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Journal articles on the topic 'Real interpolation method RIM'

Author: Grafiati

Published: 4 June 2025

Last updated: 23 June 2025

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1

Tin, Phu Tran, Tran Hoang Quang Minh, Tran Thanh Trang, and Nguyen Quang Dung. "Using real interpolation method for adaptive identification of nonlinear inverted pendulum system." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (2019): 1078–89. https://doi.org/10.11591/ijece.v9i2.pp1078-1089.

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In this paper, we investigate the inverted pendulum system by using real interpolation method (RIM) algorithm. In the first stage, the mathematical model of the inverted pendulum system and the RIM algorithm are presented. After that, the identification of the inverted pendulum system by using the RIM algorithm is proposed. Finally, the comparison of the linear analytical model, RIM model, and nonlinear model is carried out. From the results, it is found that the inverted pendulum system by using RIM algorithm has simplicity, low computer source requirement, high accuracy and adaptiveness in the advantages.

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Tin, Phu Tran, Tran Hoang Quang Minh, Tran Thanh Trang, and Nguyen Quang Dung. "Using real interpolation method for adaptive identification of nonlinear inverted pendulum system." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (2019): 1078. http://dx.doi.org/10.11591/ijece.v9i2.pp1078-1089.

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<p>In this paper, we investigate the inverted pendulum system by using real interpolation method (RIM) algorithm. In the first stage, the mathematical model of the inverted pendulum system and the RIM algorithm are presented. After that, the identification of the inverted pendulum system by using the RIM algorithm is proposed. Finally, the comparison of the linear analytical model, RIM model, and nonlinear model is carried out. From the results, it is found that the inverted pendulum system by using RIM algorithm has simplicity, low computer source requirement, high accuracy and adaptiveness in the advantages.</p>

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3

Phu, Tran Tin, Tran Minh, Anh Vu Le, Quang Dung Nguyen, and Thanh Trang Tran. "Real interpolation method for transfer function approximation of distributed parameter system." TELKOMNIKA Telecommunication, Computing, Electronics and Control 17, no. 4 (2019): 1941–47. https://doi.org/10.12928/TELKOMNIKA.v17i4.11088.

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Distributed parameter system (DPS) presents one of the most complex systems in the control theory. The transfer function of a DPS possibly contents: rational, nonlinear and irrational components. This thing leads that studies of the transfer function of a DPS are difficult in the time domain and frequency domain. In this paper, a systematic approach is proposed for linearizing DPS. This approach is based on the real interpolation method (RIM) to approximate the transfer function of DPS by rational-order transfer function. The results of the numerical examples show that the method is simple, computationally efficient, and flexible.

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Nguyen, Dung Quang. "An Effective Approach of Approximation of Fractional Order System using Real Interpolation Method." Journal of Advanced Engineering and Computation 1, no. 1 (2017): 39. http://dx.doi.org/10.25073/jaec.201711.48.

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Fractional-order controllers are recognized to guarantee better closed-loop performance and robustness than conventional integer-order controllers. However, fractional-order transfer functions make time, frequency domain analysis and simulation significantly difficult. In practice, the popular way to overcome these difficulties is linearization of the fractional-order system. Here, a systematic approach is proposed for linearizing the transfer function of fractional-order systems. This approach is based on the real interpolation method (RIM) to approximate fractional-order transfer function (FOTF) by rational-order transfer function. The proposed method is implemented and compared to CFE high-frequency method; Carlson’s method; Matsuda’s method; Chare ’s method; Oustaloup’s method; least-squares, frequency interpolation method (FIM). The results of comparison show that, the method is simple, computationally efficient, flexible, and more accurate in time domain than the above considered methods. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Phan, Van-Duc, Phu Tran Tin, Nguyen Quang Dung, Minh Tran, and Tran Thanh Trang. "Determination of all stability region of unstable fractional order system in case of bearing system." International Journal of Power Electronics and Drive Systems (IJPEDS) 10, no. 4 (2019): 1734. http://dx.doi.org/10.11591/ijpeds.v10.i4.pp1734-1741.

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In this paper, we propose and investigate the optimal tuning PID controller of unstable fractional order system by desired transient characteristics using the real interpolation method (RIM). The research shows that the main advantages of this method are drawn as the followings: 1) Carrying out an investigation of the stable region of coefficients of a PID controller using D-decomposition method; 2) Applying the method to investigate an unstable fractional order system.

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Phu, Tran Tin, Quang Dung Nguyen, Tran Minh, Phan Van-Duc, Nguyen Hoang-Nam, and Thanh Trang Tran. "Determination of all stability region of unstable fractional order system in case of bearing system." International Journal of Power Electronics and Drive System (IJPEDS) 10, no. 4 (2019): 1734–41. https://doi.org/10.11591/ijpeds.v10.i4.pp1734-1741.

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In this paper, we propose and investigate the optimal tuning PID controller of unstable fractional order system by desired transient characteristics using the real interpolation method (RIM). The research shows that the main advantages of this method are drawn as the followings: 1) Carrying out an investigation of the stable region of coefficients of a PID controller using D-decomposition method; 2) Applying the method to investigate an unstable fractional order system.

