Utilities

94aec2de-0157-4f8f-9703-0177b1515298 35 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

x β f β 1 el x X 1 el - (β 2 el^* Y 1 el + : x α β f β 1 el x α 1 el - (β 2 el^* α 2 el + : 21 sys 011 mat 12 mat

Grand champion: 1. Iterate Genfit on (x+ε), single set of initials. 2. Two parameters from initial experiment [X1, Y1]

β 1 el β 2 el 1 x β 3 el - / (sqrt * - exp * 111 mat β 1 el x * 1 Ug x / exp + ln * (β 2 el^β 3 el + 211 mat 22 mat

x φ 1 x x 2^13 mat transpose : 711 mat 12 mat

x β f β 1 el x ln * β 2 el x sqrt * + β 3 el + : 311 mat x β f β 1 el x β 2 el^- (β 1 el^sqrt β 3 el + : 411 mat 22 mat

j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

Not retained for the project in context t XFR K.p 1 α β α - (/ t - xo - α / exp * + β β α - (/ t - xo - β / exp * - (* : 511 mat 12 mat x β f β 1 el 1 β 2 el β 3 el x * - exp * + / β 4 el x 1 - exp / + : 611 mat 12 mat 21 mat

x fit b x φ * :

Utilities

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

1753503131 mat

1753503131 mat

range 13321 mat 52621 mat 103121 mat 153621 mat 203721 mat 253721 mat 303721 mat 17 mat :

region 1=> too uncertain

β 190380 38.5 31 mat 175350 30.65 31 mat 175350 30.65 31 mat 175350 30.65 31 mat 175350 30.65 31 mat 175350 30.65 31 mat 175350 30.65 31 mat 17 mat :

1753503431 mat

180360 35.5 31 mat

190380 38.5 31 mat

200400 41.6 31 mat

system

system 1 0.0022 11 0.0803 21 0.2117 31 0.3798 41 0.5776 51 0.8013 61 1.0482 71 1.3163 81 1.604 91 1.91 101 2.2333 111 2.5731 121 2.9285 131 3.2989 141 3.6838 151 4.0826 161 4.4947 171 4.9199 181 5.3578 191 5.8079 201 6.2699 211 6.7436 221 7.2286 231 7.7247 241 8.2317 251 8.7494 261 9.2774 271 9.8157 281 10.364 291 10.9221 301 11.4899 311 12.0672 321 12.6539 331 13.2498 341 13.8547 351 14.4686 361 15.0913 372 mat 1011021031041051 0.0022 61 0.0803 71 0.2117 81 0.3798 91 0.5776 101 0.8013 111 1.0482 121 1.3163 131 1.604 141 1.91 151 2.2333 161 2.5731 171 2.9285 181 3.2989 191 3.6838 201 4.0826 211 4.4947 221 4.9199 231 5.3578 241 5.8079 251 6.2699 261 6.7436 271 7.2286 281 7.7247 291 8.2317 301 8.7494 311 9.2774 321 9.8157 331 10.364 341 10.9221 351 11.4899 361 12.0672 372 mat 10110210310410510610710810910101 0.0022 111 0.0803 121 0.2117 131 0.3798 141 0.5776 151 0.8013 161 1.0482 171 1.3163 181 1.604 191 1.91 201 2.2333 211 2.5731 221 2.9285 231 3.2989 241 3.6838 251 4.0826 261 4.4947 271 4.9199 281 5.3578 291 5.8079 301 6.2699 311 6.7436 321 7.2286 331 7.7247 341 8.2317 351 8.7494 361 9.2774 372 mat 1011021031041051061071081091010101110121013101410151 0.0022 161 0.0803 171 0.2117 181 0.3798 191 0.5776 201 0.8013 211 1.0482 221 1.3163 231 1.604 241 1.91 251 2.2333 261 2.5731 271 2.9285 281 3.2989 291 3.6838 301 4.0826 311 4.4947 321 4.9199 331 5.3578 341 5.8079 351 6.2699 361 6.7436 372 mat 101102103104105106107108109101010111012101310141015101610171018101910201 0.0022 211 0.0803 221 0.2117 231 0.3798 241 0.5776 251 0.8013 261 1.0482 271 1.3163 281 1.604 291 1.91 301 2.2333 311 2.5731 321 2.9285 331 3.2989 341 3.6838 351 4.0826 361 4.4947 372 mat 10110210310410510610710810910101011101210131014101510161017101810191020102110221023102410251 0.0022 261 0.0803 271 0.2117 281 0.3798 291 0.5776 301 0.8013 311 1.0482 321 1.3163 331 1.604 341 1.91 351 2.2333 361 2.5731 372 mat 1011021031041051061071081091010101110121013101410151016101710181019102010211022102310241025102610271028102910301 0.0022 311 0.0803 321 0.2117 331 0.3798 341 0.5776 351 0.8013 361 1.0482 372 mat 17 mat :

