Finite Iteration Research Articles

An iterative method for updating undamped structural systems with connectivity constraints

Model updating is a method of correcting analytical models, such as the finite element models, by improving the correlation between the measured data and the analytical modal data. In this paper, we develop an iterative method to update undamped structural systems by using measured modal parameters. The method allows mass and stiffness matrices to be updated simultaneously. And we can obtain optimal updated matrices within finite iteration steps by choosing a special kind of initial matrix pair. More importantly, the method can preserve the physical connectivity of the original model and the updated model is in good agreement with the experimental modal data. Two real numerical examples show that the proposed method is feasible and efficient.

Real-time topology optimization based on multi-scale convolutional attention mechanism

This article proposes a deep learning model based on a multi-scale convolutional attention mechanism network SegNext for improving Topology Optimization (TO-Next), aimed at addressing the computational challenges associated with finite element iterations in traditional density-based methods. TO-Next is trained on diverse topology structures with varying loads, constraints and enriched physical information after initial iterations to enhance its generalization. Following training on three distinct decoder architectures, the optimal encoder–decoder network structure is determined. This study also investigates the algorithm's generalization capability under both single and multiple load constraints. The results indicate the superior performance and efficiency of the proposed method compared with the Solid Isotropic Material with Penalization (SIMP) method, enabling real-time generation of near-optimal topology structures within a short timeframe.

An inexact proximal linearized DC algorithm with provably terminating inner loop

Standard approaches to difference-of-convex (DC) programs require exact solution to a convex subproblem at each iteration, which generally requires noiseless computation and infinite iterations of an inner iterative algorithm. To tackle these difficulties, inexact DC algorithms have been proposed, mostly by relaxing the convex subproblem to an approximate monotone inclusion problem. However, there is no guarantee that such relaxation can lead to a finitely terminating inner loop. In this paper, we point out the termination issue of existing inexact DC algorithms by presenting concrete counterexamples. Exploiting the notion of ϵ-subdifferential, we propose a novel inexact proximal linearized DC algorithm termed tPLDCA. Despite permission to a great extent of inexactness in computation, tPLDCA enjoys the same convergence guarantees as exact DC algorithms. Most noticeably, the inner loop of tPLDCA is guaranteed to terminate in finite iterations as long as the inner iterative algorithm converges to a solution of the proximal point subproblem, which makes an essential difference from prior arts. In addition, by assuming the first convex component of the DC function to be pointwise maximum of finitely many convex smooth functions, we propose a computational friendly surrogate of ϵ-subdifferential, whereby we develop a feasible implementation of tPLDCA. Numerical results demonstrate the effectiveness of the proposed implementation of tPLDCA.

An iterative method for updating finite element models with connectivity constraints

It is well known that the analytical matrices arising from the discretization of distributed parameter systems using the finite element technique are usually symmetric and banded. How to preserve the coefficient matrices of the updated model being of the same band structure is an important yet difficult challenge for model updating in structural dynamics. In this paper, an iterative method for updating mass, damping and stiffness matrices simultaneously based on partial modal measured data is provided. By the method, the optimal updated matrices can be obtained within finite iteration steps by choosing a special kind of initial matrix triplet. The proposed approach not only preserves the physical connectivity of the original model, but also the updated model reproduces the measured modal data, which can be utilized for various finite element model updating problems. Numerical examples confirm the effectiveness of the introduced method.

MSz: An Efficient Parallel Algorithm for Correcting Morse-Smale Segmentations in Error-Bounded Lossy Compressors.

This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the discrepancies in topology between original and decompressed datasets could potentially result in erroneous interpretations or even incorrect scientific conclusions. In this paper, we focus on preserving Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting the precise reconstruction of minimum/maximum labels induced by the integral line of each vertex. The key is to derive a series of edits during compression time. These edits are applied to the decompressed data, leading to an accurate reconstruction of segmentations while keeping the error within the prescribed error bound. To this end, we develop a workflow to fix extrema and integral lines alternatively until convergence within finite iterations. We accelerate each workflow component with shared-memory/GPU parallelism to make the performance practical for coupling with compressors. We demonstrate use cases with fluid dynamics, ocean, and cosmology application datasets with a significant acceleration with an NVIDIA A100 GPU.

