Method for establishing SIL dynamic evaluation model based on Weibull distribution

Abstract

The invention relates to a method for establishing an SIL dynamic evaluation model based on Weibull distribution, and belongs to the technical field of safety protection systems. The method comprises the following steps: (1) establishing a dynamic cumulative failure probability function model based on Weibull distribution according to obtained failure data through a reliability test; (2) calculating Weibull distribution parameters by using a median rank method, a linear regression fitting method and a least square method; (3) drawing a function model image by using MATLAB software; and (4) in combination with a fault tree method, establishing an SIL dynamic evaluation model based on Weibull distribution. According to the SIL dynamic evaluation model for the final executive component of the safety instrument system based on Weibull distribution, the dynamic change trend of the final executive component PFDavg along with time obtained by the model basically accords with the reality, the accuracy of SIL evaluation is improved, and scientific method support is provided for design personnel of the safety instrument system.

Description

Technical Field

[0001] This invention relates to a method for establishing a dynamic evaluation model of Safety Instrumented System (SIL) based on Weibull distribution, and particularly to a method for establishing a dynamic evaluation model of the final actuator of a safety instrumented system based on Weibull distribution, belonging to the field of safety protection system technology. Background Technology

[0002] A Safety Instrumented System (SIS) is an instrumentation system composed of sensors, logic controllers, and final actuators capable of performing one or more safety functions. As a crucial measure for ensuring safe production, SISs are widely used in industries such as petrochemicals, natural gas, and power generation. To effectively guarantee the reliability and safety of SISs, it is necessary to calculate the Average Probability of Dangers Failure on Demand (PFD). avg The Safety Integrity Level (SIL) of an instrumented system is used to assess its reliability. The SIL, as a metric for measuring the reliability of a Safety Instrumented System (SIS), is detailed in the International Electrotechnical Commission (IEC) standard 61508 and the Chinese functional safety standard GB / T 20438-2017, which specify the relevant concepts and calculation methods for the functional safety of SIS. avg Different methods have been used to set requirements and regulations for the functional safety and safety integrity levels of Safety Instrumented Systems (SIS).

[0003] Safety Instrumented Systems (SIS) require the average probability of hazardous failure (PFD) avg The computational model for PFD typically uses a constant failure rate. In reality, the failure rate varies over time, thus leading to PFD. avg The calculation results and the Security Integrity Level (SIL) classification are not accurate enough.

[0004] The inventors discovered that the PFD calculated using the constant failure rate formula in GB / T 20438.6 is... avg An excessively high value may lead to a bias in the SIL assessment, underestimate the SIL level of the safety instrumented system, and increase the initial investment cost of the enterprise's SIS.

[0005] Therefore, a method for establishing a SIL dynamic evaluation model based on Weibull distribution is provided, applicable to the final actuators of safety instrumented systems, enabling the final actuator PFD... avg The dynamic trend of change over time is basically consistent with reality, improving the safety instrumented system (PFD). avg Ensuring the accuracy of calculation results, and providing scientific methodological support for safety instrument system designers, has become a pressing technical challenge in this field. Summary of the Invention

[0006] The main objective of this invention is to provide a method for establishing a dynamic evaluation model of SIL based on Weibull distribution, enabling the final execution element PFD to... avg The dynamic trend of change over time is basically consistent with reality, improving the safety instrumented system (PFD). avg The accuracy of the calculation results provides scientific methodological support for designers of safety instrumented systems.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for establishing a dynamic evaluation model of SIL based on Weibull distribution, the steps of which are as follows:

[0009] (1) Based on the failure data obtained from reliability tests, establish a dynamic cumulative failure probability function model based on the Weibull distribution;

[0010] (2) The Weibull distribution parameters were calculated using the median rank method, linear regression fitting method, and least squares method.

[0011] (3) Use MATLAB software to plot the function model;

[0012] (4) Combine the fault tree method to establish a dynamic evaluation model of SIL based on Weibull distribution.

