10,377 results
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2. Average Convergence Rate of Evolutionary Algorithms II: Continuous Optimisation
- Author
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Chen, Yu, He, Jun, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Li, Kangshun, editor, Li, Wei, editor, Wang, Hui, editor, and Liu, Yong, editor
- Published
- 2020
- Full Text
- View/download PDF
3. Estimating Approximation Errors of Elitist Evolutionary Algorithms
- Author
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Wang, Cong, Chen, Yu, He, Jun, Xie, Chengwang, Barbosa, Simone Diniz Junqueira, Editorial Board Member, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Pan, Linqiang, editor, Liang, Jing, editor, and Qu, Boyang, editor
- Published
- 2020
- Full Text
- View/download PDF
4. Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems
- Author
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Avvakumov, A. V., Strizhov, V. F., Vabishchevich, P. N., Vasilev, A. O., Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Dimov, Ivan, editor, Faragó, István, editor, and Vulkov, Lubin, editor
- Published
- 2019
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- View/download PDF
5. Illumination compensation algorithm for colorimetric detection of microfluidic paper-based devices with a smartphone
- Author
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Ademir Ferreira Da Silva, Mathias Steiner, Matheus Esteves Ferreira, Ricardo Luis Ohta, Jaione Tirapu-Azpiroz, and Daniel Vitor Lopes Marcondes Marçal
- Subjects
Standard test image ,Channel (digital image) ,Computer science ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Histogram matching ,Software ,Approximation error ,Color mapping ,Calibration ,RGB color model ,Computer vision ,Artificial intelligence ,business - Abstract
Colorimetric detection using microfluidic paper-based analytical devices (µPADs) and smartphones enable lowcost mobile chemical analysis solutions. However, variable illumination conditions and phone characteristics (i.e. camera hardware and software capabilities) limit the accurate interpretation and reproducibility of quantitative results. In this paper, we describe a method to automatically compensate an image captured by a smartphone camera under variable illumination conditions. By incorporating a two-step algorithm, we approximate the mobile camera picture color distribution to resemble a laboratory-grade measurement under reference illumination conditions. For every test image, the algorithm first applies a color mapping step that performs histogram matching of a set of color reference spots printed on the device to a laboratory reference measurement. After this initial correction step, a transformation matrix is computed via a least-square fit to minimize the differences between the device and the laboratory references. This matrix is then applied to the RGB channel values obtained from a µPAD to correct for illumination variations. The methodology was tested by correcting a test dataset captured using a smartphone to approximate to a calibration dataset acquired using a lab-grade camera. After correction, the relative error between the datasets fell to 10-20%, leading to an increase in classification accuracy between 12-33%. This approach enables colorimetric chemical analysis with smartphones outside the lab, removing the need to control external lighting conditions.
- Published
- 2021
6. Some observations regarding the RBF-FD approximation accuracy dependence on stencil size.
- Author
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Kolar-Požun, Andrej, Jančič, Mitja, Rot, Miha, and Kosec, Gregor
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STENCIL work ,PARTIAL differential equations ,FINITE differences ,APPROXIMATION error ,CONFERENCE papers - Abstract
When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that it affects the approximation accuracy in a particularly interesting way — the solution error oscillates under increasing stencil size. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are able to introduce a numerical quantity that could indicate whether a given stencil size is locally optimal. This work is an extension of our ICCS 2023 conference paper (Kolar-Požun et al., 2023). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Modeling of a paper-making wastewater treatment process using a fuzzy neural network
- Author
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Zhanzhan Hu, Yan Wang, Hongbin Liu, Jinquan Wan, Yongwen Ma, Huiping Zhang, Mingzhi Huang, and ChangKyoo Yoo
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Setpoint ,Model predictive control ,Fuzzy rule ,Mean squared error ,Artificial neural network ,Approximation error ,Control theory ,General Chemical Engineering ,General Chemistry ,Cluster analysis ,Fuzzy logic ,Mathematics - Abstract
An intelligent system that includes a predictive model and a control was developed to predict and control the performance of a wastewater treatment plant. The predictive model was based on fuzzy C-means clustering, fuzzy inference and neural networks. Fuzzy C-means clustering was used to identify model’s architecture, extract and optimize fuzzy rule. When predicting, MAPE was 4.7582% and R was 0.8535. The simulative results indicate that the learning ability and generalization of the model was good, and it can achieve a good predication of effluent COD. The control model was based on a fuzzy neural network model, taking into account the difference between the predicted value of COD and the setpoint. When simulating, R was 0.9164, MAPE was 5.273%, and RMSE was 0.0808, which showed that the FNN control model can effectively change the additive dosages. The control of a paper-making wastewater treatment process in the laboratory using the developed predictive control model and MCGS (monitor and control generated system) software shows the dosage was computed accurately to make the effluent COD remained at the setpoint, when the influent COD value or inflow flowrate was changed. The results indicate that reasonable forecasting and control performances were achieved through the developed system; the maximum error was only 3.67%, and the average relative error was 2%.
- Published
- 2012
8. Paper-craft from 3D polygonal models using generalized cylinders
- Author
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Fady Massarwi, Gershon Elber, and Craig Gotsman
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Developable surface ,Aerospace Engineering ,T-vertices ,Topology ,Computer Graphics and Computer-Aided Design ,Hausdorff distance ,Approximation error ,Mesh generation ,Modeling and Simulation ,Automotive Engineering ,Triangle mesh ,Polygon mesh ,Laplacian smoothing ,ComputingMethodologies_COMPUTERGRAPHICS ,Mathematics - Abstract
We introduce an algorithm for approximating a 2-manifold 3D mesh by a set of developable surfaces. Each developable surface is a generalized cylinder represented as a strip of triangles not necessarily taken from the original mesh. Our algorithm is automatic, creates easy-to-assemble pieces, and provides L"@K global error bounds. The algorithm consists of three stages. In the first stage, the mesh is segmented into meaningful components. The second stage approximates each of the mesh components in 3D by a set of triangle strips with smooth (non-jagged) boundaries that guarantee a maximal user-defined error relative to the original mesh. Finally, these strips are unfolded to the plane, resulting in flat patterns, which may be cut and assembled from paper. The approximation quality is controlled by a user-supplied parameter specifying the allowed Hausdorff distance between the input mesh and its piecewise-developable approximation. The strips generated by our algorithm may be parameterized to conform with the parameterization of the original mesh, if given, to facilitate texture mapping. We demonstrate this by physically assembling paper-craft models from the strips generated by our algorithm when run on several polygonal 3D mesh data sets.
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- 2008
9. Space‐efficient estimation of empirical tail dependence coefficients for bivariate data streams.
- Author
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Gregory, Alastair and Jana, Kaushik
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BIVARIATE analysis ,MARGINAL distributions ,COPULA functions ,RIVERS ,APPROXIMATION error ,PAPER arts - Abstract
This article proposes a space‐efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream‐length invariant error bounds, utilizes recent work on the development of a summary for bivariate empirical copula functions. The work in this paper accurately approximates a bivariate empirical copula in the tails of each marginal distribution, therefore modeling the tail dependence between the two variables observed in the data stream. Copulas evaluated at these marginal tails can be used to estimate the tail dependence coefficients. Modifications to the space‐efficient bivariate copula approximation, presented in this paper, allow the error of approximations to the tail dependence coefficients to remain stream‐length invariant. Theoretical and numerical evidence of this, including a case‐study using the Los Alamos National Laboratory netflow data‐set, is provided within this article. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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10. New method of determining the plane deformation of paper
- Author
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L. S. Yamnikov
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Scanner ,Plane (geometry) ,Computer science ,Approximation error ,Applied Mathematics ,Acoustics ,Measuring instrument ,Paper specimen ,Deformation (meteorology) ,Compression (physics) ,Instrumentation - Abstract
A description is given of a new method and a new measuring instrument for determining the plane deformation of banknotes, securities, and other commercial documents. The deformation unit models the compression of a paper specimen, while a scanner and computer operating on a specially developed program provide for measurement of strains on the order 2.0–5.0 mm with an absolute error no greater than ±10 μm.
- Published
- 1998
11. Phosphorus Analysis in Wastewater: Best Practices White Paper
- Author
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D. Scott Smith
- Subjects
Wastewater ,chemistry ,Approximation error ,Phosphorus ,Environmental engineering ,chemistry.chemical_element ,Environmental science ,Sewage treatment ,Replicate ,Colorimetry ,Effluent ,Volume concentration - Abstract
Phosphorus (P) monitoring at wastewater treatment plants is essential as phosphorus (as total phosphorus) is an important main constituent regulated in treatment plant effluents. Recent trends are towards increasingly lower phosphorus limits, requiring reliable lower and lower phosphorus measurements. There is a long history of P analysis in dilute matrices; i.e., river and lake water and best practices have been developed. These best practices for surface waters are reported herein. Potential issues in wastewater P analysis by colorimetry include pH, proton to molybdenum ratio, color development time, and digestion method. Of equal importance are the QA/QC measurement protocols implemented by wastewater analysis labs; demonstrably well performing examples from Coeur d'Alene, Spokane, and the City of Las Vegas are presented. Total reactive phosphorus is an ambiguous analytical measurement because the quantitative results depend strongly on color development time. For low level analysis, long path lengths have advantages in more precisely resolving low concentrations. Replicate measurements are essential, especially for low level P samples, in order to capture the true value of the sample within variability. When dealing with low concentrations, even a small absolute error is a large relative error; thus, replicate measurements are essential to estimate true concentrations for dilute phosphorus samples. This title belongs to WERF Research Report Series ISBN: 9781780407807 (eBook)
- Published
- 2016
12. Invited discussion paper small-sample distributional properties of nonlinear regression estimators (a geometric approach)
- Author
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Andeej Pizman
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Statistics and Probability ,Mathematical optimization ,Heuristic ,Gaussian ,Estimator ,Probability density function ,Conditional probability distribution ,Edgeworth series ,symbols.namesake ,Approximation error ,symbols ,Applied mathematics ,Statistics, Probability and Uncertainty ,Nonlinear regression ,Mathematics - Abstract
The paper is mainly a survey of the topic how to approximate the probability density of the parameter estimator in a nonlinear regression model. A short presentation of the geometry of the model and a heuristic discussion of the model and a heuristic discussion of the “irregularities” of the estimates are given. In the model with Gaussian errors we present the asymptotic normal approximation, the approximationby the second order Edgeworth expansion, a conditional density of BARNDORFF-NIELSEN, and mainly the approximation called “flat” or “saddlepoint” approximation, which will be shown to have several interesting properties. Further, we present the possibility of improving the approximation in some models, the extension of the approximation to some cases of nongaussian errors, and besides the maximum likelihood estimator we consider also the weighted least-squares estimator, with the weights not depending on the error concariance matrix.
- Published
- 1990
13. L1 Adaptive Fault-Tolerant Control for Nonlinear Systems Subject to Input Constraint and Multiple Faults.
- Author
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Zhou, Yan, Liu, Huiying, and Guo, Huijuan
- Subjects
FAULT-tolerant control systems ,TIME-varying systems ,NONLINEAR systems ,LINEAR systems ,APPROXIMATION error - Abstract
This paper investigates an L1 adaptive fault-tolerant control scheme for nonlinear systems with input constraint, external disturbances, and multiple faults, which include actuator faults and sensor faults. Faults and input constraint are important factors that affect the stability and performance of a control system. Actuators and sensors are the most vulnerable components, with the former receiving more attention in comparison. In this paper, sensor faults are first transformed into pseudo-actuator faults through the augmented matrix approach, which facilitates their handling together with actuator faults. Saturation constraints on the control signal are not conducive to the design of the controller. The conversion of an input-saturated function to a time-varying linear system is completed based on function approximation and Lagrange's mean value theorem. Moreover, a nonlinear system with unknown input gain and uncertainties is constructed using these methods. Next, an L1 adaptive fault-tolerant controller is designed to cope with uncertainties, including system uncertainties, external disturbances, faults, and approximation errors. In the L1 adaptive controller, the online estimation of the time-varying parameters allows for updating of the system state, while the combination of the two is transmitted to the control law such that it can compensate for the effects of the uncertainties. The stability and performance boundaries are further derived using the Lyapunov theory and the L1 reference system. Finally, simulations are carried out to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor.
- Author
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Li, Wan-Li, Li, Jiong, Ye, Ji-Kun, Shao, Lei, and Zhou, Chi-Jun
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REINFORCEMENT learning ,DEEP reinforcement learning ,MACHINE learning ,NONCONVEX programming ,CONVEX programming ,ALGORITHMS ,APPROXIMATION error - Abstract
To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Control of cross-directional systems with approximate symmetries.
- Author
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Kempf, Idris, Goulart, Paul J., and Duncan, Stephen R.
- Subjects
- *
SEMIDEFINITE programming , *APPROXIMATION error , *SYMMETRY , *LIGHT sources , *LINEAR dynamical systems , *COMPUTATIONAL complexity , *LYAPUNOV stability - Abstract
Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries undermine the ability to decouple the system, resulting in the loss of any potential complexity reduction. To address this, we propose substituting an approximation with exact structural symmetries for the original system model, thereby introducing an approximation error. We focus on internal model controllers for cross-directional systems encountered in large-scale and high-speed control problems of synchrotrons or the process industry and characterise the stability, performance, and robustness properties of the resulting closed loop. While existing approaches replace the original system model with one that minimises the Frobenius norm of the approximation error, we show that this can lead to instability or poor performance. Instead, we propose approximations that are obtained from semidefinite programming problems. We show that our proposed approximations can yield stable systems even when the Frobenius norm approximation does not. The paper concludes with numerical examples and a case study of a synchrotron light source with inexact structural symmetries. Exploiting structural symmetries in large-scale and high-speed systems enables faster sampling times and the use of more advanced control techniques, even when the symmetries are approximate. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Development of a new permeability tester of paper
- Author
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Kentaro Yamamoto, Akihiko Iwasaki, Mineko Iwasaki, Zenichi Miyagi, and Shichio Hara
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Paperboard ,Materials science ,business.industry ,Electrical engineering ,Pressure differential ,Mechanics ,Permeation ,law.invention ,Volumetric flow rate ,Permeability (earth sciences) ,Pressure measurement ,law ,Approximation error ,Air permeability specific surface ,visual_art ,visual_art.visual_art_medium ,business - Abstract
The permeability test is standardized by JIS P 8117 Testing Method for Air Permeability of Paper and Paperboard, in which the permeability is provided by Gurley's permeability TG in second, which is the elapsed time necessary for air of definite volume to permeate through definite area of paper under definite pressure differential. The measuring range of TG is prescribed between 2 and 1800 s. The method is time consuming and inefficient at the practical testing, because at least the elapsed time of TG is necessary at the test. In order to indicate TG value in a moment a new permeability tester is developed, the principle of which is similar to that of a pneumatic micrometer of back-pressure type. Assuming that flow rate of air through paper is proportional to pressure differential, working principle of the test is analysed, and a method of graduation of Gurley's permeability TG on a water column manometer is derived theoretically. And the error evaluation of the tester becomes possible. The relative error of TG due to measuring error of the manometer can be limited within 1% by giving suitable design constants at the design of the tester. The assumption of flow rate through paper is confirmed by a special operation of the tester.
