To solve above problems, the original ESN is extended to polynomial ESNs (PESNs) by employing the polynomial functions of input variables into output weights.
It was approximated by the polynomial function and subtracted by using "baseline correction" functionality of the LabSpec software.
By approximating the directional distributions of contact normal density, mean contact force and mean contact vector with polynomial expansions in unit direction vector n, the directional dependences were characterized by the coefficients of the polynomial functions, i.e., the direction tensors.
Also a PCA is used, but instead of shifting a window over the data and normalizing by the last w trials, a method similar to [13] is used: a polynomial is fitted to the content of the window and the next trial is adjusted by the value, the polynomial function would estimate.
The designer is guided in his choice by the coefficients of the polynomial function which give the effect of each parameter on energy demand.
Remote data points ("outliers") were not used for fitting the polynomials F. For each probe in the sample (element in the vector S k), the normalized value (in log-space) is calculated from the initial value by transforming it with the polynomial function F k, so that.
With the help of the polynomial function defined by (3.3). the previous divided difference can be written as (3.4).
The coefficients a and b are then expressed by the following polynomial functions for the horizontal value u: Fig. 12 Modeling errors using combined functions for a, b, and H in LUT method a={a}_0+{a}_1u+{a}_n{u}^n+cdots +{a}_n{u}^n, (15) b={b}_0+{b}_n{u}^n_2{u}^2+cdots +{b}_n{u}^n, (16).
The LABSPEC 2.0 software (HORIBA Scientific, France) was utilized to remove the autofluorescence background by the 4th polynomial function and smooth the SERS spectra by the Savitzky-Golay smoothing.