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Dao, Sy Luat. "MODELLING AND EVALUATING ELASTIC LINKS IN MULTI-MOTOR AUTOMATIC ELECTRICAL DRIVING SYSTEMS BY USING THE NUMERICALMETHOD." Journal of Science and Technique 15, no. 2 (2020): 88–97. http://dx.doi.org/10.56651/lqdtu.jst.v15.n02.145.

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The paper proposes a new approach for solving the problem of determining the optimal estimation model of the elastic linkage element in multi-motor automatic driving systems using the real interpolation method (RIM). Algorithms and programs based on the RIM have been built for a two-motor electromechanical driving model to approximate the original transfer function that describes the elastic linkage element containing inertialand transcendent components by the transfer function in a rational fraction form. Besides,providing a specific function form, the program also calculates estimation errors for different approximate transfer functions, thereby allowing to determine the structure and parameters of the optimal estimation model.

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Tran Tin, Phu, Le Anh Vu, Minh Tran, Nguyen Quang Dung, and Tran Thanh Trang. "Optimal tuning PID controller of unstable fractional order system by desired transient characteristics using RIM." Indonesian Journal of Electrical Engineering and Computer Science 14, no. 3 (2019): 1177. http://dx.doi.org/10.11591/ijeecs.v14.i3.pp1177-1188.

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<p>In this paper, we propose the method of tuning a conventional PID controller for unstable transient characteristics. The results show that: 1) This is the novel practical method based on the desired settling time and overshoot percentage; 2) The results are close to the desired parameters; 3) The novel method can tune an unstable fractional order system by real interpolation method (RIM); 4) The novel method is simplicity and computer efficiency; 5) The novel method can find an optimal solution for tuning task in both academic and industrial purposes.</p>

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Dung, Nguyen Quang, and Tran Hoang Quang Minh. "A Innovation Identification Approach of Control System by Irrational (Fractional) Transfer." Indonesian Journal of Electrical Engineering and Computer Science 3, no. 2 (2016): 336. http://dx.doi.org/10.11591/ijeecs.v3.i2.pp336-342.

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<p>In this paper, an innovative algorithm of identification of control system, described by irrational transfer function with distributed parameter characteristics - with irrational components, is proposed. Algorithm is based on real interpolation method (RIM). Parameters of irrational transfer function can be identified by its experimental transient responses. Each of them can be represented by an analytic expression, table or graph. The proposed method is computationally efficient, simple and practical, as is illustrated by numerical examples. In the furure, the method can be used for tuning the controller and for direct application construction of adaptive controllers, working on the identification principle.</p>

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Yang, Ying, and Yusen Wei. "RANDOM INTERPOLATION AVERAGE FOR ECG SIGNAL DENOISING USING MULTIPLE WAVELET BASES." Biomedical Engineering: Applications, Basis and Communications 25, no. 04 (2013): 1350042. http://dx.doi.org/10.4015/s1016237213500427.

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The random interpolation average (RIA) is a simple yet good denoising method. It firstly employed several times of random interpolations to a noisy signal, then applied the wavelet transform (WT) denoising to each interpolated signal and averaged all of the denoised signals to finish the denoising process. In this paper, multiple wavelet bases and the level-dependent threshold estimator were used in the RIA scheme so that it can be more suitable for the electrocardiogram (ECG) signal denoising. The synthetic ECG signal, real ECG signal and four types of noise were used to perform comparison experiments. The results show that the proposed method can provide the best signal to noise ratio (SNR) improvement in the deoising applications of the synthetic ECG signal and the real ECG signals. For the real ECG signals denoising, the average SNR improvement is 5.886 dB, while the result of the RIA scheme with single wavelet basis (RIAS), the fully translation-invariant [TI (fully)] and the WT denoising using hard thresholding [WT (hard)] are 5.577, 5.274 and 3.484 dB, respectively.

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Petikam, Lohit, Ken Anjyo, and Taehyun Rhee. "Shading Rig: Dynamic Art-directable Stylised Shading for 3D Characters." ACM Transactions on Graphics 40, no. 5 (2021): 1–14. http://dx.doi.org/10.1145/3461696.

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Despite the popularity of three-dimensional (3D) animation techniques, the style of 2D cel animation is seeing increased use in games and interactive applications. However, conventional 3D toon shading frequently requires manual editing to clean up undesired shadows or add stylistic details based on art direction. This editing is impractical for the frame-by-frame editing in cartoon feature film post-production. For interactive stylised media and games, post-production is unavailable due to real-time constraints, so art-direction must be preserved automatically. For these reasons, artists often resort to mesh and texture edits to mitigate undesired shadows typical of toon shaders. Such edits allow real-time rendering but are limited in resolution, animation quality and lack detail control for stylised shadow design. In our framework, artists build a “shading rig,” a collection of these edits, that allows artists to animate toon shading. Artists pre-animate the shading rig under changing lighting, to dynamically preserve artistic intent in a live application, without manual intervention. We show our method preserves continuous motion and shape interpolation, with fewer keyframes than previous work. Our shading shape interpolation is computationally cheaper than state-of-the-art image interpolation techniques. We achieve these improvements while preserving vector quality rendering, without resorting either to high texture resolution or mesh density.