xy system 1 j el : sub range 1 j el 1 el : end range 1 j el 2 el : 31 line

empirical convenient approximation 1 K.gk / μ V.gk * x + (32 / (^* x μ V.gk * + (32 /^K.gk / ≡

Explorer

j 4 :

xy 11 mat 1011021031041051061071081091010101110121013101410151 0.0022 161 0.0803 171 0.2117 181 0.3798 191 0.5776 201 0.8013 211 1.0482 221 1.3163 231 1.604 241 1.91 251 2.2333 261 2.5731 271 2.9285 281 3.2989 291 3.6838 301 4.0826 311 4.4947 321 4.9199 331 5.3578 341 5.8079 351 6.2699 361 6.7436 372 mat 11 mat

XY system 1 j el sub end 12 submatrix : X XY 1 col : Y XY 2 col : n X rows : 13 mat XY X Y augment : data XY o 5 black plot : 41 line

The classical 2nd order XFR system

in some ways: undefined xo X 1 el - : 141 -

XFR 2nd order system ... Kp [Process gain], α,β [Dynamics] x β f β 3 el 1 β 1 el β 2 el β 1 el - (/ x xo + (- β 1 el / exp * + β 2 el β 2 el β 1 el - (/ x xo + (- β 2 el / exp * - (* :

β β 1 j el :

x c 1 xo - x ≤ (x 375 ≤ (& cases :

Absolute  residuals δ j 1 X rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

xo - 1 xo - 1 - 2 2 mat x β f x c * XY o 5 black plot 3 1 sys

bar δ Error :

bar 0 2 1 sys

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.0177

NOTES: 1. "system" is extracted from "Project Tesla_CBG_R1 [optimized].sm" 2. In this XFR model, β1, β2 are tentative, not exclusive of others.

experimental 2 parameter model function
  β [1,2].... X1, Y1 initial experiment. β 1 el x X 1 el - (β 2 el^* Y 1 el +

phenomenological XFR 'one' paramater.
β1, β2 are constants ... β3 scale β 3 el 1 β 1 el β 2 el β 1 el - (/ x xo + (- β 1 el / exp * + β 2 el β 2 el β 1 el - (/ x xo + (- β 2 el / exp * - (*

datumY Y Y rows el : datumX X X rows el : 21 mat 6.2699 35121 mat

xo - 141

x u 1 xo - x ≤ (cases :

The mother XFR phenomenological

x β f x u * xo - 10 xo - 10 - 2 2 mat datumX datumY + 20 red 1 5 mat 3 1 sys

xo 2 - :

α β t XFR 11 α β α - (/ t xo + (- α / exp * + β β α - (/ t xo + (- β / exp * - (* :

Demo for demonstrating the XFR shifted by xo, modeled [α,β]

1 2 x XFR x u * 2 4 x XFR x u * 3 6 x XFR x u * 3 1 sys