Статті в журналах з теми "Gaussian interpolation function"
Щоб переглянути інші типи публікацій з цієї теми, перейдіть за посиланням: Gaussian interpolation function.
Оформте джерело за APA, MLA, Chicago, Harvard та іншими стилями
Ознайомтеся з топ-50 статей у журналах для дослідження на тему "Gaussian interpolation function".
Біля кожної праці в переліку літератури доступна кнопка «Додати до бібліографії». Скористайтеся нею – і ми автоматично оформимо бібліографічне посилання на обрану працю в потрібному вам стилі цитування: APA, MLA, «Гарвард», «Чикаго», «Ванкувер» тощо.
Також ви можете завантажити повний текст наукової публікації у форматі «.pdf» та прочитати онлайн анотацію до роботи, якщо відповідні параметри наявні в метаданих.
Переглядайте статті в журналах для різних дисциплін та оформлюйте правильно вашу бібліографію.
1
Sydorenko, Yuliia V., and Mykola V. Horodetskyi. "Modification of the Algorithm for Selecting a Variable Parameter of the Gaussian Interpolation Function." Control Systems and Computers, no. 6 (290) (December 2020): 21–28. http://dx.doi.org/10.15407/csc.2020.06.021.
Повний текст джерелаАнотація:
The paper presents an algorithm for selecting the optimal value of the variable parameter α of the Gaussian interpolation function to obtain the smallest possible error when interpolating the tabular data. The results of the algorithm are checked on a sample of elementary mathematical functions. For comparison, the interpolation data of the Lagrange polynomial are given. The paper presents the results of Gaussian interpolation at different α, conclusions are made about the need to applying the algorithm for selecting of its optimal value.
2
Sydorenko, I., and M. Horodetskyi. "ANALYSIS OF GAUSSIAN INTERPOLATION FUNCTION ALGORITHM ON ELEMENTARY ALGEBRAIC FUNCTIONS." Modern problems of modeling 19 (September 8, 2020): 134–45. http://dx.doi.org/10.33842/2313-125x/2020/19/134/145.
Повний текст джерела
3
Dutra e Silva Júnior, Élvio Carlos, Leandro Soares Indrusiak, Weiler Alves Finamore, and Manfred Glesner. "A Programmable Look-Up Table-Based Interpolator with Nonuniform Sampling Scheme." International Journal of Reconfigurable Computing 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/647805.
Повний текст джерелаАнотація:
Interpolation is a useful technique for storage of complex functions on limited memory space: some few sampling values are stored on a memory bank, and the function values in between are calculated by interpolation. This paper presents a programmable Look-Up Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can also be reconfigured to minimize the approximation error on specific portions of the interpolated function’s domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a study case, the proposed interpolator was used as the core of a programmable noise generator—output signals drawn from different Probability Density Functions were produced for testing FPGA implementations of chaotic encryption algorithms. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518.
4
Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 02 (June 1996): 481–99. http://dx.doi.org/10.1017/s0001867800048588.
Повний текст джерелаАнотація:
We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t, s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.
5
Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 2 (June 1996): 481–99. http://dx.doi.org/10.2307/1428068.
Повний текст джерелаАнотація:
We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t,s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.
6
Hartman, Eric, and James D. Keeler. "Predicting the Future: Advantages of Semilocal Units." Neural Computation 3, no. 4 (December 1991): 566–78. http://dx.doi.org/10.1162/neco.1991.3.4.566.
Повний текст джерелаАнотація:
In investigating gaussian radial basis function (RBF) networks for their ability to model nonlinear time series, we have found that while RBF networks are much faster than standard sigmoid unit backpropagation for low-dimensional problems, their advantages diminish in high-dimensional input spaces. This is particularly troublesome if the input space contains irrelevant variables. We suggest that this limitation is due to the localized nature of RBFs. To gain the advantages of the highly nonlocal sigmoids and the speed advantages of RBFs, we propose a particular class of semilocal activation functions that is a natural interpolation between these two families. We present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks, and, very importantly, are more accurate than RBF networks in the presence of irrelevant inputs. On the Mackey-Glass and Coupled Lattice Map problems, the speedup over sigmoid networks is so dramatic that the difference in training time between RBF and gaussian bar networks is minor. Gaussian bar architectures that superpose composed gaussians (gaussians-of-gaussians) to approximate the unknown function have the best performance. We postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics, which we call automatic connection pruning, is an important factor in the success of this representation.
7
Khalili, Mohammad Amin, and Behzad Voosoghi. "Gaussian Radial Basis Function interpolation in vertical deformation analysis." Geodesy and Geodynamics 12, no. 3 (May 2021): 218–28. http://dx.doi.org/10.1016/j.geog.2021.02.004.
Повний текст джерела
8
Shen, Qiang, and Longzhi Yang. "Generalisation of Scale and Move Transformation-Based Fuzzy Interpolation." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 3 (May 20, 2011): 288–98. http://dx.doi.org/10.20965/jaciii.2011.p0288.
Повний текст джерелаАнотація:
Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and reduce system complexity. In particular, the scale and move transformation-based approach is able to handle interpolation with multiple antecedent rules involving triangular, complex polygon, Gaussian and bell-shaped fuzzy membership functions [1]. Also, this approach has been extended to deal with interpolation and extrapolation with multiple multi-antecedent rules [2]. However, the generalised extrapolation approach based on multiple rules may not degenerate back to the basic crisp extrapolation based on two rules. Besides, the approximate function of the extended approach may not be continuous. This paper therefore proposes a new approach to generalising the basic fuzzy interpolation technique of [1] in an effort to eliminate these limitations. Examples are given throughout the paper for illustration and comparative purposes. The result shows that the proposed approach avoids the identified problems, providing more reasonable interpolation and extrapolation.
9
Lee, Lung-fei. "INTERPOLATION, QUADRATURE, AND STOCHASTIC INTEGRATION." Econometric Theory 17, no. 5 (September 25, 2001): 933–61. http://dx.doi.org/10.1017/s0266466601175043.
