1,085 results
Search Results
2. 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
- Subjects
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
- Full Text
- View/download PDF
3. 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
4. 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
- Subjects
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
5. Approximating Bézier curves with least square polygons.
- Author
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Li, Yajuan, Zhang, Meng, Jin, Wenbiao, and Deng, Chongyang
- Subjects
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
6. 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
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7. 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
8. 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
9. 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.
- Subjects
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
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10. 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
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11. 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
- Subjects
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
12. 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
13. 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
14. 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
15. Predictor-Based Neural Dynamic Surface Control of a Nontriangular System With Unknown Disturbances.
- Author
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Yang, Yang, Chen, Didi, Liu, Qidong, Zhang, Tengfei, Liu, Aaron, and Yue, Wenbin
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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
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16. On asymptotic convergence rate of random search.
- Author
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Tarłowski, Dawid
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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
17. On approximation and estimation of distribution function of sum of independent random variables.
- Author
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Midhu, N. N., Dewan, Isha, Sudheesh, K. K., and Sreedevi, E. P.
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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
18. An adaptive bearing rigid formation control of multi-agent systems with nonlinear dead-zone inputs.
- Author
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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
19. Approximation Conjugate Gradient Method for Low-Rank Matrix Recovery.
- Author
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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
20. A Bayesian approach to online estimation of airgap spatial variation in induction machines with static eccentricity.
- Author
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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
21. A SECOND-ORDER NUMERICAL METHOD FOR PSEUDO-PARABOLIC EQUATIONS HAVING BOTH LAYER BEHAVIOR AND DELAY PARAMETER.
- Author
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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
22. TUNING OF THE EQUILIBRATED RESIDUAL METHOD FOR APPLICATIONS IN GENERAL, DIRECT AND INVERSE PIEZOELECTRICITY.
- Author
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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
23. A Loss Landscape Perspective and Simulations for Imaging Inverse Problems based on AI and Neuron Network Training Method.
- Author
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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
24. Comparative analysis of approximating functions for electric steel magnetizing curves.
- Author
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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
25. A Subaperture Motion Compensation Algorithm for Wide-Beam, Multiple-Receiver SAS Systems.
- Author
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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
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26. A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems.
- Author
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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
27. Approximating Kolmogorov complexity.
- Author
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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
28. 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
29. Algebraic Multi-Layer Network: Key Concepts.
- Author
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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
30. On the Rate of Convergence of Greedy Algorithms.
- Author
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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]
- Published
- 2023
- Full Text
- View/download PDF
31. Experimental investigation for the operational performance improvement of cryogenic piston-type pump using subcooling effect for liquid hydrogen stations.
- Author
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Kim, Kyoung Joong, Bae, Junhyuk, and Jeong, Sangkwon
- Subjects
- *
LIQUID hydrogen , *PUMPING machinery , *CRYOGENIC liquids , *RECIPROCATING pumps , *APPROXIMATION error , *LIQUID nitrogen - Abstract
This paper investigates the impact of subcooling degree and exhaust pressure on the performance of a high-pressure piston pump for pressurizing cryogenic liquid. We fabricate a lab-scale cryogenic liquid pump, conduct experiments with liquid nitrogen, and observe the significant effect of subcooling changes on the pump performance. The lab-scale pump achieves up to 30 bar of exhaust pressure and up to 45.4 g exhaust mass per cycle. This paper introduces the concept of duty cycle for the exhaust mass as a measure of pump performance. The results show that as the subcooling degree and the exhaust pressure increase, the duty cycle and the exhaust mass also increase, improving the pump performance. However, the increase in performance does not happen proportionally, and an optimal subcooling degree must be selected. This paper establishes a generalized computational model to predict the pump performance, achieving the mean absolute errors of 1.8 bar and 0.3 g/s in pressure and mass flow rate, respectively. The model can predict the exhaust mass during one stroke cycle of the pump with an approximation error of 10 %. In addition, the model predicts that pressurizing liquid hydrogen to 900 bar requires subcooling degree and its duty cycle cannot reach 100 % by reduction of specific volume. The findings suggest that subcooling can be used to enhance cryogenic liquid pump performance, and the optimal subcooling degree can be determined during the design of piston pumps to achieve high pressure. [Display omitted] • A piston-type tension-assisted cryogenic liquid pump was developed. • We identified the performance indicator of the pump as duty cycle. • This paper investigated the effect of the parameters on the duty cycle. • Subcooling degree effect on liquid hydrogen is predicted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Improved rates for a space–time FOSLS of parabolic PDEs.
