First-order Method Research Articles

Ultra-low frequency and broadband flexural wave attenuation using an inertant nonlinear metamaterial beam

Attenuation of elastic waves in the extremely low frequency range is a considerable challenge. While linear acoustic metamaterials can manipulate elastic waves, their effectiveness is often limited to a narrow frequency range. The present paper proposes a novel inertant nonlinear metamaterial beam to address the challenging problem of the ultra-low frequency broadband flexural wave attenuation. The amplitude-frequency response and dispersion relations of the flexural waves are obtained using the first-order harmonic balance method, where four different resonant units are investigated and the resulting band gaps are compared. Finite element (FE) simulations are also conducted to evaluate the transmission spectra of the flexural vibration through a finite metamaterial beam. The good consistency between the band gaps predicted by the analytical model and the FE simulation verifies the correctness and effectiveness of the developed analytical approach. The results of this study demonstrate that introducing the inertance and softening nonlinearity into the resonant units can significantly widen the flexural wave band gaps within the low-frequency range. This finding provides a viable solution for engineering applications that require low-frequency vibration suppression and isolation.

Parameter Study and Optimization of Static Performance for a Hybrid Cable-Stayed Suspension Bridge

The hybrid cable-stayed and suspension (HCSS) bridge is known for its stability and cost-effectiveness, with significant application potential. This study examined the static performance of an HCSS bridge with a 1440 m main span. A finite element model (FEM) was developed to assess key parameters, such as the span-to-rise ratio, cable-to-hanger ratio, pylon stiffness, steel–concrete interface, and cable stiffness. Through FEM analysis and parameter optimization using the zero-order and first-order optimization methods in an ANSYS module, key design variables were optimized. The results show that an inappropriate span-to-rise ratio negatively impacts mid-span girder forces, while increasing the cable-stayed area enhances the overall stiffness. Main cable stiffness plays a crucial role in load-bearing and deformation control. Significant force differences were observed between stay and hanger cables, with axial force in the main girder increasing from the side span to the pylon under dead load. Bending moments in the transition region varied widely under combined loads. Optimizing parameters, such as the span-to-rise and cable-to-hanger ratios, significantly improved the mechanical performance of HCSS bridges, offering valuable insights for future designs.

Modal analysis of plates resting on elastic foundation based on the first-order shear deformation theory and finite element method

This paper investigates the free vibration characteristics of plate structures supported by a Pasternak elastic foundation, utilizing the first-order shear deformation theory (FSDT). FSDT simplifies the plate theory by considering only first-order shear deformation, enhancing formulation simplicity. Additionally, employing plate theory reduces computational complexity, as 2D models entail fewer degrees of freedom compared to their 3D counterparts. The finite element method (FEM) with 8-node quadrilateral element is employed for computational analysis, implemented using MATLAB. First, a comparison is made with some existing data to show the accuracy and reliability of the research. Numerical examples are then presented of the influence of the effects of thickness variation, foundation parameters and boundary conditions on frequency are investigated. The results show that the method converges very fast and reliability when compared to other research findings. The results of the research can be applied to many different engineering applications related to plates resting on elastic foundation.

Particle Virtual Element Method (PVEM): an agglomeration technique for mesh optimization in explicit Lagrangian free-surface fluid modelling

Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.

Efficient fuzzy simulations for estimating the failure credibility of engineering structures under fuzzy environment

Efficiently and accurately solving the failure credibility of a structural system plays a significant role in the engineering field under fuzzy environment. A more precise failure credibility can help assess the safety degree of the system, and then reduce the occurrence of security accidents. At present, the extended fuzzy first-order and second-moment method (EFFOSM) is effective to analyze failure credibility for some occasions. However, when it comes to complicated performance functions and fuzzy inputs, the accuracy of EFFOSM is greatly reduced and its efficiency also needs to be improved. To overcome the above shortcomings, this paper proposes two types of novel fuzzy simulation algorithms, namely uniform discretization algorithm (UDA) and bisection simulation algorithm (BSA). For the system involving frequently-encountered continuous and strictly monotone performance functions of regular LR fuzzy interval inputs, these two algorithms are designed to estimate failure credibility with higher efficiency and accuracy. Subsequently, with the aid of the linearization and regularization procedures in EFFOSM, the application of UDA and BSA is extended to non-monotone performance functions of irregular LR fuzzy intervals. To evaluate and verify the performance of the proposed two algorithms, their comparisons with EFFOSM are conducted through some numerical examples and practical problems. The results show that the proposed two algorithms outperform EFFOSM in terms of accuracy and efficiency, and also have wider application range for estimating the failure credibility of strictly monotone performance functions involving regular LR fuzzy interval inputs. Meanwhile, BSA is slightly better than UDA for the less runtime.