- Published
- 1985
17. Approximating Bézier curves with least square polygons.
- Author
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Li, Yajuan, Zhang, Meng, Jin, Wenbiao, and Deng, Chongyang
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LEAST squares ,POLYGONS ,GEOMETRIC approach ,PIECEWISE linear approximation ,APPROXIMATION error ,COMPUTER-aided design - Abstract
Approximating Bézier curve by polygon is a traditional technique in computer-aided geometric design, and there are several methods for constructing such polygons. In this paper, we propose to approximate Bézier curve by the least square polygon (LSP). LSP was derived by least square fitting which minimizes the integral of approximating errors. We provide a closed formula for the vertices of LSP. Because of its optimization method, LSP has lower approximation errors than existing approximating polygons. This observation is verified by many numerical examples we tested and several typical examples are included in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. Brenke-type polynomials-based robust adaptive control of cooperative multiple manipulators without velocity measurements.
- Author
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Deylami, Ali and Izadbakhsh, Alireza
- Subjects
ADAPTIVE control systems ,ROBUST control ,POLYNOMIAL approximation ,VELOCITY measurements ,APPROXIMATION error - Abstract
This paper proposes Brenke-type polynomials for uncertainty approximation in adaptive control of cooperative electrically driven manipulators. The contribution of this paper is reducing the number of signals needed in the construction of the regressor vector for uncertainty approximation due to the simplicity of Brenke-type polynomials in comparison with other alternatives. It is verified that uniformly bounded stability of the tracking/approximation errors can be assured if the Brenke-type polynomials are utilised as regressors. Moreover, it has been assumed that velocity signals are not available for feedback. Different trajectories, including simple and highly complicated and fast paths, have been tested in simulation results. The results are also compared with four state-of-the-art powerful approximation methods to show the accuracy and efficiency of the proposed controller structure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. A machine-learning approach based on 409 treatments to predict optimal number of iodine-125 seeds in low-dose-rate prostate brachytherapy
- Author
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Luc Ollivier, Ulrike Schick, G. Goasduff, Nicolas Boussion, Dimitris Visvikis, Antoine Valeri, Gurvan Dissaux, and Olivier Pradier
- Subjects
Original Paper ,Mean squared error ,business.industry ,medicine.medical_treatment ,Brachytherapy ,machine-learning ,Machine learning ,computer.software_genre ,prostate cancer ,Low-Dose Rate Brachytherapy ,low-dose-rate brachytherapy ,Support vector machine ,Oncology ,Abacus (architecture) ,Approximation error ,radioactive seeds ,Test set ,Medicine ,Radiology, Nuclear Medicine and imaging ,Artificial intelligence ,business ,computer ,Prostate brachytherapy - Abstract
Purpose Low-dose-rate brachytherapy is a key treatment for low-risk or favorable intermediate-risk prostate cancer. The number of radioactive seeds inserted during the procedure depends on prostate volume, and is not easy to predict without pre-planning. Consequently, a large number of unused seeds may be left after treatment. The objective of the present study was to predict the exact number of seeds for future patients using machine learning and a database of 409 treatments. Material and methods Database consisted of 18 dosimetric and efficiency parameters for each of 409 cases. Nine predictive algorithms based on machine-learning were compared in this database, which was divided into training group (80%) and test group (20%). Ten-fold cross-validation was applied to obtain robust statistics. The best algorithm was then used to build an abacus able to predict number of implanted seeds from expected prostate volume only. As an evaluation, the abacus was also applied on an independent series of 38 consecutive patients. Results The best coefficients of determination R2 were given by support vector regression, with values attaining 0.928, 0.948, and 0.968 for training set, test set, and whole set, respectively. In terms of predicted seeds in test group, mean square error, median absolute error, mean absolute error, and maximum error were 2.55, 0.92, 1.21, and 7.29, respectively. The use of obtained abacus in 38 additional patients resulted in saving of 493 seeds (393 vs. 886 remaining seeds). Conclusions Machine-learning-based abacus proposed in this study aims at estimating the necessary number of seeds for future patients according to past experience. This new abacus, based on 409 treatments and successfully tested in 38 new patients, is a good alternative to non-specific recommendations.
- Published
- 2021
20. The role of an objective function in the mathematical modelling of wide-angle X-ray diffraction curves of semi-crystalline polymers
- Author
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Małgorzata Rabiej and Stanisław Rabiej
- Subjects
Diffraction ,Work (thermodynamics) ,Mathematical optimization ,Materials science ,relative error ,Biochemistry ,Inorganic Chemistry ,absolute error ,Quality (physics) ,objective function ,Structural Biology ,Approximation error ,Tacticity ,General Materials Science ,mathematical modelling ,Physical and Theoretical Chemistry ,polymers ,chemistry.chemical_classification ,Polymer ,Condensed Matter Physics ,Research Papers ,Amorphous solid ,Condensed Matter::Soft Condensed Matter ,chemistry ,X-ray crystallography ,diffraction curves - Abstract
The choice of an objective function in constructing a mathematical model of an experimental wide-angle X-ray diffraction curve of semi-crystalline polymers is discussed., To decompose a wide-angle X-ray diffraction (WAXD) curve of a semi-crystalline polymer into crystalline peaks and amorphous halos, a theoretical best-fitted curve, i.e. a mathematical model, is constructed. In fitting the theoretical curve to the experimental one, various functions can be used to quantify and minimize the deviations between the curves. The analyses and calculations performed in this work have proved that the quality of the model, its parameters and consequently the information on the structure of the investigated polymer are considerably dependent on the shape of an objective function. It is shown that the best models are obtained employing the least-squares method in which the sum of squared absolute errors is minimized. On the other hand, the methods in which the objective functions are based on the relative errors do not give a good fit and should not be used. The comparison and evaluation were performed using WAXD curves of seven polymers: isotactic polypropylene, polyvinylidene fluoride, cellulose I, cellulose II, polyethylene, polyethylene terephthalate and polyamide 6. The methods were compared and evaluated using statistical tests and measures of the quality of fitting.
- Published
- 2021
21. ON SIMULTANEOUS APPROXIMATION AND COMBINATIONS OF LUPAS TYPE OPERATORS.
- Author
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SINHA, T. A. K., SINGH, K. K., and SHARMA, AVINASH K.
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POSITIVE operators ,LINEAR operators ,APPROXIMATION error - Abstract
The purpose of the present paper is to study a sequence of linear and positive operators which was introduced by A. Lupas. First, we obtain estimate of moments of the operators and then prove a basic convergence theorem for simultaneous approximation. Further, we find error in approximation in terms of modulus of continuity of function. Finally, we establish a Voronovskaja asymptotic formula for linear combination of the above operators. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Disturbance Observer-Based Adaptive Fault Tolerant Control with Prescribed Performance of a Continuum Robot.
- Author
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Xu, Shoulin
- Subjects
ROBOT dynamics ,ROBOT control systems ,APPROXIMATION error ,LYAPUNOV functions ,ACTUATORS - Abstract
This paper studies an adaptive fault tolerant control (AFTC) scheme for a continuum robot subjected to unknown actuator faults, dynamics uncertainties, unknown disturbances, and prescribed performance. Specifically, to deal with uncertainties, a function approximation technique (FAT) is employed to evaluate the unknown actuator faults and uncertain dynamics of the continuum robot. Then, a nonlinear disturbance observer (DO) is developed to estimate the unknown compounded disturbance, which contains the unknown disturbances and approximation errors of the FAT. Furthermore, the prescribed error bound is treated as a time-varying constraint, and the controller design method is based on an asymmetric barrier Lyapunov function (BLF), which is operated to strictly ensure the steady-state and transient performance of the continuum robot. Afterwards, the simulation results validate the effectiveness of the proposed AFTC in dealing with the unknown actuator faults, uncertainties, unknown disturbances, and prescribed performance. Finally, the effectiveness of the proposed AFTC scheme is verified through experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Fast and precise approximation of Minkowski sum of two rotational ellipsoids with a superellipsoid.