FINC: An Efficient and Effective Optimization Method for Normalized Cut.

The optimization methods for solving the normalized cut model usually involve three steps, i.e., problem relaxation, problem solving and post-processing. However, these methods are problematic in both performance since they do not directly solve the original problem, and efficiency since they usually depend on the time-consuming eigendecomposition and k-means (or spectral rotation) for post-processing. In this paper, we propose a fast optimization method to speedup the classical normalized cut clustering process, in which an auxiliary variable is introduced and alternatively updated along with the cluster indicator matrix. The new method is faster than the conventional three-step optimization methods since it solves the normalized cut problem in one step. Theoretical analysis reveals that the new method is able to monotonically decrease the normalized cut objective function and converge in finite iterations. Moreover, we have proposed efficient methods for adjust two regularization parameters. Extensive experimental results show the superior performance of the new method. Moreover, it is faster than the existing methods for solving the normalized cut.

Multistage Competitive Opinion Maximization With Q-Learning-Based Method in Social Networks.

Competitive opinion maximization (COM) aims to determine some individuals (i.e., seed nodes) from social networks, propagating the desired opinions toward a target entity to their neighbors through social relationships when facing with its competitors (components) and maximize the opinion spread after the specific time. Current studies on COM are still in its infancy, while the only work merely considers the scenario that the strategy of competitors is known but ignores the unknown scenario. In addition, previous studies on COM cannot easily address the situation where some users might dynamically change their opinions. To address the COM issue, we investigate the multistage COM and propose a brand-new Q-learning-based opinion maximization framework (QOMF). Our QOMF consists of two components: dynamic opinion propagation and seeding process. We formulate the COM problem by maximizing relative effective opinions. To produce a dynamic opinion series more realistically, we design an opinion propagation model by joining the activation process and a dynamic opinion process. Moreover, we also verify that the opinion propagation model can reach convergence within finite iterations. To acquire the seed nodes, we design a multistage Q-learning seeding scheme by considering known and unknown competitor strategies, respectively. Experimental results on three real datasets demonstrate that the proposed method outperforms the benchmarks on reaching relatively effective opinions.

Data-Driven Robust Finite-Iteration Learning Control for MIMO Nonrepetitive Uncertain Systems.

This work considers three main problems related to fast finite-iteration convergence (FIC), nonrepetitive uncertainty, and data-driven design. A data-driven robust finite-iteration learning control (DDRFILC) is proposed for a multiple-input-multiple-output (MIMO) nonrepetitive uncertain system. The proposed learning control has a tunable learning gain computed through the solution of a set of linear matrix inequalities (LMIs). It warrants a bounded convergence within the predesignated finite iterations. In the proposed DDRFILC, not only can the tracking error bound be determined in advance but also the convergence iteration number can be designated beforehand. To deal with nonrepetitive uncertainty, the MIMO uncertain system is reformulated as an iterative incremental linear model by defining a pseudo partitioned Jacobian matrix (PPJM), which is estimated iteratively by using a projection algorithm. Further, both the PPJM estimation and its estimation error bound are included in the LMIs to restrain their effects on the control performance. The proposed DDRFILC can guarantee both the iterative asymptotic convergence with increasing iterations and the FIC within the prespecified iteration number. Simulation results verify the proposed algorithm.

