Aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network

Abstract

The invention discloses an aviation activity risk assessment method based on an interval hesitant Z-number and a Bayesian network, and the method defines the hesitant degree of the interval Z-number, the credibility of the interval Z-number, an interval hesitant fuzzy Z-number weighted average operator, an expert weight adjustment method and an attribute weight value determination model, and can achieve the prior probability mathematical expression of a Bayesian network node. And aviation activity probability risk assessment is carried out through mathematical reasoning of a Bayesian network model, and then importance analysis of nodes is carried out, so that corresponding risk management and control measures can be implemented.

Description

Technical Field

[0001] The present invention relates to the technical field of risk assessment, and in particular to an aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network. Background Art

[0002] With the increasing maturity of aviation technology, the fields of civil air transport and military aviation have accelerated their development, becoming a key engine driving military transformation and improving people's lives worldwide. In actual operations, although improvements in technology and management capabilities have led to a gradual decline in the number of aviation accidents, several fatal crashes still occur. In actual operations, aviation activities are often affected by a combination of factors, including lack of personnel skills, fragility of aircraft equipment, complex environments, and management deficiencies. Even the slightest negligence can result in fatal crashes. Therefore, conducting aviation risk assessments and promptly identifying potential risks in aviation activities are of great significance for accident prevention and improving aviation safety.

[0003] Because the human, aircraft, environment, and management elements of aviation activities are difficult to effectively quantify, expert assessment is often used to determine the probability of occurrence of these elements, ultimately determining the risk probability of aviation activities. However, in actual operations, the accuracy of expert assessment information is difficult to effectively measure. To address the cognitive uncertainty and fuzziness of expert assessment information, an interval-valued hesitant fuzzy Z-number method is introduced to determine the risk probability of nodes. This method can simultaneously account for the uncertainty and reliability of expert assessment information, ensuring the objectivity and accuracy of aviation activity risk assessment results. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide an aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network, which comprises the following steps:

[0005] Step 1: Build a risk assessment indicator system for heavy equipment airdrops;

[0006] Step 2: Use the expert scoring method to score each indicator in the heavy equipment airdrop risk assessment index system;

[0007] Step 3: Adjust the expert weight based on the interval Z-number hesitation and interval Z-number credibility;

[0008] Step 4: Determine the topology of the Bayesian network based on the heavy equipment airdrop risk assessment indicator system;

[0009] Step 5: Based on the Bayesian network, calculate the risk probability of each risk node;

[0010] Step 6: According to the risk probability of each node, the importance of the risk node in the Bayesian network or the risk uncertainty is determined by the posterior probability analysis method or the uncertainty analysis method;

[0011] Step 7: According to the importance of the node, the risk prevention is performed for the node, or according to the risk uncertainty of the node, the risk point prone to mutation is determined, and the risk prevention is performed for the node.

[0012] Further, the specific steps of step 3 include:

[0013] Step 3.1: Let The interval Z-number hesitancy is represented as:

[0014]

[0015] And

[0016]

[0017] Wherein, n is the number of elements in the interval hesitancy fuzzy Z-number, and is the variance of the interval hesitancy fuzzy Z-number.

[0018] Step 3.2: Let The interval Z-number reliability is represented as:

[0019] R(Z i )=1-Φ(Z i );

[0020] Step 3.3: The interval Z-number reliability is introduced, and the calculation formula of the expert weight is improved as:

[0021]

[0022] Wherein, ω' k represents the support degree for the node risk probability, ω k (k=1,…,q) represents the kth expert weight, and j (j=1,…,J) represents the jth attribute of the evaluation index.

[0023] Step 3.4: ω' k is normalized, and the attribute weight of each index of the evaluation expert is represented as:

[0024]

[0025] Wherein, ω" kTo evaluate the attribute weight of each index by experts.

[0026] Further, the specific steps of step 5 include:

[0027] Step 5.1: define the calculation formula of node risk probability as:

[0028]

[0029] Wherein, a' j represents the support of the jth attribute to the evaluation index; is the left interval number of the expert integrated evaluation result, is the right interval number of the expert integrated evaluation result, is the integrated weight of all experts;

[0030] Step 5.2: normalize a' j to obtain the normalized risk probability:

[0031]

[0032] Wherein, J represents the number of attributes of the node.

