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Journal articles on the topic 'Smoothed functional algorithms'
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1
Bhatnagar, Shalabh. "Adaptive Newton-based multivariate smoothed functional algorithms for simulation optimization." ACM Transactions on Modeling and Computer Simulation 18, no. 1 (December 2007): 1–35. http://dx.doi.org/10.1145/1315575.1315577.
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Bhatnagar, Shalabh, and Vivek S. Borkar. "Multiscale Chaotic SPSA and Smoothed Functional Algorithms for Simulation Optimization." SIMULATION 79, no. 10 (October 2003): 568–80. http://dx.doi.org/10.1177/0037549703039988.
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Ghoshdastidar, Debarghya, Ambedkar Dukkipati, and Shalabh Bhatnagar. "Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions." ACM Transactions on Modeling and Computer Simulation 24, no. 3 (May 2, 2014): 1–26. http://dx.doi.org/10.1145/2628434.
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Ghoshdastidar, Debarghya, Ambedkar Dukkipati, and Shalabh Bhatnagar. "Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms." Automatica 50, no. 10 (October 2014): 2606–14. http://dx.doi.org/10.1016/j.automatica.2014.08.021.
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Prasad, H. L., L. A. Prashanth, Shalabh Bhatnagar, and Nirmit Desai. "Adaptive Smoothed Functional Algorithms for Optimal Staffing Levels in Service Systems." Service Science 5, no. 1 (March 2013): 29–55. http://dx.doi.org/10.1287/serv.1120.0035.
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Lakshmanan, K., and Shalabh Bhatnagar. "Quasi-Newton smoothed functional algorithms for unconstrained and constrained simulation optimization." Computational Optimization and Applications 66, no. 3 (September 15, 2016): 533–56. http://dx.doi.org/10.1007/s10589-016-9875-4.
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NOROUZZADEH, P., B. RAHMANI, and M. S. NOROUZZADEH. "FORECASTING SMOOTHED NON-STATIONARY TIME SERIES USING GENETIC ALGORITHMS." International Journal of Modern Physics C 18, no. 06 (June 2007): 1071–86. http://dx.doi.org/10.1142/s0129183107011133.
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We introduce kernel smoothing method to extract the global trend of a time series and remove short time scales variations and fluctuations from it. A multifractal detrended fluctuation analysis (MF-DFA) shows that the multifractality nature of TEPIX returns time series is due to both fatness of the probability density function of returns and long range correlations between them. MF-DFA results help us to understand how genetic algorithm and kernel smoothing methods act. Then we utilize a recently developed genetic algorithm for carrying out successful forecasts of the trend in financial time series and deriving a functional form of Tehran price index (TEPIX) that best approximates the time variability of it. The final model is mainly dominated by a linear relationship with the most recent past value, while contributions from nonlinear terms to the total forecasting performance are rather small.
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Kostjukov, V. A., M. Y. Medvedev, and V. Kh Pshikhopov. "Algorithms for Planning Smoothed Individual Trajectories of Ground Robots." Mekhatronika, Avtomatizatsiya, Upravlenie 23, no. 11 (November 3, 2022): 585–95. http://dx.doi.org/10.17587/mau.23.585-595.
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The article is devoted to the development of an algorithm for constructing the trajectory of a robotic platform moving in an environment with obstacles. This algorithm is based on the application of a special local optimization procedure at each planning step and allows us to obtain feasible program trajectories without increasing the computational complexity of algorithms compared to existing methods. The algorithm is based on the application of the improved method of potential fields and subsequent smoothing of the resulting trajectory. The improving of the potential field method consists in a new way of detecting and avoiding local minima. When a local minimum is detected, it is added to the map as an additional obstacle, which makes it possible to avoid it during further trajectory planning. To circumvent obstacles that can be approximated by polygons, the method of the effective point to the obstacle is proposed, which is the equivalent of the latter in relation to the current location of the moving robotic platform when using this planning method. A two-stage technique for smoothing piecewise linear trajectories is proposed. It is assumed that there is some initial suboptimal curve found by any planning method. This curve is optimized using a functional that includes the length of the trajectory and the deviation of the optimized curve from the original curve. At the second stage, the linear segments of the planned straight line are conjugated with second-order curves. As a result, the planned trajectory of motion is a quadratic-linear curve with a smooth function of the trajectory velocity. At the same time, the proposed method of coupling rectilinear sections of the trajectory does not require sudden changes in speed when passing turns. Simulation results confirming the effectiveness of the proposed method of planning the trajectories of robots are considered and discussed.
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Vijayan, Nithia, and Prashanth L.A. "Smoothed functional-based gradient algorithms for off-policy reinforcement learning: A non-asymptotic viewpoint." Systems & Control Letters 155 (September 2021): 104988. http://dx.doi.org/10.1016/j.sysconle.2021.104988.
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Cheng, Chuen-Sheng, Pei-Wen Chen, and Yu-Tang Wu. "Phase I Analysis of Nonlinear Profiles Using Anomaly Detection Techniques." Applied Sciences 13, no. 4 (February 7, 2023): 2147. http://dx.doi.org/10.3390/app13042147.
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In various industries, the process or product quality is evaluated by a functional relationship between a dependent variable y and one or a few input variables x, expressed as y=fx. This relationship is called a profile in the literature. Recently, profile monitoring has received a lot of research attention. In this study, we formulated profile monitoring as an anomaly-detection problem and proposed an outlier-detection procedure for phase I nonlinear profile analysis. The developed procedure consists of three key processes. First, we obtained smoothed nonlinear profiles using the spline smoothing method. Second, we proposed a method for estimating the proportion of outliers in the dataset. A distance-based decision function was developed to identify potential outliers and provide a rough estimate of the contamination rate. Finally, PCA was used as a dimensionality reduction method. An outlier-detection algorithm was then employed to identify outlying profiles based on the estimated contamination rate. The algorithms considered in this study included Local Outlier Factor (LOF), Elliptic Envelope (EE), and Isolation Forest (IF). The proposed procedure was evaluated using a nonlinear profile that has been studied by various researchers. We compared various competing methods based on commonly used metrics such as type I error, type II error, and F2 score. Based on the evaluation metrics, our experimental results indicate that the performance of the proposed method is better than other existing methods. When considering the smallest and hardest-to-detect variation, the LOF algorithm, with the contamination rate determined by the method proposed in this study, achieved type I errors, type II errors, and F2 scores of 0.049, 0.001, and 0.951, respectively, while the performance metrics of the current best method were 0.081, 0.015, and 0.899, respectively.