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Liu, Dequan, Guoqing Zhou, Jingjin Huang, et al. "On-Board Georeferencing Using FPGA-Based Optimized Second-Order Polynomial Equation." Remote Sensing 11, no. 2 (2019): 124. http://dx.doi.org/10.3390/rs11020124.

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For real-time monitoring of natural disasters, such as fire, volcano, flood, landslide, and coastal inundation, highly-accurate georeferenced remotely sensed imagery is needed. Georeferenced imagery can be fused with geographic spatial data sets to provide geographic coordinates and positing for regions of interest. This paper proposes an on-board georeferencing method for remotely sensed imagery, which contains five modules: input data, coordinate transformation, bilinear interpolation, and output data. The experimental results demonstrate multiple benefits of the proposed method: (1) the computation speed using the proposed algorithm is 8 times faster than that using PC computer; (2) the resources of the field programmable gate array (FPGA) can meet the requirements of design. In the coordinate transformation scheme, 250,656 LUTs, 499,268 registers, and 388 DSP48s are used. Furthermore, 27,218 LUTs, 45,823 registers, 456 RAM/FIFO, and 267 DSP48s are used in the bilinear interpolation module; (3) the values of root mean square errors (RMSEs) are less than one pixel, and the other statistics, such as maximum error, minimum error, and mean error are less than one pixel; (4) the gray values of the georeferenced image when implemented using FPGA have the same accuracy as those implemented using MATLAB and Visual studio (C++), and have a very close accuracy implemented using ENVI software; and (5) the on-chip power consumption is 0.659 W. Therefore, it can be concluded that the proposed georeferencing method implemented using FPGA with second-order polynomial model and bilinear interpolation algorithm can achieve real-time geographic referencing for remotely sensed imagery.

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Li, Dong, Haining Ma, Hongqing Liu, et al. "An Efficient Ground Manoeuvring Target Refocusing Method Based on Principal Component Analysis and Motion Parameter Estimation." Remote Sensing 12, no. 3 (2020): 378. http://dx.doi.org/10.3390/rs12030378.

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Refocusing ground manoeuvring targets with complex motions in synthetic aperture radar (SAR) remains a challenging objective because of the large range of cell migration (RCM) and time-varying Doppler frequency modulation (DFM). By exploiting the geometric information of RCM and two-dimensional (2-D) coherently integrated gain, a fast ground manoeuvring target refocusing method using principal component analysis (PCA) and high-order motion parameter estimation is proposed. First, an efficient phase difference (PD) method and PCA are utilized to correct the RCM, and then, the energy of the ground manoeuvring target is concentrated into the same range bin. Second, by utilizing the coherently integrated cubic phase function (CICPF) that was developed in our previous work, the motion parameters are obtained accurately, and the manoeuvring target is thus well refocused into a sharp peak point based on the estimated motion parameters. The proposed method is of low computational complexity because it avoids time-consuming search and interpolation operations and demonstrates an improved anti-noise performance due to fully exploiting the 2-D coherent accumulation characteristics for estimating motion parameters and enhanced refocused imaging results for manoeuvring targets due to adopting the high-order motion model. Finally, experiments are conducted using simulated and real SAR data to show the performance of the proposed method.

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14

Roulier, Frédéric. "Geometric Morphometrics Applied to Cartography." Revue Internationale de Géomatique 32, no. 1 (2023): 17–37. http://dx.doi.org/10.32604/rig.2023.045458.

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The morphological differences between two geographical maps can be highlighted by a polycentric distance cartogram resulting from a bidimensional regression. Beyond the communicational interest of the transformations thus produced, the method makes it possible to reveal the differences in structure and therefore constitutes a real research tool. However, bidimensional regression can only compare the shape of two maps. Since the 1990s, geometric morphometrics has revolutionized the morphological analysis of natural structures (and others). It has since been applied in many fields of research but not in cartography. This article describes the theoretical and methodological bases of a method combining bidimensional regression with a geometric morphometrics approach to compare the shape of several geographical maps. Geometric morphometrics and bidimensional regression indeed share common approaches of the statistical shape analysis like homologous landmarks and interpolation grids. However, there is no software in geometric morphometrics capable of directly reading geographical data, which would facilitate the work of cartographers accustomed to GIS software. That is why we present MapMorphy, a tool specifically developed for this task. An example on ancient maps illustrates the method.

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Qin, Li, Tang, Zeng, Li, and Xu. "A Fast High-Resolution Imaging Algorithm for Helicopter-Borne Rotating Array SAR Based on 2-D Chirp-Z Transform." Remote Sensing 11, no. 14 (2019): 1669. http://dx.doi.org/10.3390/rs11141669.

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In view of the azimuth resolution of the helicopter-borne rotating array synthetic aperture radar (RoASAR) depending on the azimuth reconstruction angle and the sector distortion caused by the azimuth Deramp processing, this paper proposes an efficient helicopter-borne RoASAR high-resolution imaging algorithm based on two-dimensional (2-D) chirp-z transform (CZT). First, the high-order Taylor series expansion is performed on the slant range, and the accurate 2-D spectral expression of the point target is obtained by using the method of series reversion (MSR). Based on that, the space-variant characteristics of the range cell migration (RCM) terms are analyzed. After that, the space-variant RCM and the sector distortion effect caused by the azimuth Deramp processing are removed by using efficient 2-D CZT, thereby increasing the azimuth reconstruction angle and improving the azimuth resolution. The proposed algorithm is efficient without the interpolation operation, and it is easy to implement in real-time. Finally, the simulations are provided to verify the effectiveness of the proposed algorithm.

