FORMULATION AND ANALYSIS OF THE PROBABILITY OF DETECTION AND FALSE DETECTION FOR SUBSEA LEAK DETECTION SYSTEMS

Transcription

1 Proceedings of the 24 th International Pipeline Conference IPC24 September 29 - October 3, 24, Calgary, Alberta, Canada IPC FORMULATION AND ANALYSIS OF THE PROBABILITY OF DETECTION AND FALSE DETECTION FOR SUBSEA LEAK DETECTION SYSTEMS Alireda Aljaroudi Memorial University St. John s, NL, Canada aaa55@mun.ca Faisal Khan Memorial University St. John s, NL, Canada fikhan@mun.ca Ayhan Akinturk Memorial University St. John s, NL, Canada akinturk@mun.ca Mahmoud Haddara Memorial University St. John s, NL, Canada mhaddara@mun.ca Premkumar Thodi INTECSEA Canada St. John s, NL, Canada premkumar.thodi@intecsea.com ABSTRACT Insuring the integrity of subsea process component is one of the primary business objectives for oil and gas industry. One of the systems used to insure reliability of a pipeline, is the Leak Detection System (LDS). Different leak detection systems use different technologies for detecting and locating leaks that could result from pipelines. One technology in particular that is gaining wide acceptance by the industry is the optical leak detection systems. This technology has great potential for subsea pipelines applications. It is the most suited for underwater applications due to the ease of installation and reliable sensing capabilities. Having pipelines underwater in the deep sea present a greater challenge and a potential threat to the environment and operation. Thus, there is a need to have a reliable and effective system to provide the assurances that the monitored subsea pipeline is safe and functioning as per operating conditions. Two important performance parameters that are of concern to operators are the probability of detection and probability of false alarm. This article presents a probabilistic formulation of the probability of detection and probability of false detection for fiber optic LDS based systems. NOMENCLATURE BSS : Brillouin Stimulated Scattering CW : Continuous Wave LDS : Leak Detection System NP : Noise Power PD : PFA : Probability of False Alarm PMD : Probability of Missed Detection SNR : Signal to Noise Ratio c : Speed of Light (Km/s d : Location of The Temperature Change, dp dt : Temperature Coefficient (mw/ºc) dp : Strain Coefficient dε (mw/µε) n : Refractive Index Aeff : Effective Area of The Fiber Leff : Effective Length of The Fiber gb : Gain P o : Reference Power apb(measured) : Measured Brillouin Power PCW : Input Probe Power PP : Pulse Power α ε : Strain Coefficient Expressed In MHz/με α T : Temperature Coefficient Expressed In MHz/ºC Δε : Strain Change ΔT : Temperature Change ΔT measured : Measured Temperature Change δt : Minimum Detectable Temperature Change Va : Acoustic Velocity v B : Brillouin Frequency Shift τ : Pulse Width λ : Wavelength of the Incident Light v o : Reference Brillouin Frequency at No Strain and at the Ambient Temperature - MHz Δt : Travelled Time Xth : Threshold Temperature Change Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

2 . INTRODUCTION One of the key monitoring systems for subsea pipeline is the LDS. Its performance should be assessed regularly to insure its operability and functionality as well as reliability are maintained at all times and more importantly insure that it does not miss detect or falsely detect a pipeline leak. The consequences of such incorrect diagnosis may pose a threat to the environment or production. Based on the outcome of the assessment a decision should be made if the whole or part of the system needs to be repaired, upgraded or replaced. Generally, the key factors that affect the performance of a subsea leak detection system are missed detection and false detection. The system may reveal that a leak is happening somewhere along the pipeline when in fact the leak is not present. Likewise, the system may not declare a leak is happening when in fact it is present. The latter is termed as missed detection and the former as false detection or false alarm. Missed or false detection may not place the system out of service; however, they cause the system to fail partially. In either case, whether we have total