- Author
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Gantner, Gregor and Stevenson, Rob
- Subjects
SPACETIME ,HEAT equation ,APPROXIMATION error - Abstract
We consider the first-order system space–time formulation of the heat equation introduced by Bochev and Gunzburger (in: Bochev and Gunzburger (eds) Applied mathematical sciences, vol 166, Springer, New York, 2009), and analyzed by Führer and Karkulik (Comput Math Appl 92:27–36, 2021) and Gantner and Stevenson (ESAIM Math Model Numer Anal 55(1):283–299 2021), with solution components (u 1 , u 2) = (u , - ∇ x u) . The corresponding operator is boundedly invertible between a Hilbert space U and a Cartesian product of L 2 -type spaces, which facilitates easy first-order system least-squares (FOSLS) discretizations. Besides L 2 -norms of ∇ x u 1 and u 2 , the (graph) norm of U contains the L 2 -norm of ∂ t u 1 + div x u 2 . When applying standard finite elements w.r.t. simplicial partitions of the space–time cylinder, estimates of the approximation error w.r.t. the latter norm require higher-order smoothness of u 2 . In experiments for both uniform and adaptively refined partitions, this manifested itself in disappointingly low convergence rates for non-smooth solutions u. In this paper, we construct finite element spaces w.r.t. prismatic partitions. They come with a quasi-interpolant that satisfies a near commuting diagram in the sense that, apart from some harmless term, the aforementioned error depends exclusively on the smoothness of ∂ t u 1 + div x u 2 , i.e., of the forcing term f = (∂ t - Δ x) u . Numerical results show significantly improved convergence rates. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Stability and guaranteed error control of approximations to the Monge–Ampère equation.
- Author
-
Gallistl, Dietmar and Tran, Ngoc Tien
- Subjects
MONGE-Ampere equations ,ELLIPTIC equations ,APPROXIMATION error ,VISCOSITY solutions ,REGULARIZATION parameter ,HAMILTON-Jacobi-Bellman equation - Abstract
This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the L ∞ norm from the theory of viscosity solutions which are independent of the regularization parameter ε . They allow for the uniform convergence of the solution u ε to the regularized problem towards the Alexandrov solution u to the Monge–Ampère equation for any nonnegative L n right-hand side and continuous Dirichlet data. The main application are guaranteed a posteriori error bounds in the L ∞ norm for continuously differentiable finite element approximations of u or u ε . [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Exploratory Landscape Validation for Bayesian Optimization Algorithms.
- Author
-
Agasiev, Taleh and Karpenko, Anatoly
- Subjects
OPTIMIZATION algorithms ,APPROXIMATION error ,COMPUTATIONAL complexity ,PROBLEM solving ,APPROXIMATION algorithms ,GAUSSIAN processes - Abstract
Bayesian optimization algorithms are widely used for solving problems with a high computational complexity in terms of objective function evaluation. The efficiency of Bayesian optimization is strongly dependent on the quality of the surrogate models of an objective function, which are built and refined at each iteration. The quality of surrogate models, and hence the performance of an optimization algorithm, can be greatly improved by selecting the appropriate hyperparameter values of the approximation algorithm. The common approach to finding good hyperparameter values for each iteration of Bayesian optimization is to build surrogate models with different hyperparameter values and choose the best one based on some estimation of the approximation error, for example, a cross-validation score. Building multiple surrogate models for each iteration of Bayesian optimization is computationally demanding and significantly increases the time required to solve an optimization problem. This paper suggests a new approach, called exploratory landscape validation, to find good hyperparameter values with less computational effort. Exploratory landscape validation metrics can be used to predict the best hyperparameter values, which can improve both the quality of the solutions found by Bayesian optimization and the time needed to solve problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Asymptotic Expansion and Weak Approximation for a Stochastic Control Problem on Path Space.
- Author
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Kannari, Masaya, Naito, Riu, and Yamada, Toshihiro
- Subjects
ASYMPTOTIC expansions ,STOCHASTIC approximation ,APPROXIMATION error ,FUNCTIONALS ,MONTE Carlo method - Abstract
The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. A novel adaptive fuzzy prescribed performance congestion control for network systems with predefined settling time.
- Author
-
Qi, Xuelei, Li, Chen, Ni, Wei, and Ma, Hongjun
- Subjects
- *
ADAPTIVE control systems , *CLOSED loop systems , *APPROXIMATION error , *DIFFERENTIAL equations , *TIME-varying systems , *NONLINEAR systems - Abstract
The adaptive predefined settling time performance tracking control for a class of uncertain nonlinear network systems with fast time-varying or even abrupt reference signals is studied. In this paper, an improved performance function with time-varying boundary (following the change of reference signal) is designed to overcome the problem that the traditional prescribed performance control (PPC) can only converge to a constant in steady state. Compared with the existing adaptive finite time prescribed performance congestion control for tracking fixed value reference signals, an adaptive predefined settling time prescribed performance congestion control strategy is proposed by means of some new recursive construction (introducing nonautonomous differential equations (NDE)) and analysis innovation. In addition, the network system considered in this paper is more general. Under the framework of backstepping, NDE is used iteratively to control the approximation error with boundary inequality. It is proved theoretically that all signals of the closed-loop system are predefined settling time bounded. Finally, the effectiveness of the proposed control strategy is verified by simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Probabilistic state synthesis based on optimal convex approximation.
- Author
-
Akibue, Seiseki, Kato, Go, and Tani, Seiichiro
- Subjects
APPROXIMATION error ,DETERMINISTIC algorithms ,QUANTUM states ,CIRCUIT complexity ,SAMPLING errors - Abstract
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce the approximation error compared to conventional deterministic synthesis. In this paper, we demonstrate that the optimal probabilistic synthesis quadratically reduces the approximation error. Moreover, we show that a deterministic synthesis algorithm can be efficiently converted into a probabilistic one that achieves this quadratic error reduction. We also numerically demonstrate how this conversion reduces the T-count and analytically prove that this conversion halves an information-theoretic lower bound on the circuit size. In order to derive these results, we prove general theorems about the optimal convex approximation of a quantum state. Furthermore, we demonstrate that this theorem can be used to analyze an entanglement measure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Robust fractional-order [proportional integral derivative] controller design with specification constraints: more flat phase idea.
- Author
-
Wu, Zhenlong, Viola, Jairo, Luo, Ying, Chen, YangQuan, and Li, Donghai
- Subjects
CLOSED loop systems ,APPROXIMATION error ,INTEGRALS ,INDUSTRIAL capacity ,TIME management - Abstract
This paper presents a new design methodology for robust fractional-order controllers with more than three parameters for first-order plus dead time systems using the synthesis scheme of the 'more flat phase' idea for a fractional-order controller with [proportional integral derivative] (FO[PID]) structure. The stability region of the FO[PID] controller and the synthesis scheme with the 'more flat phase' idea are illustrated through a simulation example. The corresponding pseudo-codes of the synthesis scheme are also summarised. The implementation and approximation error of the FO[PID] controller are also discussed. Likewise, the superiority of the FO[PID] controller designed with the 'more flat phase' idea is verified by additional simulations and experimental results where the closed-loop system with FO[PID] controller is not sensitive to the variations of the loop gain, ensuring satisfactory control performance. Obtained results show high potential in practical industrial applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Stability Analysis for Incremental Adaptive Dynamic Programming with Approximation Errors.
