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Version 26.1 by Mengting Qiu on 2024/09/02 17:19
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Mengting Qiu 4.1 1 **~ Table of Contents:**
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3 {{toc/}}
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7 = 1. Instroduction =
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10 This chapter shows how to perform linear calibration.
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13 = 2. Linear calibration =
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16 In some case, the measurement and real value are in different range, but they are both linear, we have to calculate the real value with the measurement we can use a simple Linear Calibration.
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Mengting Qiu 8.1 18
19 == 2.1 Solve the linear relationship manually ==
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Mengting Qiu 7.1 22 (% style="color:blue" %)**Example:**(%%) we have a water level probe, the measurement range is 0 ~~ 10 meters, and the output is 4~~20mA, this means the when the water level is 0 meter, the output is 4mA, when the water level is 10 meters, the output is 20mA.
Mengting Qiu 4.1 23
Mengting Qiu 6.1 24 We can make a coordinate axis as below:
Mengting Qiu 4.1 25
Mengting Qiu 7.1 26 1. (% style="color:#4f81bd" %)**Y**(%%) axis is the real value, from 0~~10 meters
27 1. (% style="color:#4f81bd" %)**X**(%%) axis is the probe output , from 4~~20mA
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Mengting Qiu 6.1 29 We use two points to make the linear line: Point1(x1,y1) = (4,0), Point2(x2,y2)= (20,10).
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Mengting Qiu 7.1 31 Since the reading is linear, all (% style="color:#4f81bd" %)**probe output**(%%) and (% style="color:#4f81bd" %)**real value**(%%) is on this line, so we can calculate the real value by probe output in two steps:
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Mengting Qiu 7.1 33 * **Step1:** Get (% style="color:#4f81bd" %)**realk(Slope)**(%%) for the line:
Mengting Qiu 6.1 34
35 k=(y2-y1)/(x2-x1) = (10-0)/(20-4) =10/16= 0.625
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Mengting Qiu 7.1 37 * **Step2:** Get (% style="color:#4f81bd" %)**real value( y )**(%%):
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Mengting Qiu 7.1 39 k =(y-y1)/(x-x1)  
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Mengting Qiu 7.1 41 ~-~-> y = k*(x-x1)+y1 = 0.625 * (x-4) + 0.
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Mengting Qiu 7.1 43 ~= 0.625 * (x-4)
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Mengting Qiu 7.1 45 Thus, we can introduce x-values to the already obtained equations to derive the corresponding y-values：
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Mengting Qiu 7.1 47 When x=12 mA , y=5 meters
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Mengting Qiu 7.1 49 When x=8 mA, y=2.5 meters
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Mengting Qiu 7.1 51
Mengting Qiu 4.1 52 A more general formular:
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Mengting Qiu 22.1 54 (% style="color:blue" %)**Y=(y2-y1)/(x2-x1)* (x-x1) + y1**
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Mengting Qiu 7.1 57 Calibration Curve Schematic：
Mengting Qiu 4.1 58
Mengting Qiu 14.1 59 [[image:image-20240902114541-1.png||height="336" width="596"]]
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Mengting Qiu 8.1 62 == 2.2 Performing linear calibration curves in Excel ==
Mengting Qiu 7.1 63
Mengting Qiu 8.1 64
65 In addition, we can also perform calibration curves in Excel and directly obtain linear equations by statistics of X and Y values.
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Mengting Qiu 14.1 67 Citing the same example above, (% style="color:#4f81bd" %)**X**(%%) and (% style="color:#4f81bd" %)**Y**(%%).
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Mengting Qiu 14.1 70 === Step 1: Create chart ===
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Mengting Qiu 14.1 73 A simple spreadsheet with two columns: X values and Y values.
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Mengting Qiu 14.1 75 [[image:image-20240902160516-1.png||height="404" width="561"]]
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Mengting Qiu 14.1 77 * Start by selecting the data you want to plot in the chart.
78 * First, select the X-Value column cell, then press the Ctrl key, and finally click the Y-value column cell.
Mengting Qiu 8.1 79
Mengting Qiu 14.1 80 [[image:image-20240902160755-2.png||height="394" width="562"]]
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Mengting Qiu 22.1 82 * Go to the "(% style="color:#4f81bd" %)**Insert**(%%)" TAB, navigate to the "(% style="color:#4f81bd" %)**Chart**(%%)" menu, and then select the first option in the "(% style="color:#4f81bd" %)**Scatter**(%%)" drop-down list.
