Number Of Iterations Research Articles

A New Alternating Suboptimal Dynamic Programming Algorithm with Applications for Feature Selection

Feature selection is predominantly used in machine learning tasks, such as classification, regression, and clustering. It selects a subset of features (relevant attributes of data points) from a larger set that contributes as optimally as possible to the informativeness of the model. There are exponentially many subsets of a given set, and thus, the exhaustive search approach is only practical for problems with at most a few dozen features. In the past, there have been attempts to reduce the search space using dynamic programming. However, models that consider similarity in pairs of features alongside the quality of individual features do not provide the required optimal substructure. As a result, algorithms, which we will call suboptimal dynamic programming algorithms, find a solution that may deviate significantly from the optimal one. In this paper, we propose an iterative dynamic programming algorithm, which invertsthe order of feature processing in each iteration. Such an alternating approach allows for improving the optimization function by using the score from the previous iteration to estimate the contribution of unprocessed features. The iterative process is proven to converge and terminates when the solution does not change in three successive iterations or when the number of iterations reaches the threshold. Results in more than 95% of tests align with those of the exhaustive search approach, being competitive and often superior to the reference greedy approach. Validation was carried out by comparing the scores of output feature subsets and examining the accuracy of different classifiers learned on these features across nine real-world applications, considering different scenarios with various numbers of features and samples. In the context of feature selection, the proposed algorithm can be characterized as a robust filter method that can improve machine learning models regardless of dataset size. However, we expect that the idea of alternating suboptimal optimization will soon be generalized to tasks beyond feature selection.

Geometry optimization of a floating platform with an integrated system of wave energy converters using a genetic algorithm

This study uses a genetic algorithm(GA) to investigate the practicality of optimizing the geometry and dimensions of a floating platform, which houses pitching wave energy converters (WEC). Using frequency-domain analysis, sensitivity tests for the search start point, choice of optimized variable, number of iterations, simulation time, and contents of the search space are made. Results show that the required number of iterations to convergence increases with an increased number of optimized variables. Furthermore, for the studied platform geometry, no single global optimum exists. Instead, various combinations of characteristic features can lead to comparable performances of the integrated wave absorber. Finally, it is observed that when the solution space is controlled and made to contain a subset of potential solutions known to improve the system performance, computation time, absorption efficiency and range are observed to improve. Additionally, the GA optimum tends towards platform geometries for which the wave absorber’s resonance response corresponds to the dominating wave climate frequencies. A key contribution of this study is the controlled manipulation of the solution space to contain a subset of potential solutions that enhance system performance. This controlled approach leads to improvements in computation time, absorption efficiency, and range of the system.

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow [17] to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ∼25.7.

Solving nonlinear structural problems by associating line-search and path-following techniques

The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line-search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence.

A design of interactive review for computer aided diagnosis of pulmonary nodules based on active learning

Automatic detection of pulmonary nodule based on computer tomography (CT) images can significantly improve the diagnosis and treatment of lung cancer. However, there is a lack of effective interactive tools to record the marked results of radiologists in real time and feed them back to the algorithm model for iterative optimization. This paper designed and developed an online interactive review system supporting the assisted diagnosis of lung nodules in CT images. Lung nodules were detected by the preset model and presented to doctors, who marked or corrected the lung nodules detected by the system with their professional knowledge, and then iteratively optimized the AI model with active learning strategy according to the marked results of radiologists to continuously improve the accuracy of the model. The subset 5-9 dataset of the lung nodule analysis 2016(LUNA16) was used for iteration experiments. The precision, F1-score and MioU indexes were steadily improved with the increase of the number of iterations, and the precision increased from 0.213 9 to 0.565 6. The results in this paper show that the system not only uses deep segmentation model to assist radiologists, but also optimizes the model by using radiologists' feedback information to the maximum extent, iteratively improving the accuracy of the model and better assisting radiologists.

Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2)

Abstract. Solving the momentum balance is the computationally expensive part of simulating the evolution of ice sheets. The momentum balance is described by the nonlinear full-Stokes equations, which are solved iteratively. We use the Picard iteration and Newton's method combined with Armijo step sizes and approximately exact step sizes, respectively, to solve these equations. The Picard iteration uses either no step size control or the approximately exact step sizes. We compare the variants of Newton's method and the Picard iteration in benchmark experiments, called ISMIP-HOM experiments A, B, E1, and E2. The ISMIP-HOM experiments consist of a more realistic domain and are designed to test the quality of ice models. For an even more realistic test case, we simulate the experiments E1 and E2 with a time-dependent surface. We obtain that approximately exact step sizes greatly reduce the necessary number of iterations for the Picard iteration and Newton's method with nearly no increase in the computation time for each iteration.