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Siripunvaraporn, Weerachai, and Gary Egbert. "An efficient data‐subspace inversion method for 2-D magnetotelluric data." GEOPHYSICS 65, no. 3 (May 2000): 791–803. http://dx.doi.org/10.1190/1.1444778.
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There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much more efficient variant on the OCCAM scheme. By expressing the solution as a linear combination of rows of the sensitivity matrix smoothed by the model covariance (the “representers”), we transform the linearized inverse problem from the M-dimensional model space to the N-dimensional data space. This method is referred to as DASOCC, the data space OCCAM’s inversion. Since generally N ≪ M, this transformation by itself can result in significant computational saving. More importantly the data space formulation suggests a simple approximate method for constructing the inverse solution. Since MT data are smooth and “redundant,” a subset of the representers is typically sufficient to form the model without significant loss of detail. Computations required for constructing sensitivities and the size of matrices to be inverted can be significantly reduced by this approximation. We refer to this inversion as REBOCC, the reduced basis OCCAM’s inversion. Numerical experiments on synthetic and real data sets with REBOCC, DASOCC, NLCG, RRI, and OCCAM show that REBOCC is faster than both DASOCC and NLCG, which are comparable in speed. All of these methods are significantly faster than OCCAM, but are not competitive with RRI. However, even with a simple synthetic data set, we could not always get RRI to converge to a reasonable solution. The basic idea behind REBOCC should be more broadly applicable, in particular to 3-D MT inversion.
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Bläser, Markus, Bodo Manthey, and B. V. Raghavendra Rao. "Smoothed Analysis of Partitioning Algorithms for Euclidean Functionals." Algorithmica 66, no. 2 (April 11, 2012): 397–418. http://dx.doi.org/10.1007/s00453-012-9643-5.
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Chen, Xing-Min, and Chao Gao. "On the Convergence of Smoothed Functional Stochastic Optimization Algorithms**This work is supported by the National Natural Science Foun-dation of China under Grant 61203118, the Fundamental Research Funds for Central Universities, and the Youth Foundation of Dalian Polytechnic University under Grant QNJJ201416." IFAC-PapersOnLine 48, no. 28 (2015): 229–33. http://dx.doi.org/10.1016/j.ifacol.2015.12.130.
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An, Dongsheng, Na Lei, Xiaoyin Xu, and Xianfeng Gu. "Efficient Optimal Transport Algorithm by Accelerated Gradient Descent." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10119–28. http://dx.doi.org/10.1609/aaai.v36i9.21251.
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Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly challenging. Recently, methods based on the Sinkhorn algorithm add an entropy regularizer to the prime problem and get a trade off between efficiency and accuracy. In this paper, we propose a novel algorithm to further improve the efficiency and accuracy based on Nesterov's smoothing technique. Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which finally smooths the original non-smooth Kantorovich dual functional. The smooth Kantorovich functional can be optimized by the fast proximal gradient algorithm (FISTA) efficiently. Theoretically, the computational complexity of the proposed method is lower than current estimation of the Sinkhorn algorithm in terms of the precision. Empirically, compared with the Sinkhorn algorithm, our experimental results demonstrate that the proposed method achieves faster convergence and better accuracy with the same parameter.
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Ahn, Jong-Hoon, and In Young Kim. "Learning the Dynamics of Objects by Optimal Functional Interpolation." Neural Computation 24, no. 9 (September 2012): 2457–72. http://dx.doi.org/10.1162/neco_a_00325.
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Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.
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Bala, Nurudeen Muhammad, and Suhailan Bin Safei. "A Hybrid Harmony Search and Particle Swarm Optimization Algorithm (HSPSO) for Testing Non-functional Properties in Software System." Statistics, Optimization & Information Computing 10, no. 3 (January 9, 2021): 968–82. http://dx.doi.org/10.19139/soic-2310-5070-1039.
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An important aspect of improving software system is testing. However, it is time demanding and sometimeslabour intensive if done manually. In this paper, we developed an automatic search-based approach for testing the nonfunctional properties of a software system using hybrid harmony search and particle swarm optimization algorithms. The approach birthed a new algorithm named HSPSO, which is proposed based on the strength of HS over Genetic algorithm (GA) in terms of less adjustable parameters, quick convergence and smooth implementation. On the other hand, we propose the PSO to complement the drawback of HS in terms of time consumption problem. Besides, we used four programs for the comparative efficiency analysis of the proposed algorithm in relation to competing algorithms based on average branch coverage and execution time. The results from the analysis showed that the HSPSO algorithm was able to achieve 100% average coverage with a fewer number of generated test cases and under limited execution time.
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Fort, Jean-Claude, and Gilles Pagès. "Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method." Advances in Applied Probability 28, no. 4 (December 1996): 1072–94. http://dx.doi.org/10.2307/1428165.
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In the first part of this paper a global Kushner–Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can ‘read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.
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Fort, Jean-Claude, and Gilles Pagès. "Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method." Advances in Applied Probability 28, no. 04 (December 1996): 1072–94. http://dx.doi.org/10.1017/s0001867800027567.
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In the first part of this paper a global Kushner–Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can ‘read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.
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Nigro, Libero, and Pasi Fränti. "Two Medoid-Based Algorithms for Clustering Sets." Algorithms 16, no. 7 (July 20, 2023): 349. http://dx.doi.org/10.3390/a16070349.
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This paper proposes two algorithms for clustering data, which are variable-sized sets of elementary items. An example of such data occurs in the analysis of a medical diagnosis, where the goal is to detect human subjects who share common diseases to possibly predict future illnesses from previous medical history. The first proposed algorithm is based on K-medoids and the second algorithm extends the random swap algorithm, which has proven to be capable of efficient and careful clustering; both algorithms depend on a distance function among data objects (sets), which can use application-sensitive weights or priorities. The proposed distance function makes it possible to exploit several seeding methods that can improve clustering accuracy. A key factor in the two algorithms is their parallel implementation in Java, based on functional programming using streams and lambda expressions. The use of parallelism smooths out the O(N2) computational cost behind K-medoids and clustering indexes such as the Silhouette index and allows for the handling of non-trivial datasets. This paper applies the algorithms to several benchmark case studies of sets and demonstrates how accurate and time-efficient clustering solutions can be achieved.
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Russ, Nicholas J., Chun-min Chang, and Jing Kong. "Fast computation of DFT nuclear gradient with multiresolution*This article is dedicated to Dr. Russell J. Boyd for his distinguished career in chemical research." Canadian Journal of Chemistry 89, no. 6 (June 2011): 657–62. http://dx.doi.org/10.1139/v11-063.
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We present an efficient algorithm for evaluating the exchange-correlation contribution to the nuclear gradients of density-functional theory calculation within the local spin-density approximation. The algorithm is an extension of the multiresolution exchange-correlation (mrXC) method, which treats smooth and compact parts of the electron density separately. The nuclear gradient of the smooth density is calculated on the even-spaced grid while the compact part of the density is handled on the normal atom-centered grid (ACG). The overall formulism is still formally based on the ACG, and thus does not change the results of the existing ACG-based algorithms for all-electron density-functional theory (DFT) calculations. The variation of the positions and weights of ACG owing to the nuclear perturbation is also handled rigorously. Benchmark calculations with different basis sets and sizes of ACG show that mrXC reduces the computational cost by several times without loss of accuracy. It also lessens the impact on the CPU time when the size of the ACG is increased.
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Mahzarnia, Ali, and Jun Song. "Multivariate functional group sparse regression: Functional predictor selection." PLOS ONE 17, no. 4 (April 7, 2022): e0265940. http://dx.doi.org/10.1371/journal.pone.0265940.
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In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under a high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression under a generic Hilbert space of infinite dimension. We show the convergence of algorithms and the consistency of the estimation and the selection (oracle property) under infinite-dimensional Hilbert spaces. Simulation studies show the effectiveness of the methods in both the selection and the estimation of functional coefficients. The applications to functional magnetic resonance imaging (fMRI) reveal the regions of the human brain related to ADHD and IQ.
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Amstutz, Samuel, Charles Dapogny, and Alex Ferrer. "A consistent approximation of the total perimeter functional for topology optimization algorithms." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 18. http://dx.doi.org/10.1051/cocv/2022005.
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This article revolves around the total perimeter functional, one particular version of the perimeter of a shape Ω contained in a fixed computational domain D measuring the total area of its boundary ∂Ω, as opposed to its relative perimeter, which only takes into account the regions of ∂Ω strictly inside D. We construct and analyze approximate versions of the total perimeter which make sense for general “density functions” u, as generalized characteristic functions of shapes. Their use in the context of density-based topology optimization is particularly convenient insofar as they do not involve the gradient of the optimized function u. Two different constructions are proposed: while the first one involves the convolution of the function u with a smooth mollifier, the second one is based on the resolution of an elliptic boundary-value problem featuring Robin boundary conditions. The “consistency” of these approximations with the original notion of total perimeter is appraised from various points of view. At first, we prove the pointwise convergence of our approximate functionals, then the convergence of their derivatives, as the level of smoothing tends to 0, when the considered density function u is the characteristic function of a “regular enough” shape Ω ⊂ D. Then, we focus on the Γ-convergence of the second type of approximate total perimeter functional, that based on elliptic regularization. Several numerical examples are eventually presented in two and three space dimensions to validate our theoretical findings and demonstrate the efficiency of the proposed functionals in the context of structural optimization.
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Fu, Ying, Xiaohua Li, Lei Liang, Yi Zhang, and Jiliu Zhou. "The Restoration of Textured Images Using Fractional-Order Regularization." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/356906.
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Image restoration problem is ill-posed, so most image restoration algorithms exploit sparse prior in gradient domain to regularize it to yield high-quality results, reconstructing an image with piecewise smooth characteristics. While sparse gradient prior has good performance in noise removal and edge preservation, it also tends to remove midfrequency component such as texture. In this paper, we introduce the sparse prior in fractional-order gradient domain as texture-preserving strategy to restore textured images degraded by blur and/or noise. And we solve the unknown variables in the proposed model using method based on half-quadratic splitting by minimizing the nonconvex energy functional. Numerical experiments show our algorithm's robust outperformance.
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Santitissadeekorn, N., and E. M. Bollt. "Image Edge Respecting Denoising with Edge Denoising by a Designer Nonisotropic Structure Tensor Method." Computational Methods in Applied Mathematics 9, no. 3 (2009): 309–18. http://dx.doi.org/10.2478/cmam-2009-0019.
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AbstractWe consider image denoising as the problem of removing spurious oscillations due to noise while preserving edges in the images. We will suggest here how to directly make infinitesimal adjustment to standard variational methods of image denoising, to enhance desirable target assumption of the noiseless image. The standard regularization method is used to define a suitable energy functional to penalize the data fidelity and the smoothness of the solution. This energy functional is tailored so that the region with small gradient is isotropically smoothed whereas in a neighborhood of an edge presented by a large gradient smoothing is allowed only along the edge contour. The regularized solution that arises in this fashion is then the solution of a variational principle. To this end the associated Euler — Lagrange equation needs to be solved numerically and the half-quadratic minimization is generally used to linearize the equation and to derive an iterative scheme. We describe here a method to modify Euler — Largrange equation from commonly used energy functionals, in a way to enhance certain desirable preconceived assumptions of the image, such as edge preservation. From an algorithmic point of view, we may deem this algorithm as a smoothing by a local average with an adaptive gradient-based weight. However, this algorithm may result in noisy edges although the edge is preserved and noise is suppressed in the low-gradient regions of the image. The main focus here is to present an edge-preserving regularization in the aforementioned view point, and to provide an alternative and simple way to modify the existing algorithm to mitigate the phenomena of noisy edges without explicitly defining step where we specify an energy functional to be minimized.
