Aviation safety risk U-bowtie assessment method under mixed uncertain condition

Abstract

The invention relates to an aviation safety risk U-bowtie assessment method under a mixed uncertain condition, and belongs to the technical field of aviation risk assessment. Comprising the following steps: 1, selecting a typical aviation unsafe event to carry out qualitative risk identification and consequence analysis; 2, constructing a risk measurement index by using an opportunity theory, and improving the model into a U-bowtie model; 3, aiming at the uncertain random system under the mixed uncertain condition, respectively giving a risk measurement calculation rule in the U-bowtie model from two parts of U-FTA and U-ETA; and 4, carrying out sensitivity analysis. According to the method, the improved U-bowtie model and the risk measurement index are constructed, the risk measurement calculation rule is given, risk quantitative evaluation of unsafe events is realized, the evaluation result is more reasonable and reliable, key factors and measures are obtained through sensitivity analysis, and implementation of safety management work and improvement of the safety level are facilitated.

Description

Technical Field

[0001] The present invention relates to a U-bowtie assessment method for aviation safety risks under mixed uncertain conditions, belonging to the technical field of aviation risk assessment. Background Art

[0002] Safety is an eternal theme in aviation. Aviation activities are characterized by high technology, high investment, high risks, and severe accident consequences. To effectively alleviate and control safety risks, aviation risk management work has attracted much attention.

[0003] Compared with other safety risk analysis methods, the Bow-tie model is a risk management tool that combines qualitative and quantitative analysis, has strong visualization, and is systematic and comprehensive. On the one hand, the Bow-tie model combines the fault tree analysis method and the event tree analysis method, enabling a complete and intuitive understanding of the entire process of accident development and evolution. On the other hand, the Bow-tie model can evaluate from a global perspective whether the measures taken to prevent and control hazard sources and mitigate accident consequences are sufficient. Currently, for unsafe events in aviation activities, mainly including accidents (flight accidents, ground accidents), incident reports (flight incident reports, ground incident reports), and other unsafe events, etc., the Bow-tie model can not only conduct risk analysis from a qualitative perspective but also objectively conduct risk assessment on unsafe events from a quantitative perspective.

[0004] Compared with qualitative risk analysis, the difficulty of quantitative risk assessment lies in how to reasonably and effectively measure the risk level of unsafe events. Especially in recent years, new equipment has been successively put into service, and safety issues have shown new characteristics. A large amount of uncertainty has emerged in the risk quantitative analysis using the Bow-tie model. According to the sources of uncertainty and the different levels of understanding of uncertainty, uncertainty is divided into two categories: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty is an inherent property of the system, while epistemic uncertainty is caused by the lack of historical statistical data and experimental sample information. Aleatory uncertainty is difficult to handle or eliminate, and traditional probability theory methods are usually used in the risk quantitative analysis using the Bow-tie model; for epistemic uncertainty caused by insufficient knowledge, fuzzy theory, D-S evidence theory, cloud model, uncertainty theory, etc. are all effective solutions. However, in actual aviation activities, the occurrence of many risk events involves many factors, a wide range, and miscellaneous sources. When conducting risk quantitative analysis using the Bow-tie model, there are both parts with sufficient knowledge where effective data can be fully collected, and parts with insufficient knowledge in the case of small samples and poor information. Therefore, it is necessary to consider a more general, more complex, and more realistic situation of the existence of mixed uncertainty.

[0005] Therefore, there is an urgent need to design an aviation safety risk assessment method based on an improved Bow-tie model that considers the existence of mixed uncertainty for the risk quantification of aviation unsafe events and effectively improve the safety management level. Summary of the Invention

[0006] In view of the above problems, the present invention aims to provide an aviation safety risk U-bowtie assessment method under mixed uncertainty conditions. This assessment method can describe the risk evolution process of aviation unsafe events throughout the whole process and has the ability to handle the risk quantification problem in the coexistence of aleatory and epistemic uncertainties, so as to obtain more accurate and reliable risk quantification assessment results.

[0007] An aviation safety risk U-bowtie assessment method under mixed uncertainty conditions of the present invention is characterized by including the following steps:

[0008] Step 1: Conduct risk identification and consequence analysis for typical unsafe events during the use of aviation equipment;

[0009] Step 2: Under mixed uncertain conditions, using the opportunity theory, construct a new index for measuring the likelihood of risk occurrence: the risk measure index (Risk belief), which is used to describe the risk levels of various risk events involved in the risk assessment process of typical unsafe events. At this time, the Bow-tie model considering random and cognitive uncertainties is improved to the U-bowtie model (Uncertain Bow-tie model);

[0010] Step 3: For the uncertain random system under mixed uncertain conditions, design the risk measure calculation rules in the U-bowtie model respectively from two parts: U-FTA and U-ETA;

[0011] Step 4: On the basis of risk quantification, conduct sensitivity analysis to obtain key components of the system, key nodes of the work process, key risk factors, and key control measures, etc.

[0012] Preferably, the process of risk identification and consequence analysis for the typical unsafe events described in Step 1 includes:

[0013] (1) Sort out the materials related to aviation unsafe events, select a certain accident as the research object, and conduct qualitative risk analysis;

[0014] (2) Use the Bow-tie model to sort out various causes and risk evolution paths leading to the accident, that is, construct the fault tree and event tree that make up the Bow-tie model respectively.