- Author
-
Li, Yifei and van Kampen, Erik-Jan
- Subjects
DYNAMIC programming ,APPROXIMATION error ,INCREMENTAL motion control ,STABILITY theory ,LYAPUNOV stability ,ADAPTIVE fuzzy control ,ITERATIVE learning control - Abstract
This paper provides a convergence and stability analysis of the incremental value iteration algorithm under the influence of various errors. Incremental control is firstly used to linearize the continuous-time nonlinear system, recursive least squares (RLS) identification is then introduced to identify the incremental model online. Based on the incremental model, the value iteration algorithm is used to design an optimal adaptive controller, with an analytical optimal control law. Moreover, the convergence of the developed incremental value iteration algorithm is proved. The stability of the controller is analyzed using Lyapunov stability theory. Finally, a flight control simulation verifies the robustness of the controller to various initial conditions, as well as adaptation to actuator faults. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. Effective Mechanical Properties of Periodic Cellular Solids with Generic Bravais Lattice Symmetry via Asymptotic Homogenization.
- Author
-
Rajakareyar, Padmassun, ElSayed, Mostafa S. A., Abo El Ella, Hamza, and Matida, Edgar
- Subjects
ASYMPTOTIC homogenization ,SYMMETRY ,ELASTICITY ,SPECIFIC gravity ,UNIT cell ,APPROXIMATION error - Abstract
In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais's lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in Python with a proposed fast–nearest neighbour algorithm to accurately estimate the periodic boundary conditions of the discretized representative volume element of the lattice unit cell. Convergence studies are performed, and numerical errors caused by both voxel meshing and periodic boundary condition approximation processes are discussed in detail. It is found that the numerical error in periodicity approximation is cyclically dependent on the number of divisions performed during the meshing process and, thus, is minimized with a refined voxel mesh. Validation studies are performed by comparing the elastic properties of 2D hexagon lattices with orthogonal and non-orthogonal bases. The developed methodology was also applied to derive the effective properties of several lattice topologies, and variation of their anisotropic macroscopic properties with relative densities is presented as material selection charts. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Real-Time Ship Draft Measurement and Optimal Estimation Using Kalman Filter.
- Author
-
Dhar, S. and Khawaja, H.
- Subjects
- *
KALMAN filtering , *WORK measurement , *SHIPS , *APPROXIMATION error , *FREIGHT & freightage - Abstract
Ship operators typically depend on the visual method for draft reading, which may lead to errors or approximations, and it further introduces draft survey calculation errors and cannot provide continuous updates. Ensuring accurate real-time ship draft measurement becomes crucial for enhancing navigational safety, optimizing vessel performance, and achieving precise cargo and consumable measurements. With the current approach towards automation and remote operation of ships, the need to rely on the accuracy of the measurements provided by the sensors has increased. Although different sensor types are gradually being adopted for draft measurement, they encounter challenges in the demanding marine environment which may result in noisy and inaccurate readings. This paper aims to estimate the true draft of a ship in different conditions from noisy sensor measurements using the Kalman filter algorithm. The purpose of the algorithm is to reduce uncertainty in draft measurement that is generated from inaccuracies in the sensor or from the dynamic marine environment. The paper involves designing the Kalman Filter algorithm for draft measurement to work within the different conditions the ship may experience. Simulating different situations and analyzing the result, the application of the filter shows the advantage in real-time draft measurement in both static and dynamic conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations.