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VASYLKIVSKYI, Mykola, Alyona KOLOMIETS, and Nazarii HRABCHAK. "RESEARCH OF FUNCTIONAL PARAMETERS OF INFOCOMMUNICATION NETWORKS 6G." Herald of Khmelnytskyi National University. Technical sciences 315, no. 6(1) (December 29, 2022): 46–52. http://dx.doi.org/10.31891/2307-5732-2022-315-6-46-52.
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The work presents the results of research into 6G technology, which will allow integrating all types of access in one mobile phone, ensuring smooth switching between services. New options for the use of mobile networks, such as sensing and artificial intelligence, are considered, which form new indicators of the quality of the information service – the resolution of sensing and the probability of output. For new applications, the prospects for further research into related indicators, such as flexibility and scalability to support own artificial intelligence services and network reliability level, are considered. Prospects for the development of electronic health care based on mobile communication systems with increased requirements for reliability, availability, security and confidentiality are considered. A platform for aerial mobility of various high-resolution sensors and cameras for various industries based on unmanned aerial vehicles has been investigated. The fundamental energy limitations of calculations related to information processing, which are an important step on the way to the successful deployment of 6G wireless networks, are considered. In the design of next-generation wireless communication networks, it has been determined that traditional AI optimization algorithms (such as federated learning) usually consider the bandwidth or delay of wireless connections as a weight for distributed multiprocessor data exchange, without considering the power energy bounds between different devices in different regions. This ambiguous consideration of AI energy limitations or power costs may lead to a large divergence between the design of a wireless network and the actual deployment of AI in the future. For this reason, equal importance must be attached to green AI and green communications. Therefore, when designing the architecture of the 6G information communication system, it is necessary to fully consider the impact of artificial intelligence models, algorithms and equipment on energy consumption to provide economic benefits to customers with corresponding operating costs of the system. The peculiarities of providing users with access to Internet services at any time through the same device regardless of their location, which is one of the ultimate goals of creating effective wireless networks, are discussed. The proposed concept of green AI called Oncefor-All (once and forever), according to which it is proposed to train an information communication network with further specialization during deployment will allow for efficient logical implementation on many devices, taking into account the given resource constraints. At the same time, terrestrial and non-terrestrial 6G networks will be fully integrated at the system level, ensuring the convergence of services, radio interfaces, networks and user devices. By organically combining these two access environments into one converged multi-layer heterogeneous network covering the entire globe, 6G technology will provide users with the same service. Ensuring the global delivery of mobile services will be an important aspect of the development of the 6G network.
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Xing, Y., Sheng Feng Qin, Tai Yong Wang, P. C. Wang, and J. L. Xing. "Study on a New Design Algorithm for Smooth Manufacture." Materials Science Forum 697-698 (September 2011): 765–68. http://dx.doi.org/10.4028/www.scientific.net/msf.697-698.765.
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To realize smooth manufacture of product with complex surface, a new algorithm, design for quality control (DQC), strongly connects design model and machining model. Geometry information in popular STL file in design industry was fast obtained and then exactly input into a grid-meshing model. For meeting precision requirement of machining model, quality-control parameter was employed to control subdivision times and the result-surface machining quality. Then the designed features of aesthetics surface or functional surface were kept in smooth manufacture with optimum quality. By self developed software for DQC in Visual C++, stability and reliability of this algorithm were proved.
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Massa, Enrico, Danilo Bruno, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus I: Piecewise smooth extremals." International Journal of Geometric Methods in Modern Physics 12, no. 05 (May 2015): 1550061. http://dx.doi.org/10.1142/s0219887815500619.
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A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.
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Xu, Jiucheng, Qinchen Hou, Kanglin Qu, Yuanhao Sun, and Xiangru Meng. "A Fast Weighted Fuzzy C-Medoids Clustering for Time Series Data Based on P-Splines." Sensors 22, no. 16 (August 17, 2022): 6163. http://dx.doi.org/10.3390/s22166163.
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The rapid growth of digital information has produced massive amounts of time series data on rich features and most time series data are noisy and contain some outlier samples, which leads to a decline in the clustering effect. To efficiently discover the hidden statistical information about the data, a fast weighted fuzzy C-medoids clustering algorithm based on P-splines (PS-WFCMdd) is proposed for time series datasets in this study. Specifically, the P-spline method is used to fit the functional data related to the original time series data, and the obtained smooth-fitting data is used as the input of the clustering algorithm to enhance the ability to process the data set during the clustering process. Then, we define a new weighted method to further avoid the influence of outlier sample points in the weighted fuzzy C-medoids clustering process, to improve the robustness of our algorithm. We propose using the third version of mueen’s algorithm for similarity search (MASS 3) to measure the similarity between time series quickly and accurately, to further improve the clustering efficiency. Our new algorithm is compared with several other time series clustering algorithms, and the performance of the algorithm is evaluated experimentally on different types of time series examples. The experimental results show that our new method can speed up data processing and the comprehensive performance of each clustering evaluation index are relatively good.
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Decker, Luke, and Sergey Fomel. "A variational approach for picking optimal surfaces from semblance-like panels." GEOPHYSICS 87, no. 3 (April 11, 2022): U93—U108. http://dx.doi.org/10.1190/geo2021-0336.1.