[0015] Preferably, the construction process of the risk measure index and the improved U-bowtie model described in Step 2 includes:

[0016] (1) In the improved U-bowtie model, the risk measure index is defined as: assuming that the risk event state variable ξ is an uncertain random variable, and Ξ represents the feasible domain of abnormal or failure states (i.e., accidents) that lead to risks and losses. For example, when the temperature exceeds 80 degrees, the part fails, where the temperature is the variable ξ, and ξ≥80 is the feasible domain Ξ. The risk measure is defined as the opportunity measure of the risk event being in an abnormal state that may lead to an accident, expressed as:

[0017] θ RB =Ch{ξ∈Ξ}

[0018] At this time, the variable ξ describes the state of the risk event, and the feasible domain Ξ describes the value range of the variable ξ during an accident. When ξ∈Ξ, it is considered that the risk event is in a failure state. At this time, the risk event becomes one of the causes or one of the causes leading to the accident, expressed as:

[0019] Let Ξ = {η1, η2}, where η1 represents that the system or event Λ is in a safe state, and η2 represents that the system or event Λ is in an accident state. Then the risk measure index θ RB is the opportunity measure for the event to be in the accident state (i.e., Λ = {η2}), denoted as θ RB = Ch{Λ};

[0020] (2) If the state variable ξ degenerates into a random variable, then the risk measure index is transformed into a probability representing the likelihood of the risk event occurring, which can be calculated based on statistical data and is denoted as At this time, the system is affected by random uncertainty, and the risk measure is transformed into a risk measure based on probability theory (i.e., risk probability); if the state variable ξ degenerates into an uncertain variable, then the risk measure index is transformed into a credibility representing the credibility of the risk event occurring, which is given by expert knowledge and is denoted as At this time, the system is affected by cognitive uncertainty, and the risk measure is transformed into a risk measure based on uncertainty theory (i.e., risk credibility).

[0021] Preferably, the determination process of the risk measure calculation rule in the U-bowtie model described in step 3 includes:

[0022] (1) Considering that when there is mixed uncertainty, the uncertain random system contains both random event variables and uncertain event variables, and also contains uncertain random event variables. According to the combination of variables, the uncertain random system can be divided into two categories: If an uncertain random system can be clearly divided into several random subsystems and several uncertain subsystems, that is, there is no other part that contains both random variables and uncertain variables except the whole, and at this time there is only one uncertain random variable, the whole system, then the system is called a simple uncertain random system; If there are uncertain random subsystems in the system, then the system is called a complex uncertain random system;

[0023] According to the classification of simple and complex uncertain random systems, the corresponding calculation rules are given in the U-FTA model and the U-ETA model respectively;

[0024] (2) In U-FTA, for a simple uncertain random system, the random variable and the uncertain variable are independent of each other and form a random subsystem and an uncertain subsystem respectively. The logical gate algorithms involved rely on the product theorem of probability theory and uncertainty theory. When the basic event i is a random variable, its risk measure θ RB，Bi is transformed into describing the probability of its occurrence, which is calculated from a large amount of statistical data; when the basic event i is an uncertain variable, the risk measure is transformed into Specific reliability values and types of uncertainty distributions are given by experienced experts;

[0025] For two independent random basic events, when the two variables both belong to an "AND" gate, the risk probability of its upper-level intermediate event can be obtained by calculation; when the two variables both belong to an "OR" gate, the risk probability of its upper-level intermediate event can be obtained by the formula calculation;

[0026] For two independent uncertain basic events, when the two variables both belong to an "AND" gate, the risk reliability of its upper-level intermediate event can be obtained by calculation; when the two variables both belong to an "OR" gate, the risk reliability of its upper-level intermediate event can be obtained by the formula calculation;

[0027] According to the characteristics of a simple uncertain random system, the top event is the only uncertain random variable in the system. In the U-FTA analysis under different logic gate conditions, the calculation method of the risk measure of the top event is as follows:

[0028]

[0029] where, θ RB，CE is the risk measure value of the top event, is the risk probability of the intermediate event v of the random variable, is the risk reliability of the intermediate event t of the uncertain variable.

[0030] (3) In U-FTA, for a complex uncertain random system, since there are several uncertain random variables and there is no direct calculation formula for the logic gate algorithm of uncertain random variables, when calculating the risk measure index of the top event, the system structure function needs to be given first, and then the risk measure value of the top event is calculated indirectly. Assume that the complex system is a Boolean system, the system structure function f is a Boolean function, and it consists of n basic events BE1, BE2,..., BE n with Boolean values {0, 1}. When the Boolean value is 1, the event state is an abnormal state, and when it is 0, it is a normal state. f is the system structure function, and when f(BE1, BE2,...BE n ) = 1, the accident (top event) occurs;

[0031] Assume that an uncertain random system is a Boolean system, there is a structural Boolean function f, which contains n independent random event variables η1, η2,..., η with risk probabilities of n and m risk reliabilities of Independent uncertain event variables τ1, τ2, …, τ m , then the risk measure value of the top event CE in the uncertain random system is:

[0032]

[0033] Where

[0034]

[0035] When x i = 1 and y j = 1, it respectively indicates that the event variables η i and the event variable τ j are in the failure state; p i is the risk probability when the random event variable η i is in the failure state, and ξ j is the risk belief when the uncertain event variable τ j is in the failure state.

[0036] (4) In U - ETA, for a simple uncertain random system, the random variable and the uncertain variable are independent of each other, and can be calculated respectively according to the product theorem of probability theory and uncertainty theory. The specific calculation formula is shown in Table 2. Then the risk measure calculation method of the result event OE k on branch k is as follows:

[0037]

[0038] Where θ RB，CE is the risk measure of the top event, is the risk probability of the random variable control event i, is the risk belief of the uncertain variable control event j.

[0039] (5) In U - ETA, for a complex uncertain random system, assume that there are l result events in the event tree. The k - th result event OE k includes s branches. Among the t branches, there are respectively n independent random events η1, η2, …, η with a risk measure of n , and m independent uncertain events τ1, τ2, …, τ with a risk measure of m . Then the risk measure value of the k - th result event OE k in the uncertain random system is:

[0040]

[0041] Where k = 1, …, l, t = 1, …, s.

