scholarly journals Separating the aa-index into Solar and Hale Cycle Related Components Using Principal Component Analysis

Solar Physics ◽  
2021 ◽  
Vol 296 (5) ◽  
Author(s):  
Jouni Takalo
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Solar Cycle ◽  
Sunspot Number ◽  
High Speed ◽  
Recurrent Events ◽  
Principal Component ◽  
Component Analysis ◽  
Activity Level ◽  
Aa Index

AbstractWe decompose the monthly aa-index of Cycles 10 to 23 using principal component analysis (PCA). We show that the first component (PC1) is related to the 11-year solar cycle, and accounts for 41.5% of the variance of the data. The second component (PC2) is related to 22-year Hale cycle, and explains 23.6% of the variance of the data. The PC1 time series of the aa-index for Cycles 10 – 23 has only one peak in its power spectrum at the period 10.95 years, which is the average solar cycle (SC) period for the interval SC10 – SC23. The PC2 time series of the same cycles has a clear peak at period 21.90 (Hale cycle) and a smaller peak at 3/4 of that period. We also study the principal components of the sunspot number (SSN) for Cycles 10 – 23, and compare the mutual behavior of the PC2 components of the aa-index and SSN PCA analyses. We note that they are in the same phase in all other cycles but Solar Cycles 15 and 20. The aa-index of Cycle 20 also differs from other even aa-index cycles in its shape, especially in anomalously high peaks during its descending phase. Even though there is a coherence in the PC2 time series phases of the aa-index and sunspot number, this effect is too small to be the origin of all the differences between the shape of even and odd aa cycles. We estimate that 30% of the shape of the PC2 component of the aa-index is due to the shape of the PC2 of the sunspot number and the rest to other recurrent events in the Sun and solar wind. The first maximum of the aa-index (typical to odd cycles), during sunspot maximum, has been shown to be related to coronal mass ejections (CME), while the second maximum (typical to even cycles) in the cycle descending phase, is probably related to high-speed streams (HSS). The last events increase the activity level such that the minimum between even and odd cycle pairs is always higher than the minimum between succeeding odd and even cycle pairs.

scholarly journals Optimal Vehicle Pose Estimation Network Based on Time Series and Spatial Tightness with 3D LiDARs

2021 ◽  
Vol 13 (20) ◽  
pp. 4123
Author(s):  
Hanqi Wang ◽  
Zhiling Wang ◽  
Linglong Lin ◽  
Fengyu Xu ◽  
Jie Yu ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Pose Estimation ◽  
Point Cloud ◽  
Principal Component ◽  
Component Analysis ◽  
Evaluation Index ◽  
Evaluation Indexes ◽  
Learning Network ◽  
Estimation Algorithms

Vehicle pose estimation is essential in autonomous vehicle (AV) perception technology. However, due to the different density distributions of the point cloud, it is challenging to achieve sensitive direction extraction based on 3D LiDAR by using the existing pose estimation methods. In this paper, an optimal vehicle pose estimation network based on time series and spatial tightness (TS-OVPE) is proposed. This network uses five pose estimation algorithms proposed as candidate solutions to select each obstacle vehicle's optimal pose estimation result. Among these pose estimation algorithms, we first propose the Basic Line algorithm, which uses the road direction as the prior knowledge. Secondly, we propose improving principal component analysis based on point cloud distribution to conduct rotating principal component analysis (RPCA) and diagonal principal component analysis (DPCA) algorithms. Finally, we propose two global algorithms independent of the prior direction. We provided four evaluation indexes to transform each algorithm into a unified dimension. These evaluation indexes’ results were input into the ensemble learning network to obtain the optimal pose estimation results from the five proposed algorithms. The spatial dimension evaluation indexes reflected the tightness of the bounding box and the time dimension evaluation index reflected the coherence of the direction estimation. Since the network was indirectly trained through the evaluation index, it could be directly used on untrained LiDAR and showed a good pose estimation performance. Our approach was verified on the SemanticKITTI dataset and our urban environment dataset. Compared with the two mainstream algorithms, the polygon intersection over union (P-IoU) average increased by about 5.25% and 9.67%, the average heading error decreased by about 29.49% and 44.11%, and the average speed direction error decreased by about 3.85% and 46.70%. The experiment results showed that the ensemble learning network could effectively select the optimal pose estimation from the five abovementioned algorithms, making pose estimation more accurate.

Research for Structural Damage Identification Method Based on Stable Time Series and Principal Component Analysis

2014 ◽  
Vol 578-579 ◽  
pp. 1020-1023
Author(s):  
Jing Zhou Lu ◽  
Jia Chen Wang ◽  
Xu Zhu
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Damage Detection ◽  
Structural Damage ◽  
Computing Time ◽  
Principal Component ◽  
Component Analysis ◽  
Identification Accuracy ◽  
Frame Structure ◽  
Ar Model

In this paper, we introduce a set of techniques for time series analysis based on principal component analysis (PCA). Firstly, the autoregressive (AR) model is established using acceleration response data, and the root mean squared error (RMSE) of AR model is calculated based on PCA. Then a new damage sensitive feature (DSF) based on the AR coefficients is presented. To test the efficacy of the damage detection and localization methodologies, the algorithm has been tested on the analytical and experimental results of a three-story frame structure model of the Los Alamos National Laboratory. The result of the damage detection indicates that the algorithm is able to identify and localize minor to severe damage as defined for the structure. It shows that the suggested method can lead to less amount of computing time, high suitability and identification accuracy.

scholarly journals Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Variational Bayesian Principal Component Analysis

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2298 ◽  
Author(s):  
Wudong Li ◽  
Weiping Jiang ◽  
Zhao Li ◽  
Hua Chen ◽  
Qusen Chen ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis ◽  
Common Mode ◽  
Variational Bayesian ◽  
North East ◽  
Position Time Series ◽  
Gnss Position Time Series

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

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