- Author
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Yamada, Ryunosuke, Tsuji, Tokuo, Hiramitsu, Tatsuhiro, Seki, Hiroaki, Nishimura, Toshihiro, Suzuki, Yosuke, and Watanabe, Tetsuyou
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TIME complexity ,GRANULAR flow ,FLOW simulations ,APPROXIMATION error ,PARTICLE motion ,ELLIPSOIDS ,ROBOT motion - Abstract
In this paper, we propose a fast and accurate method for approximating the Minkowski sum of two rotational ellipsoids with a superellipsoid. The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them are computed based on Minkowski sum, whose accuracy and processing time depend on how the mesh is created. We approximate Minkowski sum with a superellipsoid function. The superellipsoid has various shapes with the value of the exponents, and the computation of the parameters including the exponents is an algebraic computation with the time complexity O (1) . As a result, approximation error is small and computation is fast in all combinations of rotational ellipsoids. In addition, collision is quickly detected by solving the inequality of superellipsoid. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Three-Dimensional Dead-Reckoning Based on Lie Theory for Overcoming Approximation Errors.
- Author
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Jeong, Da Bin, Lee, Boeun, and Ko, Nak Yong
- Subjects
APPROXIMATION theory ,APPROXIMATION error ,LIE algebras ,LIE groups ,VELOCITY - Abstract
This paper proposes a dead-reckoning (DR) method for vehicles using Lie theory. This approach treats the pose (position and attitude) and velocity of the vehicle as elements of the Lie group SE 2 (3) and follows the computations based on Lie theory. Previously employed DR methods, which have been widely used, suffer from cumulative errors over time due to inaccuracies in the calculated changes from velocity during the motion of the vehicle or small errors in modeling assumptions. Consequently, this results in significant discrepancies between the estimated and actual positions over time. However, by treating the pose and velocity of the vehicle as elements of the Lie group, the proposed method allows for accurate solutions without the errors introduced by linearization. The incremental updates for pose and velocity in the DR computation are represented in the Lie algebra. Experimental results confirm that the proposed method improves the accuracy of DR. In particular, as the motion prediction time interval of the vehicle increases, the proposed method demonstrates a more pronounced improvement in positional accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares.
- Author
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Song, Jieun and Lee, Bumjoo
- Subjects
POLYNOMIAL approximation ,LEAST squares ,MINIMUM variance estimation ,NONLINEAR functions ,APPROXIMATION error ,APPROXIMATION algorithms ,SEARCH algorithms - Abstract
In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm searches for the optimal piecewise polynomial (OPP) with the minimum computational cost while ensuring that the error is below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and numbers of intervals. The computational cost only depended on polynomial complexity, i.e., the order and the number of intervals at runtime function call. In previous studies, the user had to decide one or all of the orders and the number of intervals. In contrast, the OPP approximation algorithm determines both of them. For the optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated in ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and the random selection method for the given sample points. Afterward, whether the approximation error was below the predetermined value was examined. When the error was permissible, the combination was selected as the optimal approximation, or the next combination was examined. To verify the performance, several representative functions were examined and analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. Full-Scale Isogeometric Topology Optimization of Cellular Structures Based on Kirchhoff-Love Shells.
- Author
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Mingzhe Huang, Mi Xiao, Liang Gao, Mian Zhou, Wei Sha, and Jinhao Zhang
- Subjects
CELL anatomy ,TOPOLOGY ,GEOMETRIC analysis ,APPROXIMATION error ,GEOMETRIC modeling ,ISOGEOMETRIC analysis - Abstract
Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio. In this paper, a full-scale isogeometric topology optimization (ITO) method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed. This method utilizes high-order continuous nonuniform rational B-splines (NURBS) as basis functions for Kirchhoff-Love shell elements. The geometric and analysis models of thin shells are unified by isogeometric analysis (IGA) to avoid geometric approximation error and improve computational accuracy. The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh. Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures. To facilitate numerical implementation, the p-norm function is used to aggregate local volume constraints into an equivalent global constraint. Several numerical examples are provided to demonstrate the effectiveness of the proposed method. After simulation and comparative analysis, the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Online prediction of effluent COD in the anaerobic wastewater treatment system based on PCA-LSSVM algorithm
- Author
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Yong-Wen Ma, Ze-Jun Liu, Yan Wang, and Jin-Quan Wan
- Subjects
Biological Oxygen Demand Analysis ,Support Vector Machine ,Mean squared error ,Correlation coefficient ,Health, Toxicology and Mutagenesis ,Chemical oxygen demand ,General Medicine ,Wastewater ,010501 environmental sciences ,Soft sensor ,Pulp and paper industry ,Waste Disposal, Fluid ,01 natural sciences ,Pollution ,Shock (mechanics) ,Bioreactors ,Mean absolute percentage error ,Approximation error ,Environmental Chemistry ,Anaerobiosis ,Effluent ,Algorithms ,0105 earth and related environmental sciences ,Mathematics - Abstract
Since anaerobic wastewater treatment is a nonlinear and complex biochemical process, reasonable monitoring and control are needed to keep it operating stably and efficiently. In this paper, a least-square support-vector machine (LS-SVM) was employed to construct models for the prediction of effluent chemical oxygen demand (COD) in an anaerobic wastewater treatment system. The result revealed that the performance of the steady-state model based on LS-SVM for predicting effluent COD was acceptable, with the maximum relative error (RE) of 11.45%, the mean average percentage error (MAPE) of 0.79% and the root mean square error (RMSE) of 3.08 when training, and the performance fell slightly when testing. Even though, the correlation coefficient value (R) between the predicted value and the actual value of 0.9752 could be achieved, which means this model can predict the variation of effluent COD in general. The dynamic-state models under three kinds of shock loads, which were concentration, hydraulic, and bicarbonate buffer absent, showed good forecasting performance, the correlation coefficient values (R) all excelled 0.99. Among these three shocks, the dynamic LS-SVM model under bicarbonate buffer absent shock achieved the optimal performance and followed by the dynamic-state model under hydraulic shock. This paper provides a meaningful reference to improve the monitoring level of the anaerobic wastewater treatment process.
- Published
- 2019
28. On a paper of C. B. Dunham concerning degeneracy in mean nonlinear approximation
- Author
-
Dietrich Braess
- Subjects
Mathematics(all) ,Numerical Analysis ,Nonlinear approximation ,Mathematical optimization ,Approximation error ,Applied Mathematics ,General Mathematics ,Born–Huang approximation ,Spouge's approximation ,Degeneracy (mathematics) ,Analysis ,Mathematics ,Mathematical physics - Published
- 1973
29. Generalized multilevel B-spline approximation for scattered data interpolation in image processing.
- Author
-
Chen, Juanjuan, Huang, Ting, Cai, Zhanchuan, and Huang, Wentao
- Subjects
- *
MACHINE learning , *BURST noise , *IMAGE processing , *APPROXIMATION error , *INTERPOLATION , *DEEP learning - Abstract
This paper proposes a Generalized Multilevel B-spline Approximation (GMBA) method, which addresses scattered data interpolation problems in image processing. Mathematically, the GMBA provides a better solution for the B-spline control lattice by superimposing identical level B-splines compared with traditional Multilevel B-spline Approximation (MBA). Specifically, the GMBA allows the spacing of next control lattice to be subdivided arbitrarily or remained unchanged, which is determined by a predefined spacing set or the current error level. These improvements bring higher approximation accuracy and more flexibility for algorithm design to avoid over-fitting. In this paper, basic GMBA algorithm and its refined algorithm are compiled for image processing. Finally, six relevant cases are involved to test the GMBA, including surface approximation, image enlargement, image completion, and Salt-and-Pepper (SAP) noise removal. The experimental results show that the GMBA has better performance than the MBA in surface approximation and image processing, performs comparatively fast with the best performance on more than half of the standard test images compared with traditional algorithms, and has partially better performance even than deep learning algorithms. The GMBA can effectively recover meaningful details in images contaminated with even extremely high SAP noise level (up to 99%). • We give a generalized multilevel B-spline approximation (GMBA) method. • GMBA allows the control spacing to be subdivided arbitrarily or remained unchanged. • GMBA offers higher approximation accuracy and greater flexibility than traditional MBA. • GMBA provides superior performance and less run time than many of the state-of-the-art methods for SAP noise removal. • GMBA can recovery meaningful detail at noise levels as high as 99% for SAP noise removal. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. A comparative numerical study of finite element methods resulting in mass conservation for Poisson's problem: Primal hybrid, mixed and their hybridized formulations.