Airborne Internet: An Ultradense LEO Networks Empowered Satellite-to-Aircraft Access and Resource Management Approach

With the rapid development of low earth orbit (LEO) satellite technologies and constellation projects (like Starlink, OneWeb), the ongoing ultra-dense LEO satellite networks can provide an efficient solution to ubiquitous connection of aircraft. It is urgent to design the ultra-dense LEO network enabled satellite-to-aircraft communication for in-cabin users with high-speed Internet connectivity requirements. In this paper, we investigate the resource scheduling of ultra-dense LEO network enabled satellite-to-aircraft communication and the in-cabin communication inside aircraft in civil aviation. First, we adopt the Lyapunov optimization framework to tackle the high dynamic and fast mobility of satellites and aircraft. For the satellite-to-aircraft access and subchannel assignment, we propose a dynamic access and subchannel allocation algorithm based on matching theory, which can converge to a stable matching within a finite iterations. To guarantee customized needs of in-cabin users, we propose a power control algorithm based on the successive convex approximation technology to optimize the power allocation of satellites on each subchannel and the transmit power of aircraft for each in-cabin user, which is proven to obtain a saddle point or a local minimum with low complexity. Extensive simulations have been carried out to validate the effectiveness of the proposed resource allocation method.

Bipartite graph-based community-to-community matching in local energy market considering socially networked prosumers

The mutual influences among different energy prosumers caused by the socially connected relationship have not been modeled explicitly in the current local energy market. Hence, we first develop an iterative market clearing framework to bridge the data-driven and model-driven models of heterogeneous market participants. Then, we consider the behavior difficulty, communication channel, depth of information process, social influence, and observed peer effects in the multi-agent deep reinforcement learning (MADRL) framework in the data-driven models. Finally, we calculate the marginal market value of each C2C energy transaction with a linearized distribution network power flow model and formulate the C2C matching as a bipartite graph. We propose a recurrent Hungarian algorithm to solve the best matching schemes of C2C trading. Case studies verify that the distribution network power flow model considered in C2C energy trading successfully constrain the unit values of nodal voltages between 0.9 and 1.1. The power flow values in distribution network are constrained within the upper limits of transmission capacity for each branch. The finite iteration number of MADRL in hybrid market-clearing algorithm guarantees the normal P2P energy market operation. Moreover, the social influences for the P2P energy trading results are verified by comparing P2P trading results in different scenarios. Our proposed model can better depict the trading behaviors in communities.

Distributed adaptive optimization for microgrids

AbstractIn this article, a one‐critic Q‐learning algorithm for the adaptive optimization of the distributed microgrids is proposed to improve the charging and discharging management and optimization of batteries in microgrids. Constrained by the random power generation of sustainable energy and the high uncertainty of power load, this article presents a dynamic balance point of the remaining power of the battery pack, and the dual battery pack constitutes a dynamic power game augmented system in the charge‐discharge process. The structure of the one‐critic neural network can effectively simplify the computational complexity, and the value can converge to the optimal solution in finite iterations. Simulation experiments also prove that the Q‐learning can effectively curb the overcharge and over‐discharge behavior of the battery pack, and realize the tracking of the dynamic SOC balance point.

Inverse-Covariance-Intersection-Based Distributed Estimation and Application in Wireless Sensor Network

In a sensor network, estimation performance may degrade when unknown correlations among local estimates are not addressed carefully. This article presents a novel distributed estimation algorithm based on inverse covariance intersection (ICI) for effectively solving the cross-correlation and dynamic state estimation problems in a wireless sensor network. The intermediate results of a set of consensus filters running in parallel are utilized to realize a global fusion of estimates, which involves all agents' local estimates and improves the estimation accuracy. Meanwhile, the global consistency of the proposed algorithm can be guaranteed theoretically since the fusion process considers all local estimates jointly and in a unified way. Furthermore, besides the asymptotic performance, the boundedness and consistency of the fused estimate can be achieved under finite iterations, which demonstrates its robustness and potential in practical applications. A cooperative target tracking problem illustrates the performance of the proposed algorithm.