- Author
-
Berg, Jan Bouwe van den, Jaquette, Jonathan, and James, J. D. Mireles
- Subjects
APPROXIMATION error ,COORDINATES ,PARAMETERIZATION - Abstract
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our approximation, we decompose the stable manifold into three components: a finite dimensional slow component, a fast-but-finite dimensional component, and a strongly contracting infinite dimensional "tail". We employ the parameterization method in a finite dimensional projection to approximate the slow-stable manifold, as well as the attached finite dimensional invariant vector bundles. This approximation provides a change of coordinates which largely removes the nonlinear terms in the slow stable directions. In this adapted coordinate system we apply the Lyapunov-Perron method, resulting in mathematically rigorous bounds on the approximation errors. As a result, we obtain significantly sharper bounds than would be obtained using only the linear approximation given by the eigendirections. As a concrete example we illustrate the technique for a 1D Swift-Hohenberg equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Local tool path smoothing based on symmetrical NURBS transition curve with look ahead optimal method: experimental and analytical study.
- Author
-
Lei, Chunlin, Nukman, Yusoff, Yap, Hwa Jen, Abdelrazek, Ali H., and Luo, Mingbing
- Subjects
SURFACE finishing ,REAL-time control ,SMOOTHING (Numerical analysis) ,APPROXIMATION error ,SPLINE theory ,CURVATURE - Abstract
Linear tool path with the inherent shortcoming of tangential and curvature discontinuities leads to poor machining efficiency and surface finish. A lot of local corner smoothing methods which inset a tiny spline curve at the corners have been proposed in literature. However, there exists potential overlap of the two adjacent spline curves while smoothing, and still no optimal solution to fully use the segment length of each corner while eliminating the overlaps. To optimally eliminate the overlaps and smooth the transition curve curvature in real time, a symmetrical non-uniform rational B-spline (NURBS) curve transition based on look ahead optimal method is proposed in this paper, by scanning a set of unconstrained pre-cornering transition curve information, analysing the overlap type and backward determining the optimal transition length with curvature extreme smoothness in consideration, thus fully use the linear segment length of each corner and fully increasing the feedrate at the corners. G 2 continuity, analytical expression of the curvature extreme, approximation error constraint, and real-time performance are considered simultaneously in this paper. Simulation and real machining experiments are made to compare with the existing symmetrical rounding algorithms, the results show that the proposed method has a significant curvature decrease of 17.64% and 4.44% improvement of efficiency, and the curvature distribution of the adjacent curves are balanced, thus improved the machining velocity smoothness. In addition, the real machining experiment results validate the proposed method can work well in 125 μs real-time control period CNC system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. On global normal linear approximations for nonlinear Bayesian inverse problems.
- Author
-
Nicholson, Ruanui, Petra, Noémi, Villa, Umberto, and Kaipio, Jari P
- Subjects
INVERSE problems ,RANDOM noise theory ,GAUSSIAN measures ,PARTIAL differential equations ,APPROXIMATION error ,LINEAR operators ,INVERSE scattering transform - Abstract
The replacement of a nonlinear parameter-to-observable mapping with a linear (affine) approximation is often carried out to reduce the computational costs associated with solving large-scale inverse problems governed by partial differential equations (PDEs). In the case of a linear parameter-to-observable mapping with normally distributed additive noise and a Gaussian prior measure on the parameters, the posterior is Gaussian. However, substituting an accurate model for a (possibly well justified) linear surrogate model can give misleading results if the induced model approximation error is not accounted for. To account for the errors, the Bayesian approximation error (BAE) approach can be utilised, in which the first and second order statistics of the errors are computed via sampling. The most common linear approximation is carried out via linear Taylor expansion, which requires the computation of (Fréchet) derivatives of the parameter-to-observable mapping with respect to the parameters of interest. In this paper, we prove that the (approximate) posterior measure obtained by replacing the nonlinear parameter-to-observable mapping with a linear approximation is in fact independent of the choice of the linear approximation when the BAE approach is employed. Thus, somewhat non-intuitively, employing the zero-model as the linear approximation gives the same approximate posterior as any other choice of linear approximations of the parameter-to-observable model. The independence of the linear approximation is demonstrated mathematically and illustrated with two numerical PDE-based problems: an inverse scattering type problem and an inverse conductivity type problem. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Numerical Simulation of Fractional Power Diffusion Biosensors.