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We propose and examine a variational method for determining optimal velocity fields from semblance-like volumes using continuation. The proposed approach finds a minimal-cost surface through a volume, which often corresponds to a velocity field within a semblance scan. This allows picked velocity fields to incorporate information from gathers that are spatially near the midpoint in question. The minimization process amounts to solving a nonlinear elliptic partial differential equation, which is accomplished by changing the elliptic problem to a parabolic one and solving it iteratively until it converges to a critical point which minimizes the cost functional. The continuation approach operates by using a variational framework to iteratively minimize the cost of a velocity surface through successively less-smoothed semblance scans. The method works because a global minimum for the velocity cost functional can only exist when the semblance scan varies smoothly in space and convexly in the parameter being scanned. Using a discretization of the functional with a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm, we illustrate how the continuation approach is able to avoid local minima that would typically capture the iterative solution of an optimal velocity field determined without continuation by applying the method to seismic processing of a field data set from the Viking Graben. We then use a field data set from the Gulf of Mexico to show how the final velocity model determined by the method using continuation is largely independent of the starting velocity model, producing something resembling a global minimum. Finally, we demonstrate the versatility of the variational picking approach by using it to automatically interpret a seismic horizon from the Heidrun Field.
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Du, Yunfeng, and Huan Han. "Multiscale Approach for Bounded Deformation Image Registration." Fractal and Fractional 6, no. 11 (November 18, 2022): 681. http://dx.doi.org/10.3390/fractalfract6110681.
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Deformable image registration is a very important topic in the field of image processing. It is widely used in image fusion and shape analysis. Generally speaking, image registration models can be divided into two categories: smooth registration and non-smooth registration. During the last decades, many smooth registration models (i.e., diffeomorphic registration) were proposed. However, image with strong noise may lead to discontinuous deformation, which cannot be modelled by smooth registration. To simulate this kind of deformation, some non-smooth registration models were also proposed. However, numerical algorithms for these models are easily trapped into a local minimum because of the nonconvexity of the object functional. To overcome the local minimum of the object functional, we propose a multiscale approach for a non-smooth registration model: the bounded deformation (BD) model. The convergence of the approach is shown, and numerical tests are also performed to show the good performance of the proposed multiscale approach.
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Gao, Lei, and Jie Yu Ding. "An Improved DMOC Method with Gradient Penalty Term." Advanced Materials Research 945-949 (June 2014): 2784–87. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.2784.
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An efficient method aimed at smooth and stable control forces for optimal control problem is described. Based on the native discrete mechanics and optimal control (DMOC) method, which focus mainly on the minimization of the total control forces, a gradient penalty term is introduced to cost functional to smooth the control forces. Then vibration of control forces is overcome by limiting the total gradient of the discrete control forces. With suitable discrete cost functional and constraints, the continuous optimal control problem is transformed to an equally finite dimensional form, which can be easily solved by standard algorithms. Finally, the numerical example of orbit transferring shows the effectiveness of the improved method.
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Iskhakova, Anastasia, Maxim Alekhin, and Alexey Bogomolov. "Time-frequency transforms in analysis of non-stationary quasi-periodic biomedical signal patterns for acoustic anomaly detection." Information and Control Systems, no. 1 (February 20, 2020): 15–23. http://dx.doi.org/10.31799/1684-8853-2020-1-15-23.
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Introduction: New approaches to efficient compression and digital processing of audio signals are relevant today. Thereis a lot of interest to new pattern recognition methods which can improve the quality of acoustic anomaly detection. Purpose:Comparative analysis of methods for time-frequency transformation of audio signal patterns, including non-stationary quasiperiodicbiomedical signals in the problem of acoustic anomaly detection. Results: The study compared different time-frequencytransforms (such as windowed Fourier, Gabor, Wigner, pseudo Wigner, smoothed pseudo Wigner, Choi — Williams, Bertrand, pseudoBertrand, smoothed pseudo Bertrand, and wavelet transforms) based on systematization of their functional characteristics(such as the existence and limitedness of basis functions, presence of zero moments and biorthogonal form, opportunity oftwo-dimensional representation and inverse transformation, real time processing, time-frequency transform quality, controlof time-frequency definition, time and frequency interference suppression, relative computational complexity, fast algorithmimplementation) for the problem of biomedial signal pattern recognition. A comparative table is presented with estimates ofinformation capacity for the considered time-frequency transforms. Practical relevance: The proposed approach can solve someacoustic anomaly detection algorithm implementation problems common in non-stationary quasi-periodic processes, in order tostudy disruptive effects causing a change in the functional state of ergatic system operators.
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Song, Aiguo, Lizheng Pan, Guozheng Xu, and Huijun Li. "Adaptive motion control of arm rehabilitation robot based on impedance identification." Robotica 33, no. 9 (May 1, 2014): 1795–812. http://dx.doi.org/10.1017/s026357471400099x.
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SUMMARYThere is increasing interest in using rehabilitation robots to assist post-stroke patients during rehabilitation therapy. The motion control of the robot plays an important role in the process of functional recovery training. Due to the change of the arm impedance of the post-stroke patient in the passive recovery training, the conventional motion control based on a proportional-integral (PI) controller is difficult to produce smooth movement of the robot to track the designed trajectory set by the rehabilitation therapist. In this paper, we model the dynamics of post-stroke patient arm as an impedance model, and propose an adaptive control scheme, which consists of an adaptive PI control algorithm and an adaptive damping control algorithm, to control the rehabilitation robot moving along predefined trajectories stably and smoothly. An equivalent two-port circuit of the rehabilitation robot and human arm is built, and the passivity theory of circuits is used to analyze the stability and smoothness performance of the robot. A slide Least Mean Square with adaptive window (SLMS-AW) method is presented for on-line estimation of the parameters of the arm impedance model, which is used for adjusting the gains of the PI-damping controller. In this paper, the Barrett WAM Arm manipulator is used as the main hardware platform for the functional recovery training of the post-stroke patient. Passive recovery training has been implemented on the WAM Arm, and the experimental results demonstrate the effectiveness and potential of the proposed adaptive control strategies.
