Bayesian information gain-based structural risk analysis maintenance plan optimization method

Abstract

This invention belongs to the field of aircraft structural risk analysis technology, specifically involving a structural risk analysis and maintenance plan optimization method based on Bayesian information gain. Step 1: Select the fatigue-critical parts of interest and predict the crack size probability distribution at any time; predict the single-flight failure probability (SFPOF) at any time. Step 2: Determine the time t at which the SFPOF reaches the safety threshold. risk ; Determine t risk Is it less than the design service life? If yes, proceed to step three; otherwise, end. Step three: Calculate the previous inspection time t. previous With t risk The crack size at each time point is determined using Bayesian information gain, and the time t with the maximum information gain is determined. max(IG) Step 4: When the flight reaches the maximum information gain time t max(IG) At regular intervals, key fatigue-prone areas are inspected, and t is calculated. max(IG) Step 5: Update t max(IG) The crack size probability distribution and single-flight failure probability (SFPOF) over subsequent time are then set, while the previous inspection time t is also set. previous =t max(IG) Return to step two.

Description

Technical Field

[0001] This invention belongs to the field of aircraft structural risk analysis technology, specifically relating to a structural risk analysis and maintenance plan optimization method based on Bayesian information gain. Background Technology

[0002] The Military Aircraft Structural Integrity Guidelines (GJB775A-2012) stipulate that a risk analysis should be conducted on the structure to verify that the risk of fatigue fracture during the aircraft's design service life is sufficiently low, or to determine when inspection and maintenance should be carried out to ensure that the risk of fracture is below an acceptable threshold.

[0003] Structural fracture risk analysis incorporates various uncertainties / factors into the prediction of structural fatigue life and crack propagation life, calculating the probability of structural failure due to fatigue fracture throughout its entire lifespan. Fracture failure probability is typically characterized by the single-flight failure probability (SFPOF), which refers to the probability that the structure will fail in the current flight assuming it has not failed in previous flights, allowing for preventative maintenance prior to the current flight.

[0004] GJB775A-2012 stipulates that the probability of single flight failure (SFPOF) should be limited to 1×10⁻⁶. -7 Up to 1×10 -5 Between, if SFPOF≤10 -7 It is believed that this is sufficient to guarantee the long-term safety of the aircraft; if SFPOF > 10 -5 They believe the risk is too high and unacceptable; if 10 -7 <SFPOF≤10 -5 Risks should be mitigated through measures such as inspection, repair, replacement, and restriction of use.

[0005] Compared to inspection timing determined by deterministic damage tolerance analysis, structural fracture risk analysis calculates the probability of future flight fracture failure to determine whether it is necessary to reduce the inspection interval to ensure aircraft safety and reliability, or whether the inspection interval can be increased to reduce structural maintenance costs and improve equipment availability and integrity.

[0006] The common criterion for determining maintenance plans based on structural risk analysis is to consider both flight safety and maintenance costs simultaneously, i.e., to minimize maintenance costs while keeping the SPOF below the safety threshold. Summary of the Invention

[0007] The purpose of this invention is to propose a structural risk analysis and maintenance plan optimization method based on Bayesian information gain. Starting from the perspective of maximizing the Bayesian information gain of crack size, a criterion is proposed that simultaneously considers flight safety and Bayesian information gain, namely, maximizing the Bayesian information gain while ensuring the SFPOF is less than a safety threshold. This criterion presupposes the introduction of Bayesian inference methods into structural fracture risk analysis. By fusing external structural inspection data to update the crack size probability distribution, the uncertainty of probability prediction is reduced. This method can provide more and more effective information for structural risk analysis incorporating Bayesian inference, thereby optimizing the timing of structural inspections throughout the entire life cycle while ensuring flight safety.

[0008] The technical solution of this invention:

[0009] The structural risk analysis and maintenance plan optimization method based on Bayesian information gain includes the following steps:

[0010] Step 1: Select the key fatigue components of interest, and use a probabilistic fracture mechanics model with load spectrum, material parameters, geometric parameters, and initial crack size as inputs to predict the probability distribution of crack size at any time.

[0011] Based on fatigue fracture failure criteria and probability analysis methods, the single flight failure probability (SFPOF) at any time is predicted.