or partial failure, the performance of the system will be in jeopardy. Once we know these failures and are able to calculate the probability of their occurrences and their consequences, we can evaluate the risk and its impact on the environment and production. Irrespective of the leak detection method used, the result from which we determine the status of the pipeline is the characteristics of the received signal. All leak detection methods or systems, have one common task is to detect and declare if a leak has or has not occurred and based on the characteristics of the received signal, the quantity and location of the hydrocarbon leak can be determined. The main task under this article is to formulate the (PD) and Probability of False Detection or alternatively called Probability of False Alarm (PFA) for fiber optic distributed sensing technique used for leak detection. This is accomplished by adopting some concepts from Signal Detection Theory (SDT) and engineering probabilistic methods. There is no established method for evaluating the PD and PFA for fiber optic-based LDS. False detection results in excessive expenditure and unnecessary mobilization of equipment and personnel to the site that is thought to be leaking. On the other hand, missed detection, results in environmental and financial liabilities and unfavorable reputation. An overview about fiber optic LDS, Brillouin Stimulated Scattering (BSS) as technique for temperature sensing is provided in sections 2. Sections 3 and 4 respectively discuss PFA and PD. A summary is provided in section FIBER OPTIC BASED LDS One of the most promising condition monitoring technologies is the fiber optic distributed sensing that can perform ongoing sensing along the entire length of the monitored structure. The fiber optic acts as a sensor, providing sensing and prior warning capabilities in real time and in a continuous basis. By using distributed fiber optic sensing technology, the vibration, strain and temperature changes along the monitored object can be detected. Strain occurring on a pipeline may give indication of the existence of cracks, detecting it in advance will enable maintenance personnel to carry out corrective actions in a timely manner. Applying this technology will prevent structural failure from happening that could lead to a leak and eventually to oil spill. The same fiber optic cable used for sensing can be used to support pipeline s telecommunications requirements along the pipeline via another dedicated fiber strand. Generally, oil is transported through pipes at a temperature that is higher than the surrounding, in the event a leak happens, the temperature of the surrounding will increase, causing the light wave to scatter back to the source indicating the occurrence of a leak []. On the other hand, when a gas pipeline starts leaking, the released gas will cool down the surrounding area resulting in a cooler temperature than the normal temperatures, as a result, the sensing cable will trigger an alarm indicating a leak []. This technology can provide accurate information in real time about the status of the monitored structure, which can significantly enhance the decision-making about what mitigation actions should be considered, in the event a risk or safety issue becomes imminent. 2. Scattering When optical laser propagates through the fiber, it gets scattered in three different spectral forms as indicated in Figure. with different frequencies and intensities, Rayleigh, Raman, and Brillouin scattering [2]. The scattering is created due to impurities or change of composition and interaction of the laser light with molecules of the fiber. Rayleigh Scattering Raman Brillouin FIGURE. SCATTERING MECHANISMS The Raman-based technique can achieve sensing for a range up to 37 km, measurement time of < 3 minutes, and temperature accuracy of 3 C and can measure temperature changes only [3,5]. Brillouin scattering-based technique has the ability to sense temperature and strain changes along the fiber optic cable. The 2 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

