Alternating Direction Method Of Multipliers Research Articles

Localization of partial electrical discharges using compressive spherical frequency-difference beamforming.

Accurate localization of partial electrical discharges is essential for the diagnosis of high-voltage systems. The current study achieves this by employing an acoustic sensor array and a beamforming approach. The occurrence of a partial discharge is accompanied by the emission of high-frequency sounds in the ultrasonic range, making localization a challenging task requiring many sensors to avoid spatial aliasing. Compressive frequency-difference beamforming, as previously proposed, can be effective in addressing this issue. We expand the method to include near-field localization by utilizing a spherical wave and propose a two-step normalization process. This eliminates the bias associated with nonplanar waves and standardizes the field variables, thereby preserving only the phase and relative amplitude information. A distributed algorithm based on the alternating direction multiplier method is used to solve the associated convex optimization problem. The proposed method is demonstrated using simulated and experimental data.

An optimal scheduling strategy for electricity-thermal synergy and complementarity among multi-microgrid based on cooperative games

Multi-microgrid (MMG) systems provide an effective way to convert renewable energy into other forms of energy for low-carbon utilization. However, the coupling of multi-energy and renewable energy brings a challenge to the stable operation and dispatch of the system. Therefore, an electricity-thermal-gas-hydrogen MMG complementary optimization model based on peer-to-peer (P2P) electricity-thermal synergy is proposed. The model focuses on the coupling and conversion of electricity, hydrogen, and thermal through a hydrogen energy storage system (HESS) combined with renewable energy, and incorporates integrated demand response (IDR) and ladder-type carbon trading mechanism (LCTM). Subsequently, based on the cooperative game and the alternating direction multiplier method (ADMM), a multi-energy synergistic and complementary optimal scheduling strategy is proposed, which increases the flexibility of multi-energy sharing. In addition, a revenue allocation optimization strategy that takes into account the fairness and renewable energy consumption rate is proposed to achieve the stability of the alliance system operation. Finally, the simulation results show the effectiveness of the proposed model and strategy, realizing the complementary sharing of regional multi-energy, enabling the expansion of the boundaries of optimal energy allocation, further improving the low-carbon economic operation capability of MMG, and reducing the dependence of the system on the energy market.

An accelerated alternating direction method of multiplier for MRI with TV regularisation

Compressed Sensing (CS) is important in the field of image processing and signal processing, and CS-Magnetic Resonance Imaging (MRI) is used to reconstruct image from undersampled k-space data. Total Variation (TV) regularisation is a common technique to improve the sparsity of image, and the Alternating Direction Multiplier Method (ADMM) plays a key role in the variational image processing problem. This paper aims to improve the quality of MRI and shorten the reconstruction time. We consider MRI to solve a linear inverse problem, we convert it into a constrained optimization problem based on TV regularisation, then an accelerated ADMM is established. Through a series of theoretical derivations, we verify that the algorithm satisfies the convergence rate of O1/k2 under the condition that one objective function is quadratically convex and the other is strongly convex. We select five undersampled templates for testing in MRI experiment and compare it with other algorithms, experimental results show that our proposed method not only improves the running speed but also gives better reconstruction results.

Research on distributed optimal scheduling method based on consensus

Abstract With access to large-scale distributed power sources, the physical structure of the power grid system tends to be distributed. The application of traditional centralized optimal scheduling methods will lead to a surge in communication overhead and computational complexity, which will affect the performance and efficiency of the solution. In this paper, the minimum operating cost of the system is taken as the goal, and the distributed direct current optimal power flow (DC-OPF) optimization calculation of the photovoltaic-storage power generation system is considered to approximately solve the economic dispatch problem. The DC optimal power flow model with energy storage charging penalty is constructed. Then, the distributed optimization method based on the consensus alternating direction multiplier method (ADMM) is adopted. By decoupling the objective function and constraints of the whole system problem, the fully distributed DC-OPF calculation is realized by introducing the global consensus variable to deal with the boundary buses. Finally, the improved IEEE 30-bus example is used to test the method, and the simulation results verify the convergence and accuracy of the method.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

AbstractIn this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–Łojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.