[0013] Preferably, step (2) is as follows:

[0014] First, the estimated value of the cumulative distribution F(ti) is calculated using the median rank formula. Numerous statistical experiments have shown that if the sample size is small, it can be calculated using the following formula:

[0015]

[0016] In the formula, i represents the number of failures, and n represents the total number of failures;

[0017] Subsequently, the parameters were estimated using linear regression, and then the model parameters were obtained by applying the least squares method.

[0018] For the two-parameter Weibull distribution, by transformation, the sample points are approximately fitted to a straight line, and equation (2) becomes the following equation:

[0019]

[0020] Taking the natural logarithm twice on both sides of equation (6), we have:

[0021]

[0022] make:

[0023]

[0024] Substituting equation (8) into equation (7), we get:

[0025] y = kx + b (9)

[0026] Equation (9) can be viewed as the equation of a straight line in the Cartesian coordinate system x–y, with a slope of k and an intercept of b.

[0027] Substituting the failure data into equation (8), we can obtain the data to be observed: (x1, y1), (x2, y2), ..., (x n y n Pearson correlation coefficient is calculated using equation (10) to test the linear correlation of the data. The least squares method is applied to calculate the values ​​of k and b using equation (11). Then, a Weibull probability diagram is drawn to determine whether the failure data follows a Weibull distribution. If it follows a distribution, the values ​​of the shape parameter β and the scale parameter η in the Weibull distribution model can be calculated.

[0028]

[0029] Preferably, step (3) is as follows: by writing computer program code and using MATLAB tools to plot, the specific Weibull distribution model of this valve is obtained, including the probability density function, cumulative failure probability function, reliability function and failure rate function.

[0030] Preferably, step (4) is as follows:

[0031] Given that events M2 and M3 are independent, the probability of event M1 occurring is: P M1 (t)=P M2 (t)×P M3 (t);

[0032] Since the failure rate data follows a Weibull distribution, the failure probability P M2 (t) is the cumulative failure probability function that follows a Weibull distribution, i.e.:

[0033]

[0034] If the default invalid data is consistent, then P M2 (t)=P M3 (t);

[0035]

[0036] According to PFD avg Definition of the final execution element PFD avg_wbl，FE The calculation formula is as follows:

[0037]

[0038] Requires the average probability of hazardous failure (PFD) avg_GB The calculation formula is shown in equation (19):

[0039] PFD avg_GB =2λT (19)

[0040] By referring to the table in GB / T 20438.6 and combining the failure data experimental conditions, we take the constant λ failure rate = 0.5E-6 and substitute it into formula (19) to obtain the PFD of the final actuator. avg_GB,FE The calculation formula is as follows: The indefinite integral of formula (18) cannot be expressed by elementary functions, that is, there is no analytical closed-form solution. The integral needs to be solved by numerical methods. Therefore, code is written using MATLAB tools, the values ​​of β and η are substituted into the formula, and the integral operation is performed using the integral function. Finally, the PFD of the two calculation formulas is obtained. avg Dynamic trends.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] The final actuator PFD obtained by the SIL dynamic evaluation model of the final actuator of the safety instrumented system based on Weibull distribution in this invention avg The dynamic changes over time are basically consistent with reality, which improves the accuracy of SIL assessment and provides scientific methodological support for safety instrumented system designers.

[0043] The present invention will be further described below with reference to specific embodiments and accompanying drawings, but this does not imply any limitation on the scope of protection of the present invention. Attached Figure Description

[0044] Figure 1 This describes the process of constructing a dynamic evaluation model for the final execution element of a safety instrumented system based on Weibull distribution in Embodiment 1 of the present invention;

[0045] Figure 2 This is a Weibull probability distribution diagram from Embodiment 1 of the present invention;

[0046] Figure 3 This refers to the Weibull probability distribution model in Embodiment 1 of the present invention;

[0047] Figure 4 This is the fault tree for the final execution element in Embodiment 1 of the present invention;

[0048] Figure 5 The PFD in Embodiment 1 of the present invention avg Dynamic trend chart. Detailed Implementation

[0049] The present invention will be further described below with reference to specific embodiments. It should be understood that the following text is only used to describe one or more specific implementations of the present application and does not strictly limit the scope of protection specifically claimed in the present application. In the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other.