Повний текст джерелаАнотація:
This paper considers features in numerical and stochastic integration approaches for the evaluation of analytically intractable integrals. It provides a unification of these two approaches. Some important features in quadrature formulations, namely, interpolation and region partition, can provide a valuable device for the design of a stochastic simulator. An interpolating function can be used as a valuable control variate for variance reduction in simulation. We illustrate possible variance reduction by some numerical cases with Gaussian quadrature. The resulting simulator may also be regarded as a monitor of the approximation error of a quadrature.
10
Platte, Rodrigo B., and Tobin A. Driscoll. "Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation." SIAM Journal on Numerical Analysis 43, no. 2 (January 2005): 750–66. http://dx.doi.org/10.1137/040610143.
Повний текст джерела
11
Chen, Zhixiang, and Feilong Cao. "Spherical scattered data quasi-interpolation by Gaussian radial basis function." Chinese Annals of Mathematics, Series B 36, no. 3 (April 30, 2015): 401–12. http://dx.doi.org/10.1007/s11401-015-0907-7.
Повний текст джерела
12
Sivakumar, N. "A note on the Gaussian cardinal-interpolation operator." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (February 1997): 137–49. http://dx.doi.org/10.1017/s0013091500023506.
Повний текст джерелаАнотація:
Suppose λ is a positive number, and let , x∈Rd, denote the d-dimensional Gaussian. Basic theory of cardinal interpolation asserts the existence of a unique function , x∈Rd, satisfying the interpolatory conditions , k∈Zd, and decaying exponentially for large argument. In particular, the Gaussian cardinal-interpolation operator, given by , x∈Rd, , is a well-defīned linear map from ℓ2(Zd) into L2(Rd). It is shown here that its associated operator-norm is , implying, in particular, that is contractive. Some sidelights are also presented.
13
Léget, P. F., P. Astier, N. Regnault, M. Jarvis, P. Antilogus, A. Roodman, D. Rubin, and C. Saunders. "Improving the astrometric solution of the Hyper Suprime-Cam with anisotropic Gaussian processes." Astronomy & Astrophysics 650 (June 2021): A81. http://dx.doi.org/10.1051/0004-6361/202140463.
Повний текст джерелаАнотація:
Context. We study astrometric residuals from a simultaneous fit of Hyper Suprime-Cam images. Aims. We aim to characterize these residuals and study the extent to which they are dominated by atmospheric contributions for bright sources. Methods. We used Gaussian process interpolation with a correlation function (kernel) measured from the data to smooth and correct the observed astrometric residual field. Results. We find that a Gaussian process interpolation with a von Kármán kernel allows us to reduce the covariances of astrometric residuals for nearby sources by about one order of magnitude, from 30 mas2 to 3 mas2 at angular scales of ∼1 arcmin. This also allows us to halve the rms residuals. Those reductions using Gaussian process interpolation are similar to recent result published with the Dark Energy Survey dataset. We are then able to detect the small static astrometric residuals due to the Hyper Suprime-Cam sensors effects. We discuss how the Gaussian process interpolation of astrometric residuals impacts galaxy shape measurements, particularly in the context of cosmic shear analyses at the Rubin Observatory Legacy Survey of Space and Time.
14
Rehfeld, K., N. Marwan, J. Heitzig, and J. Kurths. "Comparison of correlation analysis techniques for irregularly sampled time series." Nonlinear Processes in Geophysics 18, no. 3 (June 23, 2011): 389–404. http://dx.doi.org/10.5194/npg-18-389-2011.
Повний текст джерелаАнотація:
Abstract. Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ18O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.
15
Sydorenko, I., and O. Shaldenko. "VISUALIZATION OF THE POLYPOINT TRANSFORMATIONS’ OBJECTS USING THE INTERPOLATION GAUSSIAN FUNCTION." Modern problems of modeling 17 (February 3, 2019): 108–14. http://dx.doi.org/10.33842/2313-125x/2019/17/108/114.
Повний текст джерела
16
Sajjad, Muhammad, Naveed Ejaz, Irfan Mehmood, and Sung Wook Baik. "Digital image super-resolution using adaptive interpolation based on Gaussian function." Multimedia Tools and Applications 74, no. 20 (July 9, 2013): 8961–77. http://dx.doi.org/10.1007/s11042-013-1570-1.
Повний текст джерела
17
Lebrenz, Henning, and András Bárdossy. "Geostatistical interpolation by quantile kriging." Hydrology and Earth System Sciences 23, no. 3 (March 20, 2019): 1633–48. http://dx.doi.org/10.5194/hess-23-1633-2019.
Повний текст джерелаАнотація:
Abstract. The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting “best linear and unbiased estimator” from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile–quantile transformation with the beta- and normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space–time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.
18
Xiao, Xiao Ping, Zi Sheng Li, and Wei Gong. "Fuzzy Fractal Interpolation Surface and its Applications." Advanced Materials Research 542-543 (June 2012): 1141–44. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1141.
Повний текст джерелаАнотація:
Tackling of uncertain data is a major problem in analysis, modeling and simulation. Fractal interpolation surface and fuzzy set method are employed to solve the issue of uncertainty in modeling irregular surface. Initial interpolation data grid point is used as the kernel of Gaussian fuzzy membership function and its fuzzy numbers can be calculated by specifying λ of λ-cut set. These fuzzy numbers are used as uncertain data, which are the boundaries of the fluctuation of initial grid, and defined as a new kind of fuzzy interpolation grids. With these interpolation grids fractal interpolation surface algorithm is applied to act on. By these definitions, experimental data for modeling rock surface is illustrated to show that how the interpolation scheme proposed in this paper enhances the controllability for manipulating uncertain data.
19
Herlinawati, Elin. "PEMILIHAN NILAI PARAMETER C PADA INTERPOLAN GAUSSIAN." Jurnal Matematika Sains dan Teknologi 20, no. 1 (March 22, 2019): 1–8. http://dx.doi.org/10.33830/jmst.v20i1.78.2019.