Balance Sparse Decomposition Method with Nonconvex Regularization for Gearbox Fault Diagnosis

As an important part of rotating machinery, gearboxes often fail due to their complex working conditions and harsh working environment. Therefore, it is very necessary to effectively extract the fault features of the gearboxes. Gearbox fault signals usually contain multiple characteristic components and are accompanied by strong noise interference. Traditional sparse modeling methods are based on synthesis models, and there are few studies on analysis and balance models. In this paper, a balance nonconvex regularized sparse decomposition method is proposed, which based on a balance model and an arctangent nonconvex penalty function. The sparse dictionary is constructed by using Tunable Q-Factor Wavelet Transform (TQWT) that satisfies the tight frame condition, which can achieve efficient and fast solution. It is optimized and solved by alternating direction method of multipliers (ADMM) algorithm, and the non-convex regularized sparse decomposition algorithm of synthetic and analytical models are given. Through simulation experiments, the determination methods of regularization parameters and balance parameters are given, and compared with the L1 norm regularization sparse decomposition method under the three models. Simulation analysis and engineering experimental signal analysis verify the effectiveness and superiority of the proposed method.

Dynamic operating envelopes embedded peer-to-peer-to-grid energy trading

A novel decentralized peer-to-peer-to-grid (P2P2G) trading mechanism considering distribution network integrity is proposed. In order to direct prosumers’ peer-to-peer (P2P) trading behavior to be grid-friendly, the proposed method incorporates Dynamic Operating Envelopes (DOEs) into the existing P2P2G trading. Moreover, DOEs are determined through negotiations between the distribution system operator (DSO) and prosumers alongside the process of P2P trading, avoiding compromising prosumers’ privacy and network parameters leakage. To reduce communication costs during P2P trading, a variant of the alternating direction method of multipliers (ADMM), i.e., communication-censored ADMM (COCA) is used to solve the P2P2G trading problem. Finally, the DOE price is shown to be comprised of several economically interpretable components. Simulations validate the effectiveness of the proposed mechanism.

Schwarz decomposition for parallel minimum lap-time problems: evaluating against ADMM

The Minimum Lap Time Problem (MLTP) remains a significant area of research, particularly in the motorsport context. This form of Optimal Control Problem (OCP) aims to minimise lap times on a specific track with a given vehicle. Various complexities in both vehicle and track models are employed across the literature to address optimal trajectory planning. While previous works have tackled MLTP as a singular task using a serial approach, the increasing model complexity and horizon length demands the utilisation of parallelisation techniques. This paper introduces a novel application of the Overlapping Schwarz Decomposition algorithm to address the MLTP. The algorithm divides the problem into smaller sub-problems based on different sectors of a track, distributing them among multiple processors. We validate and compare the Schwarz approach against a serial approach and the Alternating Direction Method of Multipliers (ADMM) in solving MLTP with over 2.5 million variables. Despite the general efficiency improvement of parallelisation compared to the serial approach, the Schwarz algorithm demonstrates superior speed, accuracy and robustness compared to ADMM. As a result of our findings, it emerges as the preferred choice when large-scale MLTPs need to be solved.

Distributed Nonconvex Optimization for Control of Water Networks with Time-coupling Constraints

AbstractIn this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are exacerbated by the transition between pressure and water quality controls. The resulting optimization problem is a nonconvex, nonlinear program with nonseparable structure across time steps. This problem proves challenging for state-of-the-art nonlinear solvers, often precluding their direct use for near real-time control in large-scale networks. To overcome this computational burden, we investigate a distributed optimization approach based on the alternating direction method of multipliers (ADMM). In particular, we implement and evaluate two algorithms: a standard ADMM scheme and a two-level variant that provides theoretical convergence guarantees for our nonconvex problem. We use a benchmarking water network and a large-scale operational network in the UK for our numerical experiments. The results demonstrate good convergence behavior across all problem instances for the two-level algorithm, whereas the standard ADMM approach struggles to converge in some instances. With an appropriately tuned penalty parameter, however, both distributed algorithms yield good quality solutions and computational times compatible with near real-time (e.g. hourly) control requirements for large-scale water networks.