Efficient Transmitter Selection Strategies for Improved Information Gathering of Aerial Vehicle Navigation in GNSS-Denied Environments

Aerial vehicle navigation in global navigation satellite system (GNSS)-denied environments by utilizing pseudorange measurements from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> terrestrial signals of opportunity (SOPs) is considered. To this end, the aerial vehicle is tasked with choosing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> most informative terrestrial SOPs. Two computationally efficient, but sub-optimal, transmitter selection strategies are proposed. These selection strategies, termed opportunistic greedy selection (OGS) and one-shot selection (OSS), exploit the additive, iterative properties of the Fisher information matrix (FIM), where OGS selects the most informative transmitters in finite iterations, while the OSS selects in one-iteration. Monte Carlo simulation results are presented comparing the OGS and OSS strategies versus the optimal (exhaustive search) selection strategy, where it is concluded that OGS performs closely to the optimal selection, while executing in a fraction of the optimal selection's time. Experimental results are presented of a U.S. Air Force high-altitude aircraft navigating without GNSS signals in (i) a rural region and (ii) a semi-urban region. The performance of the aircraft's navigation solution with the selected SOP transmitters via optimal, OGS, OSS are compared over a flight segment where the selection remained valid. The position root mean-squared error (RMSE) with the optimal, OGS, and OSS were 4.53 m, 6.28 m, 7.13 m in the rural region; and 5.83 m, 6.08 m, 6.70 m in the semi-urban region for an aircraft traversing a trajectory of 1.48 km and 1.22 km, respectively.

Distributionally robust production and replenishment problem for hydrogen supply chains

This study investigates a two-stage production and replenishment problem for the hydrogen supply chain (HSC), where the uncertainty of demand and the risk of pipeline disruptions are simultaneously considered. We model this problem by adopting a distributionally robust optimization (DRO) approach. Before realizing the demands, the decision-maker decides the hydrogen production, storage, and truck-transported replenishment policies. Then, after demands and pipeline working status are realized, the pipeline-transported replenishment policy is determined in response to the first-stage decisions. The replenishment policies are determined under differentiated service level requirements. In addition, we characterize the uncertainty and correlation of demands through a factor-based model approach to accommodate the uncertainty of the distribution of demand factors. To solve the proposed model, we propose a column and constraint generation (CCG) algorithm, which can terminate in finite iterations. Through theoretical analysis and numerical experiments, we verify that the proposed model outperforms classical benchmark models in terms of total costs and are more robust. Finally, we examine the impact of the replenishment structure on the performance of the HSC and the computational efficiency of the proposed CCG algorithm.

Logic for reasoning about bugs in loops over data sequences (IFIL)

Classic deductive verification is not focused on reasoning about program incorrectness. Reasoning about program incorrectness using formal methods is an important problem nowadays. Special logics such as Incorrectness Logic, Adversarial Logic, Local Completeness Logic, Exact Separation Logic and Outcome Logic have recently been proposed to address it. However, these logics have two disadvantages. One is that they are based on under-approximation approaches, while classic deductive verification is based on the over-approximation approach. One the other hand, the use of the classic approach requires defining loop invariants in a general case. The second disadvantage is that the use of generalized inference rules from these logics results in having to prove too complex formulas in simple cases. Our contribution is a new logic for solving these problems in the case of loops over data sequences. These loops are referred to as finite iterations. We call the proposed logic the Incorrectness Finite Iteration Logic (IFIL). We avoid defining invariants of finite iterations using a symbolic replacement of these loops with recursive functions. Our logic is based on special inference rules for finite iterations. These rules allow generating formulas with recursive functions corresponding to finite iterations. The validity of these formulas may indicate the presence of bugs in the finite iterations. This logic has been implemented in a new version of the C-lightVer system for deductive verification of C programs.

A Monotone Discretization for the Fractional Obstacle Problem and Its Improved Policy Iteration

In recent years, the fractional Laplacian has attracted the attention of many researchers, the corresponding fractional obstacle problems have been widely applied in mathematical finance, particle systems, and elastic theory. Furthermore, the monotonicity of the numerical scheme is beneficial for numerical stability. The purpose of this work is to introduce a monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. Through successful monotone discretization of the fractional Laplacian, the monotonicity is preserved for the fractional obstacle problem and the uniform boundedness, existence, and uniqueness of the numerical solutions of the fractional obstacle problems are proved. A policy iteration is adopted to solve the discrete nonlinear problems, and the convergence after finite iterations can be proved through the monotonicity of the scheme. Our improved policy iteration, adapted to solution regularity, demonstrates superior performance by modifying discretization across different regions. Numerical examples underscore the efficacy of the proposed method.