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Nguyen, Hai Thanh, Cuong Quoc Ngo, and Hung Viet Nguyen. "PR-SVM algorithm for recognition of human hand tapping using functional near infrared spectroscopy." Science and Technology Development Journal 16, no. 3 (September 30, 2013): 5–17. http://dx.doi.org/10.32508/stdj.v16i3.1607.
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Researches of human Brain Computer Interface (BCI) for the objective of diagnosis and rehabilitation have been recently increased. Cerebral oxygenation and blood flow on particular regions of human brain can be measured using a non-invasive technique – fNIRS (functional Near Infrared Spectroscopy). In this paper, a study of recognition algorithm will be described for recognizing whether one taps his/her left hand or right hand. Data with noises and artifacts collected from a multi-channel system will be pre-processed using a Savitzky- Golay filter for getting more smoothly fNIRS data. Characteristics of the filtered signals during left and right hand tapping process will be extracted using a Polynomial Regression (PR)-Support Vector Machine (SVM) algorithm. Coefficients of the polynomial determined by the PR algorithm, which correspond to Oxygen-Hemoglobin (Oxy- Hb) concentration changes, will be applied for the recognition of hand tapping. Then the SVM will be employed to validate the obtained coefficient data for the hand tapping recognition. Experimental results have been done many trials on 3 subjects to illustrate the effectiveness of the proposed method.
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Sharma, Sudhir Kumar, and Pravin Chandra. "Cascading Neural Networks Using Adaptive Sigmoidal Function." Advanced Materials Research 403-408 (November 2011): 858–65. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.858.
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This paper presents cascading neural networks using adaptive sigmoidal function (CNNASF). The proposed algorithm emphasizes on architectural adaptation and functional adaptation during training. This algorithm is a constructive approach to building cascading architecture dynamically. The activation functions used at the hidden layers’ node are belonging to the well-defined sigmoidal class and adapted during training. The algorithm determines not only optimum number of hidden layers’ node, as also optimum sigmoidal function for them. One simple variant derived from CNNASF is where the sigmoid function used at the hidden layers’ node is fixed. Both the variants are compared to each other on five regression functions. Simulation results reveal that adaptive sigmoidal function presents several advantages over traditional fixed sigmoid function, resulting in increased flexibility, smoother learning, better convergence and better generalization performance.
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Sharma, Sudhir Kumar, and Pravin Chandra. "A Constructive Algorithm with Adaptive Sigmoidal Function for Designing Single Hidden Layer Feedforward Neural Network." Advanced Materials Research 403-408 (November 2011): 3867–74. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.3867.
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In this paper we propose a constructive algorithm with adaptive sigmoidal function for designing single hidden layer feedforward neural network (CAASF). The proposed algorithm emphasizes on architectural adaptation and functional adaptation during training. This algorithm is a constructive approach to building single hidden layer neural networks dynamically. The activation functions used at non-linear hidden nodes are belonging to the well-defined sigmoidal class and adapted during training. The algorithm determines not only optimum number of hidden nodes, as also optimum sigmoidal function for the non-linear nodes. One simple variant derived from CAASF is where the sigmoidal function used at the hidden nodes is fixed. Both the variants are compared to each other on five regression functions. Simulation results reveal that adaptive sigmoidal function presents several advantages over traditional fixed sigmoid function, resulting in increased flexibility, smoother learning, better convergence and better generalization performance.
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Olypher, Andrey V., and Ronald L. Calabrese. "Using Constraints on Neuronal Activity to Reveal Compensatory Changes in Neuronal Parameters." Journal of Neurophysiology 98, no. 6 (December 2007): 3749–58. http://dx.doi.org/10.1152/jn.00842.2007.
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In this study, we developed a general description of parameter combinations for which specified characteristics of neuronal or network activity are constant. Our approach is based on the implicit function theorem and is applicable to activity characteristics that smoothly depend on parameters. Such smoothness is often intrinsic to neuronal systems when they are in stable functional states. The conclusions about how parameters compensate each other, developed in this study, can thus be used even without regard to the specific mathematical model describing a particular neuron or neuronal network. We showed that near a generic point in the parameter space there are infinitely many other points, or parameter combinations, for which specified characteristics of activity are the same as in the original point. These parameter combinations form a smooth manifold. This manifold can be extended as long as the gradients of characteristics are defined and independent. All possible variations of parameters compensating each other are simply all possible charts of the same manifold. The number of compensating parameters (but not parameters themselves) is fixed and equal to the number of the independent characteristics maintained. The algorithm that we developed shows how to find compensatory functional dependencies between parameters numerically. Our method can be used in the analysis of the homeostatic regulation, neuronal database search, model tuning and other applications.
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Nikulina, Marina, and Vladimir Antonets. "Experience in assessing heart rate variability by smoothed cardiointervalograms." Izvestiya VUZ. Applied Nonlinear Dynamics 30, no. 2 (March 31, 2022): 176–88. http://dx.doi.org/10.18500/0869-6632-2022-30-2-176-188.
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The objective of this study is to show the possibility of using the smoothing cardiointervalograms (CIG) method which is solely time domain analysis of CIG to separate and display the influence of various mechanisms of human physiological regulation systems on his heart rate. Methods.This paper shows the possibility of using the method of smoothing the cardiointervalogram by means of a moving average for its subsequent decomposition into slow and fast components. Decomposition results are visualized by line graphs and pseudo-phase portraits. Visualization settings allow us to isolate unique transients and calculate its timing. The method is applied to data obtained under different subject functional states and differing in the level of adaptation risks, the presence or absence of stress. For analysis were selected stress episodes detected using the information and telecommunication technology of event-related cardiac telemetry (ITT ERCT) presented by the Internet resource “StressMonitor”. Results.For the numerical series of RR-intervals, a clear division into fast and slow components is obtained. An algorithm for identifying the frequency content of heart rate variability has been formulated and tested. A visualization method is proposed that is convenient for comparing data obtained for different patients. A pseudo-phase portrait pattern corresponding to the moment of stress onset is found. The proposed method reduced the discreteness of identifying the stress onset moment from 10 seconds to single heart beats. Conclusion. The correspondence of the results to the verified ITT ERCT method and the Baevsky–Chernikova concept of adaptive risk has been demonstrated. This confirms the possibility of using the time cardiointervalograms smoothing method for the analysis of heart rate variability.