An optimal transport approach for 3D electrical impedance tomography

Abstract This work solves the three-dimensional inverse boundary value problem with the quadratic Wasserstein distance (W2), which originates from the optimal transportation (OT) theory. The computation of the W2 distance on the manifold surface is boiled down to solving the generalized Monge-Ampère equation, whose solution is directly related to the gradient of the W2 distance. An efficient first-order method based on iteratively solving Poisson's equation is introduced to solve the fully nonlinear elliptic equation. Combining with the adjoint-state technique, the optimization framework based on the W2 distance is developed to solve the three-dimensional electrical impedance tomography (EIT) problem. The proposed method is especially suitable for severely ill-posed and highly nonlinear inverse problems. Numerical experiments demonstrate that our method improves the stability and outperforms the traditional regularization methods.

Pollutant Dispersion of Aircraft Exhaust Gas during the Landing and Takeoff Cycle with Improved Gaussian Diffusion Model

Evaluating aviation emissions and examining the dispersion properties of contaminants are crucial for understanding atmospheric pollution. To assess the pollutant emissions and dispersion of aircraft during the landing and takeoff (LTO) cycle, and address air pollution surrounding the airport resulting from flight operations, this study evaluated emissions throughout the LTO phase based on Quick Access Recorder (QAR) data in conjunction with the first-order approximation method. An improved Gaussian diffusion model for mobile point sources was employed to examine the diffusion characteristics of contaminants. Additionally, CFD calculation outcomes for various exhaust velocities and wind speeds were utilized to validate the trustworthiness of the improved Gaussian model. The discussion also encompasses the influence of diffusion time, wind direction, wind speed, temperature gradient, and particle deposition on the concentration distribution of contaminants. The findings indicated that the Gaussian diffusion model aligned with the results of the CFD calculations. The diffusion distribution of contaminants around airports varies over time and is significantly influenced by atmospheric environmental factors, including wind direction, wind speed, and atmospheric stability. Specifically, a change in wind direction from 0° to 45° caused a shift of approximately 1000 m in the contaminant’s center. An increase in wind speed from 3 m/s to 5 m/s led to a decrease in concentration by about 15%. Furthermore, a transition in atmospheric stability from category ‘a’ (very unstable) to ‘f’ (very stable) resulted in a two-order-of-magnitude increase in contaminant concentrations.

Byzantine fault tolerance in distributed machine learning: a survey

ABSTRACT Byzantine Fault Tolerance (BFT) is crucial for ensuring the resilience of Distributed Machine Learning (DML) systems during training under adversarial conditions. Among the rising corpus of research on BFT in DML, there is no comprehensive classification of techniques or broad analysis of different approaches. This paper provides an in-depth survey of recent advancements in BFT for DML, with a focus on first-order optimisation methods, particularly, the popular one Stochastic Gradient Descent (SGD) during the training phase. We offer a novel classification of BFT approaches based on characteristics such as the communication process, optimisation method, and topology setting. This classification aims to enhance the understanding of various BFT methods and guide future research in addressing open challenges in the field. This work provides the foundations for developing robust BFT systems, using a variety of optimisation methods to strengthen resilience.