[0050] Unless otherwise specified, the components involved in the following embodiments are all commercially available conventional components, and the methods used are all methods commonly used in this technical field.

[0051] Example 1

[0052] In actual production operations, the failure of the final actuators of the safety instrumented system (PFD) has a significant impact on the safety protection system of pressure-bearing equipment. avg Since the contribution or proportion is the largest, the inventors have focused their research on the final actuator, regarding it as a key device in the safety instrumented system.

[0053] Typically, when calculating the SIL (Solution Intake) of a Safety Instrumented System (SIS), the failure rate is assumed to be constant. However, in actual operation, the failure rate curve often conforms to a function with time as the variable. To more accurately calculate the SIL of an SIS and reflect the relationship between the failure rate and time, reliability tests were conducted on a certain type of valve at Wuzhong Instrument Co., Ltd. Based on the obtained failure data, a Weibull distribution model was selected to construct a failure analysis model for the valve. The Weibull distribution parameters were calculated using the median rank method, linear regression fitting method, and least squares method to obtain the final Weibull distribution model. Then, combined with the fault tree method, a dynamic SIL assessment model for the final actuator of the SIS was established, and the PFD (Power Factor Delay) of the valve at different times was calculated. avg The value of is used to address the problem of inaccurate calculation results caused by using a constant failure rate during evaluation. The specific steps are as follows: Figure 1 As shown:

[0054] 1. Failure Analysis Model Construction

[0055] 1.1 Weibull Distribution Model

[0056] The Weibull distribution model was first proposed by the Swedish scientist Weibull when calculating the strength of a chain. It is now a commonly used model in reliability analysis to express strength and lifetime. This invention selects the two-parameter Weibull distribution model, where the probability density function (PDF) is:

[0057]

[0058] In the formula, t is the running time, t≥γ; β is the shape parameter, which determines the basic shape of the probability density curve, β>0; η is the scale parameter, which has the effect of reducing or increasing the scale of the horizontal axis, but does not affect the shape of the distribution, η>0;

[0059] The cumulative failure probability, also known as unreliability, is the probability that a tool will fail to perform its intended function under specified conditions and within a specified time. The cumulative failure probability function (CDF), denoted as F(t), is expressed as:

[0060]

[0061] Reliability is the probability that a tool will perform its intended function under specified conditions and within a specified time. The reliability function, denoted as R(t), is expressed as:

[0062]

[0063] When failure data follows a Weibull distribution, the failure rate function is used to calculate the probability of failure per unit time given that the product survives to time t. Its expression is:

[0064]

[0065] The Weibull distribution model is the foundation of life testing and reliability theory, unifying the three stages of instantaneous failure rate. In failure analysis of safety instrumented systems, different values ​​of the shape parameter β can represent different types of failure stages in the bathtub curve: when β < 1, the instrument is in the early failure period (DFR), and the failure rate gradually decreases with increasing operating time; when β = 1, the instrument is in the random failure period (CFR), the failure rate decreases to a low level and remains unchanged for a considerable period, and the Weibull distribution probability density function curve approximates an exponential distribution; when β > 1, the instrument is in the wear-out failure period (IFR), and the failure rate gradually increases with increasing operating time.

[0066] 1.2 Weibull parameter calculation

[0067] First, the cumulative distribution F(t) is calculated using the median rank formula. i The estimated value of ) Numerous statistical experiments have shown that if the sample size is small, it can be calculated using the following formula:

[0068]

[0069] In the formula, i represents the number of failures, and n represents the total number of failures;

[0070] Subsequently, the linear regression method was used for parameter estimation. The linear regression method is a commonly used method for calculating model parameters. Its principle is to transform the model to make it linear, and then apply the least squares method to obtain the model parameters.