Research on image recognition of tomato leaf diseases based on improved AlexNet model

Aiming at the problems that the traditional image recognition technology is challenging to extract useful features and the recognition time is extended; the AlexNet model is improved to improve the effect of image classification and recognition. This study focuses on 8 types of tomato leaf diseases and healthy leaves. By using HOG and LBP weighted fusion to extract image features, a tomato leaf disease recognition model based on the AlexNet model is proposed, and transfer learning is used to train the AlexNet model. Transfer the knowledge learned by the AlexNet model on the PlantVillage image dataset to this model while reducing the number of fully connected layers. Keras deep learning framework and programming language Python were used. The model was implemented, and the classification and identification of tomato leaf diseases were carried out. The recognition rate of feature-weighted fusion classification is higher than that of serial and parallel methods, and the recognition time is the shortest. When the weight coefficient ratio of HOG and LBP is 3:7, the image recognition rate is the highest, and its value is 97.2 %. From the model performance curve See, when the number of iterations is more than 150 times, the training set and test accuracy rate both exceed 97 %, the loss rate shows a gradient decline, and the change is relatively stable; compared with the traditional AlexNet model, HOG + LBP + SVM model, and VGG model, improved AlexNet model has the highest recognition rate, and it has high recall value, accuracy, and F1 value; Compared with the latest convolutional neural network disease recognition models, improved AlexNet model recognition accuracy was 98.83 %, and the F1 value was 0.994. It shows that the model has good convergence performance, fast prediction speed, and low loss rate and can effectively identify 8 types of tomato leaf images, which provides a reference for the research on crop disease identification.

Dynamical properties of a small heterogeneous chain network of neurons in discrete time

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark–Sacker, double Neimark–Sacker, flip- and fold-Neimark–Sacker, and 1 : 1 and 1 : 2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Energy-efficient data collection in UAV-assisted semantic awareness IoT network

Semantic communication shows great potential in reducing data redundancy and improving data collection efficiency in the Internet of Things (IoT) networks. However, IoT devices have limited energy storage capacity, so it is not possible to transmit semantic information to cloud center all the time. To this end, we propose an energy-efficient uploading mechanism in the UAV-assisted semantic awareness data collection system. Specially, we minimize the maximum energy consumption of IoT devices via jointly optimizing user scheduling and UAV trajectory. Since the formulated optimization problem is non-convex, we propose an efficient iterative algorithm to obtain a feasible solution. As the number of iterations increases, the user min–max energy consumption gradually converges to a steady state. Simulation results show that the proposed algorithm has good convergence. In addition, the simulation results of our proposed scheme show that the system performance is greatly improved compared with the conventional bit information transmission and non-optimization schemes.

K-Means Algorithm for Clustering Students Based on Areas of Expertise (A Case Study)

Every student of the Software Engineering Technology study program, the Computer and Informatics Department of the Politeknik Negeri Medan in the lecture process is required to take all the courses in the curriculum. From the courses in the curriculum, there are several subject groups that shape student expertise, such as Software Engineering, System Analyst, Database Administrator, and IT Entrepreneur. It is hoped that this expertise will later be used as a reference by students in carrying out their thesis at the end of lectures. The purpose of this study is to group students based on their respective expertise based on data processing of student course scores related to each skill. The data used is data on student scores for batches of 2020 and 2021 with a range of courses from semester 1 to semester 3. The data is tested by implementing the K-Means algorithm. The results of the tests that have been carried out show the grouping of students based on their expertise, with 7 times the number of iterations. Then, data testing was carried out with the RapidMiner application to get the results of the distribution of cluster members obtained, including 12 students occupying Software Engineer skills, 21 students with System Analyst skills, 5 students with Database Administrator skills, and 31 students with IT Entrepreneur skills, along with the distribution chart. Thus, the K-Means algorithm is quite good at grouping students based on their expertise

Enhanced frequency and time domain feature extraction for communication infrastructure type classification using optical fiber sensing

We present a feature extraction method for a feedforward-type neural network (FNN) designed to realize a distributed acoustic sensing (DAS) technique that suits conventional optical fiber. This is, to the best of our knowledge, the first trial in which an FNN is used to interpret the field communication infrastructure type surrounding optical cables. Three classes are taken to represent the field environment: the cable tunnel (class 1), circular duct (class 2), and overhead area (class 3). We investigate and compare frequency- and time-domain feature extraction. We also show that the frequency-domain features yielded by spectral envelope shape (SES) processing have better performance than simple fast Fourier transform features. Two types of time-domain features are verified: one is the short-time maximum magnitude (STMM), which shows the largest value in the time frame, and the other is the short-time average magnitude (STAM), which indicates the average value in a time frame. Note that all features are optimized for multi-class classification. In this paper, we present the suitable number of both features and the number of training iterations. An accuracy rate of 79.0% is achieved using FNN analysis with the features studied here. Furthermore, by considering the similarity of neighboring classes, classes are refined into higher probability classes. As a result, accuracy is improved to 87.2%.