Повний текст джерелаАнотація:
Interpolation is to find a function which passes through a number of given data points. The interpolant that we used is a Gaussian function which has a parameter value of c. Selection of this parameter affects the results of interpolation. This study discusses a method that we used in selecting the optimum parameter of c. This method is inspired by a RMS (Root Means Square)error. Suppose with is the set of data points. Define the error vector with
gk - yk - Fk(xk), k E{1, 2, ..., n} ,
where is the function value in and is the interpolant which is obtained by deleting a point from the given data set. Furthermore, the optimum parameter value of c is selected by minimizing the error vector g. The result of selecting parameter values depends on the amount of data and the distribution of known data.
Interpolasi adalah pencarian fungsi melalui sejumlah titik data yang diberikan. Interpolan yang digunakan pada artikel ini adalah fungsi Gaussian yang memiliki nilai parameter . Pemilihan nilai parameter mempengaruhi hasil interpolasi. Artikel ini membahas metode yang digunakan dalam pemilihan parameter yang optimum. Metode ini terinspirasi dari galat RMS (Root Means Square). Misalkan dengan adalah himpunan titik data yang diberikan. Didefinisikan vektor galat dengan
gk - yk - Fk(xk), k E{1, 2, ..., n} ,
adalah nilai fungsi di dan adalah interpolan yang diperoleh dengan menghapus satu titik dari himpunan data yang diberikan. Selanjutnya, nilai parameter yang optimum dipilih dengan cara meminimumkan vektor galat . Hasil dari pemilihan nilai parameter bergantung pada banyaknya data dan sebaran data yang diketahui.
20
Li, Yang, Zhong Baorong, Xu Xiaohong, and Liang Zijun. "Application of a semivariogram based on a deep neural network to Ordinary Kriging interpolation of elevation data." PLOS ONE 17, no. 4 (April 22, 2022): e0266942. http://dx.doi.org/10.1371/journal.pone.0266942.
Повний текст джерелаАнотація:
The Ordinary Kriging method is a common spatial interpolation algorithm in geostatistics. Because the semivariogram required for kriging interpolation greatly influences this process, optimal fitting of the semivariogram is of major significance for improving the theoretical accuracy of spatial interpolation. A deep neural network is a machine learning algorithm that can, in principle, be applied to any function, including a semivariogram. Accordingly, a novel spatial interpolation method based on a deep neural network and Ordinary Kriging was proposed in this research, and elevation data were used as a case study. Compared with the semivariogram fitted by the traditional exponential model, spherical model, and Gaussian model, the kriging variance in the proposed method is smaller, which means that the interpolation results are closer to the theoretical results of Ordinary Kriging interpolation. At the same time, this research can simplify processes for a variety of semivariogram analyses.
21
YE, GUI-BO, and DING-XUAN ZHOU. "SVM LEARNING AND Lp APPROXIMATION BY GAUSSIANS ON RIEMANNIAN MANIFOLDS." Analysis and Applications 07, no. 03 (July 2009): 309–39. http://dx.doi.org/10.1142/s0219530509001384.
Повний текст джерелаАнотація:
We confirm by the multi-Gaussian support vector machine (SVM) classification that the information of the intrinsic dimension of Riemannian manifolds can be used to illustrate the efficiency (learning rates) of learning algorithms. We study an approximation scheme realized by convolution operators involving the Gaussian kernels with flexible variances. The essential analysis lies in the study of its approximation order in Lp (1 ≤ p < ∞) norm as the variance of the Gaussian tends to zero. It is different from the analysis for approximation in C(X) since pointwise estimations do not work any more. The Lp approximation arises from the SVM case where the approximated function is the Bayes rule and is not continuous, in general. The approximation error is estimated by imposing a regularity condition that the approximated function lies in some interpolation spaces. Then, the learning rates for multi-Gaussian regularized classifiers with general classification loss functions are derived, and the rates depend on the intrinsic dimension of the Riemannian manifold instead of the dimension of the underlying Euclidean space. Here, the input space is assumed to be a connected compact C∞ Riemannian submanifold of ℝn. The uniform normal neighborhoods of the Riemannian manifold and the radial basis form of Gaussian kernels play an important role.
22
YANG, BO, JAN FLUSSER, and TOMÁŠ SUK. "STEERABILITY OF HERMITE KERNEL." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 04 (June 2013): 1354006. http://dx.doi.org/10.1142/s0218001413540062.
Повний текст джерелаАнотація:
Steerability is a useful and important property of "kernel" functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high efficiency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by the Gaussian function with different powers, defined as the Hermite kernel. Certain special cases of such kernel, Hermite polynomials, Hermite functions and Gaussian derivatives are discussed in detail. Correspondingly, these cases demonstrate that the Hermite kernel is a powerful and effective tool for image processing. Furthermore, the steerability of the Hermite kernel is proved with the help of a property of Hermite polynomials revealing the rule concerning the product of two Hermite polynomials after coordination rotation. Consequently, any order of the Hermite kernel inherits steerability. Moreover, a couple sets of an explicit interpolation function and basis function can be directly obtained. We provide some examples to verify steerability of the Hermite kernel. Experimental results show the effectiveness of steerability and its potential applications in the fields of image processing and computer vision.
23
Sharma, Kaushal, Harinder P. Singh, Ranjan Gupta, Ajit Kembhavi, Kaustubh Vaghmare, Jianrong Shi, Yongheng Zhao, Jiannan Zhang, and Yue Wu. "Stellar spectral interpolation using machine learning." Monthly Notices of the Royal Astronomical Society 496, no. 4 (June 23, 2020): 5002–16. http://dx.doi.org/10.1093/mnras/staa1809.