- Author
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Oliari, Victor B., Hancco Ancori, Ricardo J., and Devloo, Philippe R.B.
- Subjects
- *
FINITE element method , *CONSERVATION of mass , *APPROXIMATION error , *LINEAR systems , *CONDENSATION - Abstract
This paper presents a numerical comparison of finite-element methods resulting in local mass conservation at the element level for Poisson's problem, namely the primal hybrid and mixed methods. These formulations result in an indefinite system. Alternative formulations yielding a positive-definite system are obtained after hybridizing each method. The choice of approximation spaces yields methods with enhanced accuracy for the pressure variable, and results in systems with identical size and structure after static condensation. A regular pressure precision mixed formulation is also considered based on the classical RT k space. The simulations are accelerated using Open multi-processing (OMP) and Thread-Building Blocks (TBB) multithreading paradigms alongside either a coloring strategy or atomic operations ensuring a thread-safe execution. An additional parallel strategy is developed using C++ threads, which is based on the producer-consumer paradigm, and uses locks and semaphores as synchronization primitives. Numerical tests show the optimal parallel strategy for these finite-element formulations, and the computational performance of the methods are compared in terms of simulation time and approximation errors. Additional results are developed during the process. Numerical solvers often fail to find an accurate solution to the highly indefinite systems arising from finite-element formulations, and this paper documents a matrix ordering strategy to stabilize the resolution. A procedure to enable static condensation based on the introduction of piecewise constant functions that also fulfills Neumann's compatibility condition, and yet computes an average pressure per element is presented. • Numerical comparison of the mixed, primal hybrid, and other locally conservatives finite element methods. • Introduction of a twice hybridized primal hybrid method, yielding a positive definite matrix after static condensation. • Comparison of multi-threaded strategies and thread-safety mechanisms. • A numerical procedure to stabilize the linear system resolution for indefinite matrices is described. • A general procedure that enables static condensation and fulfills Neumann's compatibility condition. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. An Improved Rational Approximation of Bark Scale Using Low Complexity and Low Delay Filter Banks.
- Author
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Hareesh, V. and Bindiya, T. S.
- Subjects
- *
FILTER banks , *FINITE impulse response filters , *STANDARD deviations , *APPROXIMATION algorithms , *APPROXIMATION error - Abstract
This paper proposes an algorithm to obtain the sampling factors to model any frequency partitioning so that it is realized using low complexity rational decimated non-uniform filter banks (RDNUFBs). The proposed algorithm is employed to approximate the Bark scale to find a rational frequency partitioning that can be realized using RDNUFBs with less approximation error. The proposed Bark frequency partitioning is found to reduce the average deviation in centre frequency and bandwidth by 65.04% and 48.50%, respectively, and root-mean-square bandwidth deviation by 54.46% when compared to those of the existing perceptual wavelet approximation of Bark scale. In the first filter bank design approach discussed in the paper, a near-perfect reconstruction partially cosine modulated filter bank is employed to obtain the improved Bark frequency partitioning. In the second design approach, the hardware complexity of the PCM-based RDNUFB is reduced by deriving the channels with different sampling factors from the same prototype filter by the method of channel merging. There is a considerable reduction of 40.83% in the number of multipliers when merging of partially cosine modulated channels is employed. It is also found that both the proposed approaches can reduce the delay by 95.17% when compared to the existing rational tree approximation methods and hence, are suitable for real-time applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Multivariate data analysis of capacitance frequency scanning for online monitoring of viable cell concentrations in small-scale bioreactors
- Author
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Christian Grimm, Marek Hoehse, Stefanie Blioch, Gerhard Greller, Jochen Scholz, Sabrina Metze, and Jens Matuszczyk
- Subjects
0106 biological sciences ,Multivariate statistics ,Cell Survival ,Computer science ,Process analytical technology ,Cell Culture Techniques ,CHO Cells ,Electric Capacitance ,Capacitance frequency scanning ,01 natural sciences ,Biochemistry ,Signal ,Capacitance ,Analytical Chemistry ,Mammalian cell culture ,03 medical and health sciences ,Bioreactors ,Cricetulus ,Robustness (computer science) ,Approximation error ,010608 biotechnology ,Animals ,Biomass ,030304 developmental biology ,0303 health sciences ,Process (computing) ,Correction ,Equipment Design ,MVDA (multifrequency permittivity, impedance spectroscopy, small-scale bioreactor, process monitoring and control) ,Multivariate Analysis ,Capacitance probe ,Biological system ,PAT ,Research Paper - Abstract
Viable cell concentration (VCC) is one of the most important process attributes during mammalian cell cultivations. Current state-of-the-art measurements of VCC comprise offline methods which do not allow for continuous process data. According to the FDA’s process analytical technology initiative, process monitoring and control should be applied to gain process understanding and to ensure high product quality. In this work, the use of an inline capacitance probe to monitor online VCCs of a mammalian CHO cell culture process in small-scale bioreactors (250 mL) was investigated. Capacitance sensors using single frequency are increasingly common for biomass monitoring. However, the single-frequency signal corresponds to the cell polarization that represents the viable cell volume. Therefore single-frequency measurements are dependent on cell diameter changes. Measuring the capacitance across various frequencies (frequency scanning) can provide information about the VCC and cope with changing cell diameter. Applying multivariate data analysis on the frequency scanning data successfully enabled direct online monitoring of VCCs in this study. The multivariate model was trained with data from 5 standard cultivations. The model provided a prediction of VCCs with relative errors from 5.5 to 11%, which is a good agreement with the acceptance criterion based on the offline reference method accuracy (approximately 10% relative error) and strongly improved compared with single-frequency results (16 to 23% relative error). Furthermore, robustness trials were conducted to demonstrate the model’s predictive ability under challenging conditions. The process deviations in regard to dilution steps and feed variations were detected immediately in the online prediction of the VCC with relative errors between 6.7 and 13.2%. Thus in summary, the presented method on capacitance frequency scanning demonstrates its suitability for process monitoring and control that can save batches, time, and cost. Graphical abstract Electronic supplementary material The online version of this article (10.1007/s00216-019-02096-3) contains supplementary material, which is available to authorized users.
- Published
- 2019
33. Predictor-Based Neural Dynamic Surface Control of a Nontriangular System With Unknown Disturbances.
- Author
-
Yang, Yang, Chen, Didi, Liu, Qidong, Zhang, Tengfei, Liu, Aaron, and Yue, Wenbin
- Subjects
NONLINEAR systems ,NOISE measurement ,APPROXIMATION error ,NONLINEAR dynamical systems ,CLOSED loop systems ,ADAPTIVE control systems ,BRUSHLESS electric motors - Abstract
For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
34. On asymptotic convergence rate of random search.
- Author
-
Tarłowski, Dawid
- Subjects
APPROXIMATION error ,STOCHASTIC processes ,CONTINUOUS functions ,MARKOV processes ,DIFFERENTIAL evolution ,COMPUTER simulation - Abstract
This paper presents general theoretical studies on asymptotic convergence rate (ACR) for finite dimensional optimization. Given the continuous problem function and discrete time stochastic optimization process, the ACR is the optimal constant for control of the asymptotic behaviour of the expected approximation errors. Under general assumptions, condition ACR < 1 implies the linear behaviour of the expected time of hitting the ε - optimal sublevel set with ε → 0 + and determines the upper bound for the convergence rate of the trajectories of the process. This paper provides general characterization of ACR and, in particular, shows that some algorithms cannot converge linearly fast for any nontrivial continuous optimization problem. The relation between asymptotic convergence rate in the objective space and asymptotic convergence rate in the search space is provided. Examples and numerical simulations with use of a (1+1) self-adaptive evolution strategy and other algorithms are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. On approximation and estimation of distribution function of sum of independent random variables.