RFOR-DQHFEM: Hybrid relaxed first-Order reliability and differential quadrature hierarchical finite element method for multi-physics reliability analysis of conical shells

In this current work, a hybrid reliability analysis and theoretical frequency technique are suggested for the reliability response of conical shells. Two levels of analyses are proposed as the main loop of the reliability method for finding the failure probability and the second level applied in the main loop for giving the performance function of frequency applied in conical shell structures with multi-physics vibration analysis. A dynamical adjusting procedure is proposed for computing the relaxed factor using the enough descent condition inside the reliability method. The superior convergence rate is considered for selecting the relaxed factor of the proposed first-order reliability method named RFORM. An elastic-electro-mechanical model based on the Higher-Order Shear Deformation Theory (HSDT) is extended for frequency analysis of conical shells. The innovative numerical procedure named Differential Quadrature Hierarchical Finite Element Method (DQHFEM) as a robust framework for giving the vibration behavior of studied mechanical structures is applied for solving motion equations. The developing DQHFEM and RFORM are applied for the laminated, nanocomposite, and piezoelectric conical shell structures with multi-source uncertainties. Increasing the volume percentage of nanoparticles from 0% to 10% significantly enhances the reliability index, with carbon nanoparticles showing a 132% increase, silica nanoparticles showing a 97% increase, and other nanoparticles showing an approximate 40% increase. Also, as moisture content increases from 0% to 30%, the reliability index for a thickness-to-large-radius ratio of 0.2 drops by about five times. Excessive moisture levels (above 20%) result in a negative reliability index, indicating a hazardous condition.

Physics-informed Neural Network for Force-free Magnetic Field Extrapolation

In this paper, we propose a physics-informed neural network extrapolation method that leverages machine learning techniques to reconstruct coronal magnetic fields. We enhance the classical neural network structure by introducing the concept of a quasi-output layer to address the challenge of preserving physical constraints during the neural network extrapolation process. Furthermore, we employ second-order optimization methods for training the neural network, which are more efficient compared to the first-order optimization methods commonly used in classical machine learning. Our approach is evaluated on the widely recognized semi-analytical model proposed by Low and Lou. The results demonstrate that the deep learning method achieves high accuracy in reconstructing the semi-analytical model across multiple evaluation metrics. In addition, we validate the effectiveness of our method on the observed magnetogram of active region.

Semi-Markov process-driven maintenance scheduling for Tainter gate system considering multiplelimit states

In extended periods of operation, Taiwan’s reservoir electromechanical systems increasingly require substantial maintenance. This research adopts the semi-Markov process, which accommodates non-exponential distribution of state durations, to formulate optimal maintenance strategies for Tainter gate systems that are noted for their prolonged dormancy and significant operational uncertainties. The methodology initiates with the estimation of failure probabilities across four condition states, analyzing deterioration through the Weibull distribution for both general and latent limit states. The general limit state accounts for time-induced deterioration and effects of dormancy using a Bayesian–Weibull first-order reliability method, while the latent limit state addresses activation failures. Employing the semi-Markov process, an annual transition matrix is computed and combined with failure probabilities to assess the Tainter gates’ system reliability. To identify the most efficient maintenance schedule, a genetic algorithm is applied, targeting the minimization of failure probabilities for both limit states below predefined thresholds and cost reduction. Numerical simulations validate the framework’s efficacy, demonstrating its potential to enhance maintenance planning objectivity and decrease dependence on subjective assessments. The findings highlight the predominance of the general limit state in dictating system failure and underscore the risk Tainter gates face during transition from dormancy to activation, emphasizing the need for thorough monitoring.

Probabilistic assessments of running ductile fractures in dense-phase and supercritical CO2 pipelines

Running ductile fracture (RDF) is a severe failure mode of high-pressure pipelines. Dense-phase and supercritical CO2 pipelines are particularly susceptible to RDF due to the unique characteristics of the depressurization process resulting from a fracture of the pipeline. The present study carries out probabilistic analyses of RDF in dense-phase and supercritical CO2 pipelines. The well-known Battelle two-curve method is employed to establish the limit state function for RDF by comparing the arrest pressure with the saturation pressure. The arrest pressure is computed using the Battelle through-wall crack model with the adjustment recently proposed in the literature. The saturation pressure is computed based on the one-dimensional isentropic decompression assumption and a rigorous equation of state. The first-order reliability method is employed to evaluate the probabilities of RDF in hypothetical CO2 pipelines designed per DVN-RP-F104 with representative pipe attributes and initial operating conditions by considering uncertainties in the relevant pipe geometric and material properties. The analysis results indicate that the probability of RDF can vary by several orders of magnitude depending on the pipe attributes and initial operating conditions. Furthermore, the results shed light on the key uncertainties associated with the pipe geometric and material properties that influence the probability of RDF.