Cooperative energy interaction for neighboring multiple distribution substation areas considering demand response

With the growing integration of renewable energy into medium- and low-voltage distribution networks, the distribution substation area (DSA) has emerged, encompassing energy storage and loads. This paper introduces an energy interaction framework for multiple DSAs aimed at enhancing local renewable energy consumption. The energy interaction issue among various DSAs is modeled as a Nash bargaining problem to encourage energy exchanges. However, the variability in pricing and internal demand response may influence scheduling decisions, necessitating further investigation. To address price forecast errors, scenarios are developed using a stochastic programming approach to represent price uncertainties while adjusting the DSA’s load accordingly. Optimal power flow constraints are integrated into the model to bolster power system operation security. Additionally, the transmission capacity can impact scheduling outcomes and operational costs. The influence of transmission limitations on operational strategies is examined within the allowable capacity. To solve this issue, the bargaining model is divided into two subproblems, and an enhanced alternating direction multiplier method (ADMM) is used to maintain the privacy of DSAs. The simulation results obtained using the IEEE-33 bus system indicate that energy interaction among multiple DSAs significantly lowers operating costs and facilitates the integration of renewable energy.

Model optimization and acceleration method based on meta-learning and model pruning for laser vision weld tracking system

Purpose This paper aims to propose a lightweight, high-accuracy object detection model designed to enhance seam tracking quality under strong arcs and splashes condition. Simultaneously, the model aims to reduce computational costs. Design/methodology/approach The lightweight model is constructed based on Single Shot Multibox Detector (SSD). First, a neural architecture search method based on meta-learning and genetic algorithm is introduced to optimize pruning strategy, reducing human intervention and improving efficiency. Additionally, the Alternating Direction Method of Multipliers (ADMM) is used to perform structural pruning on SSD, effectively compressing the model with minimal loss of accuracy. Findings Compared to state-of-the-art models, this method better balances feature extraction accuracy and inference speed. Furthermore, seam tracking experiments on this welding robot experimental platform demonstrate that the proposed method exhibits excellent accuracy and robustness in practical applications. Originality/value This paper presents an innovative approach that combines ADMM structural pruning and meta-learning-based neural architecture search to significantly enhance the efficiency and performance of the SSD network. This method reduces computational cost while ensuring high detection accuracy, providing a reliable solution for welding robot laser vision systems in practical applications.

Peer-to-peer energy trading framework for an autonomous DC microgrid using game theoretic approach

Peer-to-peer (P2P) electricity trading has become the next generation of energy management strategies that economically benefits prosumers by trading electricity as goods and services. The P2P electricity market is expected to support the grid to minimize reserve requirements, lower investment and operational costs, reduce peak demand, and improve reliability. This study proposes a peer-to-peer (P2P) energy trading framework for an autonomous DC microgrid. The motivation is to overcome several issues related to P2P reported in the literature: the lack of physical microgrid modeling, absence of an energy management system (EMS) before the P2P trading simulation, and full autonomy of P2P participants. To address these shortcomings, a framework that integrates physical layer (modeling of the microgrid), information layer (EMS), and application layer (P2P trading scheme) is suggested. The P2P market clearance utilizes a non-cooperative game theory incorporating the alternating direction method of multipliers (ADMM) algorithm. To demonstrate the proposed framework, the P2P trading of four households (prosumers) that consists of rooftop PV, local energy storage (LES), and independent community energy storage (CES) is simulated. The objective is to prove the effectiveness of P2P trading in comparison with a framework without it. The MATLAB simulation results show that the system that utilizes P2P trading can reduce the daily overall cost of energy by 47.48 %, that is, from $28.85 (without P2P) to $15.15 (with P2P). This study demonstrated the benefits of P2P energy trading for prosumers and promoted the development of the energy market.

