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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.

The dynamic modeling and simulation of a rotating flexible hub-beam based on different discretization methods of the deformation fields are studied. For a rotating flexible cantilever beam, assumed mode method, finite element method (FEM), Bezier interpolation method (BIM), and B-spline interpolation method (BSIM) are adopted to describe the deformation field of flexible beam and to construct unified. By means of Lagrange’s equation of the second kind, taking into account both longitudinal and transverse deformations, as well as longitudinal shortening in the longitudinal deformation caused by transverse bending deformation, dynamic simulation software based on four different discretization methods is prepared, and simulation examples are given for dynamic problems of the hub-beam. The simulation results show that FEM has a low computing efficiency, and the deformation of a flexible beam discretized by FEM cannot be guaranteed second derivative continuous at the element nodes. BIM and BSIM can be used as new discretization methods to effectively describe the deformation fields of flexible beams and have high computing efficiencies, perfectly meeting the needs of actual projects. Therefore, BIM and BSIM have good performance and application value in multi-flexible-body system dynamics.

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.

Most massive stars are members of a binary or a higher-order stellar system, where the presence of a binary companion can decisively alter their evolution via binary interactions. Interacting binaries are also important astrophysical laboratories for the study of compact objects. Binary population synthesis studies have been used extensively over the last two decades to interpret observations of compact-object binaries and to decipher the physical processes that lead to their formation. Here, we present POSYDON, a novel, publicly available, binary population synthesis code that incorporates full stellar structure and binary-evolution modeling, using the MESA code, throughout the whole evolution of the binaries. The use of POSYDON enables the self-consistent treatment of physical processes in stellar and binary evolution, including: realistic mass-transfer calculations and assessment of stability, internal angular-momentum transport and tides, stellar core sizes, mass-transfer rates, and orbital periods. This paper describes the detailed methodology and implementation of POSYDON, including the assumed physics of stellar and binary evolution, the extensive grids of detailed single- and binary-star models, the postprocessing, classification, and interpolation methods we developed for use with the grids, and the treatment of evolutionary phases that are not based on precalculated grids. The first version of POSYDON targets binaries with massive primary stars (potential progenitors of neutron stars or black holes) at solar metallicity.

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.

Strontium isotope ratios (87Sr/86Sr) are gaining considerable interest as a geolocation tool and are now widely applied in archaeology, ecology, and forensic research. However, their application for provenance requires the development of baseline models predicting surficial 87Sr/86Sr variations (\"isoscapes\"). A variety of empirically-based and process-based models have been proposed to build terrestrial 87Sr/86Sr isoscapes but, in their current forms, those models are not mature enough to be integrated with continuous-probability surface models used in geographic assignment. In this study, we aim to overcome those limitations and to predict 87Sr/86Sr variations across Western Europe by combining process-based models and a series of remote-sensing geospatial products into a regression framework. We find that random forest regression significantly outperforms other commonly used regression and interpolation methods, and efficiently predicts the multi-scale patterning of 87Sr/86Sr variations by accounting for geological, geomorphological and atmospheric controls. Random forest regression also provides an easily interpretable and flexible framework to integrate different types of environmental auxiliary variables required to model the multi-scale patterning of 87Sr/86Sr variability. The method is transferable to different scales and resolutions and can be applied to the large collection of geospatial data available at local and global levels. The isoscape generated in this study provides the most accurate 87Sr/86Sr predictions in bioavailable strontium for Western Europe (R2 = 0.58 and RMSE = 0.0023) to date, as well as a conservative estimate of spatial uncertainty by applying quantile regression forest. We anticipate that the method presented in this study combined with the growing numbers of bioavailable 87Sr/86Sr data and satellite geospatial products will extend the applicability of the 87Sr/86Sr geo-profiling tool in provenance applications.

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.