[0071] For a two-parameter Weibull distribution, the sample points can be approximated as a straight line through transformation, and equation (2) can be transformed into the following equation:

[0072]

[0073] Taking the natural logarithm twice on both sides of equation (6), we have:

[0074]

[0075] make:

[0076]

[0077] Substituting equation (8) into equation (7), we get:

[0078] y = kx + b (9)

[0079] Equation (9) can be viewed as the equation of a straight line in the Cartesian coordinate system x–y, with a slope of k and an intercept of b.

[0080] Substituting the failure data into equation (8), we can obtain the data to be observed (x1, y1), (x2, y2), ..., (xn, yn). The Pearson correlation coefficient is calculated using equation (10) to test the linear correlation of the data. The least squares method is applied, and the values ​​of k and b are calculated using equation (11). Then, the Weibull probability diagram is drawn to determine whether the failure data follows a Weibull distribution. If it follows a distribution, the values ​​of the shape parameter β and the scale parameter η in the Weibull distribution model can be calculated.

[0081]

[0082] 1.3PFD avg calculate

[0083] To ensure the proper functioning of the safety instrumented system in emergency situations, preventative maintenance must be performed regularly, with one inspection and maintenance session scheduled per cycle. Assuming the equipment's inspection and testing cycle is T, and based on the Weibull distribution, the average probability of hazardous failure (PFD) is... avg_wbl The calculation formula is shown in equation (12):

[0084]

[0085] 2 Case Analysis

[0086] 2.1 Data Calculation

[0087] Because the safety instrumented system operates in a low-requirement mode, activating at most once a year, it is difficult to collect field failure data for the final actuators. The data in this invention is based on reliability tests conducted by Wuzhong Instrument Co., Ltd. on this valve model. One aspect of this test involved accelerating the valve's operation at a frequency of once per hour. The raw failure data is shown in Table 1, where i represents the number of failures, t... i Indicates the time when the i-th failure occurs;

[0088] This type of valve typically fails once every 8,000 to 10,000 operations. Therefore, time correction needs to be applied to the valve based on actual application conditions. For simplified calculation, the time t in Table 1 is used as an example. i Expanded to 1000 times its original size;

[0089] Table 1 Failure data for a certain type of valve

[0090] Table 1 Failure data for a certain type of valve

[0091] Serial number i <![CDATA[Time t i / h]]> Serial number i <![CDATA[Time t i / h]]> Serial number i <![CDATA[Time t i / h]]> 1 11 16 123 31 227.2 2 23.5 17 134.2 32 231.4 3 28.4 18 136.2 33 239.3 4 40.6 19 158.1 34 251.2 5 50.7 20 169.4 35 275 6 53.2 21 170 36 276.2 7 61.1 22 173.4 37 281 8 71.1 23 175 38 283.4 9 82.5 24 178.5 39 317.1 10 90.6 25 180.2 40 352 11 91.3 26 191.6 41 391 12 97.6 27 197.6 42 487.1 13 101.8 28 207.4 43 732.2 14 102.7 29 212.4 — — 15 107.9 30 218.1 — —

[0092] Substituting the corrected valve failure data from Table 1 into equation (8), we calculate: k = 1.4579, b = -17.8475, then β = k = 1.4579, η = 207288.5835. We then plot the Weibull probability diagram, as follows: Figure 2 As shown in the figure, the blue solid line is the fitted line. From the Weibull probability distribution diagram, it can be roughly seen that the vast majority of data points are distributed around the fitted line. The Pearson correlation coefficient r = 0.99452 is calculated by equation (10), which means that the data shows a strong linear correlation. The Weibull hypothesis is valid, that is, the failed data follows the Weibull distribution.

