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The temperature and Pressure sensors plays a vital role in Nuclear Power Plant. The Rosemount temperature sensors are used to produce the exact temperature and pressure measurement of the nuclear power plant. The sensors that supply real data must respond quickly to the safety systems of NPP. Dynamic measurement of the sensors will indicate the undesirable process activity. In this project the Dimensionality of the Original dataset can be reduced by using Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Single Value Decomposition (SVD). Finally the Response Time of the sensors are computed.
In NPP, Instrumentation and control (IC) systems must be accurate to properly sense and communicate the process variables and have a quick response time. To ensure better accuracy and Dynamic Response Time of temperature and pressure sensors of NPP. Steady state measurement and fast dynamic response time are one of the first requirements in Nuclear Power Plant operation. Process to sensor interface is a second requirement. For example, the temperatures of the fluid in plants are measured by using sensors which are installed securely in thermowells to the process piping. Thermowell must be designed in a good manner and installed to give proper support to protect the temperature sensors and also to optimize better Accuracy in response time of the Nuclear Power Plant.
Rosemount Nuclear Pressure Transmitters are designed for exact pressure measurement in plant operation. The transmitters were qualified by per KTA3505, which is a type testing of measuring sensors of the safety systems. Rosemount Pressure Transmitters have similar construction and performance. Absolute (AP), Gauge (GP) and differential (DP) configurations are of Rosemount pressure range options units. Though an isolating diaphragm (valves) the process pressure is transmitted and a fluid which contains silicon oil to a sensing valves in the middle of the sensor. Similarly, the reference pressure is transmitted to the other side of the sensing valves in NPP.
Capacitance plates are placed on both sides of the sensing diaphragm which helps to detect the position of the sensing diaphragm. Nuclear specifications like seismic (i.e.) sweep between 5-35Hz. Steam pressure (or) Temperature of 1600C (3200F). Performance specifications based on Zero-based calibration spans. The accuracy may of Â±0.2% of calibrated span. Drift is of Â±0.2% URL (Upper Range Limit) for 30 months.
The response time of Rosemount Pressure Transmitters is 63.2% at 37.80C (1000F). Applications of Rosemount Pressure Transmitters are Pressurized Water Reactors (PWR), valve chambers, annulus and auxiliaries. Based on the performance of process instrumentation the plant power level is set among all other factors. The plant is allowed to produce more power based on the performance of the process instrumentation on measurement assurance basis. For example, there was an in active temperature sensors are found in one U.S Nuclear Power Plant was informed by the regulators. The regulators could operate only at 100% power level, and the response time of its safety system was 6.0 seconds or less. However, if the response time is degraded to above 6.0 seconds, the temperature instrumentation is ordered to decrease the power production level.
H.M.Hashemian proposed the advances in sensor system monitoring techniques. It would seem to follow that nuclear utilities around the world would be applying the true techniques to optimize up time and to provide additional condense in the output of processing sensors.
I.Warshawsky said what is required to keep the error in steady state temperature measurement less than an arbitrarily prescribed amount and to estimate the lag in response to temperature changes occurring under prescribed conditions.
D.W.Mitchell et.al, proposed an Instrumentation and controls technology which focus areas that have applications in Nuclear Power Plant digital upgrades as well as in new plants. Korsah et.al, suggested a modified IC architectures in new plants. They focused on Sensor and measurement systems. Hrvoje proposed Resistance Temperature Detectors (RTD) by-pass manifold system shall be replaced with fast response thermowell mounted RTDs.
David Roverso proposed the dynamic empirical modelling techniques for the process diagnostics. Three practical applications of Aladdin Transient Classifier to Nuclear Power Plants, that showed the system-wide, Component wide and recognition of faults diagnostic model. Eric Blocher et.al, proposed the methods for effective detection and mitigation of aging mechanism in Nuclear Power Plant.
R.L.Shepard and R.M.Carroll proposed that, In LMFBRs, Primary coolant temperature sensors response time is critical to the nuclear power plant safety must be verified, because in this reactor the temperature of the liquid sodium is measured by using thermocouples which are installed on the plant. R.L.Shepard proposed an LCSR test (Loop Current Step Response) for calculating response time of temperature and pressure sensors.
T.W.Kerlin proposed that the analytical basis approach for response time calculation. Thie and Joseph proposed that noise analysis for dynamic response time of pressure transmitters. Joe applied the noise analysis to various applications on nuclear reactors, manufacturing industries and fossil power plants. Upadhaya applied the noise analysis technique on process condition monitoring in numerous industrial applications.