[0012] Step 2: Based on the risk threshold criterion, determine the time t it takes for the single-flight failure probability (SFPOF) to reach the safety threshold. risk ; Determine t risk If the service life is less than the design life, proceed to step three; otherwise, end the process.

[0013] Step 3: Based on the probability distribution of crack size at any time and time t risk Calculate the previous inspection time t previous With t risk The crack size at each time point is determined using Bayesian information gain, and the time t at which the information gain reaches its maximum value is determined. max(IG) ;

[0014] Step 4: When the flight reaches the maximum information gain time t max(IG) Regularly inspect key fatigue-prone areas; if cracks are found, repair them immediately, according to t max(IG) The probability distribution of crack size before inspection and the probability distribution of initial crack size after repair are used to calculate t. max(IG) Probability distribution of crack size after inspection;

[0015] Step 5: Based on t max(IG) The probability distribution of crack size after time inspection is updated. max(IG)The probability distribution of crack size at subsequent times and the single flight probability of failure SFPOF. At the same time, let the previous inspection time t previous =t max(IG) ;

[0016] Return to step two.

[0017] Furthermore, in step one, the fatigue fracture failure criteria include: the fracture toughness criterion, which means that the maximum stress intensity factor during flight exceeds the material fracture toughness;

[0018] The remaining strength criterion, which means that the maximum load during flight exceeds the structural remaining strength;

[0019] The critical crack size criterion, which means that the crack size expands to the critical value.

[0020] Furthermore, in step two, the risk threshold criterion is: the single flight probability of failure SFPOF should be less than the safety threshold, and the safety threshold is related to the aircraft reliability requirement, generally taken as 10 -7 .

[0021] Furthermore, in step two, t risk is the time corresponding to when the single flight probability of failure SFPOF exactly equals the safety threshold.

[0022] Furthermore, in step three, the calculation process of the Bayesian information gain of the crack size at each time point between the previous inspection time t previous and t risk is as follows:

[0023] (1) According to the probability distribution of crack size at any time, calculate the expected value of the crack detection probability PCD at each time point in [t previous , t risk . The calculation formula is:

[0024] PCD = ∫POD(a)·f(a)·da

[0025] where PCD represents the expected value of the crack detection probability; POD(a) represents the crack detection probability function; f(a) represents the probability distribution function of the crack size before inspection; a is the crack size;

[0026] (2) Simulate the inspection results at each time point in [t previous , t risk through random sampling. Randomly draw a sample between [0, 1], represented by x. If x ≤ PCD, it means the inspection result is "yes" for cracks, denoted as hit. If PCD < x ≤ 1, it means the inspection result is "no" for cracks, denoted as miss;

[0027] (3) Based on the inspection result of "present / absent" cracks, perform a Bayesian update on the crack size probability distribution before inspection to obtain the crack size probability distribution after inspection, as shown in the following formula:

[0028]

[0029]

[0030] Where f(a) is the probability distribution function of crack size before inspection, f(y|a) is the likelihood function, y∈{hit,miss}; and f(a|y) is the probability distribution function of crack size after inspection.

[0031] (4) Calculate the relative entropy, i.e., the KL (Kullback-Leibler) divergence, based on the crack size probability distributions before and after inspection. This divergence is used to characterize the Bayesian information gain IG, where IG = D. KL The calculation formula is:

[0032]

[0033] or

[0034]

[0035] Where p(a) and q(a) represent the prior probability distribution of crack size before inspection and the posterior probability distribution of crack size after inspection, respectively.

[0036] Furthermore, in step three, t max(IG) For [t] previous ,t risk The time corresponding to the maximum information gain between [ ].

[0037] Furthermore, in step four, the formula for calculating the probability distribution of the inspected crack size is as follows:

[0038]

[0039] Among them, f after (a) represents the probability distribution function of crack size after inspection; f R,k (a) represents the probability distribution function of crack size after the k-th type of repair; f(a) represents the probability distribution function of crack size before inspection; PCD k The expected value of the crack detection probability for the k-th type of repair is represented by the following formula:

[0040]

[0041] Wherein, POD(a) represents the crack detection probability function; [a1,a2] represents the crack size range corresponding to the k-th type of repair.

[0042] Furthermore, in step three, if no check was performed previously, then t previous =0.

