CN117852198B - Model fusion-based digital twin prediction method for multi-scale cracks of aircraft structure - Google Patents
Model fusion-based digital twin prediction method for multi-scale cracks of aircraft structure Download PDFInfo
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Abstract
The invention discloses a model fusion-based digital twin prediction method for multi-scale cracks of an aircraft structure. Firstly, establishing a digital twin model of an aircraft structure, acquiring load data to load the digital twin model of the aircraft structure, finding a dangerous area in the aircraft structure, and constructing a local model of the dangerous area, so that multi-scale analysis of the aircraft structure is realized, the calculation efficiency is improved, and the real-time performance of digital twin prediction is ensured; a plurality of crack extension prediction models are selected, crack extension prediction results are obtained based on a particle filtering algorithm, a novel time-varying model fusion algorithm is provided, an optimization function is established by using a prediction error square sum minimization strategy, the prediction results of the plurality of models are subjected to weighted fusion, the influence of the uncertainty of the aircraft structural material parameters and the uncertainty of the model form on the prediction results is reduced by the method, and the accuracy of the crack length prediction results is effectively improved.
Description
Technical Field
The invention relates to the field of multi-scale crack growth analysis, in particular to a multi-scale crack growth digital twin prediction method based on model fusion.
Background
Most structural failures of aircraft are caused by fatigue fracture, and cyclic loads cause critical parts of the structure to initiate cracks and promote continuous expansion of the cracks, severely affecting structural integrity and reliability. The traditional aircraft structure maintenance concept is based on a safety management concept of damage tolerance, and each part of the aircraft is detected by adopting a fixed maintenance period. However, due to the difference of flight tasks of each aircraft, the load history experienced by each aircraft is different, and the differences of different structures exist in the aspects of original material defects and manufacturing errors, the individual differences and uncertainties are required to be fully considered, and a high-fidelity prediction model of crack propagation of the aircraft structural component is established, so that the maintenance interval can be scientifically and reasonably determined. On the other hand, the physical mechanism of crack propagation is complex, and because of mechanism cognition limitation, different crack propagation models have certain model form uncertainty, so that the accuracy of prediction results obtained based on the models is different, and the accuracy of crack propagation prediction is affected.
The digital twin is a novel systematic modeling and simulation integration technology aiming at complex physical objects, physical entities can be mapped to a virtual model, performance simulation and damage prediction of an aircraft structure in the whole life cycle can be realized by constructing a digital twin model of crack propagation of the aircraft structure, and load change data of the aircraft can be obtained in the aircraft flight process by installing a sensor at the aircraft fatigue dangerous position, so that maintenance and repair strategies of the aircraft are guided, and the safety and reliability of the aircraft operation are ensured.
Digital twinning of aircraft structures involves a multi-scale model, the overall aircraft size can reach 10 2 m, and the fatigue crack size is typically 10 -3 m. Therefore, how to realize the cross-scale crack propagation prediction is one of the key technical points of the invention.
In addition, during the course of crack growth studies, many scholars have proposed many crack growth models, and the models established by different modelers may differ in expression form due to the difference in knowledge reserves and cognitive levels. At present, common crack propagation models include a Paris model, a Walker model, a Forman model, a NASGRO model and the like, and the predicted results of the same crack may be greatly different from the different models, wherein the difference is caused by model form uncertainty, so how to reduce the influence of the model form uncertainty on the predicted results of crack propagation is a problem to be solved urgently by those skilled in the art.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a model fusion-based digital twin prediction method for the multi-scale cracks of the aircraft structure, which effectively improves the calculation efficiency by constructing a digital twin overall model and a local model of the aircraft structure, ensures the real-time performance of the digital twin prediction, and simultaneously considers the uncertainty of material parameters and the uncertainty of model forms based on a particle filtering algorithm and a newly proposed time-varying model fusion algorithm, thereby effectively improving the robustness and the credibility of a crack expansion prediction result.