Повний текст джерелаАнотація:
ABSTRACT Theoretical stellar spectra rely on model stellar atmospheres computed based on our understanding of the physical laws at play in the stellar interiors. These models, coupled with atomic and molecular line databases, are used to generate theoretical stellar spectral libraries (SSLs) comprising of stellar spectra over a regular grid of atmospheric parameters (temperature, surface gravity, abundances) at any desired resolution. Another class of SSLs is referred to as empirical spectral libraries; these contain observed spectra at limited resolution. SSLs play an essential role in deriving the properties of stars and stellar populations. Both theoretical and empirical libraries suffer from limited coverage over the parameter space. This limitation is overcome to some extent by generating spectra for specific sets of atmospheric parameters by interpolating within the grid of available parameter space. In this work, we present a method for spectral interpolation in the optical region using machine learning algorithms that are generic, easily adaptable for any SSL without much change in the model parameters, and computationally inexpensive. We use two machine learning techniques, Random Forest (RF) and Artificial Neural Networks (ANN), and train the models on the MILES library. We apply the trained models to spectra from the CFLIB for testing and show that the performance of the two models is comparable. We show that both the models achieve better accuracy than the existing methods of polynomial based interpolation and the Gaussian radial basis function (RBF) interpolation.
24
Zhang, Y., F. L. Litvin, N. Maruyama, R. Takeda, and M. Sugimoto. "Computerized Analysis of Meshing and Contact of Gear Real Tooth Surfaces." Journal of Mechanical Design 116, no. 3 (September 1, 1994): 677–82. http://dx.doi.org/10.1115/1.2919435.
Повний текст джерелаАнотація:
The authors propose a technique for computerized simulation and tangency of gears provided with real tooth surfaces. The deviations of real tooth surfaces from the theoretical ones are caused by the distortion of surfaces during the heat treatment and lapping. The main ideas of the proposed technique are as follows: (i) The gear real tooth surface is represented by a sum of two vector functions that determine the theoretical tooth surface and the deviations of the real surface from the theoretical one, respectively. (ii) Both vector functions mentioned above are represented in terms of the same Gaussian surface coordinates (the Gaussian coordinates of the theoretical surface). (iii) The deviations of the real surface are initially determined numerically using the data of surface coordinate measurements. The analytical representation of the vector function of deviations is based on the interpolation of a numerically given vector function by a bi-cubic spline. The interpolation provides a relatively high precision because it is accomplished for the surface of small deviations but not for the whole real surface. (iv) The computerized simulation of meshing and tangency of gears with real tooth surfaces is based on the algorithm that describes the conditions of continuous tangency of real tooth surfaces. The proposed approach is illustrated with application to the hypoid gear drive with real tooth surfaces. The data of surface deviations have been determined experimentally at the Nissan Motor Co.
25
Tian, Zhe, Seyed Amin Bagherzadeh, Kamal Ghani, Arash Karimipour, Ali Abdollahi, Mehrdad Bahrami, and Mohammad Reza Safaei. "Nonlinear function estimation fuzzy system (NFEFS) as a novel statistical approach to estimate nanofluids’ thermal conductivity according to empirical data." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (June 6, 2019): 3267–81. http://dx.doi.org/10.1108/hff-12-2018-0768.
Повний текст джерелаАнотація:
Purpose This paper aims to propose a new nonlinear function estimation fuzzy system as a novel statistical approach to estimate nanofluids’ thermal conductivity. Design/methodology/approach A fuzzy system having a product inference engine, a singleton fuzzifier, a center average defuzzifier and Gaussian membership functions is proposed for this purpose. Findings Results indicate that the proposed fuzzy system can predict the thermal conductivity of Al2O3/paraffin nanofluid with appropriate precision and generalization and it also outperforms the classic interpolation methods. Originality/value A new nonlinear function estimation fuzzy system was introduced as a novel statistical approach to estimate nanofluids’ thermal conductivity for the first time.
26
Agou, Vasiliki D., Andrew Pavlides, and Dionissios T. Hristopulos. "Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes." Entropy 24, no. 3 (February 23, 2022): 321. http://dx.doi.org/10.3390/e24030321.
Повний текст джерелаАнотація:
Modeling and forecasting spatiotemporal patterns of precipitation is crucial for managing water resources and mitigating water-related hazards. Globally valid spatiotemporal models of precipitation are not available. This is due to the intermittent nature, non-Gaussian distribution, and complex geographical dependence of precipitation processes. Herein we propose a data-driven model of precipitation amount which employs a novel, data-driven (non-parametric) implementation of warped Gaussian processes. We investigate the proposed warped Gaussian process regression (wGPR) using (i) a synthetic test function contaminated with non-Gaussian noise and (ii) a reanalysis dataset of monthly precipitation from the Mediterranean island of Crete. Cross-validation analysis is used to establish the advantages of non-parametric warping for the interpolation of incomplete data. We conclude that wGPR equipped with the proposed data-driven warping provides enhanced flexibility and—at least for the cases studied– improved predictive accuracy for non-Gaussian data.
27
Zhang, Huaiqing, Yu Chen, Chunxian Guo, and Zhihong Fu. "Application of Radial Basis Function Method for Solving Nonlinear Integral Equations." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/381908.
Повний текст джерелаАнотація:
The radial basis function (RBF) method, especially the multiquadric (MQ) function, was proposed for one- and two-dimensional nonlinear integral equations. The unknown function was firstly interpolated by MQ functions and then by forming the nonlinear algebraic equations by the collocation method. Finally, the coefficients of RBFs were determined by Newton’s iteration method and an approximate solution was obtained. In implementation, the Gauss quadrature formula was employed in one-dimensional and two-dimensional regular domain problems, while the quadrature background mesh technique originated in mesh-free methods was introduced for irregular situation. Due to the superior interpolation performance of MQ function, the method can acquire higher accuracy with fewer nodes, so it takes obvious advantage over the Gaussian RBF method which can be revealed from the numerical results.
28
Bhatt, Samir, Ewan Cameron, Seth R. Flaxman, Daniel J. Weiss, David L. Smith, and Peter W. Gething. "Improved prediction accuracy for disease risk mapping using Gaussian process stacked generalization." Journal of The Royal Society Interface 14, no. 134 (September 2017): 20170520. http://dx.doi.org/10.1098/rsif.2017.0520.
