A probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis

Abstract

The present invention belongs to the technical field of aircraft structural health monitoring, and specifically relates to a probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis. The core is to incorporate various uncertainty variables / factors into structural health monitoring and life prediction through structural fatigue fracture risk analysis, and evaluate the risk level of fatigue fracture / failure of aircraft structure during the entire life cycle; at the same time, the Bayesian reasoning method is used to integrate field use and maintenance data to update and reduce the uncertainty in probabilistic prediction, so as to improve the accuracy of structural life prediction and risk analysis, so as to achieve targeted, proactive and cost-effective maintenance decisions for each aircraft under the premise of ensuring structural safety and reliability.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft structure health monitoring, and in particular relates to a probabilistic single-machine structure health monitoring method based on fatigue fracture risk analysis. Background Art

[0002] The Military Aircraft Structural Integrity Program (GJB775A-2012) requires the establishment of a single-aircraft monitoring and analysis method to obtain actual aircraft usage data, predict the potential damage expansion of each key part of the airframe structure, and adjust the maintenance intervals of each single aircraft.

[0003] Traditional single-aircraft monitoring uses deterministic durability analysis and damage tolerance analysis methods to evaluate fatigue damage in key parts based on the actual use of the single aircraft, convert the current flight hours (FH) into equivalent flight hours under the design load spectrum or benchmark load spectrum, and compare them with the benchmark flight hours to make decision recommendations on whether to continue flying or inspect / repair.

[0004] Obviously, traditional single-machine monitoring only focuses on the changes in aircraft use (i.e., load history), without considering other uncertain factors, including geometry, material parameters, initial defect size, crack detection probability, damage state, etc. The initial defect size is a definite value (this value is related to the non-destructive testing method and POD curve), and the crack growth parameters and fracture toughness are also definite values, so the inspection cycle obtained by deterministic damage tolerance analysis is also a definite value.

[0005] All uncertainties in traditional single-machine monitoring are reflected in the dispersion coefficient, but the relationship and derivation process between the dispersion coefficient and all variable sources are usually unclear, which often leads to overly conservative maintenance strategies. In addition, the dispersion coefficient cannot accurately quantify the actual fracture risk, so the use of a universal dispersion coefficient for some key structures still has the risk of fracture failure.

[0006] The Military Aircraft Integrity Program (GJB775A-2012) clearly stipulates that risk analysis should be conducted on the structure to determine the impact of each task in the integrity program on the reliability of the aircraft structure and verify that the aircraft structure reliability requirements are met. Risk analysis should be used to determine whether the inspection interval needs to be reduced to control the safety risk to an acceptable level, or to reduce structural maintenance costs and improve equipment attendance and integrity rates. The specification does not specify the calculation method for risk analysis.

[0007] Based on the above background, the present invention proposes a probabilistic single-aircraft structural health monitoring method based on fatigue fracture risk analysis. The core of the present invention is to incorporate various uncertainty variables / factors into structural health monitoring and life prediction through structural fatigue fracture risk analysis, and evaluate the risk level of fatigue fracture / failure of the aircraft structure throughout its life cycle; at the same time, the Bayesian reasoning method is used to integrate field use and maintenance data to update and reduce the uncertainty of probabilistic prediction, so as to improve the accuracy of structural life prediction and risk analysis, thereby achieving targeted, proactive and cost-effective maintenance decisions for each aircraft under the premise of ensuring structural safety and reliability. Summary of the invention

[0008] The purpose of the present invention is to evaluate the risk of fatigue fracture / failure of aircraft structures throughout their life cycle through structural fatigue fracture risk analysis, while integrating field use and maintenance data to update and reduce the uncertainty of probability prediction, thereby improving the accuracy of structural life prediction and risk analysis, and achieving safe and economical maintenance decisions.

[0009] Technical solution of the present invention: In order to achieve the above-mentioned invention object, a probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis is proposed, comprising the following steps:

[0010] S1: Obtain the actual load spectrum of a single aircraft based on flight parameters and predict the future load spectrum; assuming that the aircraft has flown X0FH, then X0FH is the actual load spectrum of the single aircraft; after X0FH is the predicted future load spectrum;

[0011] S2: Based on the actual load spectrum of the single aircraft and the future predicted load spectrum obtained in step S1, a probabilistic fatigue analysis method is used to perform a fracture risk analysis, and the probabilistic life distribution under the damage threshold and the probability of single-flight failure over time are output; a probabilistic damage tolerance analysis method is used to perform a fracture risk analysis, and the probabilistic life distribution of a specified crack size, the probabilistic crack size distribution over time, and the probability of single-flight failure over time are output; when the flight reaches the scheduled inspection time in the structural maintenance plan, the crack detection probability is calculated, and then the probabilistic crack size distribution and the single-flight failure probability after the inspection are predicted;

[0012] Fracture risk analysis refers to calculating the probability of a structure failing due to fatigue fracture in flight. The fracture failure probability is usually represented by the single takeoff and landing failure probability (SFPOF), which refers to the probability of a structure failing in the current flight if it did not fail in the previous flight, and allows for preventive maintenance in the previous flight.