3 wavelength of the reflected wave is closely related to the changes of the surrounding temperature and strain of the fiber optic cable [4]. This technique can achieve less than one-meter spatial resolution, one-minute measuring time, and 2 ºC temperature resolution and up to 5 km sensing range [5]. The range can be extended by using fiber optic amplifiers in between. The reported strain accuracy is about micro strains [6]. As stated above, Brillouin scattering based technique outperforms Raman-based technique, as it can achieve longer sensing range, improved accuracy, less measuring time and can measure both temperature and strain. Therefore, the focus of this research is on the Brillouin-based sensing. 2.. Brillouin Scattering Brillouin scattering is caused by the fluctuations of the refractive index of the fiber. These fluctuations take place due to the variations of the fiber composition, pressure, temperature or density [7]. Along the way a vibration of the fiber molecules takes place travelling at the acoustic speed which causes variation in density and as a result the refractive index changes causing the light to scatter; this vibration is referred to as phonons. The process is called inelastic because a transfer of energy between the incident light, photons and the molecules of the fiber takes place. If the energy is transferred from the photons to the fiber material then the backscattered light is downshifted in frequency. In this case, photons lose energy. Conversely, if energy is transferred from the fiber material, the silica glass, to the photons, then the backscattered light is up shifted in frequency. Here, photons gain energy and the frequency becomes higher. The shift in frequency is called Brillouin frequency shift and is given by [7]: v B = 2nV a λ () Where v B is the Brillouin frequency shift, V a is the acoustic velocity of the phonons, n is the refractive index of the fiber and λ is the wavelength of the incident light. 2.2 Distributed Brillouin Sensing Techniques Several techniques are used for distributed Brillouin sensing. They include, Brillouin Optical Time Domain Reflectometry (BOTDR), Brillouin Optical Time Domain Analysis (BOTDA), Brillouin Optical Frequency Domain Analysis (BOFDA), Brillouin Optical Correlation-Domain Analysis (BOCDA) and Brillouin Echo Distributed Sensing (BEDS) [8]. The focus of this paper will be on BOTDA technique since it is one of the most commonly used as a monitoring technique by the industry Brillouin Optical Time Domain Analysis (BOTDA) BOTDA when used for stimulated Brillouin scheme works by launching lasers into two opposite directions, one is pulsed and the other one is continuous. The frequency difference for the two lasers can be used to measure strain and temperature along the fiber [9]. FIGURE 2. - ILLUSTRATION OF A SIMPLIFIED BOTDA SYSTEM v is called the pulsed laser or the pump signal while v 2 is called the Continuous Wave (CW) and is referred to as the probe signal. In this configuration, the power of the probe signal is transferred to the pump pulse, resulting in an increase in the intensity of the pulse as it travels along the fiber yielding a better Signal to Noise Ratio (SNR) and hence longer sensing range [-2]. The Brillouin frequency shift is dependent on material temperature and strain. The Brillouin scattering may lose or gain energy; the energy loss is called stokes process and the energy gain is called anti-stokes process. To enhance the interaction between the incident light (the pump signal) and the stokes, a probe laser is launched at the opposite side of the fiber [3-4]. For the first laser a square pulse is used, as this is usually used for timing control because the square pulses are of equal duration. Every time a pulse is sent, it will have the same time duration. From the pulse width, the spatial resolution can be determined and this is defined in Eq. 2. The spatial resolution is the smallest length of the monitored object whose temperature change can be determined. z = cτ 2n (2) Where c is the speed of light, n is the fiber optic cable refractive index and τ is the pulse width. There exists a linear relationship between the frequency shift and the changes of temperature and strain [6], [5] and [7]; the frequency shift can be expressed as: v B v o = α ε Δε + α T ΔT (3) v o is the reference Brillouin frequency at no strain and at the ambient temperature, in MHz, α ε is the strain coefficient expressed in MHz/με, α T is the temperature coefficient expressed in MHz/ºC, ΔT is the temperature change, which is 3 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

4 the difference between the measured temperature and the ambient temperature and Δε is the strain change. The strain measurement is referred to as micro strain (µε). If a fiber optic cable has an original length of meter and due to stress was stretched to.7 meter, then the strain becomes seven micro strains (7µm). From the frequency shift, sensing can be possible, but the challenge here, the shift is dependent on both strain and temperature. From the frequency shift, it is impossible to determine which change has occurred. The temperature is the determining factor for the presence or non-presence of a leak. To deal with this challenge, the fiber optic cable is held loose in close proximity to the pipe, as shown in Fig. 3.. Frequency Shift - MHz Frequency Shift - Temperature Change Plot Temperature - ºC FIGURE 4. - BRILLOUIN FREQUENCY SHIFT VERSUS TEMPERATURE FIGURE 3. - CONFIGURATION FOR TEMPERATURE AND STRAIN SENSING DETECTION The loose fiber is used to monitor the temperature change only, assuming zero strain as the fiber is held loose not attached to the pipeline, the Brillouin frequency shift can be expressed as: v B v o = α T ΔT (4) Figure 4. illustrates the linear relationship between the Brillouin frequency shift and the temperature, assuming that reference frequency at the ambient temperature is 465 MHz and the rate of change is.4 MHZ/ ºC. The Brillouin peak power can be expressed as [7]: P B = P CW e ( αl) [ exp ( g B P P L eff A eff ) ] (5) Where P CW is the input probe power, P P is the pulse power, g B is the gain, L eff and A eff are the effective length and effective area of the fiber respectively. The Brillouin power has a positive relation to the temperature, as the temperature increases, the Brillouin power increases. On the other hand, it is inversely related to strain, as strain increases, the peak Brillouin power decreases, [6] and [7]. The Brillouin peak power has a dependence on temperature and strain, [7] and [8]. P B = P O + dp dt dp ΔT + Δε (6) dε Where dp dp is the Temperature coefficient (mw/ºc), and dt dε is the strain coefficient (mw/µε). Referring to Figure 3., the fiber is laid near the pipeline, assuming zero strain; the Brillouin Power P B can be expressed as: P B = P O + dp ΔT (7) dt Either Equation 7 or Equation 4 can be used to determine the temperature change. The location of the temperature change can be determined using Eq. 8. d = CΔt 2n (8) Where d is the location of the temperature change, c is the speed of light and Δt is travelled time. 4 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

5 3. PROBABILITY OF FALSE ALARM (PFA) It is the probability of declaring a leak when in fact no leak is present. Whenever noise power exceeds a predefined noise power, a false alarm is declared. Stated differently, the PFA is described as the likelihood that the LDS will falsely detect a leak when it does not exist. The PFA is expressed in terms of the threshold, which is the minimum detectable temperature change. Any measured signal level below the established threshold will be considered as a noise signal and does not contain any true power. Within the framework of signal detection theory, the mean and standard deviation of the noise are random. Noise is modeled as a normal distribution with zero mean (μ) and standard deviation (σ): N (, σ). A false alarm occurs whenever the noise power exceeds the predefined noise power [9]. Figure 5. illustrates the noise power varying levels over time and the threshold; departure of the noise power from the baseline (the threshold power) will signal an alarm indicating false detection. In fact, the signal is mainly a noise signal that is increased in amplitude that has exceeded the threshold value due to excessive noise generated by the equipment, some frequencies interfering with the monitoring equipment or some other external factors. The noise power corresponds