Improved image denoising through fractional anisotropic diffusion and resolution-tailored differentiation in the Fourier domain

Fractional-order anisotropic diffusion-based denoising of images has been implemented in the literature through fractional differentiation in the Fourier domain. Furthermore, Fourier transform of the schemes on half-integer or integer mesh points has been used for the differentiation of images. In this paper, differentiation in the Fourier domain is proposed using schemes on fractional mesh points, aiming to enhance the performance of the algorithm. This can be regarded as employing fractional schemes at various resolutions, governed by a parameter of resolution within the range of (0.5, 1). Variations in resolution affect the pixel neighborhood by incorporating additional information from interpolated pixels. Experiments conducted on a reference image dataset, using three quantitative measures, demonstrate that the proposed method surpasses the method from the literature for higher values of the parameter of resolution. The improvement is particularly noticeable at higher noise levels, where the proposed method consistently outperforms the method from the literature across all values of the parameter of resolution. As a side effect, the proposed method is less time-consuming than the original method, as it requires higher time steps within the numerical scheme. Experiments and stability analysis show that the proposed method reduces the number of iterations by three to four times compared to the original method.

Reconstruction method for gamma-ray coded-aperture imaging based on mask and anti-mask functions

Gamma-ray coded-aperture imaging technology plays an important role in nuclear security, decommissioning of nuclear facilities, and nuclear medicine diagnosis. However, under near-field imaging condition, artifacts in the reconstructed image can interfere with identifying the shape and position of the radioactive source. In this paper, a gamma-ray coded-aperture imaging method based on mask and anti-mask functions was proposed to suppress imaging artifacts and speed up the acquisition of low-noise reconstructed images. Through simulation, the effects of the number of iterations and the thickness of the coded-aperture collimator on the imaging quality were studied, and the range of the optimal correction factor in the method was determined. Imaging experiments were conducted using a compact coded-aperture gamma camera based on CdZnTe detector to verify the applicability of the optimal correction factor range. The limitations of the proposed method were analyzed through complex-shaped source imaging simulations and multi-source imaging experiments. This method has an insufficient suppression effect on random artifacts and requires further improvement in imaging irregular radioactive sources. However, it has good imaging performance for single-point source and multi-point sources, effectively reducing regular cross-shaped and stripe-like artifacts. In the non-uniform radioactive background, it can eliminate a part of artifacts, significantly improving imaging quality. Therefore, this method has potential applications in complex radioactive environments.

Enhancing CFD solver with Machine Learning techniques

This study addresses the computational challenges in fluid flow simulations arising from demanding computational grids, required to capture the temporal and length scales involved. Our approach focuses on the pressure solver, as this is a resource-intensive component in Computational Fluid Dynamics (CFD) solvers. We achieve this by integrating a Machine Learning (ML) surrogate model with an incompressible fluid flow solver. We created two variants of an ML-enhanced CFD solver which were able to reduce the number of iterations required by the CFD pressure solver during unsteady flow simulations. Consequently, the simulations yielded comparable drag coefficients and Strouhal numbers, accompanied by an eightfold decrease in execution time. The performance enhancements are attributed to reduced computational effort per temporal iteration and early-stage forcing on the simulation dynamical behavior when using the ML-based surrogate models. This research introduces an approach to enhance the computational efficiency of fluid flow analyses by incorporating surrogate models to aid the pressure solver in CFD simulations. We propose a Hybrid CFD solver, ie. a physics-informed solver enhanced with data-driven surrogate models.

Distributed least-squares progressive iterative approximation for blending curves and surfaces

Least-squares progressive iterative approximation (LSPIA) is an effective tool for fitting data points with curves and surfaces in CAD/CAM, due to its intuitive geometric meaning and its suitability for handling mass data. However, the classic LSPIA method for blending curves and surfaces has a slow convergence rate and takes a long CPU execution time, since the spectral radius of its iteration matrix is near to 1. To achieve a reduction in CPU execution time, this paper presents a distributed least-squares progressive iterative approximation (DLSPIA) method by dividing the collocation matrix into some blocks, which are called processors. The proposed method distributes the computation of the control points progressively in a way that each processor is responsible for a block of the whole point set. Combining the information obtained from the previous processors with that of the current processor, the DLSPIA method can progressively and quickly approximate the least-squares fitting result of the original data set block by block via distributed computation. And the algorithm converges within a finite number of iterations. Furthermore, the iterative formulae for blending surface fitting are expressed in matrix form, which can avoid the computation of the matrix Kronecker product to reduce the CPU execution time. Several numerical examples are presented to demonstrate the superiority of the proposed method compared with the previous methods.