Mengting Qiu 14.1 83 * A chart will appear with the data points in the two columns.
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85 [[image:image-20240902161202-3.png||height="453" width="824"]]
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Mengting Qiu 22.1 87 * Right-click on one of the blue dots and select the (% style="color:#4f81bd" %)**"Add Trendline" **(%%)option.
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89 [[image:image-20240902161711-4.png||height="490" width="681"]]
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91 * A straight line will appear on the chart.
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Mengting Qiu 22.1 93 On the right side of the screen, the Format Trendline menu will appear. Check the boxes next to (% style="color:#4f81bd" %)**"Show formulas on chart" **(%%)and (% style="color:#4f81bd" %)**"Show R-squared values on chart"**(%%).
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Mengting Qiu 22.1 95 The R-squared value is a statistic that tells you how well the line fits the data. The best R-squared value is **1.000**, which means that every data point touches the line.
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Mengting Qiu 22.1 97 Because the ideal data example is used, the R-squared value in this case is 1.
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Mengting Qiu 22.1 99 As the difference between the data points and the line increases, the R-squared value decreases, with **0.000** being the lowest possible value.
Mengting Qiu 14.1 100
Mengting Qiu 22.1 101 The equation is of the form (% style="color:blue" %)**"y = kx + b"**(%%),(% style="color:blue" %)** **(%%)where (% style="color:blue" %)**k**(%%) is the slope and (% style="color:blue" %)**b**(%%) is the y-intercept of the line.
Mengting Qiu 14.1 102
Mengting Qiu 22.1 103 [[image:image-20240902161857-5.png||height="559" width="1103"]]
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105 * Calibration is complete. The user can customize the chart by editing the title and adding the axis title.
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107 [[image:image-20240902163527-7.png||height="349" width="656"]]
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110 === Step 2: Calculate the line equation and R-squared statistic ===
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112 * Write the Slope formula in the formula bar according to the original x and y values statistics table.
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114 [[image:image-20240902164104-8.png||height="503" width="492"]]
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117 * Write Intercept formula in the formula bar according to the original x and y value statistics table.
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119 [[image:image-20240902164156-9.png||height="525" width="488"]]
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122 * Write Correl's squared formula in the formula bar based on the original x and y statistics table.
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124 The CORREL function returns "R", so we have to square it to compute "R squared".
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126 [[image:image-20240902164503-11.png||height="523" width="743"]]
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129 * These values match those shown in the chart.
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131 [[image:image-20240902164910-12.png||height="420" width="897"]]
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134 === Step 3: Set up formulas to quickly calculate X and Y values. ===
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Mengting Qiu 4.1 143 = 3. Case examples =
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146 Some case for example which we can use Linear Calibration:
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Mengting Qiu 7.1 149 (% style="color:blue" %)**Case 1: Calibrate Microwave Radar Readling.**
Mengting Qiu 4.1 150
151 The microwave radar reading might effect by the OUM(Object Under Measured), but the reading still linear. In this case, we can measure the closest(x1,y1) and the farthest point(x2,y2). Where the x is reading in platform, y is the real value. And use above method to calibrate.
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Mengting Qiu 7.1 154 (% style="color:blue" %)**Case 2: Calibrate the Soil EC base on SE01 soil sensor raw EC reading.**
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156 The SE01 probe is calibrated via mineral soil. The reading for other soil will be different by still in linear, In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of Raw EC, y is the real EC for the soil. And use above method to calibrate
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Mengting Qiu 7.1 159 (% style="color:blue" %)**Case 3: use water level probe to calibrate for oil.**
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161 Oil has different density vs water, but we can still use the immersion type water level pressure sensor to get the oil level. In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of water level, y is the oil level. And use above method to calibrate
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Mengting Qiu 7.1 164 (% style="color:red" %)**Notice for Linear Calibrate:**
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166 1. k(Slope) is very important, We can measure more points to calculate the most accuracy k.
Mengting Qiu 7.1 167 1. Make sure the mapping is linear, and choose two calibrate points as "far" as possible.
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