The technical scheme of the invention is as follows:
step 1, establishing a digital twin model of an aircraft structure;
Step 2, acquiring load data, acquiring a borne load history from an aircraft solid structure, loading a digital twin model of the aircraft structure according to the load history, finding a dangerous area (a stress concentration position) in the aircraft structure, constructing a local model of the dangerous area, loading the digital twin model of the aircraft structure by combining the acquired historical load data with the load data acquired by a sensor on line, obtaining a response of the dangerous area, and compiling a load spectrum of the dangerous area of the aircraft structure according to the response;
Step 3, introducing initial cracks into the local model, loading the local model according to the load spectrum obtained in the step2, carrying out fracture mechanics simulation on the local model containing the initial cracks, and fitting out crack front edge evolution tracks and stress intensity factors;
And 4, firstly selecting a plurality of crack extension prediction models, obtaining a crack extension prediction result of each single model based on particle filtering, providing a new time-varying model fusion algorithm, establishing an optimization function by using a prediction error square sum minimization strategy, solving the optimization function by selecting subset simulation, obtaining the optimal weight coordinates of each model at an observation point, fitting the weight function of each model at different moments, carrying out non-negative and normalization processing on the weight function, carrying out weighted fusion on the prediction results of the models, and finally constructing a fused model.
In the step 2, preferably, the dangerous area local model is compared with the aircraft structure digital twin integral model, and the dangerous area local model needs to divide the grid of the position of the crack more carefully so as to ensure the accuracy of crack stress intensity factors and evolution track fitting.
Preferably, in step 3, a local model containing the initial crack is loaded based on the programmed load spectrum, and the stress intensity factor of the crack and the crack front evolution track of the next step are fitted through fracture mechanics simulation.
Preferably, in step 4, the established post-fusion model is expressed as:
，
In the above-mentioned method, the step of, Represents the model after fusion, N represents the load cycle number,/>For/>Weight function of individual model,/>Representing the selection/>And (5) predicting a single model by crack propagation.
Preferably, the weighting functionThe form of the t th degree polynomial is as follows:
，
Wherein the method comprises the steps of For/>Weight coefficients of the model weight functions, and the weight functions/>Meets the following constraint conditions:
，
。
Preferably, in step 3, the optimization function established by using the prediction error square sum minimization strategy is expressed as:
，
wherein G j is a crack propagation observation value of the j-th observation point data, where j=n-x, …, n-1, n; n is the total number of the current observed data, and x+1 is the number of the observed data selected by the fitting weight function.
Preferably, in step 4, the non-negative and normalized weighting function is specifically: firstly, judging whether a weight function of each model is smaller than 0 or not:
，
l i (N) is a weight function of the ith model after non-negative treatment;
And then carrying out normalization treatment:
，
q i (N) is a weight function after non-negative and normalization processing is carried out on the ith model;
establishing a fused model of the current step based on the normalized weight function, wherein the fused model is expressed as follows:
。
The beneficial effects are that:
1. The invention provides a solution to the multi-scale problem of the aircraft structure digital twin model, firstly, the aircraft structure digital twin model is constructed, and the stress concentration area in the aircraft structure is obtained through loading, and is set as a dangerous area, and then, a local model of the dangerous area is constructed.
2. According to the invention, the parameter uncertainty of the material is taken into consideration through the particle filtering algorithm, the observation value of crack growth is obtained through off-line ground detection and other modes based on the digital twin technology, and the update of the predicted value of crack growth and the update of particles are realized when each observation value is obtained, so that the influence of the parameter uncertainty of the material on the prediction of crack growth is effectively reduced.
3. Compared with the traditional model fusion method, the method has the advantages that the influence of the differences of the crack expansion models on the predicted result is considered, and the influence of model form uncertainty on the predicted result is effectively reduced, so that the predicted result is more accurate.