[0043] The beneficial effects of this invention are:

[0044] This invention proposes a structural risk analysis and maintenance plan optimization method based on Bayesian information gain, which can provide more and more effective information for structural risk analysis incorporating Bayesian inference, thereby optimizing the timing of structural inspections throughout the entire life cycle while ensuring flight safety. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the structural risk analysis and maintenance plan optimization method based on Bayesian information gain.

[0046] Figure 2 This is a schematic diagram of the SFPOF variation curve over flight time (excluding inspections);

[0047] Figure 3 A schematic diagram of the SFPOF variation curve over flight time (the timing of the inspection is determined according to the Bayesian information gain criterion);

[0048] Figure 4 This is a schematic diagram of the SFPOF variation curve over flight time (the timing of inspection is determined according to the risk threshold criterion). Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0050] This invention is based on structural fatigue fracture risk analysis incorporating Bayesian inference. It updates the probability distribution of crack size using Bayesian methods by fusing structural inspection data, and adopts the crack size Bayesian information gain maximization criterion to optimize the structural maintenance plan throughout the entire life cycle while ensuring flight safety.

[0051] The solution of the present invention includes the following steps:

[0052] S1: Select the key fatigue components of interest, use a probabilistic fracture mechanics model, and use the load spectrum, material parameters, geometric parameters, and initial crack size as inputs to predict the crack size probability distribution at any time; and predict the single-flight failure probability (SFPOF) at any time based on fatigue fracture failure criteria and probabilistic analysis methods.

[0053] In step S1, the probabilistic fracture mechanics model is based on deterministic damage tolerance analysis, assuming that the initial crack size, material parameters, etc. are random variables, and uses a linear elastic fracture mechanics model to calculate the probability distribution of crack size over time.

[0054] In step S1, the fatigue fracture failure criteria include: fracture toughness criterion, which refers to the maximum stress intensity factor exceeding the material fracture toughness during flight; residual strength criterion, which refers to the maximum load exceeding the structural residual strength during flight; and critical crack size criterion, which refers to the crack size extending to a critical value. Among these, the fracture toughness criterion is the most commonly used.

[0055] S2: Based on the risk threshold criterion, determine the time t for the single-flight failure probability (SFPOF) to reach the safety threshold. risk ; Determine t risk If the service life is less than the design life, proceed to step S3; otherwise, end.

[0056] In step S2, the risk threshold criterion states that the probability of single flight failure (SFPOF) should be less than a safety threshold. The safety threshold is related to the aircraft reliability requirements and is generally taken as 10. -7 .

[0057] In step S2, t risk It is the time when the single flight failure probability (SFPOF) is exactly equal to the safety threshold.

[0058] S3: Based on the probability distribution of crack size at any time and time t risk Calculate the previous inspection time t previous With t risk The crack size at each time point is determined using Bayesian information gain, and the time t with the maximum information gain is determined. max(IG) ;

[0059] In step S3, if no check was performed previously, then t previous =0

[0060] In step S3, the previous inspection time t is calculated. previous With t risk The Bayesian information gain (IG) for crack size at each time point is calculated using the following steps:

[0061] (1) Based on the crack size distribution at any time, calculate the crack size distribution at [t]. previous ,t risk The expected probability of crack detection (PCD) at each time point between [time points] is calculated using the following formula:

[0062] PCD=∫POD(a)·f(a)·da

[0063] Among them, PCD represents the expected value of the crack detection probability; POD(a) represents the crack detection probability function; f(a) represents the probability distribution function of the crack size before inspection, and a is the crack size.

[0064] (2) Simulate the inspection results at each time point between [t previous , t risk by random sampling. The method is as follows: Randomly draw a sample between [0, 1], denoted as x. If x ≤ PCD, it means the inspection result is "yes" for cracks, denoted as hit. If PCD < x ≤ 1, it means the inspection result is "no" for cracks, denoted as miss.

[0065] (3) According to the inspection results of "yes / no" for cracks, perform Bayesian update on the probability distribution of the crack size before inspection to obtain the probability distribution of the crack size after inspection. The calculation formula is as follows:

[0066]

[0067] Among them

[0068] Among them, f(a) is the probability distribution function of the crack size before inspection (i.e., the prior probability distribution), f(y|a) is the likelihood function, and y ∈ {hit, miss}; f(a|y) is the probability distribution function of the crack size after inspection (i.e., the posterior probability distribution).