- Author
-
Dapsys, Ignas and Ciegis, Raimondas
- Subjects
FRACTIONAL powers ,COMPUTER simulation ,LINEAR operators ,MATHEMATICAL models ,APPROXIMATION error ,BIOSENSORS - Abstract
The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Global toolpath smoothing for CNC machining based on B-spline approximation with tool tip position adjustment.
- Author
-
Hua, Li, Huang, Nuodi, Yi, Bowen, Zhao, Yanzheng, and Zhu, Limin
- Subjects
NUMERICAL control of machine tools ,SPLINE theory ,LEAST squares ,CURVES ,APPROXIMATION error - Abstract
B-spline curve approximation is widely used for fitting linear toolpaths to improve machining quality and efficiency in CNC machining. For a high-quality smoothing method, the control of both approximation error and curve curvature needs to be taken into account. To reduce the maximum curve curvature while meeting the precision requirements, a B-spline approximation scheme with tool tip position adjustment is proposed in this paper. Toolpaths are first divided into several subdivisions according to the discrete curvature of each tool tip point. For subdivisions that need adjustment, tool tip positions are adjusted to minimize the maximum discrete curvature. An existing approximation method named energy-term-incorporated progressive and iterative approximation for least square fitting (ELSPIA) is selected and improved to fit the adjusted toolpaths and lower the chord errors. For improving the numerical stability of the ELSPIA method, the way of searching appropriate foot point parameters is discussed in this paper. Deviation expansion factors of tooltip points are also defined to make the ELSPIA method suitable for fitting the adjusted toolpaths. Both simulations and experimental studies are conducted to prove that the proposed method can significantly decrease the maximum curvature of fitted B-spline curves and improve the machining efficiency without exceeding the tolerance. For example, experimental results show that for the tested butterfly and rabbit toolpaths, the proposed method can improve the machining efficiency by 2.61% and 2.37%, compared with the ELSPIA method without tool tip position adjustment. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Ground-Based MIMO-SAR Fast Imaging Algorithm Based on Geometric Transformation.
- Author
-
Dan, Qihong, Yu, Chunrui, Huang, Shisheng, Lai, Tao, Huang, Haifeng, Chen, Wu, and Weng, Duojie
- Subjects
SYNTHETIC aperture radar ,APPROXIMATION error ,MIMO radar ,INTERPOLATION algorithms ,ALGORITHMS - Abstract
Ground-based multiple-input multiple-output synthetic aperture radar (MIMO-SAR) is a new type of deformation monitoring sensor that has the advantages of no mechanical motion and fast echo acquisition. Ground-based MIMO-SAR can significantly improve the data rate of deformation monitoring. In this paper, a fast imaging algorithm tailored for ground-based MIMO-SAR data is proposed, which can be applied in both far-field and near-field scenarios. First, the phase center approximation error of the non-collinear array in the near field is analyzed. Then, a fast imaging algorithm based on geometric transformation for the coherent synthesis of subimages is put forward. The algorithm uses the geometric transformation to convert the subaperture imaging results into the full aperture coordinate system, which avoids the point-by-point interpolation calculation and further reduces the computational cost of the subimage coherent synthesis algorithm. Simulations and experiments show that the algorithm can achieve high-precision focusing imaging, and its operation efficiency is significantly improved compared with the algorithm based on interpolation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Analytic approximation of nonlinearities with memory.