Drawings
FIG. 1 is a schematic representation of the response transfer from an aircraft wing overall model to a skin panel partial model in accordance with the present invention;
FIG. 2 is a schematic illustration of a skin panel geometry model meshing in accordance with one embodiment of the present invention;
FIG. 3 is a schematic diagram of crack extension leading edge evolution trace according to an embodiment of the present invention;
FIG. 4 is a load spectrum with 10000 cycles generated according to TWIST standard load spectrum;
FIG. 5 is a Paris single model crack growth prediction based on particle filtering in one embodiment of the invention;
FIG. 6 is an enlarged view of a portion of FIG. 5;
FIG. 7 is a single model crack growth prediction result NASGRO based on particle filtering in one embodiment of the invention;
FIG. 8 is a graph showing the predicted crack growth of the fused model based on the time-varying model fusion algorithm in one embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Taking an aircraft wing structure digital twin model as an example:
Step 1: and constructing a digital twin model of the aircraft wing structure according to the real wing.
Step 2: the method comprises the steps of obtaining flight history data from an aircraft wing entity, and combining with the fact that sensors are installed on a real aircraft wing to obtain the flight data of the wing in the aircraft flight process on line, so that loading of the digital twin model of the aircraft wing structure is achieved. The aircraft wing simulation model is generallyM-level, whereas crack propagation is typically analyzed in units of/>M-level, if the crack is directly introduced into the digital twin model of the aircraft wing for analysis, the analysis difficulty is high and the calculation time is extremely long, and in order to solve the problem, the invention provides a cross-scale crack propagation analysis method.
Based on a digital twin technology, aircraft wing load data are obtained through sensors, an aircraft wing integral model is loaded, response of a dangerous area (a stress concentration position) in the aircraft wing is obtained through real-time simulation, a local model of the dangerous area is built, for an aircraft wing structural model, a skin is a part which is most prone to crack generation, a local skin plate model can be built to analyze crack expansion, as shown in fig. 1, the aircraft wing integral model response is gradually transmitted to the local skin plate model, and integral-local multi-scale analysis is achieved.
More specifically, for the expansion analysis of skin cracks, the tensile stress is a main factor for causing crack expansion, other factors can be basically ignored, and only the change of the tensile stress response of a dangerous area of the whole aircraft wing model is required to be read, and the load spectrum of the local model is compiled according to the tensile stress response of the dangerous area.
Step 3: in this embodiment, there is a plane through crack with a length of 2mm at the middle edge of the skin panel, and the grids around the crack are re-divided, as shown in fig. 2, the grids around the crack of the skin panel are more finely divided, and the local model of the skin containing the crack is loaded according to the load spectrum compiled in the step 2, and the specific load spectrum of the skin containing the crack can be compiled according to different aircraft types and different aircraft structures.
Step 4: in the process of crack propagation, 5 times of crack length detection are carried out, 5 times of discrete crack length observation data are obtained, and the model update (comprising crack length update and grid repartition) of the local skin plate containing the cracks is realized every time an observation value is obtained, and meanwhile, the update of a predicted value of crack propagation and the update of the distribution and weight of particles in particle filtering are realized.
Based on a particle filtering algorithm, 2 models of the most classical Paris model and NASGRO model are respectively selected as prediction models of crack propagation, and relevant parameters of the Paris model and the NASGRO model can be obtained through test fitting and are supplemented by utilizing an existing database.
Paris expansion model:
，
NASGRO expansion model:
。
The Paris model prediction result, NASGRO model prediction result and 95% confidence interval based on the particle filtering algorithm are shown in fig. 5 and 7 respectively, and fig. 6 is a partial enlarged view in the rectangular frame of fig. 5, and the enlargement ratio is 500%. As can be seen from fig. 5 to fig. 7, based on the digital twin technique, both models update the predicted result of crack growth with the observed values, but between the two observed values, the predicted curve of crack growth is obtained based on the predicted model entirely, and different predicted results of crack growth may be obtained by adopting the Paris model and the NASGRO model.