to the temperature measurement error and the power corresponds to the measurement of temperature. Every signal has two elements, power and noise that respectively correspond to measured temperature and error as indicted in Eq. 9 to 4. The noise affects the final accuracy of estimated T. The variance corresponds to the noise power or measurement error and the square of the mean corresponds to the power amplitude or measurement. Referring to Eq. 7, the power has noise term that results in error in the measurement of temperature - Measured power signal = Power + Noise: P B = P B(measured) + NP () Where P B(measured) is the measured Brillouin power and NP is the noise power. Both the P B(measured) and NP are measured at a given point in time. After obtaining the values of the measured power, the temperature change can be determined. ΔT = ΔT measured + ε () ε is a random measurement error that corresponds to noise in the signal with a mean of and variance σ 2. The Brillouin power P B in Eq. 7 is the measured Brillouin power. Substituting Eq. 7 into Eq., ΔT can be expressed as: T = P B(measured) P o dp dt + ε (2) False Alarms Due to Noise Power Noise Threshold Power Using Eq. and Eq., the temperature change (ΔT) is given as: ΔT = P B(measured) P o dp dt NP + dp dt (2.) The Mean of the Noise Time FIGURE 5. ILLUSTRATION OF NOISE SIGNAL 3. Power Signal and Temperature Relationship Where P o is the reference power taken at the reference temperature change (this is not to be confused with the threshold temperature change) and dp dt is the temperature coefficient (mw/ºc). The first term in Eq. 2. corresponds to measured temperature and the second term corresponds to measurement error (ε). Mainly, the measured temperature change is obtained from a set of n measurements, ΔT, ΔT 2 ΔT n is expressed as: The signal to noise ratio is defined as: ΔT measured = ΔT + ΔT 2 + n ΔT n (3) SNR = μ2 σ 2 (9) σ ΔT = ΔT measured ± n (4) 5 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

6 Where ΔT measured is the measured temperature change, σ is the standard deviation of the measurement error and n is the number of samples or the number of measurements. The system performs number of scanning, where the system at every scan measures the temperature of the monitored pipeline. At every scan the measured temperature at each point along the monitored pipeline is recorded. At the end of the scanning, the averages of measured temperatures as well as the variance of measurement errors are taken. 3.2 Probability Density Function of the Noise Signal Figure 6. depicts the probability density for noise power. As shown in the Figure that the shaded area in the right side of the Figure represents the failure region. This is the probability that the noise power (measurement error) exceeds the predetermined threshold. The threshold represents the minimum detectable temperature change. As stated earlier, the false detection occurs in the event the noise power exceeds the predetermined threshold power or lowest detectable temperature change. down from time to time and as a result, the summation of the different signal levels becomes zero. When the measured signal level is greater than the threshold change, a false alarm will be declared. Referring to Fig. 6, let us define ΔT as X and ΔT th as X th, then the probability of false alarm becomes: PFA = 2πσ2 n e Xth X 2 2σ 2 n dx (5) Where Xth is the threshold temperature change, σ 2 is the variance of the measured temperature changes, n is the number of measurements or samples. Integrating Eq. 5 yields: PFA = erf 2 [ Xth 2σ2 ( n )] (6) Where erf is the error function. Then the threshold is calculated as: Xth = 2σ2 n erf ( 2PFA) (7) FIGURE 6. AMPLITUDE DISTRIBUTION OF THE THE NOISE POWER SIGNAL The PFA is expressed in terms of the threshold and the noise power level (σ 2 ). The threshold will be either the lowest detectable power or the lowest detectable temperature change. The main task of the system is to detect if the received signal power level has exceeded the threshold. Therefore, to determine the PFA, the threshold and the number of data samples need to be determined. Assuming that the noise power level (σ 2 ) is known