Advances in Data Science and Adaptive Analysis

Load spectrum is the basement of reliability analysis. Selecting a suitable operator for a certain model in a typical experiment field is of benefit to the acquisition of load spectrum. Different operating performances caused by different operators have the characteristics of multiple evaluation indicators. In this paper, a comprehensive evaluation method based on median damage is proposed. The method is applied to evaluate the actual operating performances in the experiment field of the excavator. Comparative results show that the proposed method is feasible, and will be more convenient when more indicators are involved. The proposed method provides a theoretical reference for the compiling of load spectrum acquisition specification, and proposes an additional method for the evaluation of the operating performances.

Singular spectrum analysis (SSA) is a nonparametric spectral decomposition of a time series into arbitrary number of interpretable components. It involves a single parameter, window length $L$, which can be adjusted for the specific purpose of the analysis. After the decomposition of a time series, similar series are grouped to obtain the interpretable components by consulting with the $w$-correlation matrix. To accomplish better resolution of the frequency spectrum, a larger window length $L$ is preferable and, in this case, the proper grouping is crucial for making the SSA decomposition. When the $w$-correlation matrix does not have block-diagonal form, however, it is hard to adequately carry out the grouping. To avoid this, we propose a novel algorithm for the adaptive orthogonal decomposition of the time series based on the SSA scheme. The SSA decomposition sequences of the time series are recombined and the linear coefficients are determined so as to maximizing its squared norm. This results in an eigenvalue problem of the Gram matrix and we can obtain the orthonormal basis vectors for the $L$-dimensional subspace. By the orthogonal projection of the original time series on these basis vectors, we can obtain adaptive orthogonal decomposition of the time series without the redundancy of the original SSA decomposition.

This research develops a toolkit for snow-cover area calculation and display (SACD) based on the Interactive Multisensor Snow and Ice Mapping System (IMS). The paper uses the Tibetan Plateau region as an example to describe the toolkit’s method, results, and usage. The National Snow and Ice Data Center (NSIDC) provides to the public IMS a well-used system for monitoring the snow and ice cover. The newly developed toolkit is based on a simple shoe-lace formula for a grid box area on a sphere and can be conveniently used to calculate the total area of snow cover given the IMS data. The toolkit has been made available as an open source Python software on GitHub. The toolkit generates the time series of the daily snow-covered area for any region over the Northern Hemisphere from 4 February 1997. The toolkit also creates maps showing snow and ice coverage with an elevation background. The Tibetan Plateau (TP) region $(25^{\circ }$–$45^{\circ }$N)$\times (65^{\circ }$–$105^{\circ }$E) is used as an example to demonstrate our work on SACD. The IMS products at 24, 4, and 1km resolutions include each grid’s latitude and longitude coordinates that are used to calculate the grid box’s area using the shoe-lace formula. The total TP area calculated by the sum of the areas of all the grid boxes approximates the true spherical TP surface area bounded by $(25^{\circ }$–$45^{\circ }$N) $\times (65^{\circ }$–$105^{\circ }$E) with a difference 0.046% for the 24km grid and 0.033% for the 4km grid. The differences in the snow-cover area reported by the 24km and 4km grids vary between $-2.34$% and 6.24%. The temporal variations of the daily TP snow cover are displayed in time series from 4 February 1997 to present with 4km and 24km resolutions.