[0069] (4) Calculate the relative entropy, that is, the KL (Kullback-Leibler) divergence, according to the probability distributions of the crack sizes before and after inspection. It is used to characterize the Bayesian information gain IG, and IG = D KL , and the calculation formula is:

[0070]

[0071] Or

[0072]

[0073] Among them, p(a) and q(a) respectively represent the prior probability distribution of the crack size before inspection and the posterior probability distribution of the crack size after inspection.

[0074] In the step S3, t max(IG) is the time corresponding to the maximum value of the information gain between [t previous , t risk .

[0075] S4: When flying to the time t max(IG) corresponding to the maximum value of the information gain, inspect the fatigue critical parts of concern. If cracks are detected, repair them immediately. According to tmax(IG) The probability distribution of crack size before inspection and the probability distribution of initial crack size after repair are used to calculate t. max(IG) Probability distribution of crack size after inspection;

[0076] In step S4, the probability distribution of crack size after inspection is calculated using the following formula:

[0077]

[0078] Among them, f after (a) represents the probability distribution function of crack size after inspection; f R,k (a) represents the probability distribution function of crack size after the k-th type of repair; f(a) represents the probability distribution function of crack size before inspection; PCD k The expected value of the crack detection probability for the k-th type of repair is represented by the following formula:

[0079]

[0080] Wherein, POD(a) represents the crack detection probability function; [a1,a2] represents the crack size range corresponding to the k-th type of repair.

[0081] S5: According to t max(IG) The probability distribution of crack size after time inspection is updated. max(IG) The crack size probability distribution and single-flight failure probability (SFPOF) over subsequent time are calculated, while the previous inspection time t is set. previous =t max(IG) Return to step S2.

[0082] Example 1

[0083] Taking a key part of the fuselage frame of an aircraft as an example, the design life of the aircraft is 5000 FH, where FH represents flight hours.

[0084] Following step S1, a probabilistic fracture mechanics model is used, taking the design load spectrum, material parameters, geometric parameters, and initial crack size of the affected area as inputs, to predict the crack size probability distribution at any given time. Based on the fracture toughness failure criterion, the single-flight failure probability (SFPOF) at any given time is predicted, such as... Figure 2 This is the curve showing the change of SFPOF over flight time (the thick black curve represents the expected SFPOF at a 50% confidence level, and the thin gray curve represents the expected SFPOF at 5% and 95% confidence levels).

[0085] Following step S2, based on the risk threshold criterion, determine the expected SFPOF value at a 50% confidence level to reach the safety threshold of 10. -7 Time t risk ,according to Figure 2It can be seen that t risk =900FH,t risk Less than the design service life (5000FH);

[0086] Following step S3, calculate the Bayesian information gain of the crack size at each time point between [0, 900FH], and determine the time t corresponding to the maximum information gain. max(IG) =50FH;

[0087] Following step S4, inspect the area at 50°FH. Assuming that any crack is repaired immediately upon detection, calculate the probability distribution of the crack size after inspection.

[0088] Following step S5, update the crack size probability distribution and single-flight failure probability (SFPOF) after 50FH. Figure 3 The updated SPOF curves are those after the 50FH check (the thick black curve represents the expected SPOF at 50% confidence, and the thin gray curve represents the expected SPOF at 5% and 95% confidence). Let t previous =50FH; Return to step S2.

[0089] Repeat steps S2 to S5, from Figure 3 It can be seen that the next risk threshold time t risk Once the flight time exceeds 5000 FH, the timing of all inspections is determined. Therefore, by adopting the criterion of simultaneously considering flight safety and maximizing Bayesian information gain, only one inspection needs to be scheduled at 50 FH throughout the entire lifespan.

[0090] For comparison, the timing of inspections is also determined according to the risk threshold criterion, such as... Figure 4 As shown, two inspections need to be scheduled over the entire lifecycle, at 900FH and 4350FH respectively. Therefore, in this example, the number of inspections determined by the Bayesian information gain maximization criterion is less than that determined by the risk threshold criterion, making the former superior.