In order to reduce uncertainty of model forms, the invention fuses predicted data of 2 models by detecting the obtained crack length data based on the proposed time-varying model fusion algorithm. In this embodiment, two models, namely a Paris model and a NASGRO model, are selected for model fusion, and the established fused model is shown in the following formula:
，
In the above-mentioned method, the step of, Represents the model after fusion, N represents the load cycle number,/>For/>Weight function of individual model,/>，/>The Paris model and NASGRO model are shown, respectively. /(I)The form of the t th degree polynomial is as follows:
，
Wherein the method comprises the steps of For/>Weight coefficients of the model weight functions; and weight function/>Meets the following constraint conditions:
，
。
The key to model fusion is to determine a weight function . According to the method, the optimal weight of each model is solved by calculating the prediction error square sum of different models and applying a strategy of minimizing the prediction error square sum. Based on the digital twin technology, the observed value of the crack can be obtained through off-line ground detection and other modes, and the weight function of different models is updated every time when one observed value is obtained, so that the optimal weight ratio of each model at the current moment is obtained.
The optimization problem established by using the prediction error square sum minimization strategy is as follows:
，
for/> Crack growth observations at individual observation points, wherein/>；/>For the total number of the current observation data,/>In order to ensure the credibility of the prediction result, the number of the observation data selected for the fitting weight function does not need to be selected in the process of fitting the weight function, and only a plurality of newly acquired observation point data need to be selected.
In this example, the degree of coincidence of the predicted results of the 2 prediction models with the true crack growth value could not be obtained until the 1 st observation data was obtained, and the weighting function of the 2 models was set to be constant. After the 1 st observation point data is obtained, wherein the observation point data comprises the load cycle number/>, recorded when the 1 st observation data is obtainedAnd current crack growth observations/>First based on observation of crack growth/>Updating the local skin plate model is achieved, an optimization function is established by utilizing a prediction error square sum minimization strategy, the optimization problem is solved by utilizing a subset simulation algorithm to obtain the optimal weights of different models at the observation points, and the optimal weight coordinates of each single model at the 1 st observation point are obtained，/>Subscript/>Represents the/>Optimal weight of each model at the 1 st observation point is fitted with a weight function polynomial/>, of each single model through a function fitting method(Because each single model has only 1 optimal weight coordinate, the fitted weight function is a 0 th degree polynomial). Similarly, after obtaining the 2 nd observation point data, the same steps are utilized to update the local model and obtain the optimal weight coordinates of each single model of each model at the 2 nd observation pointFitting the weight function of each model again to obtain a weight function/>After obtaining the 3 rd observation data, fitting the weight function of each model again by using the optimal weight coordinates of 3 observation points to obtain/>, wherein the/>, is obtained by using the 1 st polynomialFor the polynomial of degree 2, in this embodiment, the best weight coordinates of the latest 3 observations are selected to fit the weight function of each model. More specifically, after the optimal weight coordinates of the 4 th observation value are obtained, the optimal weight coordinates of the 2 nd observation point, the 3 rd observation point and the 4 th observation point are selected to fit the weight function of each model. Because only the best weight coordinate fit weight function for the last 3 observations is chosen, we will/>The form of the polynomial of degree 2 is set as follows:
Finally obtaining a polynomial through a mathematical fitting method Is/>。
Non-negative and normalized treatment of weight:
In particular, if the weighting function is not aligned Constraint may lead to the situation that the model weights finally obtained are negative numbers or that the sum of the weights is greater than 1, and in order to solve these problems, non-negative and normalization processing is required for the weights.
Firstly, judging whether a weight function of each model is smaller than 0 or not:
，
for/> A weight function of the model after non-negative treatment;
Normalization:
，
for/> A weight function of the model after non-negative and normalization processing;
And finally, establishing a fused model of the current step based on the normalized weight function:
。
Fig. 8 shows the predicted result of the fused model on crack propagation, and it can be seen from the figure that the predicted result of the fused model is closer to the observed value of each time, so that the influence of uncertainty of the model form on the predicted result is effectively reduced.