Повний текст джерелаАнотація:
Maps of infectious disease—charting spatial variations in the force of infection, degree of endemicity and the burden on human health—provide an essential evidence base to support planning towards global health targets. Contemporary disease mapping efforts have embraced statistical modelling approaches to properly acknowledge uncertainties in both the available measurements and their spatial interpolation. The most common such approach is Gaussian process regression, a mathematical framework composed of two components: a mean function harnessing the predictive power of multiple independent variables, and a covariance function yielding spatio-temporal shrinkage against residual variation from the mean. Though many techniques have been developed to improve the flexibility and fitting of the covariance function, models for the mean function have typically been restricted to simple linear terms. For infectious diseases, known to be driven by complex interactions between environmental and socio-economic factors, improved modelling of the mean function can greatly boost predictive power. Here, we present an ensemble approach based on stacked generalization that allows for multiple nonlinear algorithmic mean functions to be jointly embedded within the Gaussian process framework. We apply this method to mapping Plasmodium falciparum prevalence data in sub-Saharan Africa and show that the generalized ensemble approach markedly outperforms any individual method.
29
BALASUBRAMANIAN, D., MURALI C. KRISHNA, and R. MURUGESAN. "MULTI-OBJECTIVE GA-OPTIMIZED INTERPOLATION KERNELS FOR RECONSTRUCTION OF HIGH RESOLUTION EMR IMAGES FROM LOW-SAMPLED K-SPACE DATA." International Journal of Computational Intelligence and Applications 08, no. 02 (June 2009): 127–40. http://dx.doi.org/10.1142/s1469026809002539.
Повний текст джерелаАнотація:
The low-frequency instrumentation and imaging capabilities facilitate electron magnetic resonance imaging (EMRI) as an emerging non-invasive imaging technology for mapping free radicals in biological systems. Unlike MRI, EMRI is implemented as a pure phase–phase encoding technique. The fast bio-clearance of the imaging agent and the requirement to reduce radio frequency power deposition dictate collection of reduced k-space samples, compromising the quality and resolution of the EMR images. The present work evaluates various interpolation kernels to generate larger k-space samples for image reconstruction, from the acquired reduced k-space samples. Using k-space EMR data sets, acquired for phantom as well as live mice, the proposed technique is critically evaluated by computing quality metrics viz. signal-to-noise ratio (SNR), standard deviation error (SDE), root mean square error (RMSE), peak signal-to-noise ratio (PSNR), contrast-to-noise ratio (CNR) and Lui's error function (F(I)). The quantitative evaluation of 24 different interpolation functions (including piecewise polynomial functions and many windowed sinc functions) to upsample the k-space data for the Fourier EMR image reconstruction shows that at the expense of a slight increase in computing time, the reconstructed images from upsampled data, produced using Spline-sinc, Welch-sinc, and Gaussian-sinc kernels, are closer to reference image with minimal distortion. Support of the interpolating kernel is a characteristic parameter deciding the quality of the reconstructed image and the time complexity. In this paper, a method to optimize the kernel support using genetic algorithm (GA) is also explored. Maximization of the fitness function has two conflicting objectives and it is approached as a multi-objective optimization problem.
30
Zdunek, Rafał, and Tomasz Sadowski. "Image Completion with Hybrid Interpolation in Tensor Representation." Applied Sciences 10, no. 3 (January 22, 2020): 797. http://dx.doi.org/10.3390/app10030797.
Повний текст джерелаАнотація:
The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.
31
Gu, Mengyang, Debarun Bhattacharjya, and Dharmashankar Subramanian. "GaSPing for Utility." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (April 3, 2020): 2637–44. http://dx.doi.org/10.1609/aaai.v34i03.5648.
Повний текст джерелаАнотація:
High-consequence decisions often require a detailed investigation of a decision maker's preferences, as represented by a utility function. Inferring a decision maker's utility function through assessments typically involves an elicitation phase where the decision maker responds to a series of elicitation queries, followed by an estimation phase where the state-of-the-art for direct elicitation approaches in practice is to either fit responses to a parametric form or perform linear interpolation. We introduce a Bayesian nonparametric method involving Gaussian stochastic processes for estimating a utility function from direct elicitation responses. Advantages include the flexibility to fit a large class of functions, favorable theoretical properties, and a fully probabilistic view of the decision maker's preference properties including risk attitude. Through extensive simulation experiments as well as two real datasets from management science, we demonstrate that the proposed approach results in better function fitting.
32
Zhang, Yongjun, Xunwei Xie, Xiang Wang, Yansheng Li, and Xiao Ling. "Adaptive Image Mismatch Removal With Vector Field Interpolation Based on Improved Regularization and Gaussian Kernel Function." IEEE Access 6 (2018): 55599–613. http://dx.doi.org/10.1109/access.2018.2871743.
Повний текст джерела
33
Chen, Zhaoxue, and Hao Chen. "New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model." Journal of Biomedical Optics 19, no. 7 (July 11, 2014): 076009. http://dx.doi.org/10.1117/1.jbo.19.7.076009.
Повний текст джерела
34
Guitton, Antoine, and Jon Claerbout. "Interpolation of bathymetry data from the Sea of Galilee: A noise attenuation problem." GEOPHYSICS 69, no. 2 (March 2004): 608–16. http://dx.doi.org/10.1190/1.1707081.
Повний текст джерелаАнотація:
We process a bathymetry survey from the Sea of Galilee. This data set is contaminated with non‐Gaussian noise in the form of spikes inside the lake and at the track ends. There is drift on the depth measurements leading to vessel tracks in the preliminary depth images. The drift comes from different seasonal and human conditions during data acquisition, e.g., wind and water levels. We derive an inversion scheme that produces a much‐reduced noise map of the Sea of Galilee. This inversion scheme includes preconditioning and iteratively reweighted least squares with the proper weighting function to remove the non‐Gaussian noise. We remove the ship tracks by adding a modeling operator inside the inversion that accounts for the drift in the data. We then approximate the model covariance matrix with a prediction error filter that enhances details inside the lake. Unfortunately, the prediction error filter slightly degrades the frequency content of the final depth map. Our images of the Sea of Galilee show ancient shorelines and, inside the lake, rifting features.
