Nuclear power plants measure the dynamic response of their safety-related pressure, level, and flow transmitters for one or more of at least four reasons:
- To comply with a plant’s technical specifications and/or regulatory requirements regarding response-time testing.
- In troubleshooting, to identify sensor or sensing-line problems, including blockages, voids, and leaks.
- To manage component aging, estimate residual life, and assess the reliability of pressure-sensing systems.
- To establish objective sensor replacement schedules.
Why nuclear plants measure the dynamic response of pressure sensors and their associated sensing lines is better understood than how to do the measuring. To address that problem, this article explains a noise analysis technique that will accurately measure these dynamic responses.
The noise analysis technique provides a passive method for dynamically testing pressure-sensing systems. It generates the response time for both a pressure transmitter and its sensing lines simultaneously. The test can be performed remotely while a plant is operating, does not require that transmitters be removed from service, does not interfere with plant operation, and can be performed on several transmitters simultaneously. Those benefits result in an attractive bottom line, because tests that can be run without interrupting the demand for high nuclear plant capacity factors are a big plus in today’s competitive markets.
Basic definitions
The noise analysis technique is based on analyzing the natural fluctuations that exist at the output of pressure transmitters while a plant is operating. These fluctuations (noise) are caused by the turbulence induced by the flow of water in the system, by vibration, and by other naturally occurring phenomena.
The noise analysis test has three steps: data acquisition, data qualification, and data analysis.
Data acquisition. A pressure transmitter’s normal output is a DC signal on which the process noise (AC signal) is superimposed. That noise is extracted from the transmitter output by removing the signal’s DC component and amplifying the AC component. This is easily accomplished by using commercial signal-conditioning equipment, including amplifiers, filters, and other components. The AC signal is then digitized using a high sampling rate (1 or 2 kHz) and stored for subsequent analysis. The analysis may be performed in real time as data are collected or off-line by retrieving the data from storage.
Figure 1 illustrates a 50-second record of noise data from a pressure transmitter in a nuclear power plant. For each transmitter (or each group of transmitters), about an hour of such noise data is typically recorded for use in the analysis.
1. Collect the data. A short noise data record from a pressure transmitter in an operating nuclear power plant. Source: AMS and Springer-Verlag
Data qualification. The raw data must first be thoroughly scanned and screened before any analysis can begin. This is normally accomplished using data qualification algorithms embedded in software, which check for the stationary and linear attributes of the raw data and look for other abnormalities.
For example, the raw data’s amplitude probability density (APD) is plotted and examined for skewness. The top APD in Figure 2 is perfectly symmetrical about the mean value of the data and fits the Gaussian distribution (the bell-shaped curve) that is superimposed on the APD. A Gaussian distribution is also referred to as a normal distribution. A skewed APD (see the lower plot of Figure 2) could be caused by any number of anomalies in the data, including the nonlinearity of the sensor from which the data are retrieved.
2. Manipulate the data. Normal and skewed APDs of noise signals from nuclear plant pressure transmitters. Source: AMS and Springer-Verlag
In addition to APD for noise data qualification, the mean, variance, skewness, and flatness of each block of raw data are calculated and scanned to verify that no saturated blocks, extraneous effects, missing data, or other undesirable characteristics are present. Any data block that has an anomaly is removed from the record before it is analyzed.
Data analysis. Noise data are analyzed in the frequency domain and/or time domain. For frequency domain analysis, the noise signal’s power spectral density (PSD) is first obtained through an FFT algorithm or its equivalent. Next, a mathematical model of the pressure-sensing system is fit to the PSD, from which the system’s response time is calculated. The PSDs of nuclear plant pressure transmitters have various shapes, depending on the plant, the transmitter installation and service, the process conditions, and other effects (Figure 3).
3. Examine the data. Examples of power spectral densities of nuclear plant pressure transmitters. Source: AMS and Springer-Verlag
For time domain analysis, the noise data are processed using a univariate autoregressive (AR) modeling program. This provides the impulse response (the response to a narrow pressure pulse) and the step response, from which the system’s response time is calculated. Typically, the noise data are analyzed in both the frequency domain and time domain, and the results are averaged to obtain the system’s response time.
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