[0093] 2.2 Drawing the Weibull distribution model

[0094] By writing computer program code and using MATLAB tools for plotting, the specific Weibull distribution model of this valve is obtained, and the probability density function is as follows: Figure 3 As shown in the upper left of (a); the cumulative failure probability function is as follows Figure 3 As shown in the upper right of (b); the reliability function is as follows Figure 3 As shown in the lower left of (c); the failure rate function is as follows Figure 3 As shown in the lower right of the middle (d);

[0095] 2.3 Probability Density Function Analysis

[0096] The larger the β value of the probability density function, the sharper the peak shape and the higher the data concentration. The peak time point corresponds to the most likely failure period. The peak position t can be calculated by equation (13). slope_max ≈93668, and combined with Figure 3 The probability density function graph in the upper left of (a) indicates that the valve is most likely to fail during this time period, and targeted inspections can be strengthened.

[0097]

[0098] 2.4 Cumulative Failure Probability Function Analysis

[0099] B10 life is a metric used to measure product reliability. It indicates that after a certain period of operation, it is expected that 10% of the products will fail. B10 life can be calculated using the following formula.

[0100] t B10 =η·(-ln(0.9)) 1 / β (14)

[0101] Median lifetime refers to the lifetime of a product when its reliability drops to 0.5, that is, the lifetime corresponding to a reliability R = 0.5, where it is expected that 50% of the products will fail. The median lifetime can be calculated using the following formula.

[0102] t 50 =η·(ln 2) 1 / β (15)

[0103] Characteristic lifetime is an important parameter in product reliability analysis, used to evaluate the expected life of a product at a specific reliability level. It refers to the product's lifespan at a reliability level of R(t) = e -1 The runtime at approximately 0.368 refers to the natural result in the Weibull CDF formula when t = η, i.e., F(t) = 1 - e^(-η / t). -1 ≈0.632, it is estimated that 63.2% of the products will fail before this time. The scale parameter η can directly reflect the lifespan at this time. In actual engineering, tracking the change of η value can assess the stability of the production process.

[0104] right Figure 3 Analyzing the cumulative failure probability function graph in the upper right corner, the function curve is S-shaped, which roughly determines the range of β value as (1,3). This indicates that the failure rate of this valve gradually increases with the increase of operating time. Furthermore, it can be seen that the slope of the function curve is large in the early stage, indicating that the valve has a high risk of early failure. The maximum slope point corresponds to the peak value in the PDF curve, which means that failure is most likely to occur during this period. At this time, the environmental control should be optimized and regular preventive maintenance should be carried out.

[0105] Substituting β = 1.4579 and η = 207288.5835 into equations (14) and (15), we can calculate the lifetime t of B10. B10 ≈44281, median lifetime t 50 ≈161211, characteristic lifetime t η If the value is approximately 207289, the following maintenance strategy can be implemented: preventive inspection every 100,000 hours and mandatory replacement every 200,000 hours. This method can verify whether the valve quality meets the designed engineering standards, and improve the valve's service life by increasing the η value through process improvement.

[0106] 2.5 Reliability Function and Failure Rate Function Analysis

[0107] Depend on Figure 3 As can be seen from the function graphs in the lower left and lower right, the reliability function curve is monotonically decreasing, and the reliability decreases continuously with time; the failure rate function curve is monotonically increasing, and the failure rate increases continuously with time, but the rate of increase of failure rate gradually slows down; combining the function graphs and the shape parameter β value, the wear-out failure period (IFR) of the valve in the bathtub curve can be determined, and the maintenance and replacement strategy of the valve can be formulated according to the actual situation of the project.

[0108] 3. Final Execution Component SIL Dynamic Evaluation Model

[0109] Two valves of this model are used in a petrochemical company in Tianjin and constitute the final element (FE) system of a 2oo2 voting architecture. The final element will only experience a critical failure when both valves fail simultaneously. A critical failure fault tree is constructed for the final element as follows: Figure 4 As shown:

[0110] Given that events M2 and M3 are independent, the probability of event M1 occurring, as shown in the fault tree, is: P M1 (t)=P M2 (t)×P M3 (t);

[0111] Since the failure rate data of this valve assembly follows a Weibull distribution, the failure probability P M2(t) is the cumulative failure probability function that follows a Weibull distribution, i.e.:

[0112]