35
Rashidinia, J., G. E. Fasshauer, and M. Khasi. "A stable method for the evaluation of Gaussian radial basis function solutions of interpolation and collocation problems." Computers & Mathematics with Applications 72, no. 1 (July 2016): 178–93. http://dx.doi.org/10.1016/j.camwa.2016.04.048.
Повний текст джерела
36
Li, Xueying, Wenquan Zhu, Zhiying Xie, Pei Zhan, Xin Huang, Lixin Sun, and Zheng Duan. "Assessing the Effects of Time Interpolation of NDVI Composites on Phenology Trend Estimation." Remote Sensing 13, no. 24 (December 10, 2021): 5018. http://dx.doi.org/10.3390/rs13245018.
Повний текст джерелаАнотація:
The accurate evaluation of shifts in vegetation phenology is essential for understanding of vegetation responses to climate change. Remote-sensing vegetation index (VI) products with multi-day scales have been widely used for phenology trend estimation. VI composites should be interpolated into a daily scale for extracting phenological metrics, which may not fully capture daily vegetation growth, and how this process affects phenology trend estimation remains unclear. In this study, we chose 120 sites over four vegetation types in the mid-high latitudes of the northern hemisphere, and then a Moderate Resolution Imaging Spectroradiometer (MODIS) MCD43A4 daily surface reflectance data was used to generate a daily normalized difference vegetation index (NDVI) dataset in addition to an 8-day and a 16-day NDVI composite datasets from 2001 to 2019. Five different time interpolation methods (piecewise logistic function, asymmetric Gaussian function, polynomial curve function, linear interpolation, and spline interpolation) and three phenology extraction methods were applied to extract data from the start of the growing season and the end of the growing season. We compared the trends estimated from daily NDVI data with those from NDVI composites among (1) different interpolation methods; (2) different vegetation types; and (3) different combinations of time interpolation methods and phenology extraction methods. We also analyzed the differences between the trends estimated from the 8-day and 16-day composite datasets. Our results indicated that none of the interpolation methods had significant effects on trend estimation over all sites, but the discrepancies caused by time interpolation could not be ignored. Among vegetation types with apparent seasonal changes such as deciduous broadleaf forest, time interpolation had significant effects on phenology trend estimation but almost had no significant effects among vegetation types with weak seasonal changes such as evergreen needleleaf forests. In addition, trends that were estimated based on the same interpolation method but different extraction methods were not consistent in showing significant (insignificant) differences, implying that the selection of extraction methods also affected trend estimation. Compared with other vegetation types, there were generally fewer discrepancies between trends estimated from the 8-day and 16-day dataset in evergreen needleleaf forest and open shrubland, which indicated that the dataset with a lower temporal resolution (16-day) can be applied. These findings could be conducive for analyzing the uncertainties of monitoring vegetation phenology changes.
37
del Giudice, Vincenzo, and Pierfrancesco de Paola. "Geoadditive Models for Property Market." Applied Mechanics and Materials 584-586 (July 2014): 2505–9. http://dx.doi.org/10.4028/www.scientific.net/amm.584-586.2505.
Повний текст джерелаАнотація:
Geoadditive models represent efficient and flexible tools, useful in modeling realistically complex situations. Mainly they are based on semi-parametric regressions often integrated by Kriging techniques for the spatial interpolation of surfaces. One of the choices to be made for determination of interpolated surfaces regards the specific function to be used to estimate the unknown values. The choice may currently occur between exponential, gaussian, linear, rational or spherical functions. In this working paper a geoadditive model based on penalized spline functions has been proposed, in order to obtain improvements in forecasting of interpolated surfaces respect to usual Kriging techniques. The main aim of this study is the identification of methodology in able to define and delineate the real estate market scenarios for urban areas through analysis of property values and their spatial distribution.
38
Bawazeer, Saleh A., Saleh S. Baakeem, and Abdulmajeed A. Mohamad. "New Approach for Radial Basis Function Based on Partition of Unity of Taylor Series Expansion with Respect to Shape Parameter." Algorithms 14, no. 1 (December 22, 2020): 1. http://dx.doi.org/10.3390/a14010001.
Повний текст джерелаАнотація:
Radial basis function (RBF) is gaining popularity in function interpolation as well as in solving partial differential equations thanks to its accuracy and simplicity. Besides, RBF methods have almost a spectral accuracy. Furthermore, the implementation of RBF-based methods is easy and does not depend on the location of the points and dimensionality of the problems. However, the stability and accuracy of RBF methods depend significantly on the shape parameter, which is primarily impacted by the basis function and the node distribution. At a small value of shape parameter, the RBF becomes more accurate, but unstable. Several approaches were followed in the open literature to overcome the instability issue. One of the approaches is optimizing the solver in order to improve the stability of ill-conditioned matrices. Another approach is based on searching for the optimal value of the shape parameter. Alternatively, modified bases are used to overcome instability. In the open literature, radial basis function using QR factorization (RBF-QR), stabilized expansion of Gaussian radial basis function (RBF-GA), rational radial basis function (RBF-RA), and Hermite-based RBFs are among the approaches used to change the basis. In this paper, the Taylor series is used to expand the RBF with respect to the shape parameter. Our analyses showed that the Taylor series alone is not sufficient to resolve the stability issue, especially away from the reference point of the expansion. Consequently, a new approach is proposed based on the partition of unity (PU) of RBF with respect to the shape parameter. The proposed approach is benchmarked. The method ensures that RBF has a weak dependency on the shape parameter, thereby providing a consistent accuracy for interpolation and derivative approximation. Several benchmarks are performed to assess the accuracy of the proposed approach. The novelty of the present approach is in providing a means to achieve a reasonable accuracy for RBF interpolation without the need to pinpoint a specific value for the shape parameter, which is the case for the original RBF interpolation.