First-Order Algorithms for Robust Optimization Problems via Convex-Concave Saddle-Point Lagrangian Reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first-order approaches, based on online convex optimization, have been proposed as alternatives for the case of large-scale problems. However, existing first-order methods are either stochastic in nature or involve a binary search for the optimal value. We show that this problem can also be solved with deterministic first-order algorithms based on a saddle-point Lagrangian reformulation that avoid both of these issues. Our approach recovers the other approaches’ [Formula: see text] convergence rate in the general case and offers an improved [Formula: see text] rate for problems with constraints that are affine both in the decision and in the uncertainty. Experiment involving robust quadratic optimization demonstrates the numerical benefits of our approach. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Veni.191E.035] and the Israel Science Foundation [Grant 1460/19]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0200 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0200 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Comparative analysis of seismic response and vulnerability of laminated bamboo frame structure under near-field and far-field earthquake actions

The study offers an evaluation of seismic response and vulnerability for a five-story laminated bamboo frame structure, assessing the effectiveness of seismic intensity measures across various damage thresholds and the modeling uncertainties involved. A structural finite element model was developed in OpenSees software, utilizing the Pinching4 model to accurately represent the non-linear characteristics of T-shaped steel connections in beam-column joints. Two collections of earthquake records, one consisting of pulse-like near-field and the other of far-field events, were utilized to examine the structure's nonlinear behavior. Additionally, vulnerability curves for various damage states were generated using the multiple stripe analysis technique, applied to both ground motion datasets. The applicability of 24 seismic intensity measures was also analyzed across various damage limit states. The modeling uncertainty under different seismic actions was further estimated using a first-order second-moment method. Ultimately, the annual collapse probability of the structure are elucidated. Research indicates that due to the influence of joint stiffness, the overall structure demonstrates dynamic characteristics that are predominantly of the first mode shape. The spectral acceleration associated with the fundamental period achieves a reduced logarithmic standard deviation in the vulnerability analysis across various limit states. Other IMs considering higher mode effects or softening period actions no longer predominate. In most cases, the modeling uncertainty under far-field seismic action is higher than that under near-field, especially at the severe damage limit states by using an efficient intensity measure. The laminated bamboo frame structure faces a much higher collapse risk in near-field than in far-field conditions.

Statistically optimal firstorder algorithms: a proof via orthogonalization

Abstract We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$ (and possibly some labels ${\boldsymbol{y}}\in{\mathbb{R}}^{n}$) and would like to estimate a coefficient vector ${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by ${\boldsymbol{X}}$ or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix ${\boldsymbol{X}}$ is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as ‘Bayes AMP’). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to \infty $, $n/d\to \delta $, and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

Center-to-face momentum interpolation and face-to-center flux reconstruction in Euler-Euler simulation of gas-solid flows

In order to resolve the pressure checkerboard field problem with collocated grid, it is essential to employ the momentum interpolation method when formulating the pressure equation, and the flux reconstruction method when updating the cell-centered velocity fields. In this study, we first derive a momentum interpolation method for Euler-Euler simulation of gas-solid flows, which is independent of the time step, the transient term discretization scheme, the under-relaxation factor and the shape of grid; a complete first-order flux reconstruction method is then proposed to update the cell-centered velocities. Their effectiveness are proved by simulating the hydrodynamics of solids settlement, gas-solid fixed bed, bubbling fluidized bed and circulating fluidized bed riser, and then comparing the simulation results to the theoretically known solutions. Their superiority over the standard solver of OpenFOAM® in suppressing the high-frequency oscillations and enhancing the smoothness and accuracy is also proved. Finally, the difficulty in fully eliminating the high-frequency oscillations is attributed to the insufficiency of current methods in handling the situations where the independent variables undergo abrupt change.