- Author
-
Perev, Kamen
- Subjects
- *
MATHEMATICAL formulas , *TANGENT function , *APPROXIMATION error , *HYPERBOLIC functions , *MEMORY - Abstract
This paper considers the problem of analytic approximation of nonlinearities with memory. The mathematical models for nonlinearities with memory used in the paper are differential-based, rate dependent and two-valued, involving the input signal velocity in its description. The nonlinear characteristics, considered in the paper, are the shifted unpolarized relay with hysteresis, relay with hysteresis and dead zone, and relay with hysteresis and saturation. Explicit formulas for their mathematical models are presented, containing the ideal relay as basic element in their description. The analytic approximation for nonlinearities with memory reduces to the problem of rational function approximation of the ideal relay switching behavior. The discontinuous jumps are presented by hyperbolic tangent functions, where the exponential terms are approximated by using the chained fraction method. The error of approximation is reduced by introducing a parameter in the hyperbolic tangent presentation and the corresponding errors of approximation are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Prediction and modeling of the basic properties of biomass after torrefaction pretreatment
- Author
-
Zhongqing Ma, Yunchao Li, Jialong Xu, Zhou Yicong, Huang Ming, Wenbiao Zhang, Youyou Yang, Songzhen Zhou, and Zhouyang Hu
- Subjects
Fuel Technology ,Approximation error ,Palm kernel ,Lignocellulosic biomass ,Biomass ,Heat of combustion ,Raw material ,Pulp and paper industry ,Torrefaction ,Pyrolysis ,Analytical Chemistry ,Mathematics - Abstract
Torrefaction is a promising and effective pretreatment technology to upgrade biomass into a more homogeneous and hydrophobic fuel with higher calorific value and energy density. The main objective of this study was to establish a torrefaction model to predict the basic properties (ultimate and proximate analysis, mass and energy yields) of torrefied biomass. Three groups of lignocellulosic biomass, namely woody biomass (Chinese fir), herbaceous biomass (corn stalk), and shell-like biomass (palm kernel shell), were used as raw material to establish the model. First, the simulation process was carried out on the entire torrefaction stage (200–300 °C) based on the linear fitting method. Then, in order to obtain a more accurate model, the model was established by using two-stage torrefaction process (mild stage with 200–250 °C and severe stage with 250–300 °C) and the quadratic equation. Further, the model was validated based on the torrefaction results from literature reports by using the analysis of variance. Result showed that the values of statistical parameters (relative error and mean absolute error) were less than 5%. This indicated that the simulated two-stage torrefaction model obtained by using the quadratic equation can, in general, aid in providing prediction of basic properties of woody torrefied biomass with higher accuracy. This study is helpful for the design of large scale torrefaction equipment and optimization of the torrefaction process.
- Published
- 2021
50. Approximate Multipliers Using Static Segmentation: Error Analysis and Improvements.
- Author
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Strollo, Antonio Giuseppe Maria, Napoli, Ettore, De Caro, Davide, Petra, Nicola, Saggese, Gerardo, and Di Meo, Gennaro
- Subjects
IMAGE processing ,APPROXIMATION error ,POWER (Social sciences) ,MULTIPLIERS (Mathematical analysis) ,COMPUTER arithmetic ,IMAGE segmentation - Abstract
Approximate multipliers are used in error-tolerant applications, sacrificing the accuracy of results to minimize power or delay. In this paper we investigate approximate multipliers using static segmentation. In these circuits a set of $m$ contiguous bits (a segment of $m$ bits) is extracted from each of the two $n$ -bits operand, the two segments are in input to a small $m\times m$ internal multiplier whose output is suitably shifted to obtain the result. We investigate both signed and unsigned multipliers, and for the latter we propose a new segmentation approach. We also present simple and effective correction techniques that can significantly reduce the approximation error with reduced hardware costs. We perform a detailed comparison with previously proposed approximate multipliers, considering a hardware implementation in 28 nm technology. The comparison shows that static segmented multipliers with the proposed correction technique have the desirable characteristic of being on (or close to) the Pareto-optimal frontier for both power vs normalized mean error distance and power vs mean relative error distance trade-off plots. These multipliers, therefore, are promising candidates for applications where their error performance is acceptable. This is confirmed by the results obtained for image processing and image classification applications. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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