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Compressors are important components in various power systems in the field of energy and power. In practical applications, compressors often operate under non-design conditions. Therefore, accurate calculation on performance under various operating conditions is of great significance for the development and application of certain power systems equipped with compressors. To calculate and predict the performance of a compressor under all operating conditions through limited data, the interpolation method was combined with a support vector machine (SVM). Based on the known data points of compressor design conditions, the interpolation method was adopted to obtain training samples of the SVM. In the calculation process, preliminary screening was conducted on the kernel functions of the SVM. Two interpolation methods, including linear interpolation and cubic spline interpolation, were used to obtain sample data. In the subsequent training process of the SVM, the genetic algorithm (GA) was used to optimize its parameters. After training, the available data were compared with the predicted data of the SVM. The results show that the SVM uses the Gaussian kernel function to achieve the highest prediction accuracy. The prediction accuracy of the SVM trained with the data obtained from linear interpolation was higher than that of cubic spline interpolation. Compared with the back propagation neural network optimized by the genetic algorithm (GA-BPNN), the genetic algorithm optimization of extreme learning machine neural network (GA-ELMNN), and the genetic algorithm optimization of generalized regression neural network (GA-GRNN), the support vector machine optimized by the genetic algorithm (GA-SVM) has a better generalization, and GA-SVM is more accurate in predicting boundary data than the GA-BPNN. In addition, reducing the number of original data points still enables the GA-SVM to maintain a high level of predictive accuracy.

In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.

In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. We then extend the

Spatial interpolation of precipitation data is an essential input for hydrological modelling. At present, the most frequently used spatial interpolation methods for precipitation are based on the assumption of stationary in spatial autocorrelation and spatial heterogeneity. As climate change is altering the precipitation, stationary in spatial autocorrelation and spatial heterogeneity should be first analysed before spatial interpolation methods are applied. This study aims to propose a framework to understand the spatial patterns of autocorrelation and heterogeneity embedded in precipitation using Moran's I, Getis–Ord test, and semivariogram. Variations in autocorrelation and heterogeneity are analysed by the Mann–Kendall test. The indexes and test methods are applied to the 7-day precipitation series which are corresponding to the annual maximum 7-day flood volume (P-AM7FV) upstream of the Changjiang river basin. The spatial autocorrelation of the P-AM7FV showed a statistically significant increasing trend over the whole study area. Spatial interpolation schemes for precipitation may lead to better estimation and lower error for the spatial distribution of the areal precipitation. However, owing to the changing summer monsoons, random variation in the spatial heterogeneity analysis shows a significant increasing trend, which reduces the reliability of the distributed hydrological model with the input of local or microscales.

As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, and the dimension of the approximation space is systematically determined by a probability threshold. This random sampling procedure avoids large candidate sample sets for high-dimensional parameters, and the probability based stopping criterion can efficiently control the dimension of the approximation space. Numerical experiments are conducted to demonstrate the computational efficiency of SDEIM, which include separation of variables for general nonlinear functions, e.g., exponential functions of the Karhu nen–Loève (KL) expansion, and constructing reduced order models for FitzHugh–Nagumo equations, where symmetry among limit cycles is well captured by SDEIM.

High-spatial-resolution and long-term climate data are highly desirable for understanding climate-related natural processes. China covers a large area with a low density of weather stations in some (e.g., mountainous) regions. This study describes a 0.5′ (∼ 1 km) dataset of monthly air temperatures at 2 m (minimum, maximum, and mean proxy monthly temperatures, TMPs) and precipitation (PRE) for China in the period of 1901–2017. The dataset was spatially downscaled from the 30′ Climatic Research Unit (CRU) time series dataset with the climatology dataset of WorldClim using delta spatial downscaling and evaluated using observations collected in 1951–2016 by 496 weather stations across China. Prior to downscaling, we evaluated the performances of the WorldClim data with different spatial resolutions and the 30′ original CRU dataset using the observations, revealing that their qualities were overall satisfactory. Specifically, WorldClim data exhibited better performance at higher spatial resolution, while the 30′ original CRU dataset had low biases and high performances. Bicubic, bilinear, and nearest-neighbor interpolation methods employed in downscaling processes were compared, and bilinear interpolation was found to exhibit the best performance to generate the downscaled dataset. Compared with the evaluations of the 30′ original CRU dataset, the mean absolute error of the new dataset (i.e., of the 0.5′ dataset downscaled by bilinear interpolation) decreased by 35.4 %–48.7 % for TMPs and by 25.7 % for PRE. The root-mean-square error decreased by 32.4 %–44.9 % for TMPs and by 25.8 % for PRE. The Nash–Sutcliffe efficiency coefficients increased by 9.6 %–13.8 % for TMPs and by 31.6 % for PRE, and correlation coefficients increased by 0.2 %–0.4 % for TMPs and by 5.0 % for PRE. The new dataset could provide detailed climatology data and annual trends of all climatic variables across China, and the results could be evaluated well using observations at the station. Although the new dataset was not evaluated before 1950 owing to data unavailability, the quality of the new dataset in the period of 1901–2017 depended on the quality of the original CRU and WorldClim datasets. Therefore, the new dataset was reliable, as the downscaling procedure further improved the quality and spatial resolution of the CRU dataset and was concluded to be useful for investigations related to climate change across China. The dataset presented in this article has been published in the Network Common Data Form (NetCDF) at https://doi.org/10.5281/zenodo.3114194 for precipitation (Peng, 2019a) and https://doi.org/10.5281/zenodo.3185722 for air temperatures at 2 m (Peng, 2019b) and includes 156 NetCDF files compressed in zip format and one user guidance text file.