Wang.C et.al used the similar noise analysis in medical field for monitoring the heart functionality. Keith Holbert proposed the efficient application of the noise analysis technique for diagnostics of sensing line problems in power plants. H.M.Hashemian proposed that In-Situ response time testing of RTDs and validating the noise analysis technique for pressure transmitters in Nuclear Power Plant.
Pressure Transmitter 1
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Response Time (RT) (Stamp & Ramp)
Pressure Transmitter 3
Fig 1: System Design
Model Parameters ï€ ï€¨ï´ï€±ï€¬ï€ ï´ï€²ï€¬ï´ï€³ï€®ï€®)
Computing Response Time (RT) (Stamp & Ramp)
Apply Correction Factor
Results in Single Response Time (ï´ï€©ï€ in Seconds
Fig 2: Flow Chart
Principal Component Analysis (PCA):
The Principal Component Analysis is the most widely used technique for dimensionality reduction. It makes the data easier to use and reduce noises in the data. This can be applied to high-dimensional dataset for retrieving effective dimensionally reduced dataset. And it's a useful tool for pattern recognition and time series production. Hardware implementation cost and complexity also reduced by PCA. In PCA, the original dataset is transformed from its original coordinate system new coordinate system.
In this project the PCA applied on process variables of sensors, in order to get reduced dataset. Covariance of matrix and Eigen values are computed and correlated values also removed. The result shows that the graph between principal component analysis and Percentage of variance.
ReconMat and Eigen values of the original dataset,
[[ 3.03093000e+03 2.56400000e+03 2.18773330e+03 ..., 1.64749105e-02
[ 3.09578000e+03 2.46514000e+03 2.23042220e+03 ..., 2.00999984e-02
[ 2.89492000e+03 2.53201000e+03 2.17703330e+03 ..., 2.45000041e-02
[ 2.94492000e+03 2.45076000e+03 2.19544440e+03 ..., 1.62000082e-02
[ [5.34151979e+07 2.17466719e+07 8.24837662e+06 2.07388086e+06
1.31540439e+06 4.67693557e+05 2.90863555e+05 2.83668601e+05
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00] ]
Reduced dataset from the Original dataset is,
This result shows that how effectively PCA works on high-dimensional data of processed values of sensors in Nuclear Power Plant.
Fig 3: shows the result of Principal Component Analysis Vs Percentage of Variance.
Fig 4: shows the result of observed response time Vs RTDs.
Independent Component Analysis:
Independent Component Analysis is an unsupervised dimensionality reduction method to provide better data representation. And ICA is a multivariate data analysis process for high-dimensional dataset. More essential information is provided by ICA, that resulting in performance improvement and flexibility. Based on non-Gaussianity ICA provides fast independence measure experience on dimensionally large dataset.
ICA is a necessary pre-processing step for classification. Unlike Principal Component Analysis, even in non-gaussian data it shows interesting features over datasets. For example, Cocktail-party problem, where two people are speaking simultaneously. And the two microphones are located in different places. The microphones give two different recorded signals. It leads to the complexity of separate the different sound sources by the human. Independent Component Analysis is easily separate the sound sources without any anxiety about the positions of the microphones. In this project ICA separates the featured data from the original dataset in order to reduce the dimension.
Singular Value Decomposition:
Singular Value Decomposition is tool used for dimensionality reduction of high-dimensional dataset. It provides the simplified data from the largest dataset. SVD removes noise and redundancy data. SVD used for retrieving the important features of the data. SVD based on taking the high dimensional dataset and reducing it to a lower dimensional dataset that exhibits the substructure of the original dataset. If there is a variation below any threshold value, SVD simply ignores it and greatly reduce the data.
Computing the Response Time:
Based on the processed values from Principal Component Analysis (PCA), Independent Component Analysis (ICA), and Single Value Decomposition (SVD) the response time of the sensors are computed. Dynamic response time of the Pressure Transmitter is essential for power production in power plants. The overall response time of the sensors can be computed by the following formula.
= Over all time constant.
= ith modal time constant.
Ln = natural logarithm operator.
Results and Discussions:
The response time of the temperature and pressure sensors in NPP should be dynamic in order to avoid plant accidents. By Using PCA the correlated values are removed from the original coordinate system and the Response time of the temperature sensors are also computed. The processed values are given to the input of logistic regression for classifying at which temperature the NPP continues its power production.