DAS and Sensor Errors

The universal definition for an error is the difference between the measured value and the true value of the measurand (Bolton, 1992; Dunn, 2014; Ida, 2013; McGrath and Ni Scanaill, 2013b; Regtien et al., 2004). Mathematically, it is expressed as:

•_{•= !"#$•!% '"($! − *•$! '"($! ( 2.15 )} Kularatna (2003) defines an error as the difference between the measured value and the true value of the measurand after all corrections have been made. The definition of Kularatna (2003) suggests that some form of corrections or adjustment must be made on the measured value before the final error of measurement is computed. In the real world, there is no such a thing as a true value, as this is actually a theoretical concept (Salicone, 2013). This means the true value is unknown and, therefore, indeterminate (Regtien et al., 2004). Thus, the error magnitude will be unknown (Kularatna, 2003a), which would render equation( 2.15 ) invalid. In practice, the true value is referenced to some absolute or agreed standard (ibid.). Through the referenced standard, this true value can be accepted as having a negligible uncertainty for measurement purposes (Joint Committee for Guides in Metrology (JCGM/WG 2), 2012;

Department of Electrical and Mining Engineering 36 Regtien, 2004). Uncertainty is defined as an estimate of the possible error in a measurement (Kularatna, 2003a). It can be argued that if the true value is estimated to have a very small error – thus negligible uncertainty – and this value is traceable to some standard, then the error can be obtained from equation( 2.15 ).

In the context of sensors, there are two kinds of errors: systematic errors and random errors. They are important in engineering applications and contribute negatively to sensor

performance. In practice, an error is expressed in terms of equation( 2.15 ) or as a percentage of the input full scale (IFS) or percentage of the output full scale (OFS) (Bolton, 1992; Ida, 2013; Johnson, 2000).

2.3.2.1 Systematic Errors

Systematic error is defined “as the closeness of agreement of the mean value of a number of

consecutive measurements of a variable that maintains its value static” (Bagajewicz and

Chmielewski, 2010:4). In addition, the Joint Committee for Guides in Metrology (JCGM/WG 2), 2012:22) defines it “as a component of measurement error that in replicate measurements

remains constant or varies in a predictable manner”. Both definitions essentially mean that

systemic errors are errors that are reproducible (McGrath and Ni Scanaill, 2013b), predictable, constant (Ida, 2013) and inherently present in any measurement done by a sensor. They may be classified as intrinsic errors (Finkelstein, 2014), which are the result of inherent

imperfections in sensors.

The source of systematic error may be due to many factors such as manufacturing deficiency, material imperfections, signal transmission, aging, calibration errors, and operational errors (Beaty and Fink, 2013; Ida, 2013; McGrath and Ni Scanaill, 2013b), and these error sources must be characterised by the manufacturer. Because of their predictable and constant nature, sensor errors resulting due to systematic errors can be corrected using compensation methods such as feedback (at system level), filtering and calibration (Joint Committee for Guides in Metrology (JCGM/WG 2), 2012; McGrath and Ni Scanaill, 2013b).

2.3.2.2 Random Errors

Random errors are accidental by nature and fluctuate in an unpredictable manner (Beaty and Fink, 2013). They follow the laws of chance, and they do not have a consistent magnitude and polarity (Christiansen et al., 2005b). These errors will result in different error values each time a measurement is taken. Because of their unpredictable nature, they may be considered as noise because they carry no information (McGrath and Ni Scanaill, 2013b). In a great deal of literature, random errors are viewed and are assumed to follow Gaussian distribution (Bich, 2012; Finkelstein, 2014; McGrath and Ni Scanaill, 2013b). Random error can, therefore, be modelled and analysed using statistical tools such as averages, dispersion from the average and probability distribution of errors (Cooper and Helfrick, 1985; Finkelstein, 2014; Kularatna, 2003b).

The fact that noise signals are random signals by nature and they may be superimposed on the measured signal, taking averages of a number of measured values over a period of time might reduce the effect of noise (Bolton, 1992). This basically means the arithmetic average of various observations or measurements should be used to minimise the effects of random errors (Christiansen et al., 2005a).

The source of random errors within the context of sensors may be due to an external source (McGrath and Ni Scanaill, 2013b) such as noise in the measurand, environmental noise, transmission noise and internal noise (D’Apuzzo and Liguori, 1999). In practice, manufacturers usually characterise the internal noise of the sensor.

The above sensor characteristics (errors) are usually specified for laboratory conditions. It is thus essential to known the effects of operating environment conditions, if sensors are used under conditions that are different from the conditions they were calibrated in (ibid.). In practice, these effects are not adequately specified and documented by manufacturer

datasheets. Therefore, tests should be performed to characterise the environmental effects on the stated errors specified by the manufacturer (D’Apuzzo and Liguori, 1999; Fraden, 2010). Environmental effects usually affecting sensor specification consists of temperature effects,

Department of Electrical and Mining Engineering 38 pressure effects, acceleration effects, vibration effects and mounting effects (ibid.).

2.3.3 4-20mA Transmission Protocol

It is a fact that signal levels generated by some sensors are very low (i.e. thermocouple generate 10-50µV/ºC (Ida, 2013)) and not suitable for transmission. It is obvious that signal amplification is essential for a useable signal to be transmitted (Morris, 2001). Analogue voltage signals suffer signal attenuation, especially over a long distance, due to wire resistance and are easily susceptible to noise.

Because of transmission limitations of a varying voltage signal, in the industry, a varying current signal is used in sensor signal transmission and is known as a 4-20mA current loop interface (DeNatale et al., 2003; Dudojc, 2008; Johnson, 2000; Lohiya and Talbar, 1998; McMillan, 1999; Morris and Langari, 2012; Morris, 2001; Pereira, 2004). This interface has inherently high noise immunity (McMillan, 1999; Morris and Langari, 2012), and this is because it is a differential signal. This view is disputed by Dudojc (2008:5), who argues that it is only theoretical; he concludes that the “level of noise immunity depends mainly on the

properties of the transmitter”.

The 4-20mA current loop interface uses current in the range of 4mA to 20mA to represent the output signal of a sensor (Morris and Langari, 2012). In practice, the output current is usually scaled and has a linear relationship to the measurand (DeNatale et al., 2003; Dos Reis Filho, 1989; Dudojc, 2008; Lohiya and Talbar, 1998; Pereira, 2004). The 4mA current is the lower limit or minimum value of the measurand, and the 20mA is the upper limit or maximum value of the measurand (International Society of Automation (ISA), 2012; Pereira, 2004). The interface has an inherent fault detection, which is indicated by zero current.

Figure 2.8 Sensor with 4-20ma current loop interface

A typical sensor with 4-20mA current loop interface may be represented by Figure 2.8. It consists of a sensor, which performs the sensing and produces an output electrical signal, which is usually a very small voltage or current (Fraden, 2010) and non-linear (de Barros Soldera et al., 2012; Hosticka, 2007; Niu, 2012) in response to input stimulus. It is followed by a signal conditioner that may perform functions such as signal amplification, filtering and linearisation (McMillan, 1999; Niu, 2012; Nuccio and Spataro, 2002). The signal conditioner is followed by voltage-to-current converter (Morris and Langari, 2012), which provides the 4- 20mA output signal. In the industry, these sensors are known as 4-20mA current loop

transmitters (Chaipurimas et al., 2010; International Society of Automation (ISA), 2012; Pereira, 2004) and must comply with the ANSI and ISA signal transmission standards, especially the ANSI/ISA-50.00.01-1975 (R2012) standard.