Domain decomposition is involved in Fluid-Structure Interaction (FSI) analysis to speed up their computations. Non-matched meshes always exist in the interface of these different domains which brings data exchange problem. A load transfer method is investigated in this article to deal with non-matching meshes between fluid and structure. The local nearest neighbor searching algorithm was used in this method to match fluid nodes and structural elements, while thin plate splines with tension were used to deal with data transfer between non-matching meshes in FSI computations, and the corresponding matrix equations for the target points are presented. Implementations of the obtained algorithms were used to solve the one-way FSI problem of the CRH380C high-speed train and the relative error of transferred results was analyzed. The statistical parameters under two algorithms, the TPS model and the model combining both TPS model and nearest interpolation model were compared and the results indicate that the latter can transfer data more accurately.

A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. The original empirical interpolation method (EIM) is a modification of POD that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD. We propose a discrete empirical interpolation method (DEIM), a variant that is suitable for reducing the dimension of systems of ordinary differential equations (ODEs) of a certain type. As presented here, it is applicable to ODEs arising from finite difference discretization of time dependent PDEs and/or parametrically dependent steady state problems. However, the approach extends to arbitrary systems of nonlinear ODEs with minor modification. Our contribution is a greatly simplified description of the EIM in a finite-dimensional setting that possesses an error bound on the quality of approximation. An application of DEIM to a finite difference discretization of the one-dimensional FitzHugh-Nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long-time integration that fully captures nonlinear limit cycle behavior. We also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results. [PUBLICATION ABSTRACT]

Let ( A 0 , A 1 ) be a compatible couple of normed spaces. We study the interrelation of the general K -interpolation spaces of the couple ( A 0 + A 1 , A 0 ∩ A 1 ) with those of the couples ( A 0 , A 1 ) , ( A 0 + A 1 , A 0 ) , ( A 0 + A 1 , A 1 ) , ( A 0 , A 0 ∩ A 1 ) , and ( A 1 , A 0 ∩ A 1 ) .

Precipitation has a strong and constant impact on different economic sectors, environment and social activities all over the world. An increasing interest for monitoring and estimating the precipitation characteristics can be claimed in the last decades. However, in some areas, the ground-based network is still sparse and the spatial data coverage insufficiently addresses the needs. In the last decades, different interpolation methods provide an efficient response for describing the spatial distribution of precipitation. In this study, we compare the performance of seven interpolation methods used for retrieving the mean annual precipitation over the mainland Portugal, as follows: local polynomial interpolation (LPI), global polynomial interpolation (GPI), radial basis function (RBF), inverse distance weighted (IDW), ordinary cokriging (OCK), universal cokriging (UCK) and empirical Bayesian kriging regression (EBKR). We generate the mean annual precipitation distribution using data from 128 rain gauge stations covering the period 1991 to 2000. The interpolation results were evaluated using cross-validation techniques and the performance of each method was evaluated using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), Pearson’s correlation coefficient (R) and Taylor diagram. The results indicate that EBKR performs the best spatial distribution. In order to determine the accuracy of spatial distribution generated by the spatial interpolation methods, we calculate the prediction standard error (PSE). The PSE result of EBKR prediction over mainland Portugal increases from south to north.