[0033] Further, when calculating the node risk probability, the expert integrated evaluation result is calculated by interval hesitant fuzzy weighted average operator, and the interval hesitant fuzzy Z-number weighted average operator is:

[0034]

[0035] Wherein, WA is the weighted average operator; ω = (ω1, ω2, …, ω n ) T is the Z i number weight vector, and ω i ∈ [0, 1],

[0036] Further, the specific steps of determining the importance or risk uncertainty of the risk node in step 6 include:

[0037] 1) Posterior probability analysis method

[0038] Step 1: calculate the new risk probability by the following formula:

[0039]

[0040] Wherein, P(X i ) represents the prior probability of node X i , P(O) represents the risk probability of aviation activity failure, and P(O|X i) represents node X i The probability of failure of aviation activities under the conditions of occurrence;

[0041] Step 2: Calculate the difference △ between the posterior probability and the prior probability of the node using the following formula to obtain the probability change of the node;

[0042] △=P(X i |O)-P(X i );

[0043] Step 3: Obtain the importance of risk nodes by comparing △;

[0044] 2) Uncertainty analysis methods

[0045] Step 1: Calculate the entropy of the risk node using the following formula:

[0046] H(X i )=-P(X i )log2P(X i )

[0047] Among them, H(X i ) represents node X i Entropy;

[0048] Step 2: Express the conditional entropy of two random variables as:

[0049]

[0050] Among them, H(X i |O) represents a given random variable O, X i The conditional entropy of

[0051] Step 3: Get the random variable X by the following formula i and the uncertainty of O:

[0052] I(X i ; O)=|H(X i )-H(X i |O)|

[0053] Among them, I(X i ; O) means O contains X i The amount of information.

[0054] Therefore, the present invention adopts the above-mentioned aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network, which has the following beneficial effects:

[0055] The application constructs an aviation activity risk assessment index system by analyzing specific aviation activities, and constructs an aviation activity risk assessment Bayesian network, so as to carry out aviation activity risk assessment; the application processes expert evaluation information by using an interval hesitation Z-number based method, determines the risk probability of each node in the aviation activity risk assessment Bayesian network, and determines the aviation activity risk probability according to the Bayesian network calculation rule; meanwhile, the application carries out importance analysis based on the Bayesian network topology, determines the risk factors that have greater influence on aviation activities, and facilitates targeted prevention.

[0056] The technical solutions of the application will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The technical principle diagram of the risk assessment method of the application.

[0058] Figure 2 The risk assessment Bayesian network.

[0059] Figure 3 The re-airdrop risk assessment index system. DETAILED DESCRIPTION

[0060] In the description of the application, it should be noted that, unless otherwise explicitly specified and limited, the embodiments are only used to illustrate the application and not to limit the scope of the application. In addition, it should be understood that, after reading the content taught by the application, those skilled in the art can make various modifications or changes to the application, and these equivalent forms also fall within the scope defined by the appended claims of the application.

[0061] The application proposes an aviation activity risk assessment method based on interval hesitation Z-number and Bayesian network, and first introduces the basic theory thereof.

[0062] 1. Interval hesitation fuzzy set

[0063] The interval hesitation fuzzy set can use precise values to describe the membership degree, and can also use multiple intervals to express the preferences of experts.

[0064] It includes the following definitions:

[0065] Definition 1 Let X = {x1, x2, …, x n} be a non-empty set, and D[0,1] represent a set consisting of all closed sub-intervals of the interval [0,1]:

[0066]

[0067] wherein, is a set consisting of several interval numbers, and represents the xi The elements in ∈X belong to the set The set of all possible interval memberships of is also called interval hesitant fuzzy element;

[0068] and

[0069]

[0070] In the formula, [γ L ,γ U ] is the number of intervals on the interval [0,1];

[0071] In particular, when γ L =γ U When , the interval hesitant fuzzy element degenerates into a hesitant fuzzy element.

[0072] Definition 2: and are three groups of interval hesitant fuzzy elements, then:

[0073]

[0074] Where,

[0075] Based on Definition 2, different interval-interval hesitant fuzzy elements can be aggregated, which are defined as follows:

[0076] Definition 3: is a set of interval hesitant fuzzy elements, ω=(ω1,ω2,…,ω n ) T for The weight vector of ω i ∈[0,1], The interval hesitant fuzzy weighted average operator can be expressed as:

[0077]

[0078] Definition 4: is a set of interval hesitant fuzzy elements, n is the number of elements in the interval hesitant fuzzy element, and the interval hesitation degree can be expressed as:

[0079]

[0080] Where, is the variance of the interval hesitant fuzzy element, and

[0081]

[0082] 2. Z-number method

[0083] Z-number is an ordered fuzzy number pair, usually expressed as:

[0084] Z = (A, B) (8)

[0085] where A is a description or restriction of the uncertain value and B is a reliability estimate of A.