[0042] Preferably, the sensitivity analysis process in Step 4 includes:

[0043] (1) Compare (including and ) to sort the basic events (including random basic event variables and uncertain basic event variables) by their values, and identify the "important event elements", i.e., the key basic events ranked at the top;

[0044] Among them, for random basic event variables, the Birnbaum importance calculation formula is:

[0045]

[0046] where P(OE i =1|x i =1) represents the probability that the result event occurs when event x i occurs, and P(OE i =1|x i =0) represents the risk occurrence probability of the result event when event x i does not occur;

[0047] Similarly, for uncertain basic event variables, the calculation formula for uncertainty importance is given as:

[0048]

[0049] where represents the belief that the result event occurs when event x i occurs, and represents the risk belief of the result event when event x i does not occur;

[0050] (2) For control events, with different result events as the focus, different key control events are obtained. Estimate the change in the risk level of the result event through the following two risk reduction assumptions to determine the most critical control event: 1) Quantitatively reduce the risk measure value of the input event. Assume that the risk measure value of the input event x i is reduced by 20% or 1%, and observe the reduction of the risk measure value of the output event (top event or result event); 2) Completely eliminate the risk of the input event. Assume that the risk measure value of the input event x i becomes 0, and observe the reduction of the risk measure value of the output event. At the same time, the key basic events can also be determined using the above method, and this method is also applicable to sensitivity analysis in the case of multiple event changes.

[0051] The beneficial effects of the present invention are as follows: The present invention discloses a U-bowtie assessment method for aviation safety risks under mixed uncertain conditions. Compared with the prior art, the improvements of the present invention are as follows:

[0052] (1) The present invention proposes a U-bowtie model-based aviation risk assessment method for risk assessment of aviation equipment unsafe events with both random and epistemic uncertainties (i.e., mixed uncertainties). Introducing the opportunity theory can comprehensively handle complex situations where random variables, uncertain variables, and uncertain random variables coexist. Based on sorting out and constructing the Bow-tie model of the evolution of unsafe events, the measurement of risk event variables is distinguished for simple and complex mixed situations. In addition, this method introduces and improves the Birnbaum importance for sensitivity analysis, obtains key risk factors and effective control measures, which is conducive to the implementation of risk control.

[0053] (2) Based on the Bow-tie model, this method considers the uncertain event variables and random uncertain event variables under mixed uncertain conditions and improves it to the U-bowtie model, which is more in line with the actual situation.

[0054] (3) This method determines the calculation rules for risk assessment in U-FTA and U-ETA. Combining the law of large numbers and the uncertain Boolean operation rules, a risk quantification method for the top event variable and the result event variable is given, which can handle complex situations where random uncertainty and epistemic uncertainty coexist. On the one hand, this method avoids the defects of the probability risk assessment method in the case of incomplete probability information. On the other hand, it can handle the uncertain quantities in expert credibility more properly, making the quantified results obtained from risk assessment more accurate and reliable. Description of the Drawings

[0055] Figure 1 : Flowchart of the U-bowtie assessment method for aviation safety risks under mixed uncertain conditions of the present invention;

[0056] Figure 2 : Schematic diagram of the Bow-tie model;

[0057] Figure 3 : Schematic diagram of the U-bowtie model;

[0058] Figure 4 : Simple uncertain random system diagram in U-FTA;

[0059] Figure 5 : Complex uncertain random system diagram in U-FTA;

[0060] Figure 6 : Simple uncertain random system diagram in U-ETA;

[0061] Figure 7 : Diagram of complex uncertain random system in U-ETA;

[0062] Figure 8 : Diagram of Bow-tie model for tire burst accident;

[0063] Figure 9 : Diagram of the reduction of OE3 risk level. Detailed implementation manner

[0064] In order to enable ordinary technicians in the field to better understand the technical solution of the present invention, an embodiment is given below to further describe the technical solution of the present invention.

[0065] Embodiment 1

[0066] A U-bowtie evaluation method for aviation safety risk under mixed uncertain conditions in this embodiment refers to the appendix Figures 1-7 , and includes the following steps:

[0067] Step 1: Conduct risk identification and consequence analysis on typical unsafe events during the use of aviation equipment;

[0068] In Step 1, select a certain accident as the research object, conduct qualitative risk analysis, and use the Bow-tie model to sort out various reasons and risk evolution paths leading to the accident, that is, construct the fault tree and event tree that make up the Bow-tie model respectively. Among them, this typical unsafe event is the top event (CE) in the model and is also the connection point of the fault tree and the event tree. The model generally includes two types of elements: events and logical algorithms. In the fault tree, it is divided into basic events (accident causes BE), logical gates (OR and AND), intermediate events, and key events (top event CE); in the event tree, it is divided into key events (top event), events (control events E), and result events (accident consequences OE). The basic event is the hazard source that may cause an accident, the top event is the accident itself, the control event is the mitigation and remedial measure, and the result event is a series of consequences that the accident may cause. See the appendix for the model schematic diagram Figure 2 as shown.

[0069] Step 2. Under mixed uncertain conditions, use the relevant knowledge of opportunity theory to construct a new index for measuring the likelihood of risk occurrence - risk measure index (Risk belief), so as to describe the risk levels of various risk events involved in Step 1 at this time. At this time, the Bow-tie model considering random and epistemic uncertainties is improved to the U-bowtie model (Uncertain Bow-tie model).

[0070] The construction of the U-bowtie model is divided into two parts: the Uncertain Fault Tree (U-FT) and the Uncertain Event Tree (U-ET), which are interconnected by the top event. See Appendix Figure 3 , Appendix Figure 3 An example of a U-bowtie is shown.