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16

Astashkin, S. V. "Interpolation of intersections by the real method." St. Petersburg Mathematical Journal 17, no. 2 (2006): 239–65. http://dx.doi.org/10.1090/s1061-0022-06-00902-2.

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Cai, Changpeng, Qiangang Zheng, and Haibo Zhang. "A new method to improve the real-time performance of aero-engine component level model." International Journal of Turbo & Jet-Engines 40, no. 1 (2020): 101–9. http://dx.doi.org/10.1515/tjj-2020-0033.

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Abstract In order to improve the real-time performance of aero-engine component-level models, an automatic fast positioning interpolation method is proposed. Based on the maximum parameter slope, this method can automatically determine the interpolation cut in point, change the disadvantage of low efficiency of traditional sequential interpolation from the starting point, effectively reduce the interpolation interval, thus greatly improving the efficiency of interpolation. The method is applied to the calculation of gas thermodynamic parameters and the interpolation of the characteristic of rotating parts ,so as to ameliorate the real-time performance of the single-stage flow path calculation of the component-level model. Simulation results show that, compared with the traditional method, the method proposed in this paper improves the fan characteristic calculation efficiency by 47.5%, reduces the time of single complete flow calculation by 74.3% when the dynamic and steady-state accuracy changes are less than 0.4%, which greatly improves the real-time performance of the component-level model.

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Ji, Jian Chun, Shuang Yun Shao, and Qi Bo Feng. "A Novel Method to Measure Flange Thickness and Rim Width of Wheel Sets on Line." Applied Mechanics and Materials 330 (June 2013): 237–41. http://dx.doi.org/10.4028/www.scientific.net/amm.330.237.

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The flange thickness and rim width of the wheel sets are key parameters which ensure the train security. This paper proposes a novel real-time method to measure flange thickness and rim width of wheel sets based on laser displacement sensors. Three laser displacement sensors are cramped on the steel rails. The light of sensors travels through the slit between rails, reaching a point which is 12mm below the wheel set tread. The flange thickness and rim width can be measured by three laser displacement sensors together. This non-contact method realize dynamic and real-time measurement of the wheel sets parameters. The measurement error is 0.2mm, which meet rail industry standards.

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Goncharov, Valery, Andrey Liepinsh, and Vladislav Rudnitskiy. "Numerical Method of Control Object Identification and Models Robustness Property Maintenance." Applied Mechanics and Materials 367 (August 2013): 312–16. http://dx.doi.org/10.4028/www.scientific.net/amm.367.312.

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In this paper the Real Interpolation Method is offered for the solution of systems Identification problem. The Real Interpolation Method allows to create a sufficiently cost-effective algorithmic basis and to solve all complex of Identification problems. It is based on use of a special case of the Laplace transformation, when the complex variable s =δ + jω is degenerated to real value δ.

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Zhao, Jing, Li Li, and Guo Xun Wang. "NURBS Curve Real-Time Interpolation Feed Speed Planning for CNC Machining." Applied Mechanics and Materials 635-637 (September 2014): 1394–97. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1394.

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In order to solve the problem of large amount of calculation and real time is not high in the process of NURBS real-time interpolation feed speed planning, offline feed speed planning method is proposed, the method plan speed in non real-time cycle, and generate the feed speed curve. In order to meet the machine tool dynamics constraint, the maximum acceleration and the jerk constraints were considered fully in the planning process. The simulation analysis show that the proposed method can greatly reduce the amount of computing tasks in real-time interpolation cycle, improve the real-time performance of interpolation; At the same time, the speed curve of the planning satisfies the requirement of machine tool dynamics, has the good effect of feeding speed smooth, is helpful to improve the interpolation precision.

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Zhang, Han, You Tian, and Pengfei Zhao. "Dispersion Curve Interpolation Based on Kriging Method." Applied Sciences 13, no. 4 (2023): 2557. http://dx.doi.org/10.3390/app13042557.

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Volcanic eruptions significantly impact human life. However, real-time high-precision imaging in this context still has limitations. Spatial–temporal interpolation can replace real-time data imaging, in order to obtain the state of a given volcano at any moment. The dispersion curve is interpolated in space as a foreshadowing for subsequent temporal interpolation. In this paper, kriging is applied for the interpolation of dispersion curves, and the feasibility of the process is verified through several tests. Through cross-validation, the “spherical” variogram model and universal kriging were determined. The mean relative error of the predicted dispersion curve is less than 10%, and the mean root mean square error of each predicted dispersion curve is less than 0.1. The results show that the interpolation of dispersion curves based on the kriging method is feasible. In addition, the application of kriging interpolation in ambient noise tomography can expand the imaging area, as well as complement the low ray density area. Taking the ambient noise tomography of the Changbai volcano as an example, in the deep area, the expansion multiple can reach 2.4.