[0086] Compared with other methods, Z-number can describe more uncertain information due to the reliability description of information. In normal cases, experts aggregate Z-numbers by means of distance functions or similarity, which will lead to the loss of uncertain information. Therefore, BUI functions are introduced to aggregate Z-numbers, i.e.:

[0087] Definition 5 Let Z i = (A i ,B i ),(i = 1, …, n) be a set of BUIs, C: [0, 1] n → [0, 1] be an aggregation function, then can be expressed as:

[0088]

[0089] 3. Bayesian networks

[0090] A Bayesian network is a combination of graph theory and probability theory, which can be represented by a binary tuple BN = (G, P). G represents a directed acyclic graph (DAG) composed of nodes and directed edges, and the nodes are divided into child nodes X i and parent nodes pa(X i ), representing different variables, where A(X i ) represents the set of non-descendant nodes of X i , and the directed edges represent the causal relationship between variables; P in the binary tuple represents the conditional probability table (CPT), which is used to reflect the logical relationship between nodes. When X i and pa(X i ) are conditionally independent, then:

[0091] P(X i | pa(X i ), A(X i )) = P(X i | pa(X i )) (10)

[0092] The joint probability distribution in BN can be expressed as:

[0093]

[0094] 4. Interval hesitant fuzzy Z-number

[0095] Taking into account the convenience of evaluation, the interval hesitant fuzzy Z-number weighted average operator (IVHFZWA), interval Z-number hesitation degree (IVZHD) and interval Z-number credibility (IVZCD) are defined as follows:

[0096] (1) Interval hesitant fuzzy Z-number weighted average operator

[0097] Definition 6 is a set of interval hesitant fuzzy Z-number elements (IVHFZE), ω=(ω1,ω2,…,ω n ) T Z i (i=1,2,…,n) weight vector, and ω i ∈[0,1],

[0098] Based on Definition 3 and Definition 5, the interval hesitant fuzzy Z-number weighted average operator is defined as:

[0099]

[0100] Where WA is the weighted average operator.

[0101] Using IVHFZWA allows the Z-number to reduce the information loss after integrating all expert evaluation results and reflects the membership and reliability of the integrated evaluation information. This prevents inaccurate evaluation results due to differences in expert competence. Generally speaking, experts' epistemic uncertainty can affect the rationality and accuracy of evaluation results. The reliability of expert evaluation information depends on many factors. In the case of IVHFZ (interval-valued hesitant fuzzy Z-number method), hesitancy and certainty are the criteria for measuring the reliability of evaluation information.

[0102] (2) Interval Z-number hesitation

[0103] The expert's hesitation in interval-valued hesitant fuzzy Z-number is mainly reflected in the number of IVHFEs (interval-valued hesitant fuzzy elements), the deviation and certainty of IVHFEs. Therefore, the interval Z-number hesitation is defined as:

[0104] Definition 7 is a set of interval hesitant fuzzy Z-number elements, n is the number of elements in the interval hesitant fuzzy Z-number element, and the interval Z-number hesitation degree can be expressed as:

[0105]

[0106] in,

[0107] where, is the variance of IVHFZE (Interval-Valued Hesitant Fuzzy Z-number Element).

[0108] and

[0109]

[0110] As can be seen from the variance formula, the variance can reflect the number, deviation and certainty of the interval-valued hesitant fuzzy element. The more IVHFEs, the greater the deviation, the lower the certainty, and the greater the hesitation degree.

[0111] (3) Interval Z-number credibility

[0112] In order to measure the reliability of the evaluation information, the interval Z-number credibility is defined. The higher the interval Z-number hesitation degree, the more uncertain the evaluation information of the expert, and the lower the interval Z-number credibility of the expert.

[0113] Definition 8 Let be an interval-valued hesitant fuzzy Z-number element, the interval Z-number credibility is defined as follows:

[0114] R(Z i )=1-Φ(Z i ) (14)

[0115] (4) Expert weight adjustment method

[0116] Considering the convenience of evaluation, the weights of experts are often uniformly distributed. However, due to the difference in knowledge and work experience of experts, there is a certain deviation in the evaluation result, so the weight of the expert must be adjusted in the evaluation process. Therefore, based on the interval Z-number credibility and the original expert weight, the traditional expert weight calculation formula is improved, and the improved expert weight adjustment method is proposed. By introducing the interval Z-number credibility, the evaluation result is consistent with the actual situation. The improved expert weight calculation formula is as follows:

[0117]

[0118] where, ω' k represents the support degree for the node risk probability, ω k (k=1,…,q) represents the weight of the kth expert, and j (j=1,…,J) represents the jth attribute of the evaluation index.

[0119] ω' k is normalized, and the attribute weight of the evaluation expert for the node is represented as

[0120]

[0121] (5) Method for determining risk probability

[0122] The determination of risk probability is the key to ensuring the rationality of the risk assessment results of aviation activities. Considering the value and information reliability of the comprehensive assessment results, the difference between node risk probability and decision quality can be determined.

[0123] The node risk probability is proportional to the value of the comprehensive assessment result and the reliability of the information. The calculation formula for the node risk probability is as follows:

[0124]

[0125] Assume that a node has j=1,…,J attributes, a' j Represents the support of the j-th attribute for the evaluation index, is the number of intervals on the left side of the integration result, is the number of right-hand intervals of the integration result, is the integrated weight of all experts, and the integrated result is the sum of the evaluation results of all experts on a certain risk indicator.

[0126] to a' j Normalized, the risk probability of the evaluation indicator is expressed as:

[0127]

[0128] 5. Risk Assessment

[0129] The heavy equipment airdrop process involves many factors and a complex hierarchical structure. Through expert consultation, data review, questionnaires, etc., the important risk factors of heavy equipment airdrop are determined. During the mission, the personnel involved are mainly pilots operating the aircraft, airdrop personnel responsible for executing the airdrop mission, and maintenance personnel responsible for equipment loading. From the perspective of transport aircraft and equipment, the transport aircraft's air posture and stability and flight altitude can lead to aircraft crashes and fatalities. The equipment's airborne posture, stability and airbag cushioning capacity are the guarantees for the stable descent of airdropped equipment without damage. At the same time, the reliability of transport aircraft parts and systems is also the key to preventing accidents with transport aircraft and equipment. Heavy equipment airdrops are highly dependent on the environment. Wind shear can cause severe turbulence in the transport aircraft, affecting the equipment's exit from the cabin. Atmospheric turbulence can disturb the transport aircraft, increasing the pilot's operating burden, thereby inducing dangerous situations for the transport aircraft. Ground threats can cause equipment damage after landing due to terrain or other factors. Through the above analysis, a heavy equipment airdrop risk assessment index system is established from the three perspectives of man-machine-environment, such as Figure 3 shown.

[0130] Based on the above heavy equipment airdrop risk assessment index system, the topological structure of the Bayesian network and the mathematical expression of the node probability are determined. The Bayesian network forward reasoning function of the Genie software can be used to solve the risk probability of aviation activities. The Bayesian network is as follows: Figure 2 shown.

[0131] By carrying out importance analysis, it is possible to find nodes that are more important in influencing aviation activities. The present invention uses a posteriori probability analysis method or an uncertainty analysis method to determine the importance of aviation activity risk nodes.

[0132] (1) Posterior probability analysis method

[0133] Based on the reverse reasoning function of the Bayesian network, posterior probability analysis is carried out. The posterior probability analysis of the Bayesian network mainly uses the prior probability of the node and known evidence to solve the new risk probability of the node. The calculation formula is as follows:

[0134]

[0135] Where, P(X i ) represents node X i The prior probability of P(O) represents the risk probability of failure of aviation activities, P(O|X i ) represents node X i The risk probability of failure of aviation activities under the conditions of occurrence.

[0136] The difference between the posterior probability and the prior probability of a node can reflect the probability change of the node. The calculation formula is:

[0137] △=P(X i ‖O)-P(X i ) (20)

[0138] By comparing the difference between the posterior risk probability of a node and the prior probability of the node, we can understand the importance of the risk node and take effective measures to make adjustments.

[0139] (2) Uncertainty analysis method

[0140] Entropy is an effective method for measuring the diversity of random variables and can be used to calculate the uncertainty of risk nodes in Bayesian networks. The greater the entropy of a risk node, the greater the uncertainty. This paper uses the following formula to calculate the uncertainty of risk:

[0141] H(X i )=-P(X i )log2P(X i ) (twenty one)

[0142] The conditional entropy of two random variables is expressed as:

[0143]

[0144] where H(X i |O) represents the conditional entropy of a given random variable O, X i .