Comparing the prediction errors of the two single models with the total model by adopting a time-varying model fusion algorithm, wherein the prediction errors are calculated according to the following formula:
，
representing prediction error,/> Represents the predicted crack growth in this stage,/>Representing the true crack growth at this stage, FIG. 6 vs./>And/>An alignment was performed. Table 1 compares the results of Paris model and NASGRO model prediction errors with the total model prediction error after fusion:
Table 1 model error alignment
。
As shown by the results in table 1, the prediction error is not well reduced after the 1 st model fusion, because the observation data is lacking, the weights of 2 models are directly given, but with the occurrence of the observation data, the 2 model weight functions are updated and optimized by using a strategy of square sum minimization of the prediction error, so that the influence of model form uncertainty on the prediction result is effectively reduced.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. The model fusion-based digital twin prediction method for the multi-scale cracks of the aircraft structure is characterized by comprising the following steps of:
step 1, constructing a digital twin model of an aircraft structure;
Step 2, acquiring load historical data born by an aircraft solid structure, loading the aircraft structure digital twin model according to the load historical data to obtain a dangerous area in the aircraft structure, constructing a local model of the dangerous area, loading the aircraft structure digital twin model by combining the load historical data and on-line load data acquired by a sensor to obtain a response of the dangerous area, and compiling a load spectrum of the aircraft structure dangerous area according to the response;
Step 3, introducing initial cracks into the local model, loading the local model according to the load spectrum obtained in the step2, carrying out fracture mechanics simulation on the local model containing the initial cracks, and fitting out crack front edge evolution tracks and stress intensity factors;
Step 4, selecting a plurality of crack extension prediction models, and obtaining a crack extension prediction result of each single model based on particle filtering; defining a new time-varying model fusion algorithm, fusing crack expansion prediction results of a plurality of single models based on the time-varying model fusion algorithm, and specifically, establishing an optimization function by using a prediction error square sum minimization strategy:
The established post-fusion model is expressed as:
In the above formula, g Melting and melting (N) represents the model after fusion, N represents the number of load cycles, and g 1(N),g2(N),...,gm (N) represents the selected m crack growth prediction single models; w i (N) is the weight function of the ith model, in the form of a t-th degree polynomial of the form:
wi(N)＝pi0+pi1N+...+pitNt
Where p it is the weight coefficient of the ith model weight function, and the weight function w i (N) meets the following constraints:
0≤wi(N)≤1,i＝1,2,...,m；
The optimization function established with the prediction error square sum minimization strategy is expressed as:
wherein G j is the crack growth observation at the j-th observation point, where j=n-x,..; n is the total number of current observed data, and x+1 is the number of the observed data selected by the fitting weight function;
And solving the optimization function by selecting subset simulation to obtain the optimal weight coordinate of each model at each observation point, fitting the weight function of each model at different moments, carrying out non-negative and normalization processing on the weight function, carrying out weighted fusion on the prediction results of a plurality of crack expansion prediction models, and finally constructing a fused model.
2. The model fusion-based digital twin prediction method for the multi-scale cracks of the aircraft structure according to claim 1, wherein in the step 2, the dangerous area local model performs dense division on grids of the positions where the cracks are located.
3. The model fusion-based digital twin prediction method for the multi-scale cracks of the aircraft structure according to claim 1, wherein in the step 3, a local model containing initial cracks is loaded based on a load spectrum, and the stress intensity factors of the cracks and the crack front evolution track of the next step are fitted through fracture mechanics simulation.
4. The model fusion-based digital twin prediction method for the multi-scale cracks of the aircraft structure according to claim 3, wherein in the step 4, the non-negative and normalized processing of the weight function is specifically: firstly, judging whether a weight function of each model is smaller than 0 or not:
l i (N) is a weight function of the ith model after non-negative treatment;
And then carrying out normalization treatment:
q i (N) is a weight function of the ith model after non-negative and normalization treatment;
the non-negative and normalized weight functions are expressed as a fused model of the current step:
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| CN116384193A (en) * | 2023-04-10 | 2023-07-04 | 西安理工大学 | Crack propagation prediction method based on digital twin technology and data fusion |
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