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Research Papers

Application of the Monte Carlo Method for Capacitive Pressure Transmitters Surveillance in Nuclear Power Plants

[+] Author and Article Information
C. Montalvo, M. Balbás

Amerprem Research Group, ETSI de Minas,  Technical University of Madrid (UPM), Ríos Rosas, 21, 28003 Madrid, Spain

A. García-Berrocal1

Amerprem Research Group, ETSI de Minas,  Technical University of Madrid (UPM), Ríos Rosas, 21, 28003 Madrid, Spainagustin.garciaberrocal@upm.es

J. Blázquez

Nuclear Fission Division, CIEMAT, Av. Complutense, 22, 28040 Madrid, Spain

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(3), 031014 (Apr 06, 2012) (7 pages) doi:10.1115/1.4005509 History: Received March 13, 2011; Accepted October 11, 2011; Published April 06, 2012; Online April 06, 2012

In nuclear power plants (NPPs), according to current regulations, the response time of capacitive pressure transmitters is used as an index for surveillance. Such measurement can be carried out in situ applying the noise analysis techniques to the sensor output signal. The method is well established, and it is based on the autoregressive (AR) fitting optimized by the Akaike criterion (AIC). The sensor response is influenced by the sensing line, and its length is different in each plant. Recent empirical research has proved that the sensor inner structure can be modeled with a two real poles transfer function. In the present work, it has been proved that the noise analysis applied to the simulated response of a transmitter, modeled with two poles coupled with a sensing line, gives erroneous values for the ramp time delay when the sensing line is long. Specifically, the order of the AR model supplied by the Akaike criterion is not appropriate. Therefore, a Monte Carlo method is proposed to be applied in order to establish a new criterion, based on the statistical analysis of the repeatability of the ramp time delay obtained with the AR model.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Empirical PSD in arbitrary units (a.u.) from a pressure transmitter without its sensing line [10]

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Figure 2

Electrical analogy of the pressure transmitter coupled to its sensing line

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Figure 3

Analytical PSD of the impulse response of a transmitter coupled to its sensing line

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Figure 4

Numerical simulation of the transmitter response to a white noise

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Figure 5

Autocorrelation function in arbitrary units (a.u.) of the simulated response to a driven white noise

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Figure 6

Response to a pressure ramp in arbitrary units (a.u.) obtained with an AR model and ramp time delay measurement

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Figure 7

PSD obtained through Fourier analysis (gray) and PSD estimated with an AR model (black)

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Figure 8

AR estimation of the PSD for two different sensing lines

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Figure 9

Statistical distribution of the response time (ramp time delay) of transmitter coupled with a short sensing line

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Figure 10

Response time (ramp time delay) statistical distributions of transmitters coupled to a long sensing line: (a) 31 m sensing line: τ¯=0.15  s and στ  = 0.05 s. (b) 65 m sensing line: τ¯=0.15  s and στ  = 0.05 s.

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Figure 11

(a) Monte Carlo simulation obtained with n = 5 (Akaike order) for a transmitter coupled to a short sensing line (12 m). (b) Monte Carlo simulation with n = 5 (Akaike order) for a long sensing line (26 m). (c) Monte Carlo simulation with n = 10 (higher order for high kurtosis) for a short sensing line (12 m). (d) Monte Carlo simulation with n = 10 (higher order for high kurtosis) for a long sensing line (26 m). In all cases, response time is the ramp time delay.

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Figure 12

Noise signals S1 and S2, (a) and (b), respectively, from two pressure capacitive transmitters from a NPP. The plots only show 10 s from a total record length of 300 s (sampling time Δt = 20 ms).

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Figure 13

PSD from noise signal S1 from a pressure capacitive transmitter from a NPP

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Figure 14

PSD from a sample (1000 points) taken from noise signal S1 whose record length is 15,000 points

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