A method for determining conditional probability in risk analysis

Abstract

The present invention discloses a method for determining conditional probability in risk analysis. First, the structure and function realization process of the system are analyzed, and the system simulation modeling is performed in the form of a group of physical equations using the Modelica language. Then, a risk event is injected into the system model, and through simulation, the comprehensive performance of the system after the risk event occurs is analyzed, and an event chain of risk transfer is constructed. Finally, actual disturbance data is loaded into the system simulation model, and the Monte Carlo method is used to perform repeated simulation analysis to statistically calculate the conditional probability of risk transfer. The present invention overcomes the shortcomings of traditional experience-based risk event chain construction and analysis, improves the objectivity and comprehensiveness of risk transfer event chain construction, realizes the simulation calculation of conditional probability in risk analysis, and improves the credibility of risk analysis results, which plays an important guiding role in the formulation of risk corrective measures.

Description

Technical field:

[0001] The invention relates to a method for determining conditional probability in risk analysis, and belongs to the technical field of aviation systems. Background technology:

[0002] According to the fleet risk assessment model based on TARAM (Transport Aircraft Risk Assessment Method), there is a probability of undetected failure during fleet operation, and the corresponding fleet risk R F for:

[0003]

[0004] where ε F The predicted number of faulty aircraft; μ F is the probability of failure not being detected; is the conditional probability of catastrophic consequences, i.e., the sum of the product of the conditional probabilities of the event chain, which is related to the fault type and flight time; F The severity level.

[0005] Conditional probability is defined as the probability of an unsafe outcome with a known damage rate caused by a certain risk event. Conditional probability is generally calculated by the risk transfer probability between intermediate events in the event chain. Since event chains are not easy to construct and the transfer conditional probabilities between intermediate events are difficult to determine, the calculation of conditional probability is crucial to the accuracy of fleet risk assessment.

[0006] In the existing risk conditional probability calculation methods, the key risk event chain is constructed based on subjective experience, and the method of giving the risk transfer probability in the event chain relies on historical data statistics, experimental testing, expert experience, fault tree analysis, etc. However, for the risk transfer process of a specific event, there is often a lack of data and it is impossible to estimate. Especially when the amount of data is small, the conditional probability is conservatively assumed to be 1, indicating that this unsafe event will definitely lead to some unsafe consequences, but the risk value calculated in this way is definitely too large. Therefore, the existing methods cannot guarantee the comprehensiveness of the constructed event chain and the accuracy of the conditional probability calculation, which affects the classification of event risk levels and causes unnecessary economic losses. Summary of the invention:

[0007] In order to overcome the above-mentioned deficiencies in risk analysis, such as lack of conditional probability statistics, overly conservative risk calculation values, and insufficiently comprehensive and objective event chain establishment, the present invention provides a method for determining conditional probability in risk analysis.

[0008] The technical solution adopted by the present invention is: a method for determining conditional probability in risk analysis, the specific steps are as follows:

[0009] (1) Establish a system simulation model based on Modelica, verify the accuracy of the model by performing similarity analysis on the characteristic values, characteristic change trends, and distribution patterns of the simulation data of the key parameters of the system operation and the measured data, and improve the simulation model by optimizing the modeling parameters;

[0010] (2) Treat the risk events under study as failures and inject faults into the system model, sort out the risk transfer path from risk events to unsafe consequences, and construct a risk transfer event chain;

[0011] (3) Load the actual operating data of the system into the system simulation model, perform Monte Carlo simulation analysis of the system, and calculate the conditional probability of risk transfer based on the simulation results.

[0012] Furthermore, step (1) is specifically as follows:

[0013] a. Clarify the system structure layer, divide the modeling object system into multiple levels of subsystems, sub-subsystems and even bottom-level components, split the system structure according to the different physical fields to which the components belong, and use a bottom-up approach for parts with simple hierarchical structures and a top-down approach for parts with complex multi-domain coupling;

[0014] b. Establish component models, use design documents, industry standards, and test methods to study the working principles of components, formulate quantitative descriptions of their input-output relationships and internal variable conversion relationships, and establish physical models of components in the form of a set of physical equations;

[0015] c. Optimize the simulation model, conduct similarity analysis on the characteristic values, characteristic change trends, distribution patterns, etc. of the key operating parameters of the simulated and measured systems, verify the correctness of the model, and improve the simulation model by optimizing and correcting the model parameters.

