MMU 370, Handout_1, Dr. Koksal, Dr. Sümer General Characteristics of Measurement Systems and Basic Concepts The objective in any measurement system is to establish values for certain unknown physical variables. These unknown physical variables are known as measured variables or measurands. Examples of measurands include temperature, pressure, velocity, and strain. The measurement system senses the measurand and produces a unique numerical value that describes it. A typical measurement system can be viewed as consisting three sub-systems: Measurand Sensor (Transducer) A sensor is a physical element that uses some natural phenomenon to sense the measurand and converts this sensed information into a detectable form (electrical, mechanical or optical) Examples: Spring, bourdon tube for pressure, orifice, resistance sensors, capacitance sensors, thermocouples Signal Conditioning Modifies the signal into form usable by output stage. Usually increases amplitude, power of the signal. It may also selectively filter unwanted components in the signal Examples: Gears, mirrors, lenses, amplifiers (electrical), filters (electrical) Output, Readout, Recording Provides an indication of the value of the measurand. It can also record data digitally on a computer. It could be a simple moving pointer, digital scale, oscilloscope, or a data acquistion card and a PC. MMU 370, Handout_1, Dr. Koksal, Dr. Sümer Measurement Process Errors and Related Definitions The error in a measurement system is defined as: = Measured value – True Value • Error cannot be known (unless we have another device measuring the same variable) since the “true value” is not known. • We can only estimate the uncertainty of the measurements. For instance: T = 10C 0.5C with 95% confidence. With 95% confidence, the uncertainty of the measurements is 0.5C. Error will be less than 0.5C in 95% of the measurements. Out of 100 measurements, 95 will fall in between 9.5C and 10.5C. Errors that arise in a measurement process can be classified in two groups (1998 ASME Guidelines): • Systematic (Bias, Fixed) Errors • Random (Precision) Errors Systematic Errors: consistent, repeatable errors that occur the same way when a measurement is made. For instance, a pressure gage which gives a consistent 5% low reading. Systematic errors determine the accuracy of the overall measurement process. Random Errors: Random errors are related to the scatter of the data under fixed conditions. They are unrepeatable errors. MMU 370, Handout_1, Dr. Koksal, Dr. Sümer Random errors determine the repeatability (or the precision) of the measurement process. A and B shoot at a target five times. A B Who has more systematic (bias) error? Who has more random error? Who is more accurate? Who is more precise? One can estimate: Random Error of a Measurement = Reading – Avg. of the readings Bias Error = Avg. of the readings – true value What are the sources of errors? Systematic Error Sources: Calibration errors, loading errors (insertion of the measuring device altering the measurand), defective equipment, certain consistently recurring human errors. MMU 370, Handout_1, Dr. Koksal, Dr. Sümer Remedy: High quality calibration Random Error Sources: Fluctuating experimental conditions, disturbances to the equipment, electric/magnetic fields caused by building wiring, voltage fluctuations, lighting interference. Remedy: Shielding, grounding, careful control of the external conditions. Definitions Related to Instrumentation and Instrument Errors Calibration: Relationship between the value of the input to the measurement system (instrument) and the system’s output is established with calibration. Range of an Instrument • Describes the values of a measurand to which the instrument will respond properly (input range) • Describes the values of the output from the instrument corresponding to input range (output range). • Span: Difference between the upper and lower values of the range. For instance for our transducer: ri = input span = Pmax - Pmin ro = output span = Vo, max - Vo, min (also known as FSO = full scale output) A voltmeter, for instance, with a range of 5 V, has a span of 10 V. Accuracy of an Instrument It is defined as the difference between the measured and true values. Instrument manufacturers usually state a value for accuracy as part of device MMU 370, Handout_1, Dr. Koksal, Dr. Sümer specifications obtained from calibration. It usually includes hysteresis, linearity and repeatability errors of the instrument. Typical specification would be, for instance, ± 0.2 % of FSO If FSO of a pressure gage is 100 psi and the accuracy is specified as ± 0.2 % of FSO, the uncertainty will be ± 0.2 psi. Specific Errors Related to Instruments (usually specified by the manufacturer) Hysteresis: For the same value of the measurand, different output readings may be obtained if the measurand was increasing prior to the reading than if the measurand was decreasing. This is known as hysterisis. Hysteresis can be caused by friction and mechanical flexure of internal parts. Typical specification: 0.20 % of FSO Linearity Error: Although not a requirement for a measurement system, it is highly desirable that it has a linear relationship between input and output. However, a system designed for linear input-output may show non-linear behavior known as linearity error. Typical specification: 2.0 % of FSO Sensitivity Error: Sensitivity is determined during a calibration process and error in determining the calibration constant leads to sensitivity error. Typical specification: 0.2 % of reading MMU 370, Handout_1, Dr. Koksal, Dr. Sümer Repeatability Error: Repeatability is the ability of a device to produce the same output when the same measurand is applied. Inability to repeat a measurement is known as repeatability error. Typical specification: 0.2 % of FSO Resolution Error (Reading Error) Resolution error is related to the smallest increment of input that the instrument can detect. It is usually specified by the manufacturer. If the instrument has a digital display, the reading resolution will be the last digit read. The reading resolution uncertainty (or simply reading error) will be ½ of the last digit read. For instance for a digital display of XXX.XX The reading resolution is 0.01 units The resolution uncertainty is 0.005 units.