from previously recoded data for a large population, then the noise level for the sample of interest is σ 2 /n, the standard deviation is (σ/ n), where n is the number of data samples. There is a probability of false alarm for every threshold value. The mean of the noise signal is zero, because the summation of the amplitudes of the noise power is zero. This is due to the fact that the noise power signal levels vary up and 3.3 The Minimum Detectable Temperature by Fiber Optic Based LDS The minimum detectable Brillouin frequency shift δv B as a function of SNR is expressed in Eq. 8 [2]. δv B = ΔV B 2(SNR).25 (8) ΔV B is the Brillouin spectral width of the Brillouin input signal and the SNR is signal to noise ratio. Using Eq. 8 and Eq. 3 and assuming zero strain, the minimum detectable temperature change δt can be expressed as [2]: δt = ΔV B 2α T (SNR).25 (9) Where α T is the temperature change coefficient and is expressed as MHz/ºC. δv B is the difference between the 6 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

7 reference Brillouin frequency and the measured Brillouin frequency shift (v B v o ) as indicated in Equation 3. Substituting the above Equation, Eq. 9 into Eq. 6, the PFA can be determined as a function of the threshold for the F.O based LDS. The variance of measurement has an effect on the PFA as indicated in Fig. 8 and Fig. 9, as the measurement variance increases the PFA increases. The increase or decrease of the number of sample affects the PFA and PD. This is illustrated in Fig., as the number of sample size increases the PFA decreases. PFA =.5 ( erf (.5 ΔV B α T (SNR) n.25 σ2)) (2) False Detection.3 Std. : 4 Std. : Figure 7 illustrates the PFA versus the threshold for a case where the system has a bandwidth (ΔV B ) of 2 MHz, temperature coefficient (α T) of.5mhz/ºc. The Figure reveals that as the threshold value increases the probability of false alarm decreases..4 False Detection Probability of False Alarm Probability of False Alarm FIGURE 9. PFA FOR VARIOUS TEMPERATURES USING TWO DIFFERENT STANDARD DEVIATION VALUES FIGURE 7. PFA FOR VARIOUS TEMPERATURE VALUES PD.5 PD versus PFA X:.394 Y: Sample Size:24 Probability of False Alarm Probability of False Alarm False Detection Std. : Std. : FIGURE 8. PFA FOR VARIOUS TEMPERATURES USING TWO DIFFERENT STANDARD DEVIATION VALUES PD PD PFA.5 X:.33 Y: PFA.5 X:.233 Y: Sample Size: Sample Size: PFA FIGURE. PD VERSUS PFA USING DIFFERENT SAMPLE SIZES Figure illustrates that the higher the SNR is, the lower the threshold (lowest detectable temperature change). 7 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

8 7 6 Lowest Detectable Different SNR Values Let us define the lowest detectable temperature change as X th and temperature change as X; then the PD can be expressed as: SNR PD = 2πσ2 n e Xth (X μ) 2 2σ 2 n dx (22) Lowest Detectable FIGURE. SNR VERSUS TEMPERATURE X th is the threshold temperature change and the µ is the mean value taken for every group of measurements, X is the amplitude that represents the measured temperature and σ 2 is the noise power or the measurement error. Integrating the above Equation, Eq. 22 yields: 4. PROBABILITY OF DETECTION AND MISSED DETECTION The PD is the likelihood that the LDS will correctly detect an actual leak. The Probability of Missed Detection is the probability that the system will not declare an actual leak. The signal here is a combination of true signal power and noise power that respectively correspond to measured temperature change and the measurement error of the temperature change. Figure 2 shows the probability density for power signal plus noise. Detection occurs in the event the measured signal power exceeds or equals to the predetermined threshold. FIGURE 2. AMPLITUDE DISTRIBUTION OF THE THE POWER SIGNAL Probability of Missed Detection (PMD) is expressed as: PD = Xth μ erf 2 2σ2 [ ( n )] (23) Four possible cases result from modeling the detection and false detection: PD : Leak exists and LDS indicates that leak exists PMD : Leak exists and LDS does not report the leak PFA : Leak does not exist and LDS indicates it exists POCR : Leak does not exist and LDS indicates it does not exist. - (hit) - (miss) - (false