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Zhao, Xiao Dong, Zuo Feng Zhou, Jian Zhong Cao, Long Ren, Guang Sen Liu, Hua Wang, Deng Shan Wu, and Jia Hai Tan. "Multi-Frame Super-Resolution Reconstruction Algorithm Based on Diffusion Tensor Regularization Term." Applied Mechanics and Materials 543-547 (March 2014): 2828–32. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2828.
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This paper presents a multi-frame super-resolution (SR) reconstruction algorithm based on diffusion tensor regularization term. Firstly, L1-norm structure is used as data fidelity term, anisotropic diffusion equation with directional smooth characteristics is introduced as a prior knowledge to optimize reconstruction result. Secondly, combined with shock filter, SR reconstruction energy functional is established. Finally, Euler-Lagrange equation based on nonlinear diffusion model is exported. Simulation results validate that the proposed algorithm enhances image edges and suppresses noise effectively, which proves better robustness.
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Ajo-Franklin, Jonathan B., Burke J. Minsley, and Thomas M. Daley. "Applying compactness constraints to differential traveltime tomography." GEOPHYSICS 72, no. 4 (July 2007): R67—R75. http://dx.doi.org/10.1190/1.2742496.
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Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a nonsmooth spatial process. Time-lapse imaging of flow-induced velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. By performing inversions on differenced arrival time data, the properties of the time-lapse feature can be directly constrained. We develop a differential traveltime tomography algorithm whichselects for compact solutions, i.e., models with a minimum area of support, through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously explored within the potential theory community. We compare our inversion algorithm to the results obtained by traditional Tikhonov regularization for two simple synthetic models: one including several sharp localized anomalies and a second with smoother features. We use a more complicated synthetic test case based on multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration imaging. We apply the algorithm to a [Formula: see text]-sequestration-monitoring data set acquired at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct, the addition of compactness constraints improves image quality by reducing tomographic artifacts and spatial smearing of target features.
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Ding, Liang, Hui Zhao, and Yixin Dou. "Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method." Mathematical Problems in Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/2736306.
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We consider sparse signal inversion with impulsive noise. There are three major ingredients. The first is regularizing properties; we discuss convergence rate of regularized solutions. The second is devoted to the numerical solutions. It is challenging due to the fact that both fidelity and regularization term lack differentiability. Moreover, for ill-conditioned problems, sparsity regularization is often unstable. We propose a novel dual spectral projected gradient (DSPG) method which combines the dual problem of multiparameter regularization with spectral projection gradient method to solve the nonsmooth l1+l1 optimization functional. We show that one can overcome the nondifferentiability and instability by adding a smooth l2 regularization term to the original optimization functional. The advantage of the proposed functional is that its convex duality reduced to a constraint smooth functional. Moreover, it is stable even for ill-conditioned problems. Spectral projected gradient algorithm is used to compute the minimizers and we prove the convergence. The third is numerical simulation. Some experiments are performed, using compressed sensing and image inpainting, to demonstrate the efficiency of the proposed approach.
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Chen, Jiupeng, Hongjun San, and Xing Wu. "Gait Regulation of a Bionic Quadruped Robot with Antiparallelogram Leg Based on CPG Oscillator." Complexity 2019 (November 30, 2019): 1–11. http://dx.doi.org/10.1155/2019/5491298.
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In order to shorten the research and development cycle of quadruped robot, it is significant to solve the problem of single leg weight-bearing and obtain a smooth gait switching. Firstly, a leg structure with an antiparallelogram is proposed, which greatly enhances the strength and stiffness of the leg in this paper. Secondly, the Simulink-ADAMS cosimulation platform is built and the improved Hopf oscillator is used in the control of robot. This control mode based on CPG realizes the walk and trot gait of quadruped robot. Thirdly, in order to solve the problems of breakpoints, phase-locked, and stopping of gait curve in the process of gait switching by directly replacing the gait matrix, the functional relationship between the right hind leg and duty cycle is introduced to realize the smooth transition of gait curve. The simulation results show that the proposed algorithm can achieve a smooth gait transformation within 4–6 second, which preliminarily proves the feasibility of the algorithm. Finally, the experimental platform is built and the control algorithm is written into the controller to realize the specific gait of the robot, which proves the effectiveness of the proposed method.
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Bredies, Kristian. "A forward–backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space." Inverse Problems 25, no. 1 (November 13, 2008): 015005. http://dx.doi.org/10.1088/0266-5611/25/1/015005.
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Landkammer, Philipp, and Paul Steinmann. "Application of a Non-Invasive Form Finding Algorithm to the Ring Compression Test with Varying Friction Coefficients." Key Engineering Materials 651-653 (July 2015): 1381–86. http://dx.doi.org/10.4028/www.scientific.net/kem.651-653.1381.
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It is a great challenge in the development of functional components to determine the optimal blank design (material configuration) of a workpiece according to a specific forming process, while knowing the desired target geometry (spatial configuration). A new iterative non-invasive algorithm, which is purely based on geometrical considerations, is developed to solve inverse form finding problems. The update-step is performed by mapping the nodal spatial difference vector, between the computed spatial coordinates and the desired spatial target coordinates, with a smoothed deformation gradient to the discretized material configuration. The iterative optimization approach can be easily coupled non-invasively via subroutines to arbitrary finite element codes such that the pre-processing, the solving and the post-processing can be performed by the habitual simulation software. This is exemplary demonstrated by an interacting between Matlab (update procedure for inverse form finding) and MSC.MarcMentat (metal forming simulation). The algorithm succeeds for a parameter study of a ring compression test within nearly linear convergence rates, despite highly deformed elements and tangential contact with varying friction parameters.