[0013] Assume t is the current flight, φ i Indicates that flight i has failed. Indicates that flight i has not failed (or succeeded). Since SFPOF is a conditional probability, therefore:

[0014]

[0015] Where Pr represents the fracture failure probability;

[0016] The fracture failure criterion is: the load encountered during flight exceeds the remaining strength of the structure (or the maximum stress intensity factor during flight exceeds the critical value), the crack propagates to the critical size, the fatigue damage accumulates to the damage threshold, etc.

[0017] S3: According to the output result of the fracture risk analysis in step S2, set the safety threshold of the single - flight failure probability. Optimize the out - field structure maintenance plan according to the principle that the single - flight failure probability is lower than the safety threshold and the maintenance cost of the entire maintenance plan is minimized.

[0018] S4: Determine whether the actual structural inspection and maintenance results are returned when implementing the out - field structure maintenance plan. If the structural inspection and maintenance results are generated at X i FH(X i <X0), it is necessary to diagnose and update the output result of the fracture risk analysis of X i FH in step S2, and predict the output result of the fracture risk analysis after X i FH based on the updated fracture risk analysis output result by returning to step S2.

[0019] In a possible embodiment, in step S1, obtaining the actual single - aircraft usage load spectrum specifically includes the following steps: First, based on the typical maneuver template database, use pattern recognition methods such as clustering to identify the maneuver actions of the flight parameter history, and substitute them into the "flight parameter - load" models of various maneuvers, and arrange them according to the order of landings and takeoffs and maneuvers to obtain the actual single - aircraft usage load spectrum.

[0020] In a possible embodiment, in step S1, the probability landing method is used to predict the future load spectrum of a single aircraft, which specifically includes the following steps: According to the current or planned mission profile combination, randomly allocate future landings according to the proportion or occurrence probability of each profile. Each landing is randomly selected from the historical landings of the affiliated profile, and the future load spectrum of a single aircraft can be predicted.

[0021] In a possible embodiment, in step S2, the probability fatigue analysis method assumes that the material parameters and fatigue damage thresholds are continuous random variables on the basis of deterministic fatigue analysis, uses the stress or strain fatigue analysis method, tracks the damage accumulation under the single - aircraft usage load spectrum and the future probability load spectrum, calculates the distribution of the fatigue life (usually expressed in flight hours or number of landings) when the fatigue damage reaches the threshold, and then calculates the future flight failure probability using the probability method.

[0022] The inputs are: material parameters (stress-life curve, strain-life curve, etc.), geometric dimension information (thickness, aperture, etc., which mainly affect the stress concentration factor), load spectrum (including usage and future load spectrum). All input parameters can be discrete variables or continuous random variables.

[0023] Among them, stress-life and strain-life curves usually adopt probability psN and peN curves, and geometric dimensions usually take nominal values ​​or obey normal distribution.

[0024] The outputs are: probabilistic life distribution under damage threshold, single flight failure probability over time, and failure probability within a certain time range. Among them, SFPOF is the expected value with confidence interval.

[0025] In a possible embodiment, in step S2, the probabilistic damage tolerance analysis is based on probabilistic fracture mechanics. On the basis of the deterministic damage tolerance analysis, it is assumed that the initial crack size and material parameters are random variables, and various deterministic or random crack extension models (usually a linear elastic fracture mechanics model) are used to track the crack extension under the single-machine load spectrum and the future probabilistic load spectrum, calculate the probabilistic crack size distribution over time, and then use the probabilistic method to calculate the future flight failure probability according to the fracture failure criterion.

[0026] The inputs are: initial defect size, material parameters (fracture toughness, crack growth rate parameters, etc.), geometric size information (thickness, aperture, etc., which mainly affect the geometric correction factor curve), load spectrum (including usage and future load spectrum), maximum stress per flight, crack detection probability (POD curve), defect size after repair, etc. All input parameters can be discrete variables or continuous random variables.

[0027] Among them, the initial defect size and the defect size after repair are usually assumed to obey Weibull or lognormal distribution, which are generally determined by fitting the fatigue test data of simulated parts and crack extension curves; material parameters are usually assumed to obey normal distribution or joint normal distribution, and geometric dimensions usually take nominal values ​​or obey normal distribution; the maximum stress of each flight is usually assumed to obey Gumbel distribution, which can be obtained based on the fitting of the maximum stress sample of a single flight or the derivation of the load spectrum exceedance curve; the POD curve is a representation of the non-destructive testing capability, which is generally obtained based on NDE test data and is often represented by the cumulative distribution function of the lognormal distribution or exponential distribution.

[0028] The outputs are: probabilistic life distribution for a specified crack size, probabilistic crack size distribution over time, single flight failure probability over time, and failure probability within a certain time range. Among them, SFPOF is the expected value with confidence interval.

[0029] In a possible embodiment, in step S2, the fracture failure probability (SFPOF) can be calculated using a variety of probability analysis techniques, such as conditional reliability method, first-order and second-order reliability (FORM / SORM) method, Monte Carlo sampling method, etc. In order to improve the calculation efficiency, various variance reduction techniques are usually used, including but not limited to importance sampling, stratified sampling, adaptive sampling, Latin-hypercube sampling, and response surface methods.

[0030] Taking the conditional reliability method as an example, if the fracture failure criterion is that the crack expands to the critical size or the fatigue damage accumulates to the damage threshold, the failure probability calculation method for the current flight t is:

[0031]

[0032] Wherein, h(t) is the hazard rate of the current flight t, f(·) and F(·) are the probability distribution function and cumulative distribution function of the fatigue life when the crack grows to the critical size or the damage reaches the threshold, f(t) and F(t) are the probability distribution function value and cumulative distribution function value of the current flight t, and R(t) is the cumulative survival rate of the current flight t.

[0033] Taking the conditional reliability method as an example, if the fracture failure criterion is that the load encountered in flight exceeds the residual strength of the structure (or the maximum stress intensity factor in flight exceeds the critical value), the failure probability of the current flight t is calculated as follows:

[0034]

[0035] in, represents the maximum stress σ per flight max Exceeding the residual strength σ cr The probability of H(·) is σ max Cumulative distribution function of the residual strength; X represents all variables related to the residual strength, including fracture toughness, crack size, and crack growth rate parameters; f X (X) represents the joint probability distribution of the variables, and R(t) is the cumulative survival rate of the current flight t.

[0036] In a possible embodiment, in step S2, the calculation formula for the crack detection probability is:

[0037]

[0038] Among them, PCD represents the probability of crack detection; POD represents the probability of crack detection, which is related to the nondestructive testing method, confidence level and crack size; f(a) represents the probability distribution function of the crack size before inspection, and [a1, a2] represents the crack size range corresponding to the kth type of repair.

[0039] In a possible embodiment, in step S2, the probability crack size distribution after inspection is predicted, and the calculation formula is:

[0040]

[0041] Among them, f after (a) represents the probability distribution function of crack size after inspection; PCD k represents the crack detection probability of the k-th type of repair, f R,k (a) represents the probability distribution function of the crack size after the kth type of repair; f(a) represents the probability distribution function of the crack size before inspection.

[0042] In one possible embodiment, in step S3, the maintenance cost can be attributed to the following four sources: inspection, repair, false alarm and failure. The expected costs generated by them can usually be estimated independently. For a specific maintenance plan, the estimated maintenance cost of a certain structural part is:

[0043]

[0044] Among them, E(C I )、E(C R )、E(C L )、E(C F ), E(C) represent the expected values ​​of inspection cost, repair cost, false alarm cost, failure cost and total cost respectively. and represents the inspection cost of the jth inspection and the probability of the inspection occurring, usually or 1.0; and represents the repair cost and the probability of occurrence of the k-th type of repair in the j-th inspection, where the probability of occurrence of the repair is equal to the probability of detection of a crack of the corresponding size; and represents the false alarm cost and the probability of false alarm in the jth inspection; C F represents the failure cost of the part, represents the failure probability of the part in flight i;

[0045] In practical applications, it is usually assumed that once a crack is detected, it will be repaired, and the type of repair is related to the size of the crack. For example, when the crack is small, the fastener is enlarged by one level after reaming; when the crack is longer, a reinforced corner box is used; when the crack is longer, a new part is replaced;

[0046] In a possible embodiment, in step S3, the safety threshold is 10 -7 .

[0047] In a possible embodiment, in step S4, if a structural inspection and maintenance result is generated, for the case where the structural inspection and maintenance result is a crack hit / miss, a Bayesian update may be performed according to the probabilistic crack size distribution of step S2, and the formula is as follows:

[0048]

[0049] in

[0050] Among them, f(a) is the prior probability distribution function of the crack size before inspection, f(y|a) is the likelihood function, y∈{hit,miss}; f(a|y) is the posterior probability distribution function of the crack size after inspection.

[0051] For the case where the structural inspection maintenance result is a crack size measurement (using denoted), the Bayesian update can be performed based on the probabilistic crack size distribution of step s2, as follows:

[0052]

[0053] in, represents the actual measured value of the crack size, and f(a) is the prior probability distribution function of the crack size before inspection; is the likelihood function, which needs to be obtained by using the statistical model of the POD curve, which is generally a normal distribution. is a continuous response, is the posterior probability distribution function of the crack size after inspection.

[0054] Beneficial technical effects of the present invention: The present invention incorporates various uncertainties into structural health monitoring and prediction through structural fracture risk analysis, and integrates actual aircraft use and inspection data to continuously update and reduce model / parameter uncertainties, thereby improving the accuracy of structural health status diagnosis and prediction.

[0055] As new usage and maintenance data is continuously collected, the level of uncertainty in fatigue life predictions and risk assessments is gradually reduced. This continuous probabilistic model updating ensures that the digital twin continuously reflects its physical body, enabling proactive and cost-effective maintenance decisions to be made for each aircraft.

[0056] The present invention is superior to conventional risk analysis. Conventional risk analysis can only predict the probability of fracture failure, and cannot use field structural inspection data to diagnose and update the probability model. The present invention adopts a probability update method based on Bayesian reasoning, etc., which can integrate the actual use and inspection data of the aircraft to diagnose and update the probability distribution of crack size, and then perform future probability life prediction and risk analysis based on the updated results, so as to achieve better maintenance decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to an embodiment of the present invention.

[0058] Figure 2 Schematic diagram of SFPOF prediction value with flight takeoff and landing number in embodiment 1 of the present invention

[0059] Figure 3 Schematic diagram of the comparison of the crack size probability distribution before and after updating based on the actual inspection results in the first embodiment of the present invention

[0060] Figure 4 Schematic diagram of the impact of probability distribution update based on actual inspection results on subsequent SFPOF in embodiment 1 of the present invention DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] The solution of the present invention comprises the following steps:

[0063] (1) Obtaining single-aircraft load spectrum and predicting future load spectrum based on flight parameters

[0064] The single machine load spectrum is the basic input for fatigue damage accumulation and crack growth tracking as well as fracture risk analysis.

[0065] Acquisition of load spectrum for single aircraft: First, based on the typical maneuver template database, pattern recognition methods such as clustering are used to identify the maneuver actions of the flight parameter history, and the "flight parameter-load" model of various maneuvers is substituted and arranged in the order of take-off and landing and maneuvering to obtain the actual load history of the single aircraft.

[0066] Prediction of future load spectrum of a single aircraft: The probabilistic take-off and landing method can be used to randomly allocate future take-offs and landings according to the proportion (or probability of occurrence) of each profile based on the current or planned mission profile combination. Each take-off and landing is randomly selected from the historical take-offs and landings of the corresponding profile. The prediction of future load spectrum is not limited to the probabilistic take-off and landing method, but can also be other probabilistic methods.

[0067] (2) Fracture risk analysis based on probabilistic fatigue / damage tolerance analysis

[0068] Fracture risk analysis refers to calculating the probability of a structure failing due to fatigue fracture in flight. The fracture failure probability is usually characterized by a single flight failure probability (SFPOF), which refers to the probability of a structure failing in the current flight if it has not failed in the previous flight, and allows for preventive maintenance in the previous flight.

[0069] Assume t is the current flight, φ i Indicates that flight i has failed. represents that flight i did not fail (or succeeded). Since SFPOF is a conditional probability, then:

[0070]

[0071] Where Pr represents the probability of fracture failure.

[0072] The fracture failure criteria are: the load encountered during flight exceeds the residual strength of the structure (or the maximum stress intensity factor during flight exceeds the critical value), the crack extends to the critical size, the fatigue damage accumulates to the damage threshold, etc.

[0073] a) Probabilistic fatigue analysis

[0074] Probabilistic fatigue analysis is based on deterministic fatigue analysis, assuming that material parameters and fatigue damage thresholds are continuous random variables. It uses stress or strain fatigue analysis methods to track the damage accumulation under the load spectrum of single aircraft use and the future probabilistic load spectrum, and calculates the distribution of fatigue life (usually expressed in flight hours or take-off and landing times) when the fatigue damage reaches the threshold. Then, a probabilistic method is used to calculate the probability of future flight failure.

[0075] The inputs are: material parameters (stress-life curve, strain-life curve, etc.), geometric dimension information (thickness, aperture, etc., which mainly affect the stress concentration factor), load spectrum (including usage and future load spectrum). All input parameters can be discrete variables or continuous random variables.

[0076] Among them, stress-life and strain-life curves usually adopt probability psN and peN curves, and geometric dimensions usually take nominal values ​​or obey normal distribution.

[0077] The outputs are: probabilistic life distribution under damage threshold, single flight failure probability over time, and failure probability within a certain time range. Among them, SFPOF is the expected value with confidence interval.

[0078] b) Probabilistic damage tolerance analysis

[0079] Probabilistic damage tolerance analysis is based on probabilistic fracture mechanics. On the basis of deterministic damage tolerance analysis, it assumes that the initial crack size and material parameters are random variables, and adopts various deterministic or random crack propagation models (usually linear elastic fracture mechanics models) to track the crack propagation under the load spectrum of single aircraft use and future probabilistic load spectrum, calculate the probabilistic crack size distribution over time, and then use the probabilistic method to calculate the future flight failure probability according to the fracture failure criterion.

[0080] The inputs are: initial defect size, material parameters (fracture toughness, crack growth rate parameters, etc.), geometric size information (thickness, aperture, etc., which mainly affect the geometric correction factor curve), load spectrum (including usage and future load spectrum), maximum stress per flight, crack detection probability (POD curve), defect size after repair, etc. All input parameters can be discrete variables or continuous random variables.

[0081] Among them, the initial defect size and the defect size after repair are usually assumed to obey Weibull or lognormal distribution, which are generally determined by fitting the fatigue test data of simulated parts and crack extension curves; material parameters are usually assumed to obey normal distribution or joint normal distribution, and geometric dimensions usually take nominal values ​​or obey normal distribution; the maximum stress of each flight is usually assumed to obey Gumbel distribution, which can be obtained based on the fitting of the maximum stress sample of a single flight or the derivation of the load spectrum exceedance curve; the POD curve is a representation of the non-destructive testing capability, which is generally obtained based on NDE test data and is often represented by the cumulative distribution function of the lognormal distribution or exponential distribution.

[0082] The outputs are: probabilistic life distribution for a specified crack size, probabilistic crack size distribution over time, single flight failure probability over time, and failure probability within a certain time range. Among them, SFPOF is the expected value with confidence interval.

[0083] The fracture failure probability (SFPOF) can be calculated using a variety of probability analysis techniques, such as conditional reliability method, first-order and second-order reliability (FORM / SORM) method, Monte Carlo sampling method, etc. In order to improve the calculation efficiency, various variance reduction techniques are usually used, including but not limited to importance sampling, stratified sampling, adaptive sampling, Latin-hypercube sampling, and response surface methods.

[0084] Taking the conditional reliability method as an example, if the fracture failure criterion is that the crack expands to the critical size or the fatigue damage accumulates to the damage threshold, the failure probability calculation method for the current flight t is:

[0085]

[0086] where h(t) is the hazard rate of the current flight t, f(·) and F(·) are the probability distribution function and cumulative distribution function of the fatigue life when the crack grows to the critical size or the damage reaches the threshold, and R(t) is the cumulative survival rate of the current flight t.

[0087] Taking the conditional reliability method as an example, if the fracture failure criterion is that the load encountered in flight exceeds the residual strength of the structure (or the maximum stress intensity factor in flight exceeds the critical value), the failure probability of the current flight t is calculated as follows:

[0088]

[0089] in, represents the maximum stress σ per flight max Exceeding the residual strength σ cr The probability of H(·) is σ max Cumulative distribution function of the residual intensity; X represents all variables related to the residual intensity, f X (X) represents the joint probability distribution of the variables, and R(t) is the cumulative survival rate of the current flight t.

[0090] When the flight reaches the scheduled inspection time in the structural maintenance plan, the crack detection probability is calculated, and then the probabilistic crack size distribution and the single flight failure probability after inspection are predicted.

[0091] The calculation formula for the crack detection probability is:

[0092]

[0093] Among them, PCD represents the probability of crack detection; POD represents the probability of crack detection, which is related to the nondestructive testing method, confidence level and crack size; f(a) represents the probability distribution function of the crack size before inspection, and [a1, a2] represents the crack size range corresponding to the kth type of repair.

[0094] The calculation formula for the probabilistic crack size distribution after inspection is:

[0095]

[0096] Among them, f after (a) represents the probability distribution function of crack size after inspection; PCD k represents the crack detection probability of the k-th type of repair, f R,k(a) represents the probability distribution function of the crack size after the kth type of repair; f(a) represents the probability distribution function of the crack size before inspection.

[0097] (3) Probability distribution model update based on field use and inspection and maintenance data

[0098] The structural failure probability calculated in step (2) should be considered as a nominal or estimated risk measure rather than an absolute risk measure. Aircraft field use and inspection and maintenance data are the most important feedback for risk / reliability analysis and are currently the only reliable way to verify the results of structural risk calculations.

[0099] The Bayesian reasoning method is adopted to update the crack size probability distribution and risk assessment results using the actual aircraft usage and inspection and maintenance data, and then future probabilistic life prediction and structural risk analysis are carried out based on the updated results, gradually reducing the uncertainty level of fatigue life prediction and risk assessment to improve safety and reliability.