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Astashkin, S. V., and P. Sunehag. "The real interpolation method on couples of intersections." Functional Analysis and Its Applications 40, no. 3 (2006): 218–21. http://dx.doi.org/10.1007/s10688-006-0033-0.

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Yang, Shi Qing, and Lan Fang Miao. "Research on DEM Construction Method of Interpolation." Applied Mechanics and Materials 416-417 (September 2013): 1470–74. http://dx.doi.org/10.4028/www.scientific.net/amm.416-417.1470.

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DEM construction quality directly affects a variety of applications based on DEM and terrain analysis. Giving the error in measured data, interpolation methods affect the quality of DEM. Therefore, for a certain district, choosing a better interpolation method is very important. In this paper, we constructed new DEM by three interpolation methods (inverse distance weight, spline, Kriging) on the real DEM data of loess tableland. By comparing this new DEM with the original DEM and analyzing this new DEM, we can get a better choice of interpolation for DEM construction and terrain analysis for a certain district.

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Regmi, Rajendra Prasad. "Finding of principle square root of a real number by using interpolation method." Janapriya Journal of Interdisciplinary Studies 7, no. 1 (2018): 77–83. http://dx.doi.org/10.3126/jjis.v7i1.23053.

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There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

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Zhang, Hui, and Qin Ruo Wang. "Simulation and Implementation of an Improved Inscribed Chord Interpolation Algorithm." Advanced Materials Research 756-759 (September 2013): 3220–24. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3220.

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In order to improve the shortcomings of the realization of the traditional quadratic curve interpolation inscribed chord method, this paper proposes an improved internal chord interpolation algorithm. The program flow chart of the algorithm achievement and the interpolation method of circular arc interpolation and linear interpolation of a detailed operation process is given in this paper. Finally through a calculation example the simulation is conducted, and the point by point comparison method were compared. The simulation results show the improvement on the quadratic curve interpolation in the inner string interpolation speed, good flexibility, and it worth popularizing in the interpolation algorithm for real time interpolation.

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Nie, Mingxing, Yaping Wan, and Aijun Zhou. "Real-Time NURBS Interpolation under Multiple Constraints." Computational Intelligence and Neuroscience 2022 (May 17, 2022): 1–15. http://dx.doi.org/10.1155/2022/7492762.

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NURBS interpolation is superior to traditional linear or circular interpolation in terms of code size, surface quality, and machining efficiency. However, with the increasing demands for high-accuracy and efficient machining, NURBS interpolation has faced a growing number of challenges. Many researchers are actively involved in this field with great interest. Due to the special form of NURBS curve, there is a nonlinear relationship between its curve and arc length; feed fluctuations and mechanical shocks which are caused during the interpolation process will seriously affect the surface accuracy and quality of machined parts. To solve these problems, a real-time NURBS interpolation is proposed under multiple constraints (RNIC) in this paper. First, the formulas of the constrained feedrate under geometric errors, kinematic constraints, drive constraints, and contour errors are given. Then, the two stages for the proposed interpolation are established. The former stage is offline preprocessing stage, which aims to quickly find feedrate sensitive areas (FSAs), while the latter online stage is the real-time interpolation, which is responsible for smoothing the velocity. In the preprocessing stage, we utilized FSA scan module and feedrate adjustment module to detect the FSAs and adjust the feedrate at the start/end of each subsegment by a bidirectional scanning algorithm. Each segment contains acceleration and deceleration (some contains uniform speed) stages, which can be well matched with the processing process of acceleration and deceleration. Finally, according to the proposed method and the adaptive speed adjustment method, the simulation of a “butterfly-shaped” NURBS curve using the S-shaped ACC/DEC algorithm is carried out, which verifies the reliability and effectiveness of the proposed algorithm.

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Evans, W. D., and B. Opic. "Real Interpolation with Logarithmic Functors and Reiteration." Canadian Journal of Mathematics 52, no. 5 (2000): 920–60. http://dx.doi.org/10.4153/cjm-2000-039-2.

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AbstractWe present “reiteration theorems” with limiting values θ = 0 and θ = 1 for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].

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Wang, Kun Qi, Jing Wei Yang, and Li Qun Lei. "Real-Time Control and Data Exchange Method in Software CNC System Based on PC." Applied Mechanics and Materials 241-244 (December 2012): 1392–95. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.1392.

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A new real-time control method for software CNC based on PC is proposed, and the data exchange methods are given. Both external and system clock interrupt are adopted as interpolation cycle to make up software CNC on PC. The data between the front procedures, interpolation module, and background procedures, application module, is exchanged by WDM. The method is verified in experiment, and the resolves show that the speed control and the interpolation operator are right, and whole software CNC is significantly improved.

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Sette, Robledo Mak’s Miranda, Dicesar Lass Fernandez, and Eduardo Brandani da Silva. "A Theory for Interpolation of Metric Spaces." Axioms 13, no. 7 (2024): 439. http://dx.doi.org/10.3390/axioms13070439.

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In this work, we develop an interpolation theory for metric spaces inspired by the real method of interpolation. These interpolation spaces preserve Lipschitz operators under certain conditions. We also show that this method, valid in metrics spaces, still holds in normed spaces without any algebraic structure required. Furthermore, this interpolation method for metric spaces when applied to normed spaces is equivalent to the K-method, which has been widely studied in the literature. As an application, we interpolate Fréchet sequence spaces.