- Author
-
Midhu, N. N., Dewan, Isha, Sudheesh, K. K., and Sreedevi, E. P.
- Subjects
DISTRIBUTION (Probability theory) ,RANDOM variables ,INDEPENDENT variables ,MONTE Carlo method ,APPROXIMATION error - Abstract
In this paper, we obtain an approximation for the distribution function of sum of two independent random variables using quantile based representation. The error of approximation is shown to be negligible under some mild conditions. We then use the approximation to obtain a non-parametric estimator for the distribution function of sum of two independent random variables. The exact distribution of the proposed estimator is derived. The estimator is shown to be strongly consistent and asymptotically normally distributed. Extensive Monte Carlo simulation studies are carried out to evaluate the bias and mean squared error of the estimator and also to assess the approximation error. We also compare the performance of the proposed estimator with other estimators available in the literature. Finally, we illustrate the use of the proposed estimator for estimating the reliability function of a standby redundant system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. An adaptive bearing rigid formation control of multi-agent systems with nonlinear dead-zone inputs.
- Author
-
Wang, Qin, Chen, Zitao, Yi, Yang, and Shen, Qingcheng
- Subjects
NONLINEAR systems ,ADAPTIVE fuzzy control ,MULTIAGENT systems ,APPROXIMATION error ,FUZZY systems ,PARAMETER estimation - Abstract
In this paper, an adaptive bearing rigid formation control strategy for a class of nonlinear system with unknown dead-zone inputs and external disturbance is proposed. Firstly, the I-Type fuzzy system is used to approximate the unknown nonlinear dynamics of the formation model, and the approximation errors and unknown external disturbance are eliminated by the parameter adaptive estimation. Furthermore, the adaptive dynamic estimation algorithm is utilized to estimate and compensate the unknown dead-zone parameters, effectively suppressing the impact of dead-zone on formation system performance. Finally, the stability of the formation system is proved based on LaSalle's invariance principle, and the effectiveness of the algorithm is verified by simulation results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Approximation Conjugate Gradient Method for Low-Rank Matrix Recovery.
- Author
-
Chen, Zhilong, Wang, Peng, and Zhu, Detong
- Subjects
LOW-rank matrices ,MATRIX multiplications ,SYMMETRIC matrices ,CONJUGATE gradient methods ,APPROXIMATION error ,COMPUTATIONAL complexity - Abstract
Large-scale symmetric and asymmetric matrices have emerged in predicting the relationship between genes and diseases. The emergence of large-scale matrices increases the computational complexity of the problem. Therefore, using low-rank matrices instead of original symmetric and asymmetric matrices can greatly reduce computational complexity. In this paper, we propose an approximation conjugate gradient method for solving the low-rank matrix recovery problem, i.e., the low-rank matrix is obtained to replace the original symmetric and asymmetric matrices such that the approximation error is the smallest. The conjugate gradient search direction is given through matrix addition and matrix multiplication. The new conjugate gradient update parameter is given by the F-norm of matrix and the trace inner product of matrices. The conjugate gradient generated by the algorithm avoids SVD decomposition. The backtracking linear search is used so that the approximation conjugate gradient direction is computed only once, which ensures that the objective function decreases monotonically. The global convergence and local superlinear convergence of the algorithm are given. The numerical results are reported and show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. A Bayesian approach to online estimation of airgap spatial variation in induction machines with static eccentricity.
- Author
-
Ardekani, Iman T. and Nicholson, Ruanui
- Subjects
- *
ECCENTRICS (Machinery) , *SPATIAL variation , *APPROXIMATION error , *MACHINERY , *INVERSE problems , *MACHINE performance , *JOURNAL bearings - Abstract
In this paper, we develop a method for the estimation of airgap spatial variation from the harmonics that appear in the stator's current under static eccentricity conditions. We move beyond the detection of the eccentricity fault and endeavour to quantify the severity of this fault. To achieve this, we formulate the problem as a mathematical inverse problem and attempt to solve it in the Bayesian framework using the so-called Bayesian approximation error approach. The solution takes the form of an algorithm capable of estimating the parameter(s) that characterize the spatial variation of the airgap length from noisy and limited data. Furthermore, it can quantify the uncertainty associated with the results as a byproduct of the Bayesian analysis approach employed in this paper. The results demonstrate that with each iteration of the algorithm, estimation accuracy improves, and the uncertainty of the estimated results reduces. • Bayesian approximation error analysis shows promise in monitoring electrical machines with eccentric rotors. • The paper applies Bayesian inversion for online estimation of airgap length in induction machines with eccentric rotors. • The study estimates static eccentricity ratio from limited data on harmonics of the machine line currents. • This paper gives an analytical method for calculating all inductances of induction machines under static eccentricity. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. A SECOND-ORDER NUMERICAL METHOD FOR PSEUDO-PARABOLIC EQUATIONS HAVING BOTH LAYER BEHAVIOR AND DELAY PARAMETER.
- Author
-
GUNES, Baransel and DURU, Hakkı
- Subjects
APPROXIMATION error ,ANALYTICAL solutions ,DELAY differential equations ,EQUATIONS - Abstract
In this paper, singularly perturbed pseudo-parabolic initial-boundary value problems with time-delay parameter are considered by numerically. Initially, the asymptotic properties of the analytical solution are investigated. Then, a discretization with exponential coefficient is suggested on a uniform mesh. The error approximations and uniform convergence of the presented method are estimated in the discrete energy norm. Finally, some numerical experiments are given to clarify the theory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. TUNING OF THE EQUILIBRATED RESIDUAL METHOD FOR APPLICATIONS IN GENERAL, DIRECT AND INVERSE PIEZOELECTRICITY.
- Author
-
ZBOIŃSKI, GRZEGORZ
- Subjects
PIEZOELECTRICITY ,COUPLED problems (Complex systems) ,ELECTROMECHANICAL effects ,ELECTRIC potential ,APPROXIMATION error - Abstract
This paper presents application and tuning of the equilibrated residual method (ERM) of a posteriori error estimation for coupled electromechanical problems of direct, inverse and general piezoelectricity. In these three cases, either electric potential is induced by strains or strains appear due to the applied electric potential or both phenomena occur simultaneously. The mentioned ERM is assigned for the assessment of modeling and approximation errors of the numerical finite element solution. Such error values usually serve as indication for adaptive hierarchical modeling and adaptive mesh changes within thin and/or solid piezoelectric members so as to obtain the solution of assumed accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. A Loss Landscape Perspective and Simulations for Imaging Inverse Problems based on AI and Neuron Network Training Method.
- Author
-
Mingyong Zhou
- Subjects
ARTIFICIAL intelligence ,INVERSE problems ,ELECTRICAL impedance tomography ,NEURONS ,APPROXIMATION error - Abstract
The purpose of Imaging Inverse problems are to recover original true signals/images from observations by plethora physical methods. The recovered signals/images are measured by appropriate quantity and quality measures. Given a specific physical process, imaging is classically a mathematical algorithm design to estimate the original signals/images. In this paper starting from inverse imaging problem of Electrical Impedance Tomography (EIT), we will address several aspects of loss landscape and its regularization properties of a neuron network solution for imaging inverse problems. Loss landscape and regularization strategy for imaging inverse problems is first introduced in I), and is followed by II) Sampling from unbounded landscape to bounded discrete. In III), an asymptotic approximation property when neuron network width goes to infinity is analyzed. Complexity of training and approximation error is discussed in IV). In V), case study for indicator function approximation and application in imaging EIT by neuron network is highlighted. Finally in VI), discussions will be devoted to the limitations of regularization capability of neuron network as a new tool, especially in medical imaging applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Comparative analysis of approximating functions for electric steel magnetizing curves.
