![]() ![]() Some devices may deviate from the line that we cannot precisely, or maybe we cannot predict precisely enough for the measurements we need to make. If we switched the x and y-axis, we would develop a formula for solving for Response = A 1 * (Force) + A 0 Figure 1 shows us a force-measuring device with consistent linear behavior. ![]() We can modify this formula to use coefficients, and it would become Force = B 1 * (Response) + B 0. The standard formula of y = mx + b, where m designates the slope of the line, and where b is the y-intercept that is b is the second coordinate of a point where the line crosses the y-axis. One would typically find the slope of the line, which could predict other points along the line. ![]() Straight-line equations such as y = mx + b is common for force-measuring devices shown in figure 1. ![]() Calibration Coefficients Straight Line Fits Almost any force-measuring device can be characterized using standard equations many will remember from algebra classes they may have had in high school.įigure 1 Load Cell Curve Using the Equation for a Straight Line Where Y - Values are Force and X -Values are Response (What the Instrument Reads). To use a fit above the 2nd-degree (or quadratic) requires the force-measuring device to have a resolution that exceeds 50,000 counts. The ASTM E74 standard has additional requirements for higher-order fits. We can use these equations to predict the appropriate coordinate more accurately for any point in the measurement range, typically above the first non-zero point on the curve. That output can either be the Force at a specific response or the Response when the Force is known. The higher the variance, the larger the reproducibility error in the standard uncertainty becomes, which raises the Lower Limit Factor (ASTM E74) or Reproducibility b (ISO 376). When calibrating to a standard such as ASTM E74, or ISO 376, we often refer to this grouping as between run variance. This assumes multiple measured values of the force-measuring device are grouped closely together. In simple terms, these higher-order fits give instructions on how best to predict an output given a measured input. Both Standards use observed data, and they both fit the data to a curve. These standards may use higher-order fits such as a second or third-order fit (ISO 376) or ASTM E74 allows higher-order fits up to as high as a 5th order. Plt.ASTM E74, ISO 376, and other standards may use calibration coefficients to characterize the performance characteristics of continuous reading force-measuring equipment better. Plt.plot(h, y_fit_1) # plot the equation using the fitted parameters Plt.plot(comboX, comboY, 'D') # plot the raw data Y_fit_2 = mod2(h, a, b, c) # second data set, second equation Y_fit_1 = mod1(h, a, b, c) # first data set, first equation # curve fit the combined data to the combined functionįittedParameters, pcov = curve_fit(comboFunc, comboX, comboY, initialParameters) # single data set passed in, extract separate dataĮxtract1 = comboData # first dataĮxtract2 = comboData # second data Y2 = np.array()ĭef mod1(data, a, b, c): # not all parameters are used hereĭef mod2(data, a, b, c): # not all parameters are used here This is not intended as a direct answer, but is here so that I can post formatted code. Per my comment, here is working Python code that fits two data sets to two straight lines with different slopes and a single shared offset parameter. I have used nlsLM to model the curves individually but I have been unable to find a method to model together with the shared parameters "a" and "n". # values - These are re-sampled to reduce the number of points This is a curve fitting so I have values for the following: #Parameters: These are currently guesstimates but will ultimately be Hi I am trying to curve fit 2 models (Van Genuchten & Mualem) with shared parameters in r. ![]()
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