In a measurement system for RTST, transducers are used to measure the displacement of actuator and the coupling force. Then, electronic amplifiers amplify the measured signals. Before being fed into an analog-to-digital (A/D) converter, each analog signal may be filtered by a low pass filter in order to avoid aliasing phenomenon, if it is necessary. At each A/D converter, the analog signal is digitalized into a series of discrete data.
Figure 3.4: The basic components of a channel in the measurement system Physical
quantity Transducer Amplifier A/D
converter Digital signal Filter
0
0 10 20 30 40 50
Phase lag∆ν (deg)
180 90
Frequency f (Hz) 270
The errors in measurement can be classified as error of transducer, error of electronic amplifier and filter, and finally, error of digital converter according to their sources. In addition, noise is a special error that comes from any component in the measurement system as well as from unknown sources. In this section, noise is discussed separately from the other errors.
To begin with the transducers, the major errors of a transducer are the error of sensitivity in a considered range of frequencies and the nonlinear error. These errors depend on the transducer, the environment and the electric power. The total value of these errors is approximately 1% in a laboratory environment.
It is worth discussing further the error of sensitivity. Because the sensitivity value is used to convert the measured signal into the physical quantity, the error of the measured physical quantity will be the same as the error of sensitivity. In addition, the sensitivity of a transducer may change due to usage or unknown reasons. Regarding the variation of this error with frequency, load cells with strain gauges, Linear Variable Differential Transformer (LVDT) or inductive displacement transducers are usually not considered because their responses almost do not vary in the considered range of frequencies in structural testing. On the contrary, the responses of acceleration and velocity transducers based on piezoelectric principle vary dramatically with frequency. The reason is that these types of transducers have low and high cut-off frequencies that may be in the considered range of frequencies. In highly accurate controllers, both displacement and acceleration are usually measured and controlled. In these systems, highly accurate accelerometers such as servo accelerometers with frequency range from 0 hertz to some hundred hertz should be used.
The next consideration is the error in electronic components including amplifiers and low pass filters. Both have errors of gain and phase shift. Gain error results in amplitude error of the measured values of displacement (or coupling force) while phase shift results in a phase lag between the measured signal and the actual displacement (or the actual force). Electronic amplifiers usually have small amplification error and the phase shift in semi-conductive components could be neglected in wide range of frequencies for structural applications. However, phase shift is an inherent property of filters. The commonly used filters are Butterworth, Bassel and Chebyshev filters and their phase shifting properties are slightly different.
At low frequencies, such the ones lower than 0.1 times of the cut-off frequency of the
frequencies near the cut-off frequency and should be taken into account during the evaluation of the test results.
Because the properties of transducers and electronic components may be changed, the displacement and force measurements are usually recommended to be recalibrated every year to determine the correct conversion values and to ensure that their errors are within the acceptable ranges.
Besides the errors of transducers and electronic components, errors in A/D converter are also important. Some major errors in the converter could be classified as quantization error, nonlinear error and zero drifting error.
The quantization error is caused by resolution of the converter and this error ranges from zero to half of the resolution. The resolution of an A/D converter is specified as Eq. (3.5) and the measured value in the case of no drifting error is calculated as Eq.
(3.6).
1 2 −
=
∆ VnFSR
V (3.5)
V n n
Vm =( m − o)∆ (3.6)
where ∆V is the resolution in volts that represents voltage of a digital unit, VFSR is the full-scale range in volts of the input, nr is the resolution in bits of the converter, Vm is the measured value in volts, nm is the output value of digitalization and no is the zero offset of the converter. Usually the zero offset of a converter is set at zero or half of the value of 2nr.
The nonlinear error of the converter comes from the error in the mapping of a continuous signal to discrete levels. The nonlinear error depends on the specific converter and this error is usually larger than the resolution in volts. The nonlinear error can be measured by calibrating the converter at many different levels in the full- scale range. When the nonlinear errors at different levels of signal are known, a correction of the measured data can be used to reduce the nonlinear error of the converter.
The zero drifting is one important error of the converter. This is caused by drifting the zero offset of the converter. This error is usually larger than the resolution in volts and usually does not change significantly over a short period. With a zero drifting error, the zero offset is changed and the correct value of the zero offset can be calibrated in order to avoid the effect of the zero drifting error. To measure the new value of the
zero offset, the input signal is set at zero and the zero offset can be measured as the average value of the digital output in certain duration. The difference between the actual zero offset and the declared zero offset of the converter is the zero drifting error.