[0145] H(X i ) and H(X i |O) is the uncertainty of random variables X i and O, that is:

[0146] I(X i ; O) = |H(X i )-H(X i |O)| (23)

[0147] where I(X i ; O) represents the amount of information contained in O about X i .

[0148] By solving the risk uncertainty of the node, the risk point prone to mutation can be timely alerted, and measures can be taken to prevent risks in time.

[0149] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application rather than limiting them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. The aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network is characterized by: The following steps are involved: Step 1: Build a risk assessment indicator system for heavy equipment airdrops; Step 2: Use the expert scoring method to score each indicator in the heavy equipment airdrop risk assessment index system; Step 3: Adjust the expert weight based on the interval Z-number hesitation and interval Z-number credibility; Step 4: Determine the topology of the Bayesian network based on the heavy equipment airdrop risk assessment indicator system; Step 5: Based on the Bayesian network, calculate the risk probability of each risk node; Step 6: Based on the obtained risk probability of each node, determine the importance or risk uncertainty of the risk node in the Bayesian network through posterior probability analysis method or uncertainty analysis method; Step 7: Perform risk prevention on the node based on its importance, or determine the risk point prone to mutation based on the risk uncertainty of the node and perform risk prevention on the node.

2. The aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network according to claim 1, characterized in that: The specific steps of step 3 include: Step 3.1: It is defined as a set of interval hesitant fuzzy Z-number elements, and the interval Z-number hesitation degree is expressed as: and Among them, n is the number of elements in the interval hesitant fuzzy Z-number element, is the variance of the interval hesitant fuzzy Z-number element; Step 3.2: Defined as an interval hesitant fuzzy Z-number element, the interval Z-number credibility is expressed as: R(Z i )=1-Φ(Z i ); Step 3.3: Introduce the interval Z-number credibility and improve the calculation formula of expert weight to: Among them, ω' k Represents the support for the node risk probability, ω k (k=1,…,q) represents the kth expert weight, j (j=1,…,J) represents the jth attribute of the evaluation indicator; Step 3.4: ω' k Normalize and express the attribute weights of the evaluation experts for each indicator as follows: Among them, ω” k To evaluate the attribute weights of each indicator by experts.

3. The aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network according to claim 2, characterized in that: The specific steps of step 5 include: Step 5.1: Define the calculation formula for node risk probability as: Among them, a' j Represents the support of the j-th attribute for the evaluation index; is the number of intervals on the left side of the expert integrated evaluation results, is the number of right intervals of the expert integrated evaluation results, is the integrated weight of all experts; Step 5.2: Risk probability a' for the node j Normalize and get the normalized risk probability: Where J represents the number of attributes of the node.

4. The aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network according to claim 3, characterized in that: When calculating the node risk probability, the expert integrated assessment result is calculated by the interval hesitant fuzzy weighted average operator. The interval hesitant fuzzy Z-number weighted average operator is: Where WA is the weighted average operator; ω=(ω1,ω2,…,ω n ) T Z i (i=1,2,…,n) weight vector, and ω i ∈[0,1], 5. The aviation activity risk assessment method based on interval hesitant Z-number and Bayesian network according to claim 4, characterized in that: The specific steps for determining the importance of risk nodes or risk uncertainty in step 6 include: 1) Posterior Probability Analysis Method Step 1: Calculate the new risk probability using the following formula: Among them, P(X i ) represents node X i The prior probability of P(O) represents the risk probability of failure of aviation activities, P(O|X i ) represents node X i The probability of failure of aviation activities under the conditions of occurrence; Step 2: Calculate the difference △ between the posterior probability and the prior probability of the node using the following formula to obtain the probability change of the node; △=P(X i |O)-P(X i ); Step 3: Obtain the importance of risk nodes by comparing △; 2) Uncertainty analysis methods Step 1: Calculate the entropy of the risk node using the following formula: H(X i )=-P(X i )log2P(X i ) Among them, H(X i ) represents node X i Entropy; Step 2: Express the conditional entropy of two random variables as: Among them, H(X i |O) represents a given random variable O, X i The conditional entropy of Step 3: Get the random variable X by the following formula i and the uncertainty of O: I(X i ;O)=|H(X i )-H(X i |O)| Among them, I(X i ; O) means O contains X i The amount of information.

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