# Correct use of S.V.D. regression on my data

All I(barley) know is electrical engineering. Only ever taken one basic stat class and a linear alg. class. So please use layman terms. I'm working on a wireless power transfer system. (Like those wireless power phone charging pads).There are two coils, one that sends power(Tx) and one that receives power (Rx) and materials that can increase wireless power transfer if cleverly placed in either coil. Three materials: sheet material (large and small), and ribbon material.

No material - NM, Large sheet - LS, Small sheet - SS, Ribbon material - RM

From my experiments there are 5 possibilities. 1) I did no materials, 2) SS in the Tx, 3) LS in the Tx, 4) LS in Tx and SS in Rx, 5) RM in TX.

Then wireless power transfer was tested for distances 14cm - 5.5 cm., .5 step

I recently looked into the S.V.D. (part where I'm out of my comfort zone and probably wrong) for data and regression models. I thought it was really fascinating. I made a data matrix where if the category (say no material in Rx) is satisfied it gets a 1. If not then 0 (for me this part was a shot in the dark, it was the only way I could think to make a matrix that could use the SVD). Then all distances from 14 - 5.5. Matrix is 90,7.
Ex: 14 1 0 0 1 0 0, stands for no material in Rx and SS material in Tx at 14 cm

$$\begin{pmatrix} D & NM-RX & NM-TX & SS-RX & SS-TX & LS-TX & TX-R \\ 14 & 1 & 0 & 0 & 1 & 0 & 0 \\ 14 & 1 & 0 & 0 & 0 & 1 & 0 \\ 14 & 0 & 0 & 1 & 0 & 1 & 0 \\ 14 & 1 & 0 & 0 & 0 & 0 & 1 \\ 14 & 1 & 1 & 0 & 0 & 0 & 0 \\ 13.5 & 1 & 0 & 0 & 1 & 0 & 0 \\ 13.5 & 1 & 0 & 0 & 0 & 1 & 0 \\ \vdots \end{pmatrix}$$ Then a vector containing all the matching voltages (my actual experimental data) $$\begin{pmatrix} V \\ 0.23 \\ 0.3 \\ 0.4 \\ 0.3 \\ 0.3 \\ 0.25 \\ 0.4 \\ \vdots \end{pmatrix}$$ I ran some SVD stuff on my data matrix and results. I also randomly shuffled the data/result matrix because I read that helps (which it does) but I have no idea why? The original matrix has some patterns tht mess up the SVD? One dimension is very high, which makes sense because distance is the biggest driving factor. Voltage data shoots up when the coils approach 5 cm. Then some of the other dimensions are around equal size, some are near zero. I ran a Ax = b, least squares thing. and I had some x vector that was a "best fit model?" I plotted the actual voltage results against my best fit model, and was surprised they seem accurate( to me, I have no idea)

There are definitely issues, at close distances (hopefully closer than 5 cm) the materials start affecting each other from something called mutual inductance. Inception thing where wireless voltage magnetic fields start affecting the transmitting fields. I'm wondering if that means at close distances the independent variables start becoming dependent one each other? Also my model shows for some trials, there is negative voltage which can’t be. I'm really curious if what Im doing is worth while. Original data: