curve fitting... tell me about it!!! :( [MATLAB]

[insomartin]

can't wait for a mcu code!

[z22]

Hmm paano ba i-eexplain....
Kung log yung scale ng y-axis, almost linear yung mga curves, so transform the measured resistance and the table to the log domain (parang dB lang), then use bilinear interpolation to get the RH value. Kasi kung yung raw values yung gagamitin, baka bicubic interpolation yung kailangan, eh medyo mahirap yun (I'm still reading Numerical Recipies). Pwede kaya?
If not, pwede kaya yung model na

R = SUM(i=0..5, j=0..7)a_ijTⁱH^j,

R = resistance, T = temperature, H = RH, a_ij yet to be determined.

[insomartin]

that is where i can't answeeer.
http://www.intmath.com/Exponential-logarithmic-functions/7_Graphs-log-semilog.php
sa pinaka babang page may applications. hope that could help...

madaming CNC codes na ginagamit ko using spline curves and linear interpolate. but walang source code...

[z22]

Same table, but resistance in Kohm replaced with log10(resistance in Kohm):

Code:

       15.000 25.000 35.000 45.000 55.000
------------------------------------------
20.0 |  4.000  3.699  3.491  3.243  3.068
30.0 |  3.367  3.114  2.875  2.633  2.447
40.0 |  2.740  2.491  2.279  2.061  1.857
50.0 |  2.190  1.940  1.748  1.580  1.398
60.0 |  1.708  1.491  1.301  1.176  1.041
70.0 |  1.301  1.114  0.954  0.833  0.740
80.0 |  0.919  0.756  0.623  0.519  0.431
90.0 |  0.613  0.431  0.322  0.230  0.146

Suppose the temperature is 29 degrees C. Interpolate the values between the 25 degrees and 35 degrees column:

Code:

       25.000 29.000 35.000
----------------------------
20.0 |  3.699  3.616  3.491
30.0 |  3.114  3.018  2.875
40.0 |  2.491  2.406  2.279
50.0 |  1.940  1.863  1.748
60.0 |  1.491  1.415  1.301
70.0 |  1.114  1.050  0.954
80.0 |  0.756  0.703  0.623
90.0 |  0.431  0.388  0.322

If the measured resistance is 100K, log10(100) = 2. Interpolate again using the 29 degrees column, the RH is 47%

Tanong ko lang po, paano yung mapping from resistance to measured ADC value, check ko sana sa generated table.

[marcelino]

very simple yung circuit na ginawa ko... parang ganito:


RE0 = HIGH;
some_delay(x);    //to emulate half of my preferred frequency (half lang.)
var0 = read_adc();
RE0 = LOW;
some_delay(x);   
RE1 = HIGH;
some delay(x);
var1 = read_adc;
RE1 = LOW;
some delay();

so makikita natin na dalawang readings ang makukuha, var0 and var1.... the values presented by these two are 10-bits. so ang total nyan ay nasa 1024... actually nag-eexceed, pero ok lang yun. di naman ganun ka accurate yung ginagawa kong data gathering, but at least, i can read the changes of the resistance. i will just cheat the output by having to compare it with the existing (commercial) hygrometer. dagdag-bawas nalang siguro.

makikita natin during RE0 = HIGH, RE1 = LOW - providing a voltage divider among the 39k and the sensor. then mababasa na yung var0. in reverse, mababasa yung var1. pero i based my calculation from the reading of the 39k. so mas importante saaking yung readin of var1.

ang ginawa ko nalang ay mag set na ng table. given var1 and the temperature, hahanapin nya yung row number, which is the humidity. so kailangan ko talgang i plot ang bawat content ng axis.

eto, using cubic spline, nagawa ko to (just part of the generated values):

Code:

TEMP 23 24 25 26 27 28 29
--------------------------------------------------------------
20 5648.24 5307.00 5000.00 4724.00 4475.76 4252.03 4049.58
21 5016.94 4715.44 4443.33 4197.89 3976.39 3776.08 3594.25
22 4439.72 4174.43 3934.20 3716.74 3519.79 3341.06 3178.28
23 3913.99 3681.57 3470.33 3278.41 3103.93 2945.00 2799.76
24 3437.16 3234.43 3049.46 2880.75 2726.75 2585.94 2456.79
25 3006.64 2830.59 2669.32 2521.59 2386.19 2261.89 2147.47
26 2619.84 2467.65 2327.63 2198.81 2080.22 1970.90 1869.89
27 2274.18 2143.19 2022.12 1910.24 1806.78 1711.00 1622.17
28 1967.05 1854.79 1750.53 1653.73 1563.81 1480.22 1402.39
29 1695.88 1600.02 1510.58 1427.14 1349.28 1276.59 1208.65
30 1450.16 1372.82 1300.00 1230.99 1165.52 1103.43 1044.56
31 1240.15 1176.72 1116.52 1058.79 1003.35 950.18 899.28
32 1059.76 1007.67 957.87 909.56 862.66 817.23 773.34
33 906.16 863.16 821.78 781.25 741.53 702.74 665.01
34 776.56 740.67 705.97 671.77 638.03 604.91 572.54
35 668.15 637.68 608.18 579.04 550.23 521.90 494.16
36 578.10 551.67 526.14 500.99 476.21 451.90 428.15
37 503.63 480.13 457.57 435.55 414.03 393.08 372.74
38 441.91 420.53 400.20 380.63 361.77 343.62 326.19
39 390.14 370.37 351.77 334.17 317.50 301.71 286.74

converting to the voltage across 39k (integer value na):
value = (39k*1024)/(39k+var1)

Code:

TEMP 23 24 25 26 27 28 29
-----------------------------------------------------------
20 7 7 8 8 9 9 10
21 8 8 9 9 10 10 11
22 9 9 10 11 11 12 12
23 10 11 11 12 13 13 14
24 11 12 13 14 14 15 16
25 13 14 15 16 16 17 18
26 15 16 17 18 19 20 21
27 17 18 19 20 22 23 24
28 20 21 22 24 25 26 28
29 23 24 26 27 29 30 32
30 27 28 30 31 33 35 37
31 31 33 35 36 38 40 43
32 36 38 40 42 44 47 49
33 42 44 46 49 51 54 57
34 49 51 54 56 59 62 65
35 56 59 62 65 68 71 75
36 65 68 71 74 78 81 85
37 74 77 80 84 88 92 97
38 83 87 91 95 100 104 109
39 93 98 102 107 112 117 123

so kapag nakaread ako ng value ng 101 and the temperature is 27degrees. i put that value under 100 na kasi di naman nagexceed sa 112 (the next value with 27deg). then the humidity will be 38%RH.]

nga pala, i have decided of using cubic spline nalang... i might not include the equation on the documentation... sasabihin ko nalang na generated nalang using MATLAB.

pero baka may suggestion kayo... open pa naman.

[z22]

1. Look up table: 1491 values, simple code.
2. Smaller look up table + bilinear interpolation
3. Bicubic spline interpolation: bad idea, sobrang daming coefficients (16 per grid square)

LUT na lang...

[marcelino]

^another thing... kukunin ko lang naman yung from 15 - 35deg ... di na kasi realistic ibang temp range. (at least for time being - wait fo the global warming.)

so LUT nalang. thanks sa suggestion. and thank you for the comparison.

did you know that that table consumed 5% of my 64k ROM? hehehe pic18f4620.
may idadagdag pa akong isa after characterization ko nung moisture sensor ko, gypsum block...
(eto naman ay weight vs resistance or voltage)

[z22]

Isa pa pala, delta compression. Store mo lang yung diffrence from the last, para kasya sa isang byte, or less

[marcelino]

Isa pa pala, delta compression. Store mo lang yung diffrence from the last, para kasya sa isang byte, or less

papano yan

di ko gets... 

[z22]

Ex. may 4 akong values
900 915 923 933
10 bits each for storage = 40 bits total

Ganito gagawin
915-900=15
923-915=8
933-923=10
Yung mga differences pwedeng 4 bits lang
Ang ilalagay mo sa memory
900 15 8 10
22 bits lang kailangan

[marcelino]

Ex. may 4 akong values
900 915 923 933
10 bits each for storage = 40 bits total

Ganito gagawin
915-900=15
923-915=8
933-923=10
Yung mga differences pwedeng 4 bits lang
Ang ilalagay mo sa memory
900 15 8 10
22 bits lang kailangan

ayos yang technique na yan ah... very useful lalo na siguro kung sobrang dami ng inputs... 
nakikita ko, mas mabilis pa ang accessing ng data...
sige try ko to kung magkaroon pa ako ng time mag code. honestly, halos tapos na kasi. isa pa, 5 nodes lang naman ang babasahin ko...

nice learning! pogi mo!!!

[z22]

Mula sa table, 15 degrees column:

x[1] = 4
x[2] = 4
x[3] = 5
x[4] = 5
x[5] = 6
...
x[69]  = 906
x[70] = 916
x[71] = 927


Gagamit tayo ng linear predictor x'[n] = 3*x[n-1] - 3*x[n-2] + x[n-3] and measure its error e[n] = x'[n] - x[n].
Given na yung unang 3 values: 4, 4, 5.
Predicted 4th value: x'[4] = 3*x[3] - 3*x[2] + x[1] = 3*5 - 3*4 + 4 = 7.
Prediction error: e[4] = x'[4] - x[4] = 7 - 5 = 2.

Tuloy tuloy lang...
x'[5] = 4, e[5] = -2
x'[6] = 8, e[6] = 1
x'[7] = 8, e[7] = 0
...
x'[69] = 908, e[69] = 2
x'[70] = 916, e[70] = 0
x'[71] = 926, e[71] = -1

Ang ilalagay mo sa memory ay x[1], x[2], x[3], e[4], e[5], e[6], ..., e[69], e[70], e[71]:

4, 4, 5, 2, -2, 1, 0, -1, 2, -3, 2, -1, 1, -1, 0, 1, 0, 0, 1, 0, -2, 1, -2, 0, 0, 0, -3, 1, -2, -2, 2, 0, 6, 4, 6, 1, 3, -4, -4, -5, -4, -3, 0, 1, -1, 1, 1, -1, 1, 1, 4, 2, 0, 3, -2, 2, -3, 2, -3, -1, 0, -2, 0, 0, 1, -2, 3, -3, 2, 0, -1

Kasya na sa 4-bit signed integer yung bawat value, so yung buong table 746 bytes. Yung post ko kanina (store the difference) kailangan ng 6 bits per value.

Madali lang i-reconstruct yung actual values: x[n] = x'[n] - e[n].

[piona]

dapat may inverse curve equation basi sa R versus H values e, para ipadaan mo lang yong inputs sa equation ayos na, kahit anong values okay....

w8 gawa ako ng inverse curve function....

[piona]

Eto sampol ng R versus H inverse curve:



kailangan to para paggawa ng circuit ipadaan lang ang sensor input don sa equation okay na, either > or < the resultant values would trigger whatever, depende na lang sa application nito.

i think the thread starter wants to fit the R-H curve relationship into a formula or equation to use the sensor in the circuit at any given analog values of the sensor.

[piona]

all i got for 15degC



yong RH30 parang imposible  

[e.novacek]

Isa pa pala, delta compression. Store mo lang yung diffrence from the last, para kasya sa isang byte, or less

also known as "finite difference" technique or the difference method..

[insomartin]

i'm trying to solve this using eureqa...

and walang sin/cos/log sa flowcode... help naman.

[insomartin]