39
Rehfeld, K., and J. Kurths. "Similarity estimators for irregular and age uncertain time series." Climate of the Past Discussions 9, no. 5 (September 16, 2013): 5299–346. http://dx.doi.org/10.5194/cpd-9-5299-2013.
Повний текст джерелаАнотація:
Abstract. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many datasets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age uncertain time series. We compare the Gaussian-kernel based cross correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.
40
Rehfeld, K., and J. Kurths. "Similarity estimators for irregular and age-uncertain time series." Climate of the Past 10, no. 1 (January 16, 2014): 107–22. http://dx.doi.org/10.5194/cp-10-107-2014.
Повний текст джерелаАнотація:
Abstract. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.
41
Thanh Nha, Nguyen, Nguyen Ngoc Minh, Bui Quoc Tinh, and Truong Tich Thien. "Extended meshless moving Kriging method for crack propagation analyzing in orthotropic media." Science and Technology Development Journal 20, K8 (April 13, 2019): 20–27. http://dx.doi.org/10.32508/stdj.v20ik8.1666.
Повний текст джерелаАнотація:
Orthotropic composite material is the particular type of anisotropic materials and their products have been extensively used in a wide range of engineering applications. Study on mechanical behaviors of such materials under working conditions is very essential. In this study, an extended meshfree moving Kriging interpolation method (namely as X- MK) is presented for crack analyzing in 2D orthotropic materials models. The Gaussian function is used for constructing the moving Kriging shape functions. Typical advantages of the MK shape function are the high-order continuity and the satisfaction of the Kronecker’s delta property. To calculate the stress intensity factors (SIFs), interaction integral method is used with orthotropic auxiliary fields. Several numerical tests including static SIFs calculating and crack propagation predicting are performed to verify the accuracy of the present approach. The obtained results are compared with available refered results and they have shown a very good performance of the present method.
42
Wang, Yanghua. "The Ricker wavelet and the Lambert W function." Geophysical Journal International 200, no. 1 (November 3, 2014): 111–15. http://dx.doi.org/10.1093/gji/ggu384.
Повний текст джерелаАнотація:
Abstract The Ricker wavelet has been widely used in the analysis of seismic data, as its asymmetrical amplitude spectrum can represent the attenuation feature of seismic wave propagation through viscoelastic homogeneous media. However, the frequency band of the Ricker wavelet is not analytically determined yet. The determination of the frequency band leads to an inverse exponential equation. To solve this equation analytically a special function, the Lambert W function, is needed. The latter provides a closed and elegant expression of the frequency band of the Ricker wavelet, which is a sample application of the Lambert W function in geophysics and there have been other applications in various scientific and engineering fields in the past decade. Moreover, the Lambert W function is a variation of the Ricker wavelet amplitude spectrum. Since the Ricker wavelet is the second derivative of a Gaussian function and its spectrum is a single-valued smooth curve, numerical evaluation of the Lambert W function can be implemented by a stable interpolation procedure, followed by a recursive computation for high precision.
43
Liu, Rushan, Mingpan Xiong, and Deyuan Tian. "Relationship between Damage Rate of High-Voltage Electrical Equipment and Instrumental Seismic Intensity." Advances in Civil Engineering 2021 (January 8, 2021): 1–10. http://dx.doi.org/10.1155/2021/5104214.
Повний текст джерелаАнотація:
Based on the actual damage data of high-voltage electrical equipment in electric substations in the Wenchuan earthquake, this paper uses the cumulative Gaussian distribution function to describe the relationship between the damage rate of high-voltage electrical equipment and the instrumental seismic intensity. The instrumental seismic intensity at strong motion observation stations in the Wenchuan earthquake is calculated, and the Kriging interpolation method is used to estimate the instrumental seismic intensity at 110 kV and above voltage level substations in Mianyang, Deyang, Guangyuan, and Chengdu of Sichuan Province. A cumulative Gaussian distribution function is then used to fit the damage rate-instrumental seismic intensity relationship curve for six types of high-voltage electrical equipment such as the transformer, circuit breaker, voltage mutual inductor, current mutual inductor, isolating switch, and lightning arrester. The results show that transformers have the highest vulnerability during earthquakes, and they suffered a certain level of damage even under low instrumental intensity. The second most vulnerable equipment is the circuit breaker, followed by the lightning arrester, transformer, and isolating switch, which share a similar vulnerability curve.
44
Liu, Rushan, Mingpan Xiong, and Deyuan Tian. "Relationship between Damage Rate of High-Voltage Electrical Equipment and Instrumental Seismic Intensity." Advances in Civil Engineering 2021 (January 8, 2021): 1–10. http://dx.doi.org/10.1155/2021/5104214.
Повний текст джерелаАнотація:
Based on the actual damage data of high-voltage electrical equipment in electric substations in the Wenchuan earthquake, this paper uses the cumulative Gaussian distribution function to describe the relationship between the damage rate of high-voltage electrical equipment and the instrumental seismic intensity. The instrumental seismic intensity at strong motion observation stations in the Wenchuan earthquake is calculated, and the Kriging interpolation method is used to estimate the instrumental seismic intensity at 110 kV and above voltage level substations in Mianyang, Deyang, Guangyuan, and Chengdu of Sichuan Province. A cumulative Gaussian distribution function is then used to fit the damage rate-instrumental seismic intensity relationship curve for six types of high-voltage electrical equipment such as the transformer, circuit breaker, voltage mutual inductor, current mutual inductor, isolating switch, and lightning arrester. The results show that transformers have the highest vulnerability during earthquakes, and they suffered a certain level of damage even under low instrumental intensity. The second most vulnerable equipment is the circuit breaker, followed by the lightning arrester, transformer, and isolating switch, which share a similar vulnerability curve.
45
Boyd, John P. "Convergence and error theorems for Hermite function pseudo-RBFs: Interpolation on a finite interval by Gaussian-localized polynomials." Applied Numerical Mathematics 87 (January 2015): 125–44. http://dx.doi.org/10.1016/j.apnum.2014.09.004.
