Calibration Experimental Method SEMM 1911 PDF

Calibration Experimental Method SEMM 1911 DR MOHD KAMEIL BIN ABDUL HAMID 1  Contents Introduction to calibration. Sensitivity, Range, Accuracy and Precision of a measuring system. Sequence Calibration and Random Calibrati...

Calibration Experimental Method SEMM 1911 DR MOHD KAMEIL BIN ABDUL HAMID 1  Contents Introduction to calibration. Sensitivity, Range, Accuracy and Precision of a measuring system. Sequence Calibration and Random Calibration. Hysteresis, Linearity, Sensitivity, Zero and Repeatability Errors. Standards. 2  Introduction Definition of calibration: Applying a known value to the input of the measuring system for the purpose of observing the system’s output. Establishing the relationship between the input (independent variable) and output (dependent variable) of the measuring system. 3  Introduction Calibration involves comparing the calibrated instrument/equipment with: a primary standard. a secondary standard with higher accuracy. a known input source. 4  Introduction Example of calibration process: Correct data ??? x0 kg z0 kg Weighing Scale y0 kg 5  Introduction 100 kg 85 kg 50 kg Known input 20 kg 55 kg (standard) Weighing Scale Output (indicated values) 6  Introduction Example of calibration: Yes, Correct !! x1 kg z1 kg Weighing Scale y1 kg 7  Introduction Static calibration: Values of the measured variable(s) remain constant against time. Only the magnitude of the known input and the measured output are important. Dynamic calibration: Involves time dependent variable(s). Determine the relationship between an input of known dynamic behaviour and the measurement system output. 8  Sensitivity Slope of the graph obtained from a static calibration. Static sensitivity, K, at a particular static input, x1, is defined as: K = Kx1 = (dy/dx)x=x1 Relationship of a change in the indicated output associated with the change in the static input. The smallest change in measurement that the measuring system can detect. 9 Sensitivity 10  Range Range: maximum value – minimum value. Proper calibration should cover the range for which the measurement system is to be used. Defines the operating range for the measuring system. ri is input range, rout is output range. ri = xmax – xmin Avoid taking measurements outside the calibration range. 11  Accuracy Accuracy of the measurement refers to the ability of the measuring system to indicate a true value. True value (in this case) is the known input value during the calibration. Absolute error is the difference between the true value (known input value) applied to the system and the indicated value from the system. abs. error, e = true value – indicated value 12  Accuracy Accuracy can be determined only during the calibration, since “true value” in this context is the known input value applied to the measurement system during the calibration. Percent relative accuracy: A = 1 – (e/true value) x 100 13  Precision Precision (repeatability) is the ability of the measuring system to indicate a particular value upon repetition with independent applications of a specific input value. A measuring system can be precise while at the same time has low accuracy. 14  Sequence Calibration Applying sequential variation on the input value over the desired input range during calibration. It can be either upscale direction (increasing the input value) or downscale (decreasing the input value). Effective to identify and quantify hysteresis. Hysteresis (hysteresis error, eh) is the difference between upscale and downscale calibration. eh = yupscale – ydownscale 15  Hysteresis ro Occurs when the output is dependent on the previous value indicated by the system. Usually specified in terms of maximum hysteresis error as a percentage of full-scale output range (FSO). %eh = (eh_max / ro ) x 100 16  Random Calibration Applying the selected values of a known input in a random sequence over the intended calibration range. Breaks up hysteresis and observation errors. More closely simulate the actual measuring situation. Provides diagnostic test for delineation of several performance characteristics. Linearity error, sensitivity error, zero error and repeatability error can be quantified from a static random calibration. 17  Linearity error Many measuring equipments are designed to achieve a linear relationship between applied input (x) and indicated output (y). General form of linear static calibration: yL(x) = a0 + a1x The curve yL(x) provides a predicted output value based on the linear relationship between x and y. In reality, truly linear curve is only approximated. The relation between yL and the measured y is the measure of the non-linear behaviour of the system. linearity error, eL(x) = y(x) – yL(x) 18 Linearity error Usually specified in terms of maximum expected linearity error as a percentage of full-scale output range (FSO). %eL = (eL_max / ro ) x 100 19  Sensitivity error Scatter in the measured data during calibration affects the precision in the calibration. Sensitivity error, ek, is a statistical measure of a precision error in the estimate of the slope of calibration curve. 20 Zero error The figure shows zero error is not fixed and sensitivity is constant throughout the range. Zero error, ez, is the shift of the zero intercept of the calibration curve 21  Repeatability The ability of the system to indicate the same value upon repeated but independent application of the same input. Based on statistical measure of standard deviation, Sx, a measure of the variation in the output for a given input. Reflects only the error found under the controlled calibration conditions. Not including other errors during the actual measuring process. 22 Repeatability Usually specified in terms of maximum expected error as a percentage of full-scale output range (FSO). %er = (2Sx / ro ) x 100 23  Standard A measurement system is calibrated by comparing it with several standards whose values are already known beforehand. It could be (1) an equipment that is well trusted by the user, or, (2) an object that has well formulated physical properties, or, (3) well- accepted technique that produces values that can be trusted. 24  Unit versus dimension Dimension: physical variable used to specify the behaviour/nature of a particular system/object. Eg: length, mass, time. Unit: term that is used to measure the dimension. Eg: m, kg, s. Unit is defined by primary standard so that it can be exact and accurate. Each unit is defined by agreements internationally to avoid confusions. Considerations for primary standard: universal availability, continuous reliability, stability and minimum sensitivity to surrounding elements. 25  Unit versus dimension International Measuring System (SI) only provide standard for four basic dimensions: mass, length, time and temperature. Standard for other dimensions are derived from here. Standard Mass: defined as one unit kilogram in SI unit, is the mass of a platinium-iridium bar kept at International Bureau of Weight and Measures, France. Standard Length: defined as one metre in SI unit, equivalent to a distance travelled by light in vacuum in 3.335641 x 10 -9 sec. 26  Hierarchy of Standard Primary standard: the ultimate reference, often impractical. Secondary standard: the duplicate and close approximation of the primary standard, due to impracticality of the primary standard. Go down the hierarchy, increases chances of uncertainty/errors 27  Hierarchy of Standard Standard can also be used to refer a procedure (like standard operating procedure, SOP). The purpose of standard procedure is usually to ensure a proper way in conducting an experiment/ measurement. In Malaysia, SIRIM is responsible to maintain secondary standard for national level. Some companies also have their own standards. All calibration equipments/companies need to be calibrated/checked by SIRIM before they can do calibrations. 28