[0071] In the improved U-bowtie model, the risk measure index is defined as follows: Assume that the state variable ξ of the risk event is an uncertain random variable, and Ξ represents the feasible region of abnormal or failure states (i.e., accidents) that cause risks and losses. For example, when the temperature exceeds 80 degrees, a part fails, where the temperature is the variable ξ, and ξ ≥ 80 is the feasible region Ξ. The risk measure is then defined as the opportunity measure of the risk event being in an abnormal state that may lead to an accident, expressed as:

[0072] θ RB = Ch{ξ ∈ Ξ}

[0073] At this time, the variable ξ describes the state of the risk event, while the feasible region Ξ describes the range of values of the variable ξ during an accident. When ξ ∈ Ξ, it is considered that the risk event is in a failure state, and at this time, the risk event becomes one of the causes or a cause leading to the accident, expressed as:

[0074] Let Ξ = {η1, η2}, where η1 represents that the system or event Λ is in a safe state, and η2 represents that the system or event Λ is in an accident state. Then the risk measure index θ RB is the opportunity measure of the event being in an accident state (i.e., Λ = {η2}), denoted as θ RB = Ch{Λ}.

[0075] It should be noted that if the state variable ξ degenerates into a random variable, the risk measure index is transformed into a probability representing the likelihood of the risk event occurring, which can be calculated based on statistical data and is denoted as At this time, the system is affected by random uncertainty, and the risk measure is transformed into a risk metric based on probability theory (i.e., risk probability); if the state variable ξ degenerates into an uncertain variable, the risk measure index is transformed into a credibility representing the credibility of the risk event occurring, which is given by expert knowledge and is denoted as At this time, the system is affected by cognitive uncertainty, and the risk measure is transformed into a risk metric based on uncertainty theory (i.e., risk credibility).

[0076] Therefore, based on the risk measure index, the U-bowtie model established based on the opportunity theory is a brand-new risk analysis technique applicable to complex systems containing uncertain variables and random variables.

[0077] Step 3. For an uncertain stochastic system under mixed uncertain conditions, give the calculation rules of risk measures in the U-bowtie model.

[0078] Considering that when there is mixed uncertainty, the uncertain stochastic system contains both random event variables, uncertain event variables, and uncertain stochastic event variables. According to the combination of variables, the uncertain stochastic system can be divided into two categories: If an uncertain stochastic system can be clearly divided into several random subsystems and several uncertain subsystems, that is, there is no other part that contains both random variables and uncertain variables except the whole, and there is only one uncertain stochastic variable, which is the whole system at this time, then this system is called a simple uncertain stochastic system; if there are uncertain stochastic subsystems in the system, then this system is called a complex uncertain stochastic system.

[0079] According to the classification of simple and complex uncertain stochastic systems, and based on the structural composition of the U-bowtie model, calculation rules are given for both the U-FTA model and the U-ETA model respectively.

[0080] 1. First, the calculation rules of risk measures in U-FTA.

[0081] For uncertain fault tree analysis (U-FTA), its event elements are divided into three categories: bottom basic events BE, middle intermediate events IE, and top top events CE. The logic gates include AND gate and OR gate. According to the classification criteria of simple and complex uncertain stochastic systems, it can be obtained that:

[0082] If the intermediate event closest to the top event is a random variable or an uncertain variable, and the top event CE obtained through a single logic gate is an uncertain stochastic variable. At this time, it can be considered that in the model, several random subsystems and uncertain subsystems are conducted through a single logic gate to obtain the top event. See the appendix Figure 4 shown, which belongs to the U-FTA analysis of a simple uncertain stochastic system.

[0083] If there is at least one uncertain stochastic event variable among the intermediate event variables connecting to obtain the top event CE, at this time, there are uncertain stochastic subsystems in the subsystems connected by the same logic gate. See the appendix Figure 5 shown, which belongs to the U-FTA analysis of a complex uncertain stochastic system.

[0084] The following gives the calculation rules of risk measures in simple and complex uncertain stochastic systems in U-FTA analysis respectively:

[0085] (1) In a simple uncertain random system, random variables and uncertain variables are independent of each other, forming a random subsystem and an uncertain subsystem respectively. The logical gate algorithms involved depend on the product theorems of probability theory and uncertainty theory. When the event is a random variable, the risk measure θ RB，Bi is transformed into the probability of its occurrence, which is calculated from a large amount of statistical data; when the event is an uncertain variable, the risk measure is transformed into the numerical value of the specific credibility and the type of uncertain distribution given by experienced experts.

[0086] For two independent random basic events, when the two variables belong to the "AND" gate, the risk probability of the upper intermediate event can be calculated by ; when the two variables belong to the "OR" gate, the risk probability of the upper intermediate event can be calculated by the formula calculated.

[0087] For two independent uncertain basic events, when the two variables belong to the "AND" gate, the risk credibility of the upper intermediate event can be calculated by ; when the two variables belong to the "OR" gate, the risk credibility of the upper intermediate event can be calculated by the formula calculated.

[0088] Table 1 Logical gate algorithm formulas in U-FTA

[0089]

[0090] In summary, the specific logical gate calculation formulas for different variable combinations are summarized in Table 1. Therefore, according to the characteristics of the simple uncertain random system, the top event is the only uncertain random variable in the system. In the U-FTA analysis under different logical gate conditions, the calculation method of the risk measure of the top event is as follows.