[0113] Since the two valve groups are identical, the default failure data is the same, then P M2 (t)=P M3 (t);

[0114]

[0115] According to PFD avg Definition of the final execution element PFD avg_wbl，FE The calculation formula is as follows:

[0116]

[0117] The requirement of the 2oo2 voting architecture in "Functional Safety of Electrical / Electronic / Programmable Electronic Safety-Related Systems Part 6: Application Guidelines for GB / T 20438.2 and GB / T 20438.3" (GB / T 20438.6) for the average probability of hazardous failure (PFD) is as follows: avg_GB The calculation formula is shown in equation (19):

[0118] PFD avg_GB =2λT (19)

[0119] By referring to the table in GB / T 20438.6 and combining the failure data experimental conditions, we take the constant λ failure rate = 0.5E-6 and substitute it into formula (19) to obtain the PFD of the final actuator. avg_GB,FE The calculation formula is as follows: The indefinite integral of formula (18) cannot be expressed by elementary functions, that is, there is no analytical closed-form solution. The integral needs to be solved by numerical methods. Therefore, code is written using MATLAB tools, the values ​​of β and η are substituted into the formula, and the integral operation is performed using the integral function. Finally, the PFD of the two calculation formulas is obtained. avg Dynamic trends, such as Figure 5 As shown; the red dashed line in the figure represents the PFD. avg_GB,FE The curve shows the change, with the blue solid line representing PFD. avg_wbl,FE The variation curve is calculated using the constant failure rate formula in GB / T 20438.6, representing the PFD. avg The PFD calculated using the Weibull distribution formula is significantly higher in the early time period than that calculated using the Weibull distribution formula. avg The value is too large, which may cause deviation in the SIL assessment, underestimate the SIL level of the safety instrumented system, and increase the enterprise's investment costs.

[0120] The black markers on the blue solid line in the figure represent the characteristic lifetime points, i.e., the time points T = η, at which point the PFD... avg_wbl,FE=0.13153, indicating that there is approximately a 13.15% probability that the final actuator will fail dangerously before this time point. By finding the extreme value of the second derivative, the point of maximum curvature change of the function curve is calculated, and the inflection point time T is obtained. tp If the timeframe is approximately 90,974 hours, then preventative maintenance before the inflection point will be most effective; if you want to maintain the SIL safety level at SIL1 or SIL2, then PFD (Prophylactic Filter) is required. avg The value is less than 0.1 or 0.01, which can be determined according to PFD. avg_wbl,FE The function formula calculates the maintenance time T set before the final execution element reaches the SIL1 level allowable threshold. tv1 The maintenance time T set before reaching the SIL2 level allowable threshold is approximately 181,960 hours. tv2 ≈71,889 hours, in order to ensure the SIL safety level of the final actuator;

[0121] 4. Conclusion

[0122] (1) Based on the reliability test failure data of a certain type of valve of Wuzhong Instrument Co., Ltd., the present invention calculates the Weibull distribution parameters using methods such as linear regression fitting. The Pearson correlation coefficient and the Weibull distribution probability image both show that the failure data follows the Weibull distribution. Then, the four models of the valve in the Weibull distribution model are calculated: probability density function, cumulative failure probability function, reliability function, and failure rate function. Through theoretical analysis of the four models, the failure characteristics of the valve are summarized and various life indicators are calculated, and targeted engineering suggestions are proposed.

[0123] (2) Based on the Weibull distribution model of a certain type of valve, and combined with the fault tree method, a dynamic evaluation model of the SIL of the final actuator of the safety instrumented system was established; by comparison, it was found that the PFD calculated using the constant failure rate formula in GB / T 20438.6 was lower. avg PFD calculated by the Weibull distribution formula avg An excessively high value may bias the SIL assessment, underestimate the SIL level of the safety instrumented system, and increase the initial investment cost of the enterprise's SIS. Therefore, using the Weibull distribution model can improve the PFD of the safety instrumented system. avg The accuracy of the calculation results;

[0124] (3) The feasibility and effectiveness of the method have been verified through engineering examples, avoiding the problems of PFD in traditional models. avg The calculated deviations are of reference value for the dynamic assessment of the safety integrity level of the safety instrumented system in petrochemical plants, and provide scientific methodological support for safety instrumented system designers.