Harmonic Detection Methods and Optimization Strategies for Charger in Power Grid

The charger’s operation in the power grid will cause harmonic pollution, affecting the service life of the equipment and the quality of the power grid. The harmonic characteristics and detection during the charging process are studied. The simulation model of charger is established first using MATLAB, the results of the experiment show that odd harmonics are mainly generated during charging, and the distortion rate of the current harmonics remains between 0.231 and 0.443 during the charging process. A new wavelet neural network is proposed to detect the harmonic method. Experimental results indicate that, compared with previous detection methods, this network has better detection efficiency and accuracy for harmonics. But detection result of this network is unstable and does not even converge. A new adaptive bat algorithm with improved focusing distance is presented here to optimize the wavelet neural network, which effectively solves the defect of being sensitive to the node number of hidden layer, resulting in higher detection accuracy, faster detection speed, and stable convergence. The detection error range is reduced from −0.03 to 0.02, and the number of iterations is reduced to around 1000.

Iteration and stochastic first-order oracle complexities of stochastic gradient descent using constant and decaying learning rates

The performance of stochastic gradient descent (SGD), which is the simplest first-order optimizer for training deep neural networks, depends on not only the learning rate but also the batch size. They both affect the number of iterations and the stochastic first-order oracle (SFO) complexity needed for training. In particular, the previous numerical results indicated that, for SGD using a constant learning rate, the number of iterations needed for training decreases when the batch size increases, and the SFO complexity needed for training is minimized at a critical batch size and that it increases once the batch size exceeds that size. Here, we study the relationship between batch size and the iteration and SFO complexities needed for nonconvex optimization in deep learning with SGD using constant or decaying learning rates and show that SGD using the critical batch size minimizes the SFO complexity. We also provide numerical comparisons of SGD with the existing first-order optimizers and show the usefulness of SGD using a critical batch size. Moreover, we show that measured critical batch sizes are close to the sizes estimated from our theoretical results.

Model‐free inversion‐based iterative learning control algorithm with adaptive gain: Achieving superior robustness and convergence

AbstractThe main objective of this work is to address the challenge of simultaneously ensuring robustness and convergence performance in model‐free inversion‐based iterative learning control. Initially, this research provides a mathematical analysis of the sources of errors in the iterative process, followed by proposing a gain design guideline to enhance both convergence speed and the final value error. Based on the gain design guideline, a gain design method associated with the number of iterations is proposed, resulting in a novel model‐free inversion‐based iterative learning control algorithm. Subsequently, a robustness analysis of the proposed algorithm is conducted. Finally, a comprehensive simulation and numerical comparison of the proposed algorithm with existing MFIIC‐like algorithms are presented to demonstrate the superior performance of the proposed control algorithm.

Data‐driven predictive control of perturbed buck converters using a modified iterative feedback tuning algorithm

AbstractThe most challenging aspect of utilizing model predictive controllers (MPCs), particularly those involving power electronic applications, is the extraction of a model that accurately represents the behavior of the studied system. Concerning the use of power electronic applications, as long as an MPC is used, adjusting the controller parameters brings difficulties. In addition, as the number of elements increases, it becomes harder to get the best control law out of the model. To do away with the need for model extraction, this study presents an offline data‐driven approach in conjunction with the MPC that can optimally adjust the MPC parameters based on the iterative feedback tuning (IFT) algorithm called the iterative feedback predictive controller (IFPC). The proposed method eliminates concerns regarding selecting an optimal number of algorithm iterations, thereby reducing operating costs, by introducing a modified IFT called feedback‐based IFPC (FIFPC) while simultaneously achieving optimal MPC parameters. The proposed method is applied to a constant voltage load (CVL) connected less‐than‐ideal buck converter, that is, one with perturbed filter elements and variable loads. A robust stability analysis (RSA) is performed under normal operating conditions to investigate the robustness behavior of the proposed controller. Simulation studies are presented to evaluate the proposed controller under different scenarios, such as step and abrupt load changes and measurement noise, compared with the well‐known model‐based and data‐enabled predictive controller (DeePC) approaches in the MATLAB/Simulink environment.

A comparative study of sensitivity computations in ESDIRK-based optimal control problems

This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.