A Novel Multi-Step Cross-Decomposition Method Based on Wavelet Transform for Wind Power Prediction

One of the main approaches to improve wind power prediction accuracy is to decompose wind-speed into different frequency-band components and use them as inputs of prediction model. Among the decomposition methods, wavelet transform is widely used due to its flexibility. However, the decomposition level and wavelet function need to be selected through trail-and-error, which is also called empirical decomposition method, because the effectiveness of a certain selection depends on the characteristic of wind farm and the prediction model. Therefore, it is difficult to find a general decomposition method that can be effective on different prediction models and wind farms. Aiming at this problem, a novel multi-step cross-decomposition method is proposed in this paper. The proposed method decomposes the wind-speed and power alternatively in each step, and after three steps of decomposition, the wind-speed can be decomposed to four different frequency-band components which will be used as the input of the prediction model. The prediction errors of proposed method and several empirical decomposition methods are compared on BPNN and SVM models. The results show that the proposed method is the only effective method on two prediction models for four wind farms.

Discriminating the Influence of Correlated Factors from Multivariate Observations: the Back-to-Back Regression

Identifying causes solely from observations can be particularly challenging when i) potential factors are difficult to manipulate independently and ii) observations are multi-dimensional. To address this issue, we introduce “Back-to-Back” regression (B2B), a linear method designed to efficiently measure, from a set of correlated factors, those that most plausibly account for multidimensional observations. First, we prove the consistency of B2B, its links to other linear approaches, and show how it provides a robust, unbiased and interpretable scalar estimate for each factor. Second, we use a variety of simulated data to show that B2B outperforms least-squares regression and cross-decomposition techniques (e.g. canonical correlation analysis and partial least squares) on causal identification when the factors and the observations are partially collinear. Finally, we apply B2B to magneto-encephalography of 102 subjects recorded during a reading task to test whether our method appropriately disentangles the respective contribution of word length and word frequency - two correlated factors known to cause early and late brain responses respectively. The results show that these two factors are better disentangled with B2B than with other standard techniques.

Geometry of Infinitely Presented Small Cancellation Groups and Quasi-homomorphisms

We study the geometry of infinitely presented groups satisfying the small cancellation condition $C^{\prime }(1/8)$, and introduce a standard decomposition (called the criss-cross decomposition) for the elements of such groups. Our method yields a direct construction of a linearly independent set of power continuum in the kernel of the comparison map between the bounded and the usual group cohomology in degree 2, without the use of free subgroups and extensions.