[0016] Furthermore, step (2) is specifically as follows:

[0017] a. Event mechanism research: according to the manifestation of risk events, find out the components or subsystems related to and affected by them;

[0018] b. Under given working conditions, the input-output relationship of the faulty component is constructed through simulation, and the physical equations used for modeling are corrected. When the working data deviation before and after the component failure is large, a new empirical formula is fitted based on the test data to achieve fault modeling;

[0019] c. Conduct simulation analysis of the system with risk events under different load conditions, check the system's functional implementation and status parameters, compare with the system FMECA table, and determine whether there are any harmful failure consequences;

[0020] d. Combined with the system Modelica model, with the correlation analysis between model variables as the core, combined with the fault tree and fishbone diagram analysis methods, sort out the risk transfer path from risk events to serious consequences, and construct the risk transfer event chain.

[0021] Furthermore, step (3) is specifically as follows:

[0022] a. Use the Modelica model to load various disturbances in actual working conditions into the system simulation model, use sensors to detect random vibrations in the working environment and interference pulses in the circuits where electronic components are located, load these disturbances into the Modelica model in real time through the semi-physical simulation platform, and participate in the simulation calculation; or fit the disturbance data into a random distribution and input it into the model;

[0023] b. Based on the Monte Carlo idea, we randomly select environmental parameters, randomly take values ​​of component parameters within the tolerance range, and randomly simulate the possibility of risk events being missed and repaired in the intermediate links. We perform a large number of repeated simulations, check component state variables at key nodes based on the established risk transfer event chain, and statistically analyze the risk transfer probability at the intermediate events.

[0024] Compared with the existing risk analysis conditional probability calculation method, the construction of the risk transfer event chain in the present invention is based on the quantitative simulation of the system model, which overcomes the shortcomings of the traditional experience-based construction of risk event chains and analysis, and the established event chain is more comprehensive and objective; the calculation of the risk transfer conditional probability is derived from a large number of random simulations of various situations that may occur during the actual operation of the system, and its statistical data is more accurate and reliable. The calculated value of risk analysis tends to be accurate, which has a high guiding significance for the formulation of maintenance corrective measures and helps to improve economic benefits. Description of the drawings:

[0025] Figure 1 It is a modeling simulation calculation flow chart of the present invention.

[0026] Figure 2 It is a flow chart of system modelica modeling performed by the present invention.

[0027] Figure 3 It is a flow chart of the risk injection process of the present invention.

[0028] Figure 4 It is a simplified diagram of the risk transfer path constructed by the present invention. Specific implementation method:

[0029] The present invention will be further described below in conjunction with the accompanying drawings.

[0030] (1) Figure 2 As shown in the figure, the steps of system hierarchical modeling based on Modelica are:

[0031] a. Clarify the system structure layer. Analyze the system structure and function realization process, divide the modeling object system into multiple levels of subsystems, sub-subsystems and even bottom-level components, and split the system structure according to the different physical fields such as electrical, mechanical, hydraulic, pneumatic, etc. The parts with simple hierarchical structures are modeled in a bottom-up manner, and the parts with complex multi-field coupling are modeled in a top-down manner.

[0032] b. Establish component models. Use design documents, industry standards, and experiments to study the working principles of components, formulate quantitative descriptions of their input-output relationships and internal variable conversion relationships, and establish component physical models in the form of a set of physical equations. At the same time, by defining components as abstract types, the reusability of the model is improved through inheritance, derivation, and re-declaration, and the international standard underlying library is used to achieve the universality of the model, thus establishing a basic component model library based on Modelica. Taking the common small hole damping in hydraulics as an example, its fluid modeling formula is shown in equation (2), and the dynamic coupling equations of fluid mechanics and other components are shown in equation (3).

[0033]

[0034] q=vA (3)

[0035] Where q is the flow rate, C d is the damping coefficient, A 孔 is the piston area, p is the hydraulic pressure, ρ is the hydraulic oil density, v is the piston speed, and A is the piston area. Encapsulating the above two formulas can form a local model of the small hole damping component, and by calling it in a higher-level system model, the inheritance and reuse of the model is realized.

[0036] According to the mutual coupling mode of functions and signals between components, the interfaces of each model are defined, including different types such as mechanical interface, gas interface, logic interface, electrical interface, etc. Necessary flow variables and potential variables, such as electric potential and current, are defined in the interface. In the above formula, hydraulic pressure p is a potential variable, and it is necessary to ensure that the values ​​at both ends of the interface are equal; flow q is a flow variable, which satisfies the requirement that the sum of the values ​​at both ends is zero and obeys the generalized Kirchhoff's law. According to the structural hierarchy of the system and the functional interaction signal transmission between components, combined with specific working conditions, the overall model is established by establishing corresponding algebraic constraint equations between interfaces and connecting all component object interfaces.

[0037] c. Optimize the simulation model. Perform a similarity comparison analysis on the characteristic values, characteristic change trends, and distribution patterns of the key operating parameters obtained by simulation and the measured values ​​to verify the correctness of the model, and improve the model by optimizing and correcting the model parameters. For example, when the pressure or flow obtained by the orifice damping simulation does not match the actual measured value, the orifice damping coefficient, hydraulic oil density, etc. in formula (2) can be checked to see if they are consistent with the actual value and corrected.

[0038] (2) Figure 3 As shown in the figure, the steps of constructing the risk transfer event chain based on the Modelica model are as follows:

[0039] a. Event mechanism research. According to the manifestation of risk events, find out the components or subsystems related to and affected by them. Conduct failure mechanism research on typical unsafe events such as sensor failure, control device failure, electrical failure, etc., including system components and event impact, explain the failure form and cause of components, and explain how the system will perform after the failure of such components. For example, wear and debris of circuit components will cause the damping orifice to be blocked, which may cause the flow of the hydraulic circuit to decrease and the pressure to rise, affecting the execution speed of the actuator and hydraulic cylinder, etc.

[0040] b. Treat system risk events as a type of failure, and conduct event modeling and injection. Analyze event behavior and event signal propagation characteristics; define model correction parameters (such as signal drift coefficient, leakage coefficient, blockage coefficient, etc.), combine the component's own working principle equations and the impact of event parameters on component functions, and formulate risk events through experiments, historical data fitting, empirical formulas, etc., as shown in formula (4).

[0041] r=Kr0 (4)

[0042] Where r is the actual radius of the small hole, K is the blockage coefficient, and r0 is the design radius of the small hole.

[0043] Different types of events have different digital representations, including sudden events and component function degradation, etc. By adding internal fault behavior models and logical switches in component modules, risk injection based on the Modelica model is achieved.

[0044] c. Perform simulation analysis of the system's risk event state under different load conditions. Check the system's functional implementation and state parameters, and compare them with the system FMECA table to determine whether there are any harmful failure consequences. For example, a common failure in a hydraulic system is actuator creep, which manifests itself as an unstable actuator execution speed and an intermittent state. This state can be easily identified and marked as a failure consequence at the end of the event chain, such as Figure 4 The "A" and "B" in the diagram.

[0045] d. Event chain construction. Combine existing fault tree, fishbone diagram and other analysis methods to study the fault propagation mechanism. For the components that appear in the fault tree and fishbone diagram, extract their key variables X and Y and calculate their correlation coefficients according to formula (5). Variables with high correlation are regarded as being on the same event chain, and the components they are in are regarded as key nodes in the risk transfer process. For example, in the hydraulic system, the key variable of the hydraulic pump is the output pressure, and the key variable of the actuator is the operating speed. The simulation data of the two are correlated, and it can be seen that the two have a high correlation. It is considered that the hydraulic pump and the actuator are two key nodes on the same event chain, such as "A1" and "B1".

[0046]

[0047] Repeat the above analysis process to construct a risk transfer path diagram, such as Figure 4 As shown, there are two independent chains of events.

[0048] (3) The method for calculating the risk conditional probability of system operation events is:

[0049] Taking advantage of the Modelica model's ability to load data from other sources, various disturbances in actual working conditions are loaded into the system simulation model. Sensors are used to detect random vibrations in the working environment, interference pulses in the circuits where electronic components are located, etc., and these disturbances are loaded into the Modelica model in real time through a semi-physical simulation platform and participate in simulation calculations; or the disturbance data is fitted into a random distribution (such as a constant pressure source, the actual output of components such as hydraulic pumps often obeys a normal distribution) and input into the model to achieve a more accurate system condition construction. According to the Monte Carlo idea, random selection of environmental parameters (such as temperature, air pressure, etc.), random selection of component parameters within the tolerance range, random simulation of the possibility of risk events being missed and repaired at intermediate links, etc., are performed, and a large number of repeated simulations are performed to achieve effective simulation of various emergencies, design defects, manufacturing defects, improper maintenance and normal system degradation that may exist in reality. Based on the constructed risk transfer event chain, the component state variables at key nodes are checked, and the probability of risk transfer at intermediate events is statistically analyzed, such as for:

[0050]

[0051] Then the conditional probabilities of unsafe results A and B are:

[0052]

[0053]

[0054] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for determining conditional probability in risk analysis, characterized in that: The specific steps are as follows: (1) Establish a system simulation model based on Modelica, verify the accuracy of the model by performing similarity analysis on the characteristic values, characteristic change trends, and distribution patterns of the simulation data of the key parameters of the system operation and the measured data, and improve the simulation model by optimizing the modeling parameters; (2) Inject the risk source under study into the system model, obtain the risk transfer path from the risk source to the unsafe consequence based on the physical mechanism established in the system model, and construct the risk transfer event chain; (3) Load the actual operating data of the system onto the system simulation model, perform Monte Carlo simulation analysis of the system, and calculate the conditional probability of risk transfer based on the simulation results; Step (1) is as follows: a. Clarify the system structure hierarchy, divide the modeling object system into multiple levels of subsystems, sub-subsystems and even bottom-level components, split the system structure according to the different physical fields to which the components belong, and use a bottom-up approach for parts with simple hierarchical structures and a top-down approach for parts with complex multi-field coupling structures; b. Establish component models, use design documents, industry standards, and test methods to study the working principles of components, formulate quantitative descriptions of their input-output relationships and internal variable conversion relationships, and establish physical models of components in the form of a set of physical equations; c. Optimize the simulation model, conduct similarity analysis on the characteristic values, characteristic change trends, and distribution patterns of the key operating parameters of the simulated and measured systems, verify the correctness of the model, and improve the simulation model by optimizing and correcting the model parameters; Step (2) is as follows: a. Event mechanism research: according to the manifestation of risk events, find out the components or subsystems related to and affected by them; b. Under given working conditions, the input-output relationship of the faulty component is constructed through simulation, and the physical equations used for modeling are corrected. When the working data deviation before and after the component failure is large, a new empirical formula is fitted based on the test data to achieve fault modeling; c. Conduct simulation analysis of the system with risk events under different load conditions, check the system's functional implementation and status parameters, compare with the system FMECA table, and determine whether there are any harmful failure consequences; d. Combine the system Modelica model, focus on the correlation analysis between model variables, combine the fault tree and fishbone diagram analysis methods, sort out the risk transfer path from risk events to serious consequences, and construct the risk transfer event chain; Step (3) is as follows: a. Use the Modelica model to load various disturbances in actual working conditions into the system simulation model, use sensors to detect random vibrations in the working environment and interference pulses in the circuits where electronic components are located, load these disturbances into the Modelica model in real time through the semi-physical simulation platform, and participate in the simulation calculation; or fit the disturbance data into a random distribution and input it into the model; b. Based on the Monte Carlo concept, we randomly select environmental parameters, randomly select component parameters within the tolerance range, and randomly simulate the possibility of risk events being missed and repaired at intermediate links. We perform a large number of repeated simulations, check component state variables at key nodes based on the established risk transfer event chain, and statistically analyze the risk transfer probability at intermediate events. for: Then the conditional probabilities of unsafe results A and B are:

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