Generalized conjugate direction algorithm for solving general coupled Sylvester matrix equations

In this paper, a generalized conjugate direction algorithm (GCD) is proposed for solving general coupled Sylvester matrix equations. The GCD algorithm is an improved gradient algorithm, which can realize gradient descent by introducing matrices Pj(k) and Tj(k) to construct parameters α(k) and β(k). The matrix Pj(k) and Tj(k) are iterated in a cross way to accelerate the convergence rate. In addition, it is further proved that the algorithm converges to the exact solution in finite iteration steps in the absence of round-off errors if the system is consistent. Also, the sufficient conditions for least squares solutions and the minimum F-norm solutions are obtained. Finally, numerical examples are given to demonstrate the effectiveness of the GCD algorithm.

Enabling Fully-Decoupled Radio Access With Elastic Resource Allocation

Recently, an origin fully-decoupled radio access network (FD-RAN) inspired by neurotransmission has been proposed for B5G/6G mobile communication networks, which achieves the potentials of improving the spectrum efficiency, reducing the energy consumption and meeting personalized user requirement through profound resource cooperation. To explore new radio and networking technologies, in this paper, we propose an elastic and efficient resource allocation for the FD-RAN architecture. First, we assume that the wireless spectrum is integrated for more reasonable allocation and sharing the spectrum dynamically across frequencies, location, users, services and networks. In particular, we propose a user-BS-subchannel matching algorithm to solve the dynamic uplink and downlink spectrum division, BS cooperation and subchannel assignment problems based on the many-to-many matching model. Our algorithm is proved to converge to a stable matching within finite iterations. Then, we propose a power control algorithm for uplink and downlink transmissions to further enhance the system performance based on the successive convex approximation. The obtained power control solution is proved to achieve a Karush-Kuhn-Tucker point. Extensive simulation results demonstrate that the proposed dynamic division of uplink and downlink spectrum, BS cooperation, subchannel assignment and power control can effectively improve the network performance for the FD-RAN architecture.

The design of distributed filtering based on lattice rule

For the problem of multiple micro-target tracking and positioning, the high-dynamic and communication coupling are two cases in actual motion. The dynamic evolution and measurement among them are depicted by a nonlinear system. This paper proposes a new distributed lattice Kalman filter (DLKF) to cope with the two cases simultaneously. The prediction is based on the Cranley-Patterson shift and Korobov lattice rule to generate the low-difference sample points. The update stage is based on the weighted average consistency to fusion its innovation and the information of its neighbor. The stability of this distributed filter is proved by constructing the upper and lower bound of the Lyapunov functional. The finite steps consensus iteration strategies for the update fusion are also investigated. To evaluate the efficiency of the DLKF, it is compared with unscented Kalman filtering and its distributed form. The simulation results show that DLKF uses significantly fewer sampling points than other quasi-Monte Carlo (QMC) filters while maintaining the estimation accuracy. The computational complexity is significantly lower, which is the key factor for application to multiple micro-targets.

L∞-Convergence Analysis of a Finite Element Linear Schwarz Alternating Method for a Class of Semi-Linear Elliptic PDEs

In this paper, we prove uniform convergence of the standard finite element method for a Schwarz alternating procedure for a class of semi-linear elliptic partial differential equations, in the context of linear iterations and non-matching grids. More precisely, making use of the subsolution-based concept, we prove that finite element Schwarz iterations converge, in the maximum norm, to the true solution of the PDE. We also give numerical results to validate the theory. This work introduces a new approach and generalizes the one in [14] as it encompasses a larger class of problems.