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Bishop, Chris. "Improving the Generalization Properties of Radial Basis Function Neural Networks." Neural Computation 3, no. 4 (December 1991): 579–88. http://dx.doi.org/10.1162/neco.1991.3.4.579.
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An important feature of radial basis function neural networks is the existence of a fast, linear learning algorithm in a network capable of representing complex nonlinear mappings. Satisfactory generalization in these networks requires that the network mapping be sufficiently smooth. We show that a modification to the error functional allows smoothing to be introduced explicitly without significantly affecting the speed of training. A simple example is used to demonstrate the resulting improvement in the generalization properties of the network.
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Zhang, Yu, Liexi Xiao, Hui Zhou, and Guanhao Zhao. "Control strategy of wind power smooth grid connection based on adaptive VMD and hybrid energy storage." Journal of Renewable and Sustainable Energy 14, no. 2 (March 2022): 023306. http://dx.doi.org/10.1063/5.0077754.
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In nature, the variation of wind speed is characterized by randomness, fluctuation, and intermittence. In order to suppress the power fluctuation caused by wind speed changes in the process of wind turbine grid connection, a wind power smooth grid-connected control strategy based on the adaptive variational modal decomposition algorithm and the hybrid energy storage system is proposed. For the problem that the selection of variational modal decomposition parameters is subjective and experiential, which leads to the poor signal decomposition reduction degree, the sparrow search algorithm is proposed to optimize variational modal decomposition to realize the adaptive selection of key variational modal decomposition parameters k and α. First, the reference power of the hybrid energy storage system conforming to the grid-connected power fluctuation standard is obtained by the adaptive moving average algorithm. Then, adaptive variational modal decomposition of the reference power was performed to obtain a set of inherent modal functional components, and the low frequency and high frequency components of the modal components were allocated for lithium batteries and the supercapacitor, respectively. Finally, Matlab/Simulink was used to simulate and compare with the control strategy of low-pass filtering. The results show that the proposed algorithm realizes the selection of adaptive decomposition parameters of variational modal decomposition, solves the lag and frequency aliasing problems existing in power distribution of the low-pass filtering algorithm, and realizes the high reduction solution of reference power. The fluctuation of wind power connected to the grid is effectively suppressed.
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Pais, AIL, C. Silva, MC Marques, JL Alves, and J. Belinha. "The influence of infill density gradient on the mechanical properties of PLA optimized structures by additive manufacturing." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 6 (April 14, 2021): 1401–18. http://dx.doi.org/10.1177/14644207211007159.
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The aim of this work is the development of a novel framework for structural optimization using bio-inspired remodelling algorithm adapted to additive manufacturing. The fact that polylactic acid (PLA, E = 3145 MPa (Young’s modulus) according to the supplier for parts obtained by injection) shows a similar parameterized behavior with ductile metals, in the sense that both materials are characterized by a bi-linear elastic-plastic law, allows to simulate and prototype parts to be further constructed in ductile metals at a lower cost and then be produced with more expensive fabrication processes. Moreover, cellular materials allow for a significant weight reduction and therefore reduction of production costs. Structural optimization algorithms based on biological phenomena were used to determine the density distribution of the infill density of the specimens. Several simple structures were submitted to distinct complex load cases and analyzed using the mentioned optimization algorithms combined with the finite element method and a meshless method. The surface was divided according to similar density and then converted to stereolitography files and infilled with the gyroid structure at the desired density determined before, using open-source slicing software. Smoothing functions were used to smooth the density field obtained with the remodeling algorithms. The samples were printed with fused filament fabrication technology and submitted to mechanical flexural tests similar to the ones analyzed analytically, namely three- and four-point bending tests. Thus, the factors of analysis were the smoothing parameter and the remodeling method, and the responses evaluated were stiffness, specific stiffness, maximum force, and mass. The experimental results correlated (obtaining accuracy of 35% for the three-point bending load case and 5% for the four-point bending load case) to the numerical results in terms of flexural stiffness and it was found that the complexity of the load case is relevant for the efficiency of the functional gradient. The fused filament fabrication process is still not accurate enough to be able to experimentally compare the results based of finite element method and meshless method analyses.
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Huang, Xiong, QingLan Li, and JieLie Chen. "Tool Path Generation Algorithm Based on Rough Machining of Jade Carving Surface." Mathematical Problems in Engineering 2022 (April 15, 2022): 1–9. http://dx.doi.org/10.1155/2022/2518687.
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To improve the quality of tool paths in surface machining, different machining requirements are considered in the tool path generation algorithm. In the traditional tool path generation algorithm, due to the lack of a unified mathematical calculation framework, these requirements often need to be considered separately, but they often compete with each other, so that different requirements cannot be satisfied at the same time and the tool path cannot achieve the optimal. To resolve this issue, an extensive tool path generation algorithm framework for arbitrary surfaces was proposed. The proposed algorithm transforms the tool path calculation framework into a constrained functional optimization problem by establishing an optimization function based on the potential energy field and an inequality function based on the gradient field in the machining area. By establishing finite element approximation, the functional optimization problem is transformed into a numerical optimization problem, which reduces the difficulty of solving. According to the machining requirements of die surface such as tool path smoothness, line width constraint and cutting direction constraints were transformed into the constraints of potential energy field isopotential line, and the method of generating reciprocating cutter path and cutter contact path isosection cutter path was proposed by optimizing the method. It is evident from the simulation and machining experiments results that continuous and smooth tool paths can be generated by using this algorithm, and machining quality and machining efficiency can be improved. By adding different machining requirements into the framework, a tool path with different optimization objectives can be generated.
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Diveev, Askhat, Elena Sofronova, and Ivan Zelinka. "Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm." Mathematics 8, no. 12 (November 25, 2020): 2105. http://dx.doi.org/10.3390/math8122105.
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A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.
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Little, Max A., and Nick S. Jones. "Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2135 (June 8, 2011): 3115–40. http://dx.doi.org/10.1098/rspa.2010.0674.
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Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.