[0091]

[0092] (2) In a complex uncertain random system, due to the existence of several uncertain random variables and the lack of direct calculation formulas for the logical gate algorithms for uncertain random variables, when calculating the risk measure index of the top event, it is necessary to first give the system structure function and indirectly calculate the risk measure value of the top event. Assume that the complex system is a Boolean system, the system structure function f is a Boolean function, composed of n basic events BE1, BE2,..., BE n with Boolean values of {0, 1}. When the Boolean value is 1, the event state is an abnormal state, and when it is 0, it is a normal state. f is the system structure function, and when f(BE1, BE1,..., BE n ) = 1, the accident (top event) occurs.

[0093] Suppose an uncertain random system is a Boolean system, and there exists a structural Boolean function f, which contains n independent random event variables η1, η2, …, η with risk probabilities of n and m independent uncertain event variables τ1, τ2, …, τ with risk credibilities of m . Then the risk measure value of the top event CE in the uncertain random system is:

[0094]

[0095] where

[0096]

[0097] When x i = 1 and y i = 1, the basic event variables are in the failure state.

[0098] 2. Secondly, the risk measure calculation rules in U-ETA.

[0099] For the uncertain event tree analysis (U-ETA), its event elements are divided into two categories: control event E and result event OE, and the logical structure is similar to an OR gate. If each event branch corresponds to only one result event variable, as shown in the appendix Figure 6 shown, then it is a U-ETA analysis of a simple uncertain random system; if there are multiple branches corresponding to the same result event variable, as shown in the appendix Figure 7 shown, then it is a U-ETA analysis of a complex uncertain random system.

[0100] The following respectively gives the risk measure calculation rules for simple and complex uncertain random systems in U-ETA analysis:

[0101] (1) In a simple uncertain random system, the random variables and uncertain variables are independent of each other, and can be calculated separately according to the product theorem of probability theory and uncertainty theory. The specific calculation formula is shown in Table 2. Then the risk measure calculation method of the result event OE k on branch k is as follows.

[0102]

[0103] Table 2 Logical gate algorithm formula in U-ETA

[0104]

[0105] (2) In a complex uncertain random system, assume that there are l result events in the event tree, and the kth result event OE kIt includes s branches. In the t-th branch, there are n independent random events η1, η2, …, η with a risk measure of n , and m independent uncertain events τ1, τ2, …, τ with a risk measure of m . Then, the risk measure value of the k-th outcome event OE k in the uncertain random system is:

[0106]

[0107] where k = 1, …, l, and t = 1, …, s.

[0108] So far, the risk measures of all event variables in the U-bowtie model, that is, the typical unsafe events and their consequence events existing in the process of using aviation equipment, etc., can be reasonably quantified through probability theory, uncertainty theory, and chance theory.

[0109] Step4. On the basis of risk quantification, further conduct sensitivity analysis around the top event and consequence events in U-FTA and U-ETA. Sensitivity analysis helps to identify key components of the system, key nodes of the work process, key risk factors, and key control measures, etc., so as to improve the system safety.

[0110] This method uses the Birnbaum importance. The main work is divided into two parts: 1) Evaluate the difference in the influence degree of each basic event on the outcome event, identify the weak links in the basic events that lead to the occurrence of unsafe events, and thus formulate targeted preventive measures; 2) Evaluate the difference in the influence degree of each control event on the outcome event, identify the effective measures in the control events that mitigate the consequences of unsafe events, and provide reasonable countermeasures for the disposal of unsafe events.

[0111] In the U-bowtie model, for the random basic event variable, the formula for calculating the Birnbaum importance is:

[0112]

[0113] where P(OE i = 1|x i = 1) represents the probability that the outcome event occurs when the event x i occurs, and P(OE i = 1|x i = 0) represents the risk occurrence probability of the outcome event when the event x i does not occur.

[0114] Similarly, for the uncertain basic event variable, the formula for calculating the uncertainty importance can be given as:

[0115]

[0116] Among them, represents the reliability of the result event occurring when event x i occurs, represents event x i When it does not occur, it represents the risk reliability of the result event.

[0117] By comparing (including and ), the values are sorted, and the basic events (including random basic event variables and uncertain basic event variables) are sorted to identify the "important event elements", that is, the key basic events ranked at the front.

[0118] Furthermore, for control events, with different result events as the focus, the obtained key control events are different. Generally, the change in the risk level of the result event can be estimated through the following two risk reduction assumptions, so as to determine the most critical control event. The determination of key basic events can also use the following method: (1) Quantitatively reduce the risk measure value of the input event. Assume that the risk measure value of the input event x i (θ RB，Bi or θ RB，Ei ) is reduced by 20% or 1%, and observe the reduction of the risk measure value of the output event (top event or result event); (2) Completely eliminate the risk of the input event. Assume that the risk measure value of the input event x i becomes 0, and observe the reduction of the risk measure value of the output event. At the same time, the method of risk reduction for hypothesis estimation is also applicable to sensitivity analysis in the case of multiple event changes.

[0119] Example 2

[0120] This example is a specific test case. The case description: As an important component in the aircraft landing system, once a tire bursts, it may cause serious accident consequences and endanger the safety of people and machines. For a certain new type of transportation, around the typical unsafe event of "tire burst", considering that the frequency of tire burst accidents during the use of this model is relatively low, there is insufficient fault data for some new components, while there is sufficient historical data for some general components that were used in previous models and can be used for reference. At this time, this example belongs to the quantitative risk assessment using the U-bowtie model under mixed uncertainty conditions. The specific steps are as follows:

[0121] Step1. Sort out relevant materials, conduct risk identification and consequence analysis on the "tire burst" accident, and construct a qualitative B0w-tie model as Figure 8 shown.

