Method and system for airfoil prediction using physical notification machine learning

Abstract

The invention relates to a method and system for airfoil prediction using physical notification machine learning. A method and system for airfoil prediction using physical notification machine learning introduces perturbations into nominal airfoil geometry (32) to simulate potential faults. The perturbed airfoil geometry (36) is processed by a physical notification neural network (PINN) model (28) trained on geometric and physical-based features (120, 122) to predict lift coefficients (134) to predict a state of health (50b) of the airfoil. A fault detection strategy is applied to assess a state of health under task-specific requirements (44), and a remaining useful life (50a) and a confidence limit are predicted for each task-specific requirement (44). Efficient airfoil health prediction, including precise fault simulation, allows active maintenance planning based on a predicted state of health (50) of the airfoil.

Description

Technical Field

[0001] The present invention relates generally to airfoils, and more particularly to the assessment of the health state of an airfoil. Background Art

[0002] Traditionally, the complex nature of rotor aerodynamics characterized by multiple interdependent equations and variables has made accurate and efficient analysis of airfoils a difficult challenge to solve. It is worth noting that the general helicopter (Gen Hel) flight dynamics simulation model, the comprehensive representation of its physical equations, the known high-fidelity model, the pre-calculated data and the efficiency lookup table exemplify this complexity. For example, the GenHel model encapsulates the dynamics of rigid flaps and lead-lag rotor blades, which depends on the airfoil lift and drag coefficient lookup table derived from wind tunnel experiments or high-fidelity numerical simulations (such as computational fluid dynamics (CFD)). Considering the inherent limitations, it is not practical to generate exhaustive lookup tables for all conceivable nominal and perturbed airfoil shapes or to perform expensive CFD simulations for each airfoil shape of interest to evaluate the prediction of each airfoil. In addition, in real-world vertical lift operations, rotor blades can sustain damage, potentially resulting in deviations of the lift coefficient from the expected specifications. Summary of the invention

[0003] In view of the above, there is provided a computing system comprising a processor and a memory storing executable instructions, the executable instructions, when executed by the processor, causing the processor to execute an impending fault simulator, the impending fault simulator being configured to receive an input of a nominal airfoil geometry of an airfoil, simulate an impending fault in the airfoil by perturbing the nominal airfoil geometry to generate a disturbed airfoil geometry, and input the disturbed airfoil geometry into one or more physically informed neural network (PINN) models to generate a corresponding predicted airfoil lift coefficient for the disturbed airfoil geometry; and a health state assessor configured to generate a predicted health state of the airfoil based on the predicted airfoil lift coefficient for the disturbed airfoil geometry, thereby utilizing physically informed machine learning to efficiently generate airfoil predictions.

[0004] The features, functions, and advantages that have been discussed can be achieved independently in various embodiments or may be combined in yet other embodiments further details of which can be seen with reference to the following description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Figure 1 A schematic diagram of a computing system according to an example of the present disclosure is shown.

[0006] Figure 2Shows the use of Figure 1 A training function of a computing system generates a schematic diagram of multiple training models.

[0007] Figure 3 Shows Figure 1 Schematic diagram of a model trainer training an untrained model during the training phase.

[0008] Figure 4 Figure 2 shows the generation of a predicted airfoil lift coefficient based on input airfoil geometry and physics-based features. Figure 1 Schematic diagram of one of the trained models.

[0009] Figure 5 Shows Figure 1 Illustrative examples of task-specific requirements for a computing system.

[0010] Fig. 6A and Figure 6B A representative depiction of nominal airfoil geometry is shown and Figure 1 Three different variations of the disturbance airfoil geometry.

[0011] Figure 7 Shown by Figure 1 The training model or Figure 4 An example of the predicted airfoil lift coefficient generated by the trained physics-informed neural network for nominal airfoil geometry.

[0012] FIG. 8A to FIG. 8I An example of predicting the lift coefficient of an airfoil is shown, which can be obtained by Figure 1 The training model or Figure 4 A trained physics-informed neural network is generated for various perturbation airfoil geometries.

[0013] 9A to 9E An additional example of predicting the airfoil lift coefficient is shown, which can be given by Figure 1 The training model or Figure 4 A trained physics-informed neural network is generated for various perturbations in airfoil geometries and angles of attack.

[0014] Fig.10 A flow chart of a first computerized method according to an example of the present disclosure is shown.

[0015] Fig.11 A flow chart of a second computerized method according to examples of the present disclosure is shown.

[0016] Fig.12 A flow chart of a third computerized method according to examples of the present disclosure is shown.