[0100] Field use refers to: the actual flight data of a single aircraft and whether fracture failure occurs during each flight. Once the updated field use data is obtained, the risk analysis of each key component of the single aircraft will be updated to the current time using the actual use load spectrum.

[0101] Inspection data refers to: presence / absence of cracks, crack size measurements. Regardless of the inspection results, once an inspection is performed, the results can be used to update the crack size distribution before the inspection.

[0102] For crack presence / absence (hit / miss), the crack size probability distribution calculated in step (2) can be used to perform Bayesian update (the formula is as follows):

[0103]

[0104] in

[0105] Among them, f(a) is the prior probability distribution function of the crack size before inspection, f(y|a) is the likelihood function, y∈{hit,miss}, and f(y|a) is the posterior probability distribution function of the crack size after inspection.

[0106] For crack size measurements (using denoted), the crack size probability distribution calculated in step (2) can be used to perform Bayesian updating (the formula is as follows):

[0107]

[0108] Where f(a) is the prior probability distribution function of the crack size before inspection; is the likelihood function, which needs to be obtained by using the statistical model of the POD curve, which is generally a normal distribution. is a continuous response, is the prior probability distribution function of the crack size after inspection.

[0109] In practical applications, the probabilistic model should be diagnosed and updated multiple times throughout the aircraft's service life based on the aircraft's actual usage and inspection results, and then the maintenance plan for each aircraft should be re-evaluated.

[0110] (4) Optimization of field structure maintenance plan based on specified rules

[0111] When formulating a maintenance plan, the probability of structural failure and maintenance cost (i.e., economy) should be weighed. The goal is usually to maintain the SFPOF at a certain safety threshold (e.g., safety threshold = 10 in GJB775A). -7 ) and minimize maintenance costs. Other rules can also be specified, such as fixed inspection intervals, failure probability thresholds, minimization of maintenance costs or number of inspections, etc.

[0112] Maintenance costs can be attributed to four sources: inspection, repair, false alarms and failures. The expected costs of these sources can usually be estimated independently. For a specific maintenance plan, the maintenance cost of a structural part is estimated as:

[0113]

[0114] Among them, E(C I )、E(C R )、E(C L )、E(C F ), E(C) represent the expected values ​​of inspection cost, repair cost, false alarm cost, failure cost and total cost respectively. and represents the inspection cost of the jth inspection and the probability of the inspection occurring, usually or 1.0; and represents the repair cost and the probability of occurrence of the k-th type of repair in the j-th inspection, where the probability of occurrence of the repair is equal to the probability of detection of a crack of the corresponding size; and represents the false alarm cost and the probability of false alarm in the jth inspection; C F represents the failure cost of the part, represents the failure probability of this part in flight i.

[0115] In practical applications, it is usually assumed that once a crack is detected, it will be repaired, and the type of repair is related to the size of the crack. For example, when the crack is small, the fastener is enlarged by one level after reaming; when the crack is longer, a reinforced corner box is used; when the crack is longer, a new part is replaced.

[0116] The structural maintenance plan for a single machine should comprehensively weigh the failure probability and maintenance costs of all key components, and the structural maintenance plan for a fleet should weigh the failure probability and maintenance costs of all single machines. Once the optimization criteria or rules are selected, the optimal maintenance and support decisions can be made for a single machine or even a fleet based on the predicted values ​​of failure probability and maintenance costs.

[0117] Embodiment 1

[0118] like Figure 1 As shown in the figure, taking the key parts of the fuselage frame of a single machine as an example, the fracture risk analysis is carried out.

[0119] 1) The aircraft has currently flown 900 FH. According to step S1, the actual load spectrum of the single aircraft within 900 FH is obtained according to the flight parameters, and the future load spectrum after 900 FH is predicted;

[0120] 2) According to step S2, the probabilistic damage tolerance analysis method is used to perform fracture risk analysis, and the probability distribution assumptions of various inputs are listed in Table 1. Other input parameters are taken as fixed values.

[0121] The fracture failure criterion is selected as the load encountered in flight exceeding the residual strength of the structure. Assume that the current maintenance plan is: the first inspection time is 6000FH and the subsequent inspection interval is 3000FH. Since SFPOF is aimed at the failure probability of a single flight, the flight time needs to be converted into flight takeoffs and landings, and the average flight time per flight is 1.2FH.

[0122] Table 1 Probability distribution assumptions for various inputs

[0123]

[0124]

[0125] The importance sampling method is used to solve the SFPOF calculation formula by Monte Carlo integration, and it is assumed that once a crack is found during inspection, it will be repaired. The SFPOF prediction results are as follows: Figure 2 , it can be seen that: SFPOF increases with flight time until the scheduled inspection time. Since a certain proportion of crack sizes are reset after inspection (this proportion is the probability of detection (PCD)), the SFPOF after inspection is reduced.