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Cobos, Fernando, and Luz M. Fernández-Cabrera. "On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators." Canadian Mathematical Bulletin 53, no. 1 (2010): 51–57. http://dx.doi.org/10.4153/cmb-2010-009-1.

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Astashkin, S. V., and P. Sunehag. "Real method of interpolation on subcouples of codimension one." Studia Mathematica 185, no. 2 (2008): 151–68. http://dx.doi.org/10.4064/sm185-2-4.

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Weisz, F. "Interpolation between continuous parameter martingale spaces: The real method." Acta Mathematica Hungarica 68, no. 1-2 (1995): 37–54. http://dx.doi.org/10.1007/bf01874434.

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Chamorro, Diego, and Pierre-Gilles Lemarié-Rieusset. "Real interpolation method, Lorentz spaces and refined Sobolev inequalities." Journal of Functional Analysis 265, no. 12 (2013): 3219–32. http://dx.doi.org/10.1016/j.jfa.2013.08.016.

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Milman, Mario. "Higher order commutators in the real method of interpolation." Journal d'Analyse Mathématique 66, no. 1 (1995): 37–55. http://dx.doi.org/10.1007/bf02788817.

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Astashkin, S. V. "On interpolation of bilinear operators with a real method." Mathematical Notes 52, no. 1 (1992): 641–48. http://dx.doi.org/10.1007/bf01247642.

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Astashkin, S. V. "One property of functors of the real interpolation method." Mathematical Notes of the Academy of Sciences of the USSR 38, no. 3 (1985): 725–32. http://dx.doi.org/10.1007/bf01163708.

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Doktorski, Leo R. Ya. "Reiteration Formulae for the Real Interpolation Method Including L or R Limiting Spaces." Journal of Function Spaces 2020 (December 2, 2020): 1–15. http://dx.doi.org/10.1155/2020/6685993.

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We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so-called L or R limiting interpolation spaces. These spaces arise naturally in reiteration formulae for the limiting cases θ = 0 or θ = 1 . Applications to grand and small Lorentz spaces are given.

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Nguyen, Quang Huu, and Long Tien Banh. "A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS." Vietnam Journal of Science and Technology 55, no. 5 (2017): 650. http://dx.doi.org/10.15625/2525-2518/55/5/9206.

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This paper presents a method of real-time CNC interpolation for free-form NURBS curves. The interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating the parametric value u after each sampling period. With the updated value of u, a new interpolated point is calculated based on the DeBoor’s algorithm. In this paper, an efficient method of limiting chord error introduced by the interpolation algorithm is also presented with the basic idea of reducing machining feedrate at positions with a radius of curvature smaller than a critical value.

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Zang, Danfeng, Jian Li, Chuankun Li, Hengran Zhang, Zhipeng Pei, and Yixiang Ma. "Shallow Subsurface Wavefield Data Interpolation Method Based on Transfer Learning." Applied Sciences 15, no. 4 (2025): 1964. https://doi.org/10.3390/app15041964.

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The deployment density of surface sensors can significantly impact the accuracy of subsurface shallow seismic field energy inversion. With finite budget constraints, it is often not feasible to deploy a large number of sensors, resulting in limited seismic signal acquisition that hinders accurate inversion of the shallow subsurface explosions. To address the challenge of insufficient sensor signals needed for inversion, we conducted a study on a subsurface shallow wavefield data interpolation method based on transfer learning. This method is designed to increase the overall signal acquisition by interpolating signals at target locations from limited measurement points. Our research employs neural networks to interpolate real seismic data, supplementing the sampled signals. Given the lack of extensive samples from actual data collection, we devised a training approach that combines numerically simulated signals with real collected signals. Initially, we performed conventional interpolation training using a deep interpolation network with complete synthetic gather images obtained from numerical simulations. Subsequently, the feature extraction part was frozen, and the interpolation network was transferred to real datasets, where it was trained using incomplete gather images. Finally, these incomplete gather images were re-input into the trained network to obtain interpolated results at the target locations. Our study demonstrates the superiority of our method by comparing it with two other interpolation networks and validating the effectiveness of transfer learning through four sets of ablation experiments in the actual test. This method can also be applied to other shallow geological structures to generate a large number of seismic signals for energy inversion.

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Li, Wenxing, Xiaojun Mao, Wenhua Yu, and Chongyi Yue. "An Effective Technique for Enhancing Direction Finding Performance of Virtual Arrays." International Journal of Antennas and Propagation 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/728463.

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The array interpolation technology that is used to establish a virtual array from a real antenna array is widely used in direction finding. The traditional interpolation transformation technology causes significant bias in the directional-of-arrival (DOA) estimation due to its transform errors. In this paper, we proposed a modified interpolation method that significantly reduces bias in the DOA estimation of a virtual antenna array and improves the resolution capability. Using the projection concept, this paper projects the transformation matrix into the real array data covariance matrix; the operation not only enhances the signal subspace but also improves the orthogonality between the signal and noise subspace. Numerical results demonstrate the effectiveness of the proposed method. The proposed method can achieve better DOA estimation accuracy of virtual arrays and has a high resolution performance compared to the traditional interpolation method.

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Zhang, Sen, Ming Chen, and Jin Song Tang. "Shadow Detecting and Shadow Interpolation Algorithm for InSAS." Advanced Materials Research 605-607 (December 2012): 2121–25. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.2121.

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The shadow detecting algorithm based on the coherence and the Sigma filter is used to pick up the shadow of interferometric synthetic aperture sonar (InSAS), which can eliminate small separated shadow areas. To solve the problems such as great computer complexity of traditional Shepard interpolation method and large fluctuant of linear interpolation method for the large shadow area, an improved Shepard interpolation method is proposed. Interpolation boundary is picked up by using diffuse search, and interpolation source is adaptively chosen according to the size of shadow area. The method carries out a perfect tradeoff between performance and computer speed. Lake trial dataset is used to validate the performance of proposed method. The results indicate that the proposed method can eliminate the fluctuant from the linear interpolation method and can process in real time in the InSAS system.

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Zhou, Xiaoyang. "An Adapted NURBS Interpolator with a Switched Optimized Method of Feed-Rate Scheduling." Machines 12, no. 3 (2024): 186. http://dx.doi.org/10.3390/machines12030186.

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With the increasing demand for processing precision in the manufacturing industry, feed-rate scheduling is a crucial component in achieving the processing quality of complex surfaces. A smooth feed-rate profile not only guarantees machining quality but also improves machining efficiency. Although the typical offline feed-rate scheduling method possesses good processing efficiency, it may not provide an optimal solution due to the NP-hard problem caused by the feed-rate scheduling of continuous curve segments, which easily results in excess kinetic limitations and feed-rate fluctuations in a real-time interpolation. Instead, the FIR (Finite Impulse Response) method is widely used to realize interpolation in real-time processing. However, the FIR method will filter out a large number of high-frequency signals, leading to a low-processing efficiency. Further, greater acceleration or deceleration is required to ensure the interpolation passes through the segment end at a predefined feed rate and the deceleration in the feed rate profile appears earlier, which allows the interpolation to easily exceed the kinetic limitation. At present, a simple offline or online method cannot realize the global optimization of the feed-rate profile and guarantee the machining efficiency. Moreover, the current feed-rate scheduling that considers both offline and online methods does not consider the situation that the call of offline data and online prediction data will lead to a decrease in the real-time performance of the CNC system. Further, real-time feed-rate scheduling data tend to dominate the whole interpolation process, thus reducing the effect of the offline feed-rate scheduling data. Hence, based on the tool path with C3 continuity (Cubic Continuously Differentiable), this paper first presents a basic interpolation unit relevant to the S-type interpolation feed-rate profile. Then, an offline local smooth strategy is proposed to smooth the feed-rate profile and reduce the exceeding of kinetic limitations and feed-rate fluctuations caused by frequent acceleration and deceleration. Further, a global online smoothing strategy based on the data generated by offline pre-interpolation is presented. What is more, FIR login and logout conditions are proposed to further smooth the feed-rate profile and improve the real-time performance and machining efficiency. The case study validates that the proposed method performs better in kinetic results compared with the typical offline and FIR methods in both the simulation experiment and actual machining experiments. Especially, in actual processing experiments, the proposed method obtains a 28% reduction in contour errors. Further, the proposed method compared with the FIR method obtains a 15% increase in machining efficiency but only a 4% decrease compared with the typical offline method.

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Liu, Xing, Pengxin Yu, Haiduo Chen, Bihui Peng, Zhao Wang, and Fusheng Liang. "Feedrate Fluctuation Minimization for NURBS Tool Path Interpolation Based on Arc Length Compensation and Iteration." Micromachines 16, no. 4 (2025): 402. https://doi.org/10.3390/mi16040402.

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Real-time parametric interpolation plays a crucial role in achieving high-speed and high-precision multi-axis CNC machining. In the interpolation cycle, the position of the next interpolation point is required to be calculated in real-time to guide the action of the machining process. Due to the existence of the positioning error of the interpolation point, it is extremely difficult to eliminate the feedrate fluctuation, which may lead to dramatic decreases in machining quality and the driving capabilities’ saturation of each axis. A computationally efficient and precise feedrate fluctuation minimization method is proposed for the NURBS tool path interpolation in the CNC milling process. The model for the arc length and curvature, with respect to the parameter of the NURBS tool path, is established to reduce the calculation amount required by interpolation points determination. The deviation between the theoretical and actual interpolation step length is decreased by the proposed arc length compensation method to minimize the feedrate fluctuation. In addition, the interpolation points derived from the arc length compensation process are further corrected by performing the Newton iteration to restrict the feedrate fluctuation within the preset accuracy threshold. The effectiveness and superiorities of the proposed feedrate fluctuation minimization method are verified by simulation and milling experiments.

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Cerdà, Joan, and Joaquim Martín. "Interpolation restricted to decreasing functions and Lorentz spaces." Proceedings of the Edinburgh Mathematical Society 42, no. 2 (1999): 243–56. http://dx.doi.org/10.1017/s0013091500020228.