- Author
-
Guskov, Vladimir, Belousova, Nadezhda, and Samoseiko, Veniamin
- Subjects
ELECTROMECHANICAL devices ,STEEL ,LEAST squares ,ERROR functions ,APPROXIMATION error ,CURVES ,ELECTRICAL steel - Abstract
The paper considers the issue of approximation of electric steel magnetizing curves, that is critical in design of electromechanical devices of different purpose. The brief overview of literature under this subject is given. Formulas for the most common approximating functions have been considered. Real magnetizing curves for steel 1411, 2013 and 3413, for which approximation was performed, are demonstrated in tabular data and graphs. Coefficients, forming a part of approximating function formulas, were found by the least square method in Mathcad mathematical software. Comparison of the considered approximating functions under the error dispersion minimum criterion has been performed. Graphs of magnetizing curves functions with the least approximation error dispersions are given. Recommendations for selection and application of approximating functions for their use in design of electric machines have been given. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. A Subaperture Motion Compensation Algorithm for Wide-Beam, Multiple-Receiver SAS Systems.
- Author
-
Zhang, Jiafeng, Cheng, Guangli, Tang, Jinsong, Wu, Haoran, and Tian, Zhen
- Subjects
SYNTHETIC apertures ,APPROXIMATION error ,ALGORITHMS ,CELL migration ,SONAR ,AZIMUTH - Abstract
Uncompensated motion errors can seriously affect the imaging quality of synthetic aperture sonars (SASs). In the existing line-by-line motion compensation (MOCO) algorithms for wide-beam multiple-receiver SAS systems, the approximate form of the range history error usually introduces a significant approximation error, and the residual two-dimensional (2D) range cell migration (RCM) caused by aperture-dependent motion errors is not corrected, resulting in the severe defocus of the image. In this paper, in the presence of translational and rotational errors in a multiple-receiver SAS system, the exact range history error concerning the five-degree-of-freedom (DOF) motion errors of the sway, heave, yaw, pitch, and roll under the non-stop-hop-stop case is derived. Based on this, a two-stage subaperture MOCO algorithm for wide-beam multiple-receiver SAS systems is proposed. We decompose the range history error into the beam-center term (BCT) and the residual spatial-variant term (RSVT) to compensate successively. In the first stage, the time delay and phase error caused by the BCT are compensated receiver-by-receiver through interpolation and phase multiplication in the azimuth-time domain. In the second stage, the data of a single pulse are regarded as a subaperture, and the RSVT is compensated in the subaperture range-Doppler (RD) domain. We divide the range into several blocks to correct RCM caused by the RSVT in the subaperture RD domain, and the phase error caused by the RSVT is compensated by phase multiplication. After compensation, the wide-beam RD algorithm is used for imaging. Simulated and real-data experiments verify the superiority and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems.
- Author
-
Jaśkowiec, Jan and Pamin, Jerzy
- Subjects
GALERKIN methods ,APPROXIMATION error ,FINITE difference method ,QUADRILATERALS ,FINITE differences ,ERROR functions - Abstract
The paper presents a posteriori error approximation concept based on residuals in the two-dimensional discontinuous Galerkin (DG) method. The approach is relatively simple and effective in application, and it takes advantage of some unique properties of the DG method. The error function is constructed in an enriched approximation space, utilizing the hierarchical nature of the basis functions. Among many versions of the DG method, the most popular one is based on the interior penalty approach. However, in this paper a DG method with finite difference (DGFD) is utilized, where the continuity of the approximate solution is enforced by finite difference conditions applied on the mesh skeleton. In the DG methods arbitrarily shaped finite elements can be used, so in this paper the meshes with polygonal finite elements are considered, including quadrilateral and triangular elements. Some benchmark examples are presented, in which Poisson's and linear elasticity problems are considered. The examples use various mesh densities and approximation orders to evaluate the errors. The error estimation maps, generated for the discussed tests, indicate a good correlation with the exact errors. In the last example, the error approximation concept is applied for an adaptive hp mesh refinement. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Approximating Kolmogorov complexity.
- Author
-
Ishkuvatov, Ruslan, Musatov, Daniil, and Shen, Alexander
- Subjects
KOLMOGOROV complexity ,APPROXIMATION error ,PROGRAMMING languages - Abstract
It is well known that the Kolmogorov complexity function (the minimal length of a program producing a given string, when an optimal programming language is used) is not computable and, moreover, does not have computable lower bounds. In this paper we investigate a more general question: can this function be approximated? By approximation we mean two things: firstly, some (small) difference between the values of the complexity function and its approximation is allowed; secondly, at some (rare) points the values of the approximating function may be arbitrary. For some values of the parameters such approximation is trivial (e.g., the length function is an approximation with error d except for a O (2 − d) fraction of inputs). However, if we require a significantly better approximation, the approximation problem becomes hard, and we prove it in several settings. Firstly, we show that a finite table that provides good approximations for Kolmogorov complexities of n-bit strings, necessarily has high complexity. Secondly, we show that there is no good computable approximation for Kolmogorov complexity of all strings. In particular, Kolmogorov complexity function is neither generically nor coarsely computable, as well as its approximations, and the time-bounded Kolmogorov complexity (for any computable time bound) deviates significantly from the unbounded complexity function. We also prove hardness of Kolmogorov complexity approximation in another setting: the mass problem whose solutions are good approximations for Kolmogorov complexity function is above the halting problem in the Medvedev lattice. Finally, we mention some proof-theoretic counterparts of these results. A preliminary version of this paper was presented at CiE 2019 conference (In Computing with Foresight and Industry – 15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15–19, 2019, Proceedings (2019) 230–239 Springer). [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Adaptive fuzzy PID control based on nonlinear disturbance observer for quadrotor.
- Author
-
Ghasemi, Ali and Azimi, Mohammad M
- Subjects
ADAPTIVE fuzzy control ,TRACKING algorithms ,FUZZY logic ,APPROXIMATION error ,NONLINEAR oscillators - Abstract
In this paper, the composite control of position and orientation of the quadrotor for tracking purposes are investigated. The quadrotor is an underactuated nonlinear system. So, based on the introduced virtual inputs the quadrotor is transformed into an actuated system. External disturbances and different sources of uncertainty such as input saturation are considered in the dynamic model of the quadrotor. Also, after transform implementation, some complicated terms appear which are considered as other sources of uncertainty. To guarantee the stabilization and tracking goals of the quadrotor in the perturbed model, the composite adaptive fuzzy PID-Like controller is proposed. This controller consists of three parts where the innovation of the paper appears in all terms. The main term is an adaptive fuzzy PID-like controller which able to approximate the coefficients of PID based on the decentralized fuzzy logic. Then, a H
∞ compensator based on a modified Riccati-like equation is presented; which can attenuate the fuzzy approximation errors. Also, as the last term of the composite controller, the modified disturbance observer is designed that estimates the uncertainty and disturbance. The experimental result shows that the proposed method leads to resilient stabilization and tracking in comparison with conventional methods. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
47. Algebraic Multi-Layer Network: Key Concepts.
- Author
-
Khanykov, Igor, Nenashev, Vadim, and Kharinov, Mikhail
- Subjects
PIECEWISE constant approximation ,BIG data ,HIERARCHICAL clustering (Cluster analysis) ,CLUSTER analysis (Statistics) ,NP-hard problems ,APPROXIMATION error - Abstract
The paper refers to interdisciplinary research in the areas of hierarchical cluster analysis of big data and ordering of primary data to detect objects in a color or in a grayscale image. To perform this on a limited domain of multidimensional data, an NP-hard problem of calculation of close to optimal piecewise constant data approximations with the smallest possible standard deviations or total squared errors (approximation errors) is solved. The solution is achieved by revisiting, modernizing, and combining classical Ward's clustering, split/merge, and K-means methods. The concepts of objects, images, and their elements (superpixels) are formalized as structures that are distinguishable from each other. The results of structuring and ordering the image data are presented to the user in two ways, as tabulated approximations of the image showing the available object hierarchies. For not only theoretical reasoning, but also for practical implementation, reversible calculations with pixel sets are performed easily, as with individual pixels in terms of Sleator–Tarjan Dynamic trees and cyclic graphs forming an Algebraic Multi-Layer Network (AMN). The detailing of the latter significantly distinguishes this paper from our prior works. The establishment of the invariance of detected objects with respect to changing the context of the image and its transformation into grayscale is also new. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. On the Rate of Convergence of Greedy Algorithms.
