Flashcards in Semester 2 Deck (31):
What is the relationship between precision and significant figures?
The higher the significant figures, the higher the precision.
What does precision refer to?
The limit of error in a measurement or variable.
What does accuracy refer to?
Closeness to the true value of a variable.
How is precision/uncertainty preserved in a calculation?
When multiplying, dividing or using other functions, the answer should have the same number of significant figures as the smallest in the calculation.
How is precision/uncertainty preserved when adding or subtracting?
The answer should have the same number of decimal places as the smallest used in the calculation.
Ideally, what is the relationship between the input and output of and an instrumentation system?
Linear and is defined by the sensitivities.
How do you find sensitivity, k, from a output range/input range graph?
It is the slope of the graph:
k = slope = Δo/ΔI
What is sensitivity in terms of the output?
k(I - Imin) + Omin = O
O = output
What "other inputs" can affect a system?
Modifying input and interfering input
What does modifying input (Im) do?
Modified the linear sensitivity I.e temperature in strain gauges.
What does interfering input (Ii) do?
Interferes with the zero condition, therefore changing the static reference.
What does an error band do?
Defines for a particular input, the output will be within +\- ΔO
What combines to give an overall statistical behaviour?
Random effects in I, Im and Ii.
The random fluctuations in Im, Ii and I (overall statistical behaviour) can be assumed to have what kind of function?
Gaussian probability density function around the mean value
How is accuracy of a measurement system quantified?
Using measurement error E
E = measured value - true value
What does the error band centred around the ideal output represent?
The accuracy of the system
When does a bridge become more linear?
When r >> 1
What Is the bridge ratio when maximum sensitivity occurs?
r = 1
How can bridges be linearised?
A combination of sensors (with equal characteristics) and negative feedback.
What is the force given by Newtons 2nd law, Hooke's law and resistive damping?
F = ma +rv + ky
How can non-linearity be removed in a bridge?
- 2 strain gauges to be used in an adjacent arm (R1 and R2)
-R1 in tensile (+) and R2 in compressive (-) strains.
What is stress?
σ = force/area
What is the effect of stress called?
Strain, which is defined as the fractional change in length.
ε = Δl/l
What is Youngs modulus (E)?
E = σ/ε
When a material extends in length due to strain, there is a decrease in cross sectional area, what does this result in?
Two opposing strains are produced; longitudinal and transversal, which are related by Poissons ratio.
What damping ratio gives optimum response and settling times?
What is a major limitation of a hydrophone?
It has a very high output impedance, effectively making it a current source.5
How should the strain gauges in a bridge be arranged to eliminate interfering inputs?
The strain gauges under longitudinal strain in opposite arms and similarly for compressive strain.
How do you determine the static error in a measurement system?
Assume all of the statistical variations may be combined as a linear sum of the component variances. In addition the variances must be scaled using the partial derivatives of the model equations.
How is an error band use to analyse a system?
The statistical variation takes into account any modifying, interfering, offset, non-linearities, hysteresis, parameter variations and defines the behaviour via a derivation from the linear relationship.