alarm) - (correct rejection) Figure 3 shows the PD curve versus the temperature changes at a given threshold. This is taken for a case with a threshold temperature change of.5 ºC, SNR 4 db and temperature coefficient of.6mhz/ ºC. As the Figure illustartes that the PD is directly proportional to the temperature change, the higher the temperature changes the higher the PD. According to Eq. 23, there are three parameters that need to be determined, the noise variance, the mean of the data samples and the threshold. The first two parameters are obtained from the characteristics of the received signal while the last parameter is determined as a function of PFA using Eq. 2. PMD = PD (2) 8 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

9 for Various Temperature Change Values - Threshold =.5Cº increases with SNR. It is obvious that PD increases with the increase of PFA and SNR FIGURE 3. - PD VERSUS TEMPERATURE CHANGE pfa =.4 pfa =. pfa =. PD can be expressed in terms of PFA by substituting Eq. 7 into Eq. 23 to yield: PD = 2 [erfc (erfc (2PFA) μ n ] (24) 2σ2) Where erfc is the complementary error function and erfc - is the inverse of the complementary error function. As indicated above that the power represents the true temperature measurements and noise represents the measurement error. Referring to Eq. 9 which is shown below as Eq. 25, the power will be µ 2 and noise power will be σ2 n. SNR = and, SNR = nµ σ µ2 σ 2 (25) n Equation 24 can be expressed in terms of SNR as: (26) PD = 2 [erfc (erfc (2PFA) SNR 2 ) ] (27) Figure 4 illustrates that as the PFA decreases the PD decreases for various values of SNR. Also, as the SNR increases, the PD increases. Similarly, Fig. 5 shows that PD Signal to Niose Ratio FIGURE 4. PD VERSUS SNR FOR VARIOUS PFA Different Values of SNR Values SNR =3 db SNR =2 db SNR = db SNR = 5 db FIGURE 5. PD FOR VARIOUS THRESHOLDS WITH DIFFERENT SNR VALUES The PD is expressed in terms of the threshold by substituting Equation 9 into Equation 23: PD = n [ erf [ 2 2σ 2 ( ΔV B μ)] ] (28) 2 SNR.25 α T 9 Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

10 Figure 6 illustrates that the PD increases with the increase of the temperature change. This means that there is higher probability of detection for higher temperature change. Another observation that can be noted is the increase of the SNR leads to an increase of the PD and the PFA together..9 Std:.2 Std: SNR:3dB - Tth:.6Cº - pfa:.6 SNR:2dB - Tth:2.8Cº - pfa:.39 SNR:dB - Tth:4.97Cº - pfa.83 SNR:5dB - Tth:6.6Cº - Different Values of SNR Values FIGURE 6. PD FOR VARIOUS THRESHOLDS WITH DIFFERENT PFA AND SNR VALUES FIGURE 8. PD FOR VARIOUS TEMPERATURES USING DIFFERENT STANDARD DEVIATION VALUES The larger the number of sample sizes or the larger the number of scanning the better the SNR value and the better the PD will be. Figure 9 illustrates that as the number of the sample sizes increases the PD increases when the detected T is higher than threshold. Figure 7 shows the relationship between PD and PFA, for every PD value there is a corresponding PFA value PD versus Different Numbers of Samples Sample Size:5 Sample Size: Sample Size:2 Sample Size: Probability of False Alarm FIGURE 7. - PD VERSUS PFA FIGURE 9. - PD FOR DIFFERENT SAMPLE SIZES 5. CONCLUSION The PFA and the PD have been formulated and analyzed for fiber optic based LDS. These two parameters establish the fundamental building block for assessing the performance of the LDS and assist operators to implement the course of action that might be required to enhance the reliability of the system. Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