[0122] According to the analysis, it is obtained that there are 16 basic events in the fault tree, which are conducted through logic gates and pass through 8 intermediate events to reach the top event of tire burst CE. The basic events are respectively: wheel hub crack BE1, main wheel chunk loss BE2, brake disc chunk loss BE3, fusible plug BE4, abnormal tire pressure BE5, inflation valve fracture BE6, wheel wear BE7, software instruction failure BE8, circuit short circuit BE9, control valve failure BE 10 , transfer valve failure BE 11 , hydraulic fuse failure BE 12 , brake device failure BE 13 , emergency transfer valve failure BE 14 , emergency hydraulic fuse failure BE 15 , emergency brake device failure BE 16 . In the event tree, 4 measures are taken to mitigate and control the risk of the occurrence of the top event of tire burst. The 4 control events are respectively starting the emergency brake system E1, avoiding the aircraft and buildings E2, adding isolation nets E3, and starting emergency fire-fighting measures E4. The 4 resulting events corresponding to the development are respectively the aircraft staying on the runway OE1, slight damage to the airframe OE2, severe damage to the airframe OE3, aircraft fire and casualties of personnel OE4. Among all the input events, according to whether sufficient data volume can be obtained, they can be divided into random variables and uncertain variables. Among them, the basic events BE1, BE2, BE3, BE5, BE6, BE7, BE8, BE 13 , BE 14 , BE 15 can obtain sufficient risk or failure data and can be defined as random variables with risk probabilities . Other events (BE4, BE9, BE 10 , BE 11 , BE 12 , BE 16 , E1, E2, E3, E4) are defined as uncertain variables with risk credibilities or . Through data collection and expert experience, the statistical data, distributions and parameters related to the input variables are shown in Tables 3 and 4.

[0123] Table 3 Distribution and parameters of basic event variables

[0124]

[0125]

[0126] Table 4 Distribution and parameters of control event variables

[0127]

[0128] The distribution of random variables can be determined by component types and their failure mechanisms, and distribution parameters are calculated through the collected failure data. For example, the life distribution of most electromechanical products follows a lognormal distribution, with two parameters μ and σ:

[0129]

[0130] Among them, Var and MTBF are calculated from historical data.

[0131] For most electrical products, the life distribution follows an exponential distribution, and the parameter λ = 1 / MTBF. On this basis, the failure function λ(t) of the component can be obtained, and its failure probability can be regarded as the risk occurrence probability.

[0132] The distribution of uncertain variables is generally obtained based on expert knowledge. According to the expectation theorem in the chance distribution and combined with expert experience data, the values of distribution parameters are calculated, and then the specific distribution is obtained. For example, when k = 2, for a normal uncertain distribution (when ), there is E[ξ 2 = e 2 +σ 2 (10)

[0133] For a zigzag uncertain distribution, there is

[0134]

[0135] For a linear uncertain distribution, there is

[0136]

[0137] Through the questionnaire method, the empirical data of eight experts on the distribution parameters of uncertain variables are obtained and summarized in Table 5-7. The corresponding uncertain distribution can be calculated through the above formula.

[0138] Table 5 Statistical table of empirical data of e and σ

[0139]

[0140] Table 6 Statistical table of empirical data of a, b, and c

[0141]

[0142] Table 7 Statistical table of empirical data of a and b

[0143]

[0144]

[0145] Step 2 According to the relevant data collection and the formula in Step 1, the specific values of the input variables are as follows:

[0146]

[0147] Step 3 Since the system involved in the fault tree part of the case is a complex mixed uncertain random system, when calculating the risk reliability of the top event and the result event, formulas (2)-(5) and formula (7) are adopted. First, from Figure 7 the shown Bowtie model diagram, the structure function can be obtained as follows,

[0148] f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 , y1, y2, y3, y4, y5, y6)

[0149] =(x1 ∨ x2 ∨ x3 ∨ x4 ∨ x5 ∨ x6 ∨ y1) ∨ (((x7 ∧ y2) ∨ y3 ∨ y4 ∨ y5 ∨ x8) ∧ (x9 ∨ x 10 ∨ y6))

[0150] where, x i is a random variable, and y i is an uncertain variable.

[0151] According to the calculation rule in U-FTA, the risk measure of the top event CE can be expressed as

[0152]

[0153] It is known that there are 10 basic events in the case, so the structure function f has 2 10 kinds of values. When f takes the value of 1, the number of existing situations is too large. By considering the situation where f takes the value of 0 through reverse thinking, θ RB，CE is calculated. When f = 0, one of the following conditions needs to be satisfied:

[0154] (1) x1 = x2 = x3 = x4 = x5 = x6 = 0;

[0155] (2) x8 = 1 and x9 = x 10 = 0.

[0156] Furthermore, the risk measure of the top event CE can be expressed as

[0157]

[0158] Taking as an example, calculate one of the situations where f = 0,

[0159]

[0160] Among them

[0161]

[0162] Similarly, the values for the other 9 cases where f = 0 can be calculated, and the risk credibility of the top event CE is obtained by summation as θ RB，CE = 1.48×10 -4 .

[0163] According to the calculation rules in U-ETA, the risk credibility values of the result events can be calculated respectively from the risk credibility value of the top event

[0164]

[0165] θ RB，OE2 = θ RB，CE ·[(1 - τ1) ∧ τ2 ∧ τ3] + [(1 - τ1) ∧ τ2 ∧ (1 - τ3) ∧ τ4]

[0166] = 0.445×10 -4 ,

[0167] θ RB，OE3 = 0.348×10 -4 , θ RB，OE4 = 0.970×10 -6 .

[0168] So far, the risk quantification of all variables in the Bow-tie risk analysis has been completed

[0169] Step 4 Based on the risk quantification, perform sensitivity analysis and identify the key basic events and control events. First, calculate the Bimbaum importance of each basic event, and select the two basic events BE 11 、BE 13 with higher importance after sorting. The analysis results are shown in Table 8. The basic events BE 11 、BE 13 are the key risk sources. For the control events, taking different result events as the focus, different key control events are obtained. Therefore, the sensitivity analysis results of all control events are listed in Table 9

[0170] Table 8 Sensitivity analysis of basic events

[0171]

[0172] Table 9 Sensitivity analysis of control events

[0173]

[0174] In the U-bowtie risk analysis, according to the sensitivity analysis, it can be observed that for a specific outcome event, its risk control measures include two categories:

[0175] (1) Reduce the risk level of the risk source, that is, control the likelihood of the basic event occurring;

[0176] (2) Reduce the risk level of the control measure, that is, increase the likelihood of the control event succeeding.

[0177] Taking the outcome event OE3 as an example for further analysis, to reduce the risk level of OE3, reducing the likelihood of occurrence of the basic events BE 11 、BE 13 shown in Table 8 is the first type of measure. From the analysis results in Table 9, it can be seen that controlling events E2 and E3 can reduce the risk of OE3, and reducing the failure rate of the control measure is the second type of risk control measure.

[0178] Combining the two types of measures mentioned above in pairs, observing the impact degree of the risk mitigation measure combination and individual measures on the risk level of the outcome event OE3, and using a laser chart to represent the relevant results as Figure 9 shown, the optimal risk mitigation measure combination is to simultaneously reduce the risk credibility values of E2 and BE 13 .

[0179] Therefore, the conclusion is that in actual engineering, to avoid the occurrence of the outcome event "severe damage to the airframe" OE3, the risk source that needs to be focused on is "brake device failure" BE 13 , the most effective control measure is "evade aircraft and buildings" E2, and the effect of the combined measure is significantly better than that of the single measure. Therefore, attention should be paid to both the prevention and control of risk sources and the mitigation and disposal of risk events to better carry out risk management and improve the safety level of the troops.

[0180] It can be seen from the verification of the above embodiments that for the risk assessment problem under mixed uncertain conditions, the traditional probability theory-based method is no longer applicable. Therefore, the opportunity theory is introduced and the risk assessment is carried out based on the U-bowtie model. Taking the "tire burst" unsafe event during the small-batch delivery and use of a certain new transport aircraft as an example, the main work is as follows:

[0181] (1) When conducting the risk assessment of aviation unsafe events, the situation where both random uncertainty and epistemic uncertainty exist is considered, which is more in line with special situations such as the service of new equipment;

[0182] (2) Introducing the opportunity theory for risk quantification under mixed uncertainty conditions can handle random variables, uncertain variables, and random uncertain variables simultaneously, making the evaluation results more reasonable;

[0183] (3) An improved U-bowtie model is obtained. On the one hand, it can effectively describe the evolution and development process of aviation unsafe events under mixed uncertain conditions and conduct qualitative structural analysis. On the other hand, it determines the calculation rules of risk measures in U-FTA and U-ETA to achieve effective risk quantification.

[0184] (4) In terms of sensitivity analysis, Birnbaum importance and its uncertainty improvement are adopted to determine the key risk factors affecting unsafe events and effective control measures to prevent the escalation of consequence events, which is conducive to the implementation of safety management work and the improvement of safety level.

[0185] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. An aviation safety risk U-bowtie assessment method under mixed uncertain conditions, characterized in that It includes the following steps: Step 1: Conduct risk identification and consequence analysis for typical unsafe events during the use of aviation equipment; Step 2: Under mixed uncertain conditions, using the opportunity theory, construct a new index for measuring the likelihood of risk occurrence: the risk measure index, which is used to describe the risk levels of various risk events involved in the risk assessment process of typical unsafe events. At this time, the Bow-tie model considering random and epistemic uncertainties is improved to the U-bowtie model; Step 3: For the uncertain random system under mixed uncertain conditions, design the risk measure calculation rules in the U-bowtie model from two parts: U-FTA and U-ETA respectively; Step 4: Based on risk quantification, conduct sensitivity analysis to obtain the key components of the system, key nodes of the work process, key risk factors, and key control measures.

2. The U-bowtie assessment method for aviation safety risks under mixed uncertain conditions according to claim 1, wherein: The process of risk identification and consequence analysis for the typical unsafe events described in Step 1 includes: (1) Sort out the relevant materials of aviation unsafe events, select a certain accident as the research object, and conduct qualitative risk analysis; (2) Use the Bow-tie model to sort out various causes leading to this accident and the risk evolution path, and respectively construct the fault tree and event tree that make up the Bow-tie model.

3. A U-bowtie assessment method for aviation safety risks under mixed uncertain conditions according to claim 1, characterized in that: The construction process of the risk measure index and the improved U-bowtie model described in Step 2 includes: (1) In the improved U-bowtie model, the risk measure index is defined as: Assume that the risk event state variable ξ is an uncertain random variable, Ξ represents the feasible domain of abnormal or failure states that cause risks and losses, and the risk measure is defined as the opportunity measure of the risk event being in an abnormal state that may lead to an accident, expressed as: θ RB = Ch{ξ ∈ Ξ} At this time, the variable ξ describes the state of the risk event, and the feasible domain Ξ describes the value range of the variable ξ during an accident. When ξ ∈ Ξ, the risk event is in a failure state, and at this time, the risk event becomes one of the causes or a cause leading to the accident, expressed as: Let Ξ = {η1, η2}, where η1 represents that the system or event Λ is in a safe state, and η2 represents that the system or event Λ is in an accident state. Then the risk measure index θ RB is the opportunity measure for the event to be in an accident state (i.e., Λ = {η2}), denoted as θ RB = Ch{Λ}; (2) If the state variable ξ degenerates into a random variable, the risk measure index is transformed into a probability indicating the likelihood of the occurrence of a risk event, which can be calculated based on statistical data and is denoted as At this time, the system is affected by random uncertainty, and the risk measure is transformed into a risk metric based on probability theory; if the state variable ξ degenerates into an uncertain variable, the risk measure index is transformed into a credibility indicating the size of the credibility of the occurrence of a risk event, denoted as At this time, the system is affected by cognitive uncertainty, and the risk measure is transformed into a risk metric based on uncertainty theory.

4. A U-bowtie assessment method for aviation safety risks under mixed uncertain conditions according to claim 1, characterized in that: The determination process of the risk measure calculation rules in the U-bowtie model described in Step 3 includes: (1) According to the combination of variables, the uncertain random system is divided into two categories: If an uncertain random system can be clearly divided into several random subsystems and several uncertain subsystems, that is, there is no other part except the whole that contains both random variables and uncertain variables at the same time, and at this time, there is only one uncertain random variable, the system as a whole, then the system is called a simple uncertain random system; If there are uncertain random subsystems in the system, then the system is called a complex uncertain random system; According to the classification of simple and complex uncertain random systems, design the corresponding calculation rules in the U-FTA model and the U-ETA model respectively.

5. According to the method for U-bowtie assessment of aviation safety risk under mixed uncertain conditions described in claim 4, characterized in that In the U-FTA, for a simple uncertain random system, the random variables and uncertain variables are independent of each other, and they respectively form a random subsystem and an uncertain subsystem. The logical gate algorithms involved respectively rely on the product theorem of probability theory and uncertainty theory. When the event is a random variable, the risk measure θ RB，Bi is transformed into describing the probability of its occurrence, which is calculated from a large amount of statistical data; when the event is an uncertain variable, the risk measure is transformed into The specific credibility value and the type of uncertainty distribution are given by experienced experts; For two independent random basic events, when the two variables both belong to an "AND" gate, the risk probability of its upper-level intermediate event can be obtained from Calculated; when the two variables both belong to an "OR" gate, the risk probability of its upper-level intermediate event can be calculated from the formula Calculated; For two independent uncertain basic events, when the two variables belong to the "AND" gate, the risk reliability of its upper intermediate event can be obtained from calculated; When two variables both belong to an "OR" gate, the risk credibility of its upper-level intermediate event can be calculated by the formula obtained; According to the characteristics of the simple uncertain random system, the top event is the only uncertain random variable in the system. In the U-FTA analysis under different logic gate conditions, the risk measure calculation method of the top event is as follows:

6. A method for evaluating aviation safety risk U-bowtie under mixed uncertain conditions according to claim 4, characterized in that: In the U-FTA, for complex uncertain random systems, due to the existence of several uncertain random variables and the lack of direct calculation formulas for the logic gate algorithms of uncertain random variables, when calculating the top event risk measure index, it is necessary to first give the system structure function and indirectly calculate the top event risk measure value. Assume that the complex system is a Boolean system, and the system structure function f is a Boolean function, which consists of n basic events BE1, BE2,..., BE n with Boolean values {0, 1}. When the Boolean value is 1, the event state is an abnormal state, and when it is 0, it is a normal state. f is the system structure function, and when f(BE1, BE2,... BE n ) = 1, the accident (top event) occurs; Assume that an uncertain random system is a Boolean system, and there exists a structural Boolean function f, which includes n independent random event variables η1, η2, …, η with a risk probability of n and m independent uncertain event variables τ1, τ2, …, τ with a risk credibility of m . Then, the risk measure value of the top event CE in the uncertain random system is as follows: Wherein When x i = 1 and y i = 1, the elementary event variable is in a failure state.

7. A method for evaluating aviation safety risk U-bowtie under mixed uncertain conditions according to claim 4, characterized in that: In U-ETA, for a simple uncertain random system, the random variables and the uncertain variables are independent of each other. According to the product theorem of probability theory and uncertainty theory, they are calculated separately. Then, the risk measure calculation method of the result event OE on branch k is as follows: k is as follows:

8. A method for evaluating aviation safety risk U-bowtie under mixed uncertain conditions according to claim 4, characterized in that: In U-ETA, for a complex uncertain random system, assume that there are l result events in the event tree, and the k-th result event OE k includes s branches, and the t-th branch contains n independent random events η1, η2, …, η with a risk measure of n , and m independent uncertain events τ1, τ2, …, τ with a risk measure of m . Then, the risk measure value of the k-th result event OE k in the uncertain random system is: where k = 1,..., l, t = 1,..., s.

9. A U-bowtie assessment method for aviation safety risks under a mixed uncertain condition according to claim 1, characterized in that: The sensitivity analysis process described in step 4 includes (1) Comparison Compare the value sizes, sort the random basic event variables and uncertain basic event variables, and identify the important event elements, that is, the key basic events ranked in the front; Among them, for the random basic event variable, the calculation formula for Birnbaum importance is: Among them, P(OE i = 1|x i = 1) represents the probability that the result event occurs when the event x i occurs, and P(OE i = 1|x i = 0) represents the risk occurrence probability of the result event when the event x i does not occur; For the uncertain basic event variable, the calculation formula for the uncertain importance is given as: Among them, represents the credibility of the result event occurring when event x i occurs, represents the risk credibility of the result event when event x i does not occur; (2) Determine the most critical and control events by estimating the change in the risk level of the result event through the following two risk reduction assumptions: 1) Quantitatively reduce the risk measure value of the input event: Assume that the risk measure value of the input event x i is reduced by 20% or 1%, and observe the reduction of the risk measure value of the output event; 2) Completely eliminate the risk of the input event: Assume that the risk measure value of the input event x i becomes 0, and observe the reduction of the risk measure value of the output event. At the same time, the above method can also be used to determine the key basic events, and this method is also applicable to the sensitivity analysis in the case of multiple event changes.

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