Optimization of Operation Strategy of Multi-Islanding Microgrid Based on Double-Layer Objective

The shared energy storage device acts as an energy hub between multiple microgrids to better play the complementary characteristics of the microgrid power cycle. In this paper, the cooperative operation process of shared energy storage participating in multiple island microgrid systems is researched, and the two-stage research on multi-microgrid operation mode and shared energy storage optimization service cost is focused on. In the first stage, the output of each subject is determined with the goal of profit optimization and optimal energy storage capacity, and the modified grey wolf algorithm is used to solve the problem. In the second stage, the income distribution problem is transformed into a negotiation bargaining process. The island microgrid and the shared energy storage are the two sides of the game. Combined with the non-cooperative game theory, the alternating direction multiplier method is used to reduce the shared energy storage service cost. The simulation results show that shared energy storage can optimize the allocation of multi-party resources by flexibly adjusting the control mode, improving the efficiency of resource utilization while improving the consumption of renewable energy, meeting the power demand of all parties, and realizing the sharing of energy storage resources. Simulation results show that compared with the traditional PSO algorithm, the iterative times of the GWO algorithm proposed in this paper are reduced by 35.62%, and the calculation time is shortened by 34.34%. Compared with the common GWO algorithm, the number of iterations is reduced by 18.97%, and the calculation time is shortened by 22.31%.

A novel weighted-guided tensor completion missing data imputation method for health monitoring data of planar parallel mechanism

Abstract High-end mechanical equipment plays a crucial role in the manufacturing industry, making the monitoring of its operational status highly significant. Due to various factors such as environmental influences, the absence of monitoring signals in mechanical equipment status is a common issue, leading to a decline in data quality. To ensure data quality, this paper proposes an adaptive weighted low-rank tensor missing data imputation method. Firstly, based on the motion characteristics of a planar parallel mechanism (PPM), a new low-rank tensor model is established using periodicity, sliding windows, and time series. Secondly, the tensor truncation nuclear norm is defined, and a novel rate parameter is introduced to control the truncation degree of all tensor modes, thereby obtaining weights for each dimension. Finally, within the framework of the alternating direction method of multipliers (ADMM), adaptive weights for each dimension are obtained during each iteration, completing the filling of missing data. Two types of missing patterns are studied on a PPM experimental platform, and the results showed that as the missing rate increased, the mean absolute percentage error is less than 0.018, and root mean square error is less than 0.001, and the rate of change is less than 0.08, which was significantly better than other compared algorithms.

Quaternion optimized model with sparseness for color image recovery

This paper presents a novel approach for sparse regularization of low-rank quaternion matrix optimization problems. Quaternion matrices, which extend the concept of complex numbers to four dimensions, have shown promising applications in various fields. In this work, we exploit the inherent sparsity present in different signal types, such as audio formats and images, when represented in their respective bases. By introducing a sparse regularization term in the optimization objective. We propose a regularization technique that promotes sparsity in the Quaternion Discrete Cosine Transform (QDCT) domain for efficient and accurate solutions. By combining low-rank restriction with sparsity, the optimized model is updated using a two-step Alternating Direction Method of Multipliers (ADMM) algorithm. Experimental results on color images demonstrate the effectiveness of the proposed method, which outperforms existing relative methods. This superior performance underscores its potential for applications in computer vision and related fields.

Dynamic MRI reconstruction via multi-directional low-rank tensor regularization

Compressed sensing significantly accelerates dynamic magnetic resonance imaging (MRI) by allowing the exact reconstruction of images from a small number of measurements in (k, t)-space. The similarity in three different directions of dynamic MRI makes it have a multi-directional low-rank prior. In this paper, we propose a tensor-based multi-dimensional low-rank regularization for dynamic MRI reconstruction model, termed as MDLRT, and introduce the Schatten capped p-norm to enforce the low-rank prior of multi-directional slices. We take dynamic MRI tensor as processing unit to protect its multi-channel structure and avoid losing internal information, which promises the reconstruction performance. The utilization of multi-directional low-rank characteristics adequately exploits the spatial and temporal redundancies. In addition, using Schatten capped p-norm to regularize the low-rank property realizes a better approximation to the rank than widely used surrogate functions. The proposed model is efficiently solved by the alternating direction multiplier method (ADMM), in which the fast algorithm for each sub-problem is separately developed. In comparison with state-of-the-art methods, extensive experiments on dynamic MR data demonstrate the superior performance and robustness to noise of the proposed method in terms of reconstruction accuracy.