Повний текст джерела
46
Krowiak, Artur. "Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel." Curved and Layered Structures 7, no. 1 (July 13, 2020): 56–67. http://dx.doi.org/10.1515/cls-2020-0006.
Повний текст джерелаАнотація:
AbstractThe paper extends recently developed idea of stable evaluation of the Gaussian kernel. Owing to this, the Gaussian radial basis function that is sensitive to the shape parameter can be stably evaluated and applied to interpolation problems as well as to solve differential equations, giving highly accurate results. But it can be done only with grids being the Cartesian product of sets of points, what limits the use of this idea to rectangular domains. In the present paper, by the association of an appropriate transformation with the mentioned method, the latter is applied to solve biharmonic problems on quadrilateral irregular domains. As an example, in the present work this approach is applied to solve bending as well as free vibration problem of thin plates. In the paper some strategies for the implementation of the boundary conditions are also presented and examined due to the accuracy. The numerical tests show high accuracy and usefulness of the method.
47
Li, Tanda, Guy R. Davies, Alexander J. Lyttle, Warrick H. Ball, Lindsey M. Carboneau, and Rafael A. García. "Modelling stars with Gaussian Process Regression: augmenting stellar model grid." Monthly Notices of the Royal Astronomical Society 511, no. 4 (February 21, 2022): 5597–610. http://dx.doi.org/10.1093/mnras/stac467.
Повний текст джерелаАнотація:
ABSTRACT Grid-based modelling is widely used for estimating stellar parameters. However, stellar model grid is sparse because of the computational cost. This paper demonstrates an application of a machine-learning algorithm using the Gaussian Process (GP) Regression that turns a sparse model grid on to a continuous function. We train GP models to map five fundamental inputs (mass, equivalent evolutionary phase, initial metallicity, initial helium fraction, and the mixing-length parameter) to observable outputs (effective temperature, surface gravity, radius, surface metallicity, and stellar age). We test the GP predictions for the five outputs using off-grid stellar models and find no obvious systematic offsets, indicating good accuracy in predictions. As a further validation, we apply these GP models to characterize 1000 fake stars. Inferred masses and ages determined with GP models well recover true values within one standard deviation. An important consequence of using GP-based interpolation is that stellar ages are more precise than those estimated with the original sparse grid because of the full sampling of fundamental inputs.
48
Stordal, Andreas S., and Hans A. Karlsen. "Large Sample Properties of the Adaptive Gaussian Mixture Filter." Monthly Weather Review 145, no. 7 (July 2017): 2533–53. http://dx.doi.org/10.1175/mwr-d-15-0372.1.
Повний текст джерелаАнотація:
In high-dimensional dynamic systems, standard Monte Carlo techniques that asymptotically reproduce the posterior distribution are computationally too expensive. Alternative sampling strategies are usually applied and among these the ensemble Kalman filter (EnKF) is perhaps the most popular. However, the EnKF suffers from severe bias if the model under consideration is far from linear. Another class of sequential Monte Carlo methods is kernel-based Gaussian mixture filters, which reduce the bias but maintain the robustness of the EnKF. Although many hybrid methods have been introduced in recent years, not many have been analyzed theoretically. Here it is shown that the recently proposed adaptive Gaussian mixture filter can be formulated in a rigorous Bayesian framework and that the algorithm can be generalized to a broader class of interpolated kernel filters. Two parameters—the bandwidth of the kernel and a weight interpolation factor—determine the filter performance. The new formulation of the filter includes particle filters, EnKF, and kernel-based Gaussian mixture filters as special cases. Techniques from particle filter literature are used to calculate the asymptotic bias of the filter as a function of the parameters and to derive a central limit theorem. The asymptotic theory is then used to determine the parameters as a function of the sample size in a robust way such that the error norm vanishes asymptotically, whereas the normalized error is sample independent and bounded. The parameter choice is tested on the Lorenz 63 model, where it is shown that the error is smaller or equal to the EnKF and the optimal particle filter for a varying sample size.
49
Lamb, Anthony R., and Deborah Villarroel-Lamb. "A Meshfree Approach for Simulating Fluid Flow in Fractured Porous Media." West Indian Journal of Engineering 44, no. 2 (January 2022): 38–47. http://dx.doi.org/10.47412/qpcd7447.
Повний текст джерелаАнотація:
This paper presents a meshfree approach for simulating fluid flow in fractured porous media using a novel fracture (FM) mapping approach. Fracture mapping is a continuum-based approach which simulates the flow interaction between the porous matrix and existing fractures via a transfer function. The approach simulates fluid flow through both the matrix and the fractures and is well suited to models containing sparsely spaced, unconnected fractures. The presented approach determines the fluid flow using approximating functions constructed employing the radial point interpolation method (RPIM) meshfree formulation which uses radial basis functions (RBFs) augmented with polynomials. As part of this meshfree scheme a nodal integration procedure has been implemented thereby removing the need for background integration cells that are usually required for meshfree schemes that rely on Gaussian integration. Numerical test results illustrate the methods ability to adequately describe the fluid pressure fields within a fractured porous domain
50
Yu, Meng, Qing Dong Zhang, Bo Wang, Xiao Feng Zhang, and Jian Peng. "Research on Rolling Model Based on Non-Circular Contact Arc for Cold Strip Temper Rolling." Advanced Materials Research 145 (October 2010): 223–29. http://dx.doi.org/10.4028/www.scientific.net/amr.145.223.
Повний текст джерелаАнотація:
During temper rolling, the reduction is small, the length of contact arc is short, and the elastic deformation of work roll is large. Roll shape is not circular arc, the assumption of circular roll shape is no longer applicable. In this paper, quintic B-spline function is used in interpolation operations with normal pressure distribution so that roll shape can be solved by Gaussian integration. And a rolling model based on non- circular contact arc for cold strip temper rolling is established. The calculated results show good agreement with the actual value. The model can meet manufacturing requirement of the field and receives better control effect of elongation.