Ship Hull Hybrid Structural Design Accounting for Reliability

The optimum ship hull design solution has always been a concern, and in recent years, genetic algorithms to optimise the ship hull structure have been developed. The genetic algorithm’s fundaments generate alternative solutions and compare them with pre-defined constants and objectives. The development of design solutions evolves through competition and controlled variations. Minimising the ship hull structure weight is essential in reducing the ship’s capital (construction) expenditure and increasing the cargo capacity. The risk of the ship is associated with the loss of the ship, cargo, human life, environmental pollution, etc. It is a governing factor impacted by the chosen structural design solution and the measures taken to reduce the structural weight. A genetic algorithm will be employed to study the weight minimisation of a multi-purpose ship hull structure, controlling the associated risk by accounting for several structural design variables. The risk and best design solution are defined by the probability of compressive collapse of the stiffened plates, integral ship hull structure, and the associated cost due to failure. The Pareto frontier solutions, calculated by the non-dominated sorting genetic algorithm, NSGA-II, will be employed to determine feasible solutions for the design variables. The first-order reliability method will estimate the Beta reliability index based on the topology of the stiffened plates and ship hull structure as a part of the Pareto frontier solutions. The algorithm employed will not account for any manufacturing constraints and consequences due to the encountered optimal design solution.

Frank–Wolfe and friends: a journey into projection-free first-order optimization methods

AbstractInvented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank–Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility and applicability in a wide range of contexts, combined with an account on recent progress in variants, both improving on the speed and efficiency of this surprisingly simple principle of first-order optimization.

Efficient finite element reliability analysis employing sequentially-updated surrogate model for fragility curve derivation

As the threat of natural disasters to structures intensifies, risk assessment of infrastructure has gained much importance. Fragility curves are essential tools in predicting disaster-related losses and making disaster mitigation decisions. In this paper, we propose a new method to efficiently derive accurate fragility curves for structures with high levels of nonlinearity or complexity, addressing the computational challenges of conventional finite element reliability analysis (FERA). To reduce the computational cost for calculating probability of failure in FERA, the proposed method utilizes the first-order reliability method (FORM). However, even with this approach, the computational cost of deriving the fragility curve may remain high; therefore, a surrogate model is used to further reduce costs. By training the surrogate model using the initial structural damage probabilities for a few hazard intensities, an optimal starting point can be calculated for the subsequent FORM analysis. During the fragility analysis, the surrogate model can be updated sequentially to increase the efficiency of FORM analysis continuously. In particular, the training process of the surrogate model requires no separate or additional finite element analysis because it is constructed using previous FERA results. The accuracy and efficiency of the proposed method are tested using conventional FERA and Monte Carlo simulations through a hypothetical short-column example. In addition, fragility curves are derived through a bridge flood fragility assessment considering the scour and seismic vulnerability assessment of a buried gas pipeline considering soil-structure interactions. The derived fragility curves closely match those derived using the conventional FERA, and the computational costs are reduced by 36.54 % and 52.38 %, respectively, compared with the conventional FERA, confirming its cost-effectiveness.

Estimation of video sequence homography based on a first-order estimation method

As it is a pre-processing task, estimation of video-sequence-based homography requires low computational costs and fast evaluation. However, current algorithms for video sequence tasks are commonly based on image-pair homography and do not consider the inner properties of the video sequences. Therefore they take unnecessary computational resources. In this work, we propose a novel algorithm with a first-order estimation method to fill the gap between estimation of image-pairs and video sequence homography. By considering the continuous movement of the camera, the proposed algorithm adopts a first-order estimation to accelerate the estimation process while maintaining its robustness. Instead of extracting many image features from every frame, we demonstrate that estimating a homography matrix with pixel-based texture patterns is effective and sufficient for video sequences. Experiments show that homography estimation with simple one-dimensional texture vectors, as used in our algorithm, can surpass state-of-the-art feature-based algorithms and deep-learning-based methods. This first-order estimation method was more than 40 times faster and real-time estimation used only the CPU.