[0126] 3) According to step S3, based on the above fracture risk analysis results, the total maintenance cost of the current maintenance plan is calculated according to SFPOF<10-7 Optimize the outfield structure maintenance plan according to the principle of minimizing maintenance costs.

[0127] The repair cost calculation process is as follows: Assume that once a crack is detected during inspection, repair is carried out immediately. According to the crack size, assume there are three repair types. Among them, reaming and enlarging the fastener corresponds to small cracks (a < 0.76 mm), the reinforcing gusset box corresponds to longer cracks (0.76 mm < a < 6.35 mm), and replacing the component corresponds to even longer cracks (a > 6.35 mm).

[0128] According to the crack detection probability calculation formula, estimate the occurrence probabilities of different repair types during future inspections, and the results are listed in Table 2.

[0129] Table 2 Occurrence Probabilities of Different Repair Types during Future Inspections

[0130]

[0131] Assume that the costs of the three repair types are 1000, 5000, and 15000 respectively. These values are dimensionless and only indicate the relative magnitudes of different repair costs. Further, according to the maintenance cost calculation formula, estimate the costs of different repair types during future inspections, and the results are listed in Table 3.

[0132] Table 3 Estimated Repair Costs during Future Inspections

[0133]

[0134] In addition to the repair cost, assume that the inspection cost is 500, the false alarm cost is 1000, and the failure cost is 1 million. Assume different structural maintenance plans (including the first inspection time and subsequent inspection intervals, as shown in Table 4 below), and calculate the total maintenance costs (including four sources) and the maximum SFPOF of each plan respectively. According to the principle of minimizing the maintenance cost on the premise that SFPOF is less than 10 -7 , the maintenance plan numbered 6 in Table 4 is the optimal one.

[0135] Table 4 Estimated Total Costs of Different Maintenance Plans

[0136]

[0137] 4) According to Step S4, assume that a crack is detected during the inspection at 6000 FH, and the crack measurement value is

[0138] Update the probability distribution of the crack size before inspection using the above Bayesian inference method. The comparison of the probability distribution function curves before /

[0139] after update is as Figure 3 . Two measurement values are assumed in the figure:

[0140]

[0141] Then, based on the updated crack size probability distribution, return to step s2 to update the SFPOF after 6000FH, and then adjust the subsequent structural maintenance plan. Figure 2 Only the prediction curves are compared as shown in Figure 4 There are two situations: one is that if the cracks found are not repaired, the SFPOF will quickly grow to the safety threshold (10 -7 ), the subsequent inspection interval should be advanced to 950FH, otherwise flight safety cannot be guaranteed; the other is to repair the cracks found during the inspection, then the crack size distribution is reset to the crack size distribution after repair (reinforcement corner box) in Table 1, and the SFPOF remains very low, so no inspection is required during the subsequent life cycle.

[0142] The above is only a specific embodiment of the present invention, and the present invention is described in detail. The unexplained part is a conventional technology. However, the protection scope of the present invention is not limited to this. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis, characterized in that: The steps include: S1: Obtain the actual load spectrum of a single aircraft based on flight parameters and predict the future load spectrum; assuming that the aircraft has flown X0FH, then X0FH is the actual load spectrum of the single aircraft; after X0FH is the predicted future load spectrum; S2: Based on the actual load spectrum of the single aircraft and the future predicted load spectrum obtained in step S1, a probabilistic fatigue analysis method is used to perform a fracture risk analysis, and the probabilistic life distribution under the damage threshold and the single flight failure probability over time are output; The probabilistic damage tolerance analysis method is used to perform fracture risk analysis, and the probabilistic life distribution of the specified crack size, the probabilistic crack size distribution over time, and the single flight failure probability over time are output; when the flight reaches the scheduled inspection time in the structural maintenance plan, the crack detection probability is calculated, and then the probabilistic crack size distribution and single flight failure probability after inspection are predicted; S3: according to the output result of the fracture risk analysis in step S2, a safety threshold of the single flight failure probability is set, and the field structure maintenance plan is optimized according to the principle that the single flight failure probability is lower than the safety threshold and the maintenance cost of the entire maintenance plan is minimized; S4: Determine whether the actual structural inspection and maintenance results are returned when the outfield structure maintenance plan is executed. If, within X i FH generates the structural inspection and maintenance results, where X i < X0, it is necessary to diagnose and update the fracture risk analysis output results of step S2 for X i FH, and based on the updated results, return to step S2 to predict the fracture risk analysis output results after X i FH; If a structural inspection and maintenance result is generated, for the case where the structural inspection and maintenance result is the presence / absence of cracks, a Bayesian update can be performed based on the probabilistic crack size distribution of step s2, and the formula is as follows: in Wherein, f(a) is the prior probability distribution function of the crack size before inspection, f(y|a) is the likelihood function, y∈{hit,miss}, and f(a|y) is the posterior probability distribution function of the crack size after inspection; POD is the probability of crack detection, which is related to the nondestructive testing method, confidence level and crack size; hit represents the presence of cracks and miss represents the absence of cracks; if a structural inspection and maintenance result is generated, for the case where the structural inspection and maintenance result is a crack size measurement value, Bayesian update can be performed according to the probabilistic crack size distribution of step s2, and the formula is as follows: in, represents the actual measured value of the crack size, and f(a) is the prior probability distribution function of the crack size before inspection; is the likelihood function, which needs to be obtained by the statistical model of deriving the POD curve. It is a normal distribution, where is a continuous response, is the posterior probability distribution function of the crack size after inspection.