[0017] Fig.13An implementation of an example computing environment of the present disclosure is shown. DETAILED DESCRIPTION

[0018] In view of the above problems, the present disclosure describes systems and methods for predicting lift coefficients of airfoils and assessing their health status, thereby improving the safety and efficiency of aerospace operations.

[0019] refer to Figure 1 , depicts an embodiment of a computing system 10 that includes, as a non-limiting example, a processor 12 and a memory 14 storing executable instructions 16 that, in response to being executed by the processor 12, cause the processor 12 to execute a neural network model trainer 18, an impending failure simulator 30, and a health state assessor 42.

[0020] The neural network model trainer 18 is configured to train one or more untrained physically informed neural network (PINN) models 26 to learn the lift coefficient of the airfoil using training input data 20, the training input data 20 including a set of geometric features and physics-based features of the airfoil, such as angle of attack, Reynolds number, approximate lift coefficient, and approximate pressure drag coefficient. The training input data 20 also includes the corresponding true lift coefficient as a label. The neural network model trainer 18 randomly initializes weights and biases 22 of the one or more PINN models 26 so that a unique configuration of weights and biases 22 is applied to each of the one or more PINN models 26. The training function 24 of the neural network model trainer 18 trains the one or more untrained PINN models 26 using the training input data 20 and the randomly initialized weights and biases 22 and generates one or more trained PINN models 28. The geometric features of the airfoil can be represented in the training input data 20 as a two-dimensional graph in xy coordinates.

[0021] The impending fault simulator 30 is configured to receive an input of a nominal airfoil geometry 32 of the airfoil and simulate an impending fault by perturbing the nominal airfoil geometry 32 using a prescribed airfoil deformer 34 to generate a disturbed airfoil geometry 36. The impending fault simulator 30 uses the disturbed airfoil geometry 36 as an input to one or more trained PINN models 28 to generate a corresponding predicted airfoil lift coefficient 38 for the disturbed airfoil geometry 36, which is stored in an airfoil lift coefficient database 40. The nominal airfoil geometry 32 may be provided, for example, from a publicly available airfoil coordinate database.

[0022] The prescribed airfoil deformer 34 generates various disturbed airfoil geometries 36 by sweeping through a range of disturbances, using prescribed failure mechanisms to perturb the nominal airfoil geometry 32 into the disturbed airfoil geometry 36. The prescribed failure mechanisms may include a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface corrosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface corrosion mechanism, or a combination thereof.

[0023] By inputting the disturbed airfoil geometry 36 into one or more trained PINN models 28, an impending fault or predicted value can be simulated. When the predicted airfoil lift coefficient 38 is associated with a specific disturbed airfoil geometry 36, the airfoil nominal to deformed transition can be identified based on aerodynamic forces. Therefore, the uncertainty region of the predicted airfoil lift coefficient 38 can be quantified at different operating dimensions, thereby facilitating proactive fault detection and system maintenance. The different operating dimensions can be, for example, different angles of attack or different disturbance scales of the disturbed airfoil geometry.

[0024] The state of health assessor 42 is configured to receive input from the airfoil lift coefficient database 40 that relates various disturbed airfoil geometries 36 to corresponding predicted airfoil lift coefficients 38, and generate a predicted state of health 50 for the airfoil based on the predicted airfoil lift coefficients 38 for the disturbed airfoil geometries 36 under nominal and fault detection conditions for each of the plurality of mission-specific requirements 44, thereby utilizing physics-informed machine learning to efficiently generate airfoil predictions.

[0025] The nominal condition may correspond to normal use and wear operation, while the fault detection condition may correspond to an extreme operating condition. Given a mission-specific requirement 44, an extreme operating condition identifier 46 uses a fault detection strategy to search for reasonable fault detection conditions or operating conditions outside of the mission-specific requirement 44. The extreme operating condition identifier 46 may use a failure mechanism database to identify potential problems (e.g., dynamic stalls) for each mission-specific requirement 44. The health state estimator 48 then uses such reasonable operating conditions (e.g., angle of attack limits outside of the mission-specific requirement 44) to simulate impending failures and generates a predicted health state 50 of the airfoil for each mission-specific requirement 44. The extreme operating condition identifier 46 may also synthesize such simulations of impending failures to control for deviations and variations.

[0026] Treatment response matching in historical data with appropriate extrapolation can be performed to control bias and variance. For example, a relationship between independent and dependent variables can be established in the historical data set. The independent variables are the predicted airfoil lift coefficient 38 and the perturbed airfoil geometry 36, while the dependent variable is the predicted health state 50 of the airfoil. Statistical or machