Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well. 相似文献
Surrogate models have been widely applied to correlate design variables and performance parameters in turbomachinery optimization applications. With more design variables and uncertain factors taken into account in an optimization design problem, the mathematical relations between the design variables and the performance parameters might present linear, low-order nonlinear or even high-order nonlinear characteristics, and are usually analytically unknown. Therefore, it is required that surrogate models have high adaptability and prediction accuracy for both the linear and nonlinear characteristics. The paper mainly investigates the effectiveness of an adaptive region segmentation combining surrogate model based on support vector regression and kriging model applied to a transonic axial compressor to approximate the complicated relationships between geometrical variables and objective performance outputs with different sampling methods and sizes. The purpose is to explore the prediction accuracy and computational efficiency of this adaptive surrogate model in real turbomachinery applications. Three different sampling techniques are studied: (1) uniform design; (2) Latin hypercube sampling method; (3) Sobol quasi-random design. For the low dimensional case with five variables, the adaptive region segmentation combining surrogate model performs better (not worse) than the single component surrogate in terms of prediction accuracy and computational efficiency. In the meanwhile, it is also noted that the uniform design applied to the adaptive surrogate model has more advantages over the Latin hypercube sampling method especially for the small sample size cases, both performing better than the Sobol quasi-random design. Moreover, a high dimensional case with 12 variables is also utilized to further validate the prediction advantage of the adaptive region segmentation combining surrogate model over the single component surrogate, and the computational results favor it. Overall, the adaptive region segmentation combining surrogate model has produced acceptable to high prediction accuracy in presenting complex relationships between the geometrical variables and the objective performance outputs and performed robustly for a transonic axial compressor problem.
In recent years, the parameterized level set method (PLSM) has attracted widespread attention for its good stability, high efficiency and the smooth result of topology optimization compared with the conventional level set method. In the PLSM, the radial basis functions (RBFs) are often used to perform interpolation fitting for the conventional level set equation, thereby transforming the iteratively updating partial differential equation (PDE) into ordinary differential equations (ODEs). Hence, the RBFs play a key role in improving efficiency, accuracy and stability of the numerical computation in the PLSM for structural topology optimization, which can describe the structural topology and its change in the optimization process. In particular, the compactly supported radial basis function (CS-RBF) has been widely used in the PLSM for structural topology optimization because it enjoys considerable advantages. In this work, based on the CS-RBF, we propose a PLSM for structural topology optimization by adding the shape sensitivity constraint factor to control the step length in the iterations while updating the design variables with the method of moving asymptote (MMA). With the shape sensitivity constraint factor, the updating step length is changeable and controllable in the iterative process of MMA algorithm so as to increase the optimization speed. Therefore, the efficiency and stability of structural topology optimization can be improved by this method. The feasibility and effectiveness of this method are demonstrated by several typical numerical examples involving topology optimization of single-material and multi-material structures.
Forecasting stock prices using deep learning models suffers from problems such as low accuracy, slow convergence, and complex network structures. This study developed an echo state network (ESN) model to mitigate such problems. We compared our ESN with a long short-term memory (LSTM) network by forecasting the stock data of Kweichow Moutai, a leading enterprise in China’s liquor industry. By analyzing data for 120, 240, and 300 days, we generated forecast data for the next 40, 80, and 100 days, respectively, using both ESN and LSTM. In terms of accuracy, ESN had the unique advantage of capturing nonlinear data. Mean absolute error (MAE) was used to present the accuracy results. The MAEs of the data forecast by ESN were 0.024, 0.024, and 0.025, which were, respectively, 0.065, 0.007, and 0.009 less than those of LSTM. In terms of convergence, ESN has a reservoir state-space structure, which makes it perform faster than other models. Root-mean-square error (RMSE) was used to present the convergence time. In our experiment, the RMSEs of ESN were 0.22, 0.27, and 0.26, which were, respectively, 0.08, 0.01, and 0.12 less than those of LSTM. In terms of network structure, ESN consists only of input, reservoir, and output spaces, making it a much simpler model than the others. The proposed ESN was found to be an effective model that, compared to others, converges faster, forecasts more accurately, and builds time-series analyses more easily. 相似文献
Identifying the key factors of the disaster-related information propagation process can provide decision support for disaster management. This study characterizes the effects of content types, location, and social capital of social media users on the virality of disaster-related information. We found through the Weibo dataset of the Yiliang earthquake that the virality of different types of information can vary on the basis of the social capital of users who post the information. This study fills the current research gaps by examining the individual and joint effects of the content and creator characteristics on the virality of disaster-related information. 相似文献
The Journal of Supercomputing - With the fast growth of big data applications, it has brought about a huge increase in the energy consumption for big data processing in Cloud data centers. In this... 相似文献