- Author
-
Temlyakov, Vladimir
- Subjects
BANACH spaces ,HILBERT space ,APPROXIMATION error ,GREEDY algorithms - Abstract
In this paper, a new criterion for the evaluation of the theoretical efficiency of a greedy algorithm is suggested. Using this criterion, we prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new component of this paper is that we bound the error of approximation by the product of two norms—the norm of f and the A 1 -norm of f. Typically, only the A 1 -norm of f is used. In particular, we establish that some greedy algorithms (Pure Greedy Algorithm (PGA) and its modifications) are as good as the Orthogonal Greedy Algorithm (OGA) in this new sense of the rate of convergence, while it is known that the PGA is much worse than the OGA in the standard sense. Our new results provide better bounds for the accuracy than known results in the case of small ∥ f ∥ . [ABSTRACT FROM AUTHOR]
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- 2023
- Full Text
- View/download PDF
49. Force-Sensitive Mat for Vertical Jump Measurement to Assess Lower Limb Strength: Validity and Reliability Study
- Author
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Raul Igual, Yolocuauhtli Salazar, Erik Vanegas, and Inmaculada Plaza
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leg strength ,Coefficient of determination ,Acoustics ,Capacitive sensing ,Health Informatics ,02 engineering and technology ,Upsampling ,03 medical and health sciences ,Vertical jump ,0302 clinical medicine ,Sampling (signal processing) ,vertical jump ,Approximation error ,0202 electrical engineering, electronic engineering, information engineering ,Humans ,Muscle Strength ,mobile health ,Mathematics ,lower limb strength ,Original Paper ,lcsh:T58.5-58.64 ,lcsh:Information technology ,lcsh:Public aspects of medicine ,020208 electrical & electronic engineering ,Reproducibility of Results ,lcsh:RA1-1270 ,030229 sport sciences ,force-sensitive resistor ,Power (physics) ,mHealth ,Lower Extremity ,Exercise Test ,Jump ,Sports - Abstract
Background Vertical jump height is widely used in health care and sports fields to assess muscle strength and power from lower limb muscle groups. Different approaches have been proposed for vertical jump height measurement. Some commonly used approaches need no sensor at all; however, these methods tend to overestimate the height reached by the subjects. There are also novel systems using different kind of sensors like force-sensitive resistors, capacitive sensors, and inertial measurement units, among others, to achieve more accurate measurements. Objective The objective of this study is twofold. The first objective is to validate the functioning of a developed low-cost system able to measure vertical jump height. The second objective is to assess the effects on obtained measurements when the sampling frequency of the system is modified. Methods The system developed in this study consists of a matrix of force-sensitive resistor sensors embedded in a mat with electronics that allow a full scan of the mat. This mat detects pressure exerted on it. The system calculates the jump height by using the flight-time formula, and the result is sent through Bluetooth to any mobile device or PC. Two different experiments were performed. In the first experiment, a total of 38 volunteers participated with the objective of validating the performance of the system against a high-speed camera used as reference (120 fps). In the second experiment, a total of 15 volunteers participated. Raw data were obtained in order to assess the effects of different sampling frequencies on the performance of the system with the same reference device. Different sampling frequencies were obtained by performing offline downsampling of the raw data. In both experiments, countermovement jump and countermovement jump with arm swing techniques were performed. Results In the first experiment an overall mean relative error (MRE) of 1.98% and a mean absolute error of 0.38 cm were obtained. Bland-Altman and correlation analyses were performed, obtaining a coefficient of determination equal to R2=.996. In the second experiment, sampling frequencies of 200 Hz, 100 Hz, and 66.6 Hz show similar performance with MRE below 3%. Slower sampling frequencies show an exponential increase in MRE. On both experiments, when dividing jump trials in different heights reached, a decrease in MRE with higher height trials suggests that the precision of the proposed system increases as height reached increases. Conclusions In the first experiment, we concluded that results between the proposed system and the reference are systematically the same. In the second experiment, the relevance of a sufficiently high sampling frequency is emphasized, especially for jump trials whose height is below 10 cm. For trials with heights above 30 cm, MRE decreases in general for all sampling frequencies, suggesting that at higher heights reached, the impact of high sampling frequencies is lesser.
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- 2021
50. Reference Electrode Standardization Interpolation Technique (RESIT): A Novel Interpolation Method for Scalp EEG
- Author
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Lingling Zhao, Yufan Zhang, Dezhong Yao, Xue Yu, Jianfu Li, Li Dong, Fali Li, Tiejun Liu, and Yongxiu Lai
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0206 medical engineering ,02 engineering and technology ,Electroencephalography ,Reduction (complexity) ,03 medical and health sciences ,0302 clinical medicine ,REST reference ,Approximation error ,medicine ,Range (statistics) ,Humans ,Radiology, Nuclear Medicine and imaging ,EEG ,Electrodes ,Bad channels ,Mathematics ,Original Paper ,Scalp ,Radiological and Ultrasound Technology ,medicine.diagnostic_test ,business.industry ,Brain ,Pattern recognition ,Reference Standards ,020601 biomedical engineering ,Interpolation ,Neurology ,Neurology (clinical) ,Artificial intelligence ,Anatomy ,EEG preprocessing ,Spline interpolation ,business ,030217 neurology & neurosurgery ,Interpolation theory ,Network analysis - Abstract
“Bad channels” are common phenomena during scalp electroencephalography (EEG) recording that arise due to various technique-related reasons, and reconstructing signals from bad channels is an inevitable choice in EEG processing. However, current interpolation methods are all based on purely mathematical interpolation theory, ignoring the neurophysiological basis of the EEG signals, and their performance needs to be further improved, especially when there are many scattered or adjacent bad channels. Therefore, a new interpolation method, named the reference electrode standardization interpolation technique (RESIT), was developed for interpolating scalp EEG channels. Resting-state and event-related EEG datasets were used to investigate the performance of the RESIT. The main results showed that (1) assuming 10% bad channels, RESIT can reconstruct the bad channels well; (2) as the percentage of bad channels increased (from 2% to 85%), the absolute and relative errors between the true and RESIT-reconstructed signals generally increased, and the correlations between the true and RESIT signals decreased; (3) for a range of bad channel percentages (2% ~ 85%), the RESIT had lower absolute error (approximately 2.39% ~ 33.5% reduction), lower relative errors (approximately 1.3% ~ 35.7% reduction) and higher correlations (approximately 2% ~ 690% increase) than traditional interpolation methods, including neighbor interpolation (NI) and spherical spline interpolation (SSI). In addition, the RESIT was integrated into the EEG preprocessing pipeline on the WeBrain cloud platform (https://webrain.uestc.edu.cn/). These results suggest that the RESIT is a promising interpolation method for both separate and simultaneous EEG preprocessing that benefits further EEG analysis, including event-related potential (ERP) analysis, EEG network analysis, and strict group-level statistics.
- Published
- 2020
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