary variables are introduced to describe the energy transactions and storage operations, which results in an MICP recourse structure. Note that the stochastic MICP formulation could be very challenging to compute even with a moderate number of scenarios. One challenge certainly comes from integer variables that cause the problem nonconvex. Another challenge follows from the fact that the strong duality of SOCPs might not hold in general. To mitigate those two challenges, we prove that the continuous relaxation of our recourse problem has strong duality, and make use of that continuous relaxation and other enhancements to design an augmented decomposition algorithm. As revealed by our numerical tests, the proposed decomposition method outperforms PHA in both the solution quality and computational efficiency. Comparing to the PHA, our ABD method often achieves tighter bounds with trivial optimality gaps. Also, it could reduce the computation time by orders of magnitude. With the help of advanced analytical tool, the proposed planning framework can be readily implemented in real-world applications.

Dominance-based variable analysis for large-scale multi-objective problems

Optimization problems with multiple objectives and many input variables inherit challenges from both large-scale optimization and multi-objective optimization. To solve the problems, decomposition and transformation methods are frequently used. In this study, an improved control variable analysis is proposed based on dominance and diversity in Pareto optimization. Further, the decomposition method is used in a cooperative coevolution framework with orthogonal sampling mutation. The algorithm’s performances are compared against the weighted optimization framework. The results show that the proposed decomposition method has much better accuracy compared to the traditional method. The results also show that the cooperative coevolution framework with a good grouping is very competitive. Additionally, the number of search directions in orthogonal sampling can be easily configured. A small number of search directions will reduce the search space greatly while also restricting the area that can be explored and vice versa.

Applying the input\u2013output price model to identify inflation processes

We try to examine the potential of input–output price model to identify mechanisms of price formation and transmission. Contrary to previous research that focused on overcoming the specific limitations of the model, we test its overall performance. In the presented study, the historical values of the commonly used consumer price index were decomposed according to the classic input–output price model for an open economy. A sequence of ex post simulations under various assumptions was used to identify the sources of inflation. This study required the use of input–output tables in current and previous year’s prices. The proposed method of decomposition might be a starting point to create a framework for studying different aspects of inflation process.

Decomposition of Socioeconomic Changes in the Consumption of Micronutrients in Pakistan between 2006 and 2016

ABSTRACT This study is conducted to decompose inequality in four important micronutrient intakes, i.e. calcium, iodine, iron, and zinc due to socioeconomic factors during 2006–2016. For this purpose, data were taken from national-level surveys, i.e. HIES-2006 and HIICS-2016. We applied a recently proposed decomposition method based on copula function to decompose between year changes in the consumption of micronutrients into structure and composition effect. The results show that average calcium and iron intakes increased by 518.54 (mg) and 0.962 (mg), respectively, while average iodine and zinc intakes decreased by 2.009 (mg) and 3.411 (mg), respectively, during the decade. Estimates of structure effect show that calcium, iodine, and iron consumption increased on average, i.e. 525.316 (mg), 14.615 (mg), and 2.15 (mg), respectively, while zinc intake decreased by 2.735 (mg). The composition effect is negative for all the four micronutrients, implying that consumption of calcium, iodine, iron, and zinc decreased as 6.7766 (mg), 16.624 (mg), 1.189 (mg), and 0.677 (mg), respectively. The main factors of this change are household income, urbanization, provinces, and household size. The policymakers need to know the importance of socioeconomic factors to improve hidden hunger in terms of micronutrient intakes.

EFIE analyses of 3-D scattering from an object above arbitrarily rough periodic surfaces by current decomposition method

This paper addresses a three-dimensional scattering problem from a PEC object above a periodic conductive rough surface by using a decomposition method based on the separation of equivalent current density on the periodic surface as induced and perturbed current densities. The infinite solution domain is forcibly bounded by assuming that the perturbed current density caused by the object is intensively dominant in only a limited area on the periodic surface. The proposed decomposition method achieves considerable accuracy while providing an effortless computation without attempting a half-space Green's function or exercising a tapered wave illumination. This method provides a significantly superior solution to the tapered wave approach in illumination at low-grazing angles, although a plane wave is harnessed. Also, this proposed method can handle an arbitrary degree of roughness since the solution method does not contain an approximation of the surface roughness.

Artifact Removal from EEG signals using Regenerative Multi-Dimensional Singular Value Decomposition and Independent Component Analysis

The EEG signals are regularly blended with sources like Electrooculogram, Electromyogram and few other artifacts caused by physical or signal interferences. The presence of artifacts induces inaccuracy in the examination of the signals acquired. Independent Component Analysis has been predominantly utilized towards these discrepancies by isolating the artifacts from the EEG signals. Direct utilization of ICA isn't conceivable with the frameworks that are outfitted with single or few EEG channels. Distinctly using ICA to eliminate artifacts on a single channel is harder. Therefore, we combine ICA with a proposed decomposition method called Regenerative Multi-Dimensional Singular Value Decomposition (RMD-SVD) which maps the acquired signals into multivariate data after which ICA is applied on it. In our proposed scheme, the pattern of a source signal is mimicked with frequency, phase and amplitude value of the input signal using EEG sigmoid function. Both the input signal and the constructed regenerative reference signals are decomposed and the most significant singular values can be observed with the help of ICA which are the values of the pure input signal. Performance measures such as SNR, PSNR, MSE etc., in our proposed systems are analyzed under different filters and it is noticed that our proposed method of RMD-SVD indicates increased noise omitting efficiency.