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For the real interpolation method, we identify the interpolated spaces of couples of classical Lorentz spaces through interpolation of the corresponding weighted Lp-spaces restricted to decreasing functions.

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Jin, Yu-an, Yong He, Jian-zhong Fu, Zhi-wei Lin, and Wen-feng Gan. "A fine-interpolation-based parametric interpolation method with a novel real-time look-ahead algorithm." Computer-Aided Design 55 (October 2014): 37–48. http://dx.doi.org/10.1016/j.cad.2014.05.002.

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Hsu, Jerry, Tongtong Wang, Zherong Pan, Xifeng Gao, Cem Yuksel, and Kui Wu. "Real-time Physically Guided Hair Interpolation." ACM Transactions on Graphics 43, no. 4 (2024): 1–11. http://dx.doi.org/10.1145/3658176.

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Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.

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Shi, Ru Chao, Sheng Li Xu, and Ya Jun Zhang. "Simulation of Water Droplet Merging under Shock Wave Using Real Ghost Fluid Method." Applied Mechanics and Materials 444-445 (October 2013): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.628.

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This paper presents a 3D numerical simulation of water droplets merging under a given shock wave. We couple interpolation method to RGFM (Real Ghost Fluid Method) to improve the numerical accuracy of RGFM. The flow states of air-water interface are calculated by ARPS (approximate Riemann problem solver). Flow field is solved by Euler equation with fifth-order WENO spatial discretization and fourth-order R-K (Runge-Kutta) time discretization. We also employ fifth-order HJ-WENO to discretize level set equation to keep track of gas-liquid interface. Numerical results demonstrate that droplets shape has little change before merging and the merged droplet gradually becomes umbrella-shaped under the given shock wave. We verify that combination of RGFM with interpolation method has the property of reducing numerical error by comparing to the results without employment of interpolation method.

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Jin, Shangzhu. "An Alternative Backward Fuzzy Rule Interpolation Method." International Journal of Software Science and Computational Intelligence 6, no. 4 (2014): 47–71. http://dx.doi.org/10.4018/ijssci.2014100104.

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Fuzzy set theory allows for the inclusion of vague human assessments in computing problems. Also, it provides an effective means for conflict resolution of multiple criteria and better assessment of options. Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of inter-connected rule bases, situations may arise when certain crucial antecedents are absent from given observations. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deducible using conventional means. To address this issue, an approach named backward fuzzy rule interpolation and extrapolation has been proposed recently, allowing the observations which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. As such, it significantly extends the existing fuzzy rule interpolation techniques. However, the current idea has only been implemented via the use of the scale and move transformation-based fuzzy interpolation method, which utilise analogical reasoning mechanisms. In order to strengthen the versatility and feasibility of backward fuzzy interpolative reasoning, in this paper, an alternative a-cut-based interpolation method is proposed. Two numerical examples and comparative studies are provided in order to demonstrate the efficacy of the proposed work.

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Farago, Emma, and Adrian D. C. Chan. "Detection and Reconstruction of Poor-Quality Channels in High-Density EMG Array Measurements." Sensors 23, no. 10 (2023): 4759. http://dx.doi.org/10.3390/s23104759.

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High-density electromyography (HD-EMG) arrays allow for the study of muscle activity in both time and space by recording electrical potentials produced by muscle contractions. HD-EMG array measurements are susceptible to noise and artifacts and frequently contain some poor-quality channels. This paper proposes an interpolation-based method for the detection and reconstruction of poor-quality channels in HD-EMG arrays. The proposed detection method identified artificially contaminated channels of HD-EMG for signal-to-noise ratio (SNR) levels 0 dB and lower with ≥99.9% precision and ≥97.6% recall. The interpolation-based detection method had the best overall performance compared with two other rule-based methods that used the root mean square (RMS) and normalized mutual information (NMI) to detect poor-quality channels in HD-EMG data. Unlike other detection methods, the interpolation-based method evaluated channel quality in a localized context in the HD-EMG array. For a single poor-quality channel with an SNR of 0 dB, the F1 scores for the interpolation-based, RMS, and NMI methods were 99.1%, 39.7%, and 75.9%, respectively. The interpolation-based method was also the most effective detection method for identifying poor channels in samples of real HD-EMG data. F1 scores for the detection of poor-quality channels in real data for the interpolation-based, RMS, and NMI methods were 96.4%, 64.5%, and 50.0%, respectively. Following the detection of poor-quality channels, 2D spline interpolation was used to successfully reconstruct these channels. Reconstruction of known target channels had a percent residual difference (PRD) of 15.5 ± 12.1%. The proposed interpolation-based method is an effective approach for the detection and reconstruction of poor-quality channels in HD-EMG.

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Lym, S. J., and K. F. Ehmann. "A Fast Interpolation Algorithm for Temporally Nonequidistant Waypoints." Journal of Engineering for Industry 115, no. 4 (1993): 500–507. http://dx.doi.org/10.1115/1.2901796.

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An interpolation scheme applicable to temporally nonequidistant waypoints is proposed. The interpolation polynomial is based on the weighted sum of two second order polynomials derived based on four consecutive waypoints. The proposed method, while maintaining general continuity, is also amenable for fast real time applications using precomputed coefficient matrices defining the interpolation polynomials.

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