11 The analysis revealed that as the SNR increases the PD increases and so does the PFA. The simultaneous increase of the PD and the PFA presents a great challenge when designing or specifying the system. Figure 7 illustrates the direct relationship between these two parameters; the PD increases with the increase of PFA. To deal with this challenge, an acceptable PFA should be selected first from which a satisfactory threshold can be determined. Once the threshold is established, the PD can be immediately determined. The missed detection and false detection are detrimental to the system performance, and the consequences of their occurrence cost time and money. The question is which one is more costly; obviously, the consequences of missed detection will result in a greater financial burden than the consequences of the false detection. Therefore, the initial step in designing such systems is to determine the magnitude of risk that the operators can accept and tolerate in the event a missed detection takes place. Once this step gets accomplished, the performance parameters can easily be established. Future work will extend this research to develop a probabilistic performance assessment framework for monitoring process components using leak detection system. ACKNOWLEDGMENTS The authors gratefully acknowledge and appreciate the partial financial support provided by the Research & Development Corporation (RDC) of Newfoundland and Labrador, Canada. REFERENCES. Nikles, Marc, 29, Long-Distance Fiber Optic Sensing Solutions for Pipeline Leakage, Intrusion and Ground Movement Detection, Proc. of SPIE, 736, pp Ulrich, H. F & Lehrmann, E. P., 28, Telecommunications Research Trends, Nova Science Publishers Inc., New York, NY, USA. 3. Park, J., Bolognini, G., Lee, D., Kim, P., Cho, P., Pasquale, F., Park, N., 26, Raman-based Distributed Temperature Sensor with Simplex Coding and Link Optimization, IEEE Photonics Technol. Letter, 8, PP Oil & Gas Journal, 2, OGJ_Sept-6-_Walk_Frings. 5. Bao, Xiaoyi and Chen, Liang, 22, Recent Progress in Distributed Fiber Optic Sensors, Sensors 22, 2, pp ; doi:.339/s2786, - ISSN , 6. Bao, X., DeMerchant, M., Brown, A., and Bremner, T., 2, Tensile and Compressive Strain Measurement in the Lab and Field with the Distributed Brillouin Scattering Sensor, Journal of Lightwave Technology, 9 (), pp Agrawal, G. P., 2, Nonlinear Fiber Optics, Academic Press, 3rd edition, New York, USA. 8. Soto, M. A., Bolognini, G., and Pasquale, F. D, 2, Long-Range Simplex-Coded BOTDA Sensor over 2Km Distance Employing Optical Pre-Amplification, Optics Letters, 36 (2), pp Bao, X. & Chen, L., 22, Recent Progress in Distributed Fiber Optic Sensors, Sensors 22, 2, pp. ( ); doi:.339/s 2786, ISSN , Bao, X, Webb, D. J. and Jackson, D., 993, A 32-Km Distributed Temperature Sensor based on Brillouin Loss in Optical Fiber, Optics Letters, 8 (8), pp , Bao, X., Dhliwayo, Heron, D. J. and Jackson, D., 995, Experimental and Theoretical Studies on Distributed Temperature Sensor Based on Brillouin Scattering, Journal of Light wave Technology, 3(7), pp Belal, M., 2, Development of a High Spatial Resolution Temperature Compensated Distributed Strain Sensor, PhD Thesis, Physical and Applied Science Optoelectronics Research Center, University of Southampton, Southampton, UK. 3. Horiguchi, T., and Tateda, M., 989, Optical-Fiber- Attenuation Investigation Using Stimulated Brillouin Scattering between a Pulse and a Continuous Wave, Opt. Letter, 4, pp Smith, J. R, 999A, Characterization of the Brillouin Loss Spectrum for Simultaneous Distributed Sensing of Strain and Temperature, MSc. Thesis, Department of Physics, University of New Brunswick, NB, Canada. 5. Brown, K., 26, Improvement of a Brillouin Scattering based Distributed Fiber Optic Sensor, PhD Thesis, University of New Brunswick, NB, Canada. 6. Parker, T., Farhadiroushan, M., Feced, R., Handerek, V. and Rogers, A., 998, Simultaneous Distributed Measurement of Strain and Temperature from Noise- Initiated Brillouin Scattering in Optical Fibers, IEEE Journal of Quantum Elec., 34, pp Smith, J., Brown, A., DeMarchant, M. and Bao, X., 999B, Simultaneous Distributed and Temperature Measurement, Applied Optics. 38, pp Wait, P. C. and Newson, T. P., 996, Landau Placzek Ratio Applied to Distributed Fiber Sensing, Opt. Communications, 22, pp Wickens, Thomas, D., 22, Elementary Signal Detection Theory, Oxford University Press Inc., New York, NY, USA. 2. Horiguchi, T., Kurashima, T. and Koyamada, Y., 992, Measurement of Temperature and Strain Distribution by Brillouin Frequency Shift in Silica Optical Fibers, SPIE Distributed and Multiplexed Fiber Optic Sensors, Volume, 797 (). Copyright 24 by ASME Downloaded From: on 2/8/26 Terms of Use:

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