An important problem in using digital signal is that the aliasing phenomenon can cause serious errors in the digital data. Analog signal of a physical quantity could be considered as a combination of many sinusoids with different frequencies. When the sampling frequency ff is small and not sufficient for the purpose of the signal reconstruction, the aliasing phenomenon occurs. The reason is that when a sinusoid with frequency f is sampled at frequency ff , the result is indistinguishable from those of another sinusoids of frequencies | f −n⋅ ff | (n is an integer number).
Unfortunately, a reconstruction technique can only construct the lowest possible frequency. This is why the reconstructed signal in Figure 3.5 is different from that of the original analog signal.
Figure 3.5: Two different sinusoids that fit the same set of samples
A sufficient condition to prevent aliasing effect is the Nyquist condition. The maximum meaningful frequency of a digital signal is half of the sampling frequency.
This is called the Nyquist frequency. To avoid aliasing effect, noises and signals at high frequencies that are higher than the Nyquist one must be removed before digitalizing the signal. Therefore, an analog filter is used (see Figure 3.4) if the measured signal is contaminated with noises in high frequencies.
As the last issue on errors of measurement and conversion, error due to noise is discussed. Some concerned noises in the measurement and control for substructure testing are thermal noise, burst noise, electro-magnetic noise and mechanical noise.
Thermal noise or Johnson-Nyquist noise is generated by the equilibrium fluctuations
1 2 3 4 5 6 7 8 9 10 11
Discrete sample
Signal value
original analog signal reconstructed signal
filter. This is caused by the random thermal motion of electrons in the electrical conductor. This noise depends on the quality of semi-conductive material as well as the temperature. The thermal noise is usually small in a high-quality measurement device. However, it is not easy to avoid the thermal noise with the working condition in a normal laboratory.
Burst noise is a sudden change of signal that does not relate to any physical quantity in the test. This noise may happen due to an electronic shock in the electronic component or a temporary discontinuity of the connector in the measurement system. Burst noise rarely happens and it can be recognized on the measured signal. To prevent this noise, the powers for electronic components should not have an electronic shock and the connectors in the measurement system should not be discontinuous during a test.
Electro-magnetic noise is a common noise in the measurement system and it should be dealt with in order to be limited within an acceptable range. This noise may come from the effect of electronic-magnetic field in the environment surrounding the connecting cables between transducers and amplifiers as well as inside the electronic equipment.
To limit this noise, signal cables with low noise properties are required and the measurement system must be connected to the ground properly. On the other hand, the environment at the test site should not have electronic devices that generate high level of electro-magnetic fields.
Another important noise is the mechanical noise. This error of measurement can be caused by several sources such as ambient vibration at the testing site, deformation of the supporting mechanisms as well as contact condition of the transducers. This noise causes certain differences between the measured signals and the physical quantities. A good example of this error is that the shock phenomenon at the coupler of load cells can cause fluctuation in the measured force (Dorka et al. 2007). Another example is the vibrating noise of the hydraulic actuators or the shaking tables when they are controlled by a MCS controller with high values of the adaptive gains (Stoten et al.
2001).
If the frequencies of these noises are beyond the considered frequency range, a low pass filter or a band pass filter can be used to remove the effect of these noises.
Unfortunately, these noises usually exist in the same frequency range as the one of the considered quantities and the only effective way to limit effect of these noises is to set up the measurement system properly. Stiff enough connections should be used to limit deformation or unwanted vibration that causes error in measurement. Rigid columns
for referent coordinates should be well fixed and their first frequencies should be far away from the considered range of frequencies in the test. Usually, a long piano wire connection may lead to poor measurement results (Thewalt and Mahin 1987). If long wire connections are used, supporting points should be equipped to prevent horizontal vibration of the wires. For absolute movement, the absolute value that is measured directly should be better than a summed value, which is calculated from some relative quantities.
In addition, since noises in the measurement may cause poor responses of actuators, the controller should be able to deal with noises in order to achieve high accuracy in substructure testing.
4 ERROR COMPENSATION METHODS IN SUBSTRUCTURE TESTING RTST in civil engineering requires fast hydraulic systems with small time lags in order to achieve high accuracy in the test results and ensure the stability in control of test.
However, time lag in hydraulic system is usually lager than a time step (typically as 10 ms) and this usually causes large errors in RTSTs. Therefore, a big problem in RTST is to reduce time lag of hydraulic systems. Another problem, which plays an important role in RTST with sub-step control, is to compensate the error force. This chapter discusses current methods that deal with phase lag and error force compensations in RTST.