[0091] The above description is merely a specific embodiment of the present invention, providing a detailed description of the invention. Parts not covered herein are conventional techniques. However, the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A structural risk analysis and maintenance plan optimization method based on Bayesian information gain, characterized in that: The method includes the following steps: Step 1: Select the key fatigue components of interest, and use a probabilistic fracture mechanics model with load spectrum, material parameters, geometric parameters, and initial crack size as inputs to predict the probability distribution of crack size at any time. Based on fatigue fracture failure criteria and probability analysis methods, the single flight failure probability (SFPOF) at any time is predicted. Step 2: Based on the risk threshold criterion, determine the time t it takes for the single-flight failure probability (SFPOF) to reach the safety threshold. risk ; Determine t risk If the service life is less than the design life, proceed to step three; otherwise, end the process. Step 3: Based on the probability distribution of crack size at any time and time t risk Calculate the previous inspection time t previous With t risk The crack size at each time point is determined using Bayesian information gain, and the time t at which the information gain reaches its maximum value is determined. max(IG) The calculation process is as follows: (1) Based on the probability distribution of crack size at any time, calculate the crack size at [t] previous ,t risk Expected probability of crack detection at this location at each time point between [time points]. PCD The calculation formula is: in, PCD This represents the expected value of the probability of crack detection. POD ( a ) represents the crack detection probability function; f ( a () represents the probability distribution function of crack size before inspection; a It is the crack size; (2) Simulation by random sampling [t] previous ,t risk For each time point between [0,1], a sample is randomly selected from the results of the inspection. x It means that if x If PCD ≤ PCD, it indicates that the inspection result is "there" cracks, denoted as hit. If PCD < x If the value is ≤1, it means that the inspection result is "no" cracks, and is recorded as "miss". (3) Based on the inspection result of "present / absent" cracks, perform a Bayesian update on the crack size probability distribution before inspection to obtain the crack size probability distribution after inspection, as shown in the following formula: in, f ( a () represents the probability distribution function of crack size before inspection. f ( y | a ) is the likelihood function. y ∈{hit ,m iss}; f ( a | y ) represents the probability distribution function of the crack size after inspection; (4) Calculate the Kullback-Leibler (KL) divergence based on the probability distribution of crack size before and after inspection. This divergence is used to characterize the Bayesian information gain IG, where IG = D. KL The calculation formula is: or Where p(a) and q(a) represent the prior probability distribution of crack size before inspection and the posterior probability distribution of crack size after inspection, respectively; Step 4: When the flight reaches the maximum information gain time t max(IG) Regularly inspect key fatigue-prone areas; if cracks are found, repair them immediately; according to t max(IG) The probability distribution of crack size before inspection and the probability distribution of initial crack size after repair are used to calculate t. max(IG) Probability distribution of crack size after inspection; Step 5: Based on t max(IG) The probability distribution of crack size after inspection is updated. max(IG) The crack size probability distribution and single-flight failure probability (SFPOF) over subsequent time are then set, while the previous inspection time t is also set. previous =t max(IG) ; Return to step two.

2. The method according to claim 1, characterized in that: In step one, the fatigue fracture failure criterion includes: fracture toughness criterion, which refers to the maximum stress intensity factor exceeding the fracture toughness of the material during flight; The residual strength criterion refers to the maximum load during flight exceeding the residual strength of the structure. The critical crack size criterion refers to the crack size reaching a critical value.

3. The method according to claim 2, characterized in that: In step two, the risk threshold criterion is: the single flight failure probability (SFPOF) should be less than the safety threshold, which is 10. -7 .

4. The method according to claim 3, characterized in that: In step two, time t risk It is the time when the single flight failure probability (SFPOF) is exactly equal to the safety threshold.

5. The method according to claim 4, characterized in that: In step three, the information gain maximum value time t max(IG) This represents the time corresponding to the maximum information gain.

6. The method according to claim 5, characterized in that: In step four, the formula for calculating the probability distribution of crack size after inspection is as follows: in, This represents the probability distribution function of crack size after inspection; This represents the probability distribution function of the crack size after the k-th type of repair; f ( a () represents the probability distribution function of crack size before inspection; PCD k The expected value of the crack detection probability for the k-th type of repair is represented by the following formula: in, POD ( · ) represents the crack detection probability function; [ a 1, a 2] indicates the first k The range of crack sizes corresponding to the type of repair.

7. The method according to claim 6, characterized in that: In step three, if no check was performed previously, then t previous =0.

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