Guaranteed matrix recovery using weighted nuclear norm plus weighted total variation minimization

This work presents a general framework regarding the recovery of matrices equipped with hybrid low-rank and local-smooth properties from just a few measurements consisting of linear combinations of the matrix entries. Concretely, we consider the problem of robust low-rank matrix recovery using Weighted Nuclear Norm plus Weight Total Variation (WNNWTV) minimization. First of all, based on a new restricted isometry property, we prove that the WNNWTV method possesses an error bound consisting of a low-rank approximation term, a total variation approximation term, and an observation error term. It should be noted that although there are many models considering both properties, there are very few recoverable error theories about such models. Specifically, the theoretical error bound provides an automatic mechanism to reducing regularization parameters with no need for cross-validation while keeping almost the same selection result with commonly used cross-validation technique. Subsequently, the proposed method is reformulated into a regularized unconstrained problem, and we study its optimization aspects in detail based on the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on synthetic data and two applications, i.e. hyperspectral image recovery and dynamic magnetic resonance imaging recovery verified our theories and proposed algorithms.

Low-rank sparse fully-connected tensor network for tensor completion

Fully-connected tensor network (FCTN) has recently drawn lots of attention in tensor completion due to its full description of all correlations between any two modes. However, the FCTN model has multiple ranks, and existing methods often ignore the difficulty brought about by rank selection, especially when the model is rank-sensitive. To overcome this drawback, this paper proposed a low-rank sparse FCTN for tensor completion. Specifically, we theoretically show that, for a tensor with FCTN structure, its subtensor can be represented as a coefficient sum of basic tensors, where the coefficients are remained in the FCTN’s factors. This means that factors’ sparsity can improve the robustness of FCTN to larger rank selection. Moreover, according to the relation between the target tensor and its FCTN’s factors, low-rank constrain is used to enhance rank robustness. Lastly, we optimize the proposed model by the alternating direction method of multipliers (ADMM) algorithm. Experimental results show that the low-rank sparse constraint effectively improves the rank robustness of the FCTN model, and achieves excellent results compared with other state-of-the-art completion methods.

Research on cooperative operation optimization method of internet data center alliance considering diversified flexibility

With the rapid development of large-scale internet data center in China, the goal of carbon peak and carbon neutrality has put forward higher requirements for low-carbon economic operation of internet data center. Considering complementary advantages among internet data centers, this paper proposes a cooperative operation optimization method of internet data center alliance based on diversified flexibility. Firstly, a cooperative operation structure of alliance considering electricity and carbon trading between members was built, as well as the diversified flexibility model considering carbon capture and power to gas device. Then, a cooperative optimization operation model of alliance was constructed based on Nash bargaining theory, and the allocation of cooperation benefit among members can be realized based on electrical carbon contribution rate. In order to improve solution convergence, the alternating direction multiplier method is improved by penalty factor updating and correction factor modeling method. Finally, the proposed method is applied to the demonstration project of “East Data and West Computing” in Qingyang, Gansu, China, and the trial run results are consistent with the theory analysis. On the one hand, the diversified flexibility and the electricity and carbon trading between members can effectively reduce the total cost and carbon emissions of alliance. On the other hand, the cooperation benefits distribution strategy based on the electrical carbon contribution rate can effectively enhance enthusiasm of members to participate in alliance. The improved alternating direction multiplier method can achieve distributed optimization of alliance, protect the privacy of each member, and has good convergence and scalability.

A hierarchical frequency stability control strategy for distributed energy resources based on ADMM

With the large-scale distributed energy resources (DERs) interfaced by power electronic converters connected to the power grid, the traditional synchronous generation is gradually replaced, and the inertia and primary frequency regulation capability of the power system is weakened, which seriously threatens the frequency security of the power grid. In view of the above problems, a hierarchical control strategy by coordinating the distributed wind turbine (WT) and photovoltaic (PV) is presented to improve the transient frequency (TF) and steady-state frequency (SSF). For the system control level, the optimal frequency regulation coefficients of multiple WTs and PVs clustering systems are determined by the optimal control principle with minimum frequency regulation energy, while considering the constraints of TF and SSF. For the WT/PV control level, the frequency regulation coefficients of WTs and PVs are solved by the model predictive controller (MPC) and alternating direction method of multipliers (ADMM), with the minimum control cost of WT and PV. It achieves the optimal allocation of frequency regulation power and improves the computing efficiency. Finally, the validity of the proposed method is tested in the modified IEEE 10-machine 39-bus system.