[0125] Although the foregoing has described the inventive concept and embodiments in detail, those skilled in the art will recognize that various improvements and modifications can be made to the invention without departing from the scope of the claims, and such improvements and modifications should still fall within the protection scope of the invention.

Claims

1. A method for establishing a dynamic evaluation model of SIL based on Weibull distribution, the steps of which are as follows: (1) Based on the failure data obtained from reliability tests, establish a dynamic cumulative failure probability function model based on the Weibull distribution; (2) The Weibull distribution parameters were calculated using the median rank method, linear regression fitting method, and least squares method. (3) Use MATLAB software to plot the function model; (4) Combine the fault tree method to establish a dynamic evaluation model of SIL based on Weibull distribution.

2. The method for establishing the SIL dynamic evaluation model based on Weibull distribution as described in claim 1, characterized in that: Step (2) is as follows: First, the estimated value of the cumulative distribution F(ti) is calculated using the median rank formula. Numerous statistical experiments have shown that if the sample size is small, it can be calculated using the following formula: In the formula, i represents the number of failures, and n represents the total number of failures; Subsequently, the parameters were estimated using linear regression, and then the model parameters were obtained by applying the least squares method. For the two-parameter Weibull distribution, by transformation, the sample points are approximately fitted to a straight line, and equation (2) becomes the following equation: Taking the natural logarithm twice on both sides of equation (6), we have: make: Substituting equation (8) into equation (7), we get: y = kx + b (9) Equation (9) can be viewed as the equation of a straight line in the Cartesian coordinate system x–y, with a slope of k and an intercept of b. Substituting the failure data into equation (8), we can obtain the data to be observed (x1, y1), (x2, y2), ..., (xn, yn). The Pearson correlation coefficient is calculated using equation (10) to test the linear correlation of the data. The least squares method is applied, and the values ​​of k and b are calculated using equation (11). Then, the Weibull probability diagram is drawn to determine whether the failure data follows a Weibull distribution. If it follows a distribution, the values ​​of the shape parameter β and the scale parameter η in the Weibull distribution model can be calculated.

3. The method for establishing a SIL dynamic evaluation model based on Weibull distribution according to claim 2, characterized in that: Step (3) is as follows: By writing computer program code and using MATLAB tools to plot, the specific Weibull distribution model of this valve is obtained, including the probability density function, cumulative failure probability function, reliability function and failure rate function.

4. The method for establishing a SIL dynamic evaluation model based on Weibull distribution according to claim 3, characterized in that: Step (4) is as follows: Given that events M2 and M3 are independent, the probability of event M1 occurring is: P M1 (t)=P M2 (t)×P M3 (t); Since the failure rate data follows a Weibull distribution, the failure probability P M2 (t) is the cumulative failure probability function that follows a Weibull distribution, i.e.: If the default invalid data is consistent, then P M2 (t)=P M3 (t); According to PFD avg Definition of the final execution element PFD avg_wbl，FE The calculation formula is as follows: Requires the average probability of hazardous failure (PFD) avg_GB The calculation formula is shown in equation (19): PFD avg_GB =2λT (19) By referring to the table in GB / T 20438.6 and combining the failure data experimental conditions, we take the constant λ failure rate = 0.5E-6 and substitute it into formula (19) to obtain the PFD of the final actuator. avg_GB,FE The calculation formula is as follows: The indefinite integral of formula (18) cannot be expressed by elementary functions, that is, there is no analytical closed-form solution. The integral needs to be solved by numerical methods. Therefore, code is written using MATLAB tools, the values ​​of β and η are substituted into the formula, and the integral operation is performed using the integral function. Finally, the PFD of the two calculation formulas is obtained. avg Dynamic trends.

Images