2. The probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to claim 1 is characterized in that: In step S2, the probabilistic fatigue analysis method assumes that material parameters and fatigue damage thresholds are continuous random variables based on deterministic fatigue analysis, uses stress or strain fatigue analysis methods, tracks damage accumulation under a single aircraft load spectrum and future probabilistic load spectra, calculates fatigue life distribution when fatigue damage reaches the threshold, and then uses a probabilistic method to calculate future flight failure probability.

3. The probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to claim 1 is characterized in that: In step S2, the probabilistic damage tolerance analysis method is based on probabilistic fracture mechanics. On the basis of deterministic damage tolerance analysis, it is assumed that the initial crack size and material parameters are random variables, and various deterministic or random crack extension models are used to track the crack extension under the load spectrum of a single machine and the future load spectrum, and calculate the probabilistic crack size distribution over time, and then use the probabilistic method to calculate the future flight failure probability according to the fracture failure criterion.

4. A probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to any one of claims 1 to 3, characterized in that: In step S2, the specific process of calculating the single flight failure probability using the conditional reliability method is as follows: If the fracture failure criterion is that the crack grows to a critical size or fatigue damage accumulates to a damage threshold, the failure probability at the current flight t is calculated as: Wherein, h(t) is the hazard rate of the current flight t, f(·) and F(·) are the probability distribution function and cumulative distribution function of the fatigue life when the crack grows to the critical size or the damage reaches the threshold, f(t) and F(t) are the probability distribution function value and cumulative distribution function value of the current flight t, and R(t) is the cumulative survival rate of the current flight t.

5. A probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to any one of claims 1 to 3, characterized in that: In step S2, the specific process of calculating the single flight failure probability using the conditional reliability method is as follows: If the fracture failure criterion is that the load encountered in flight exceeds the residual strength of the structure, the failure probability of the current flight t is calculated as: in, represents the maximum stress σ per flight max Exceeding the residual strength σ cr The probability of H(·) is σ max Cumulative distribution function of the residual strength; X represents all variables related to the residual strength, including fracture toughness, crack size, and crack growth rate parameters; f X (X) represents the joint probability distribution of the variables, and R(t) is the cumulative survival rate of the current flight t.

6. The probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to claim 1 is characterized in that: In step S2, the calculation formula of the crack detection probability is: Where PCD represents the probability of crack detection; POD represents the probability of crack detection, which is related to the nondestructive testing method, confidence level and crack size; f(a) represents the probability distribution function of the crack size before inspection, and [a1, a2] represents the crack size range corresponding to the kth type of repair.

7. The probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to claim 1 is characterized in that: In step S2, the probability crack size distribution after inspection is predicted, and the calculation formula is: where f after (a) represents the probability distribution function of crack size after inspection; PCD k represents the crack detection probability of the k-th type of repair, f R,k (a) represents the probability distribution function of the crack size after the kth type of repair; f(a) represents the probability distribution function of the crack size before inspection.

8. The probabilistic single-machine structural health monitoring method based on fatigue fracture risk analysis according to claim 1 is characterized in that: In step S3, the maintenance cost comes from inspection, repair, false alarm and failure. The expected costs generated by them can be estimated independently. For a specific maintenance plan, the estimated maintenance cost of a certain structural part is: Among them, E(C I )、E(C R )、E(C L )、E(C F ), E(C) represent the expected values ​​of inspection cost, repair cost, false alarm cost, failure cost and total cost respectively. and represents the inspection cost of the jth inspection and the probability of the inspection occurring, usually or 1.0; and represents the repair cost and the probability of occurrence of the k-th type of repair in the j-th inspection, where the probability of occurrence of the repair is equal to the probability of detection of a crack of the corresponding size; and represents the false alarm cost and the probability of false alarm in the jth inspection; C F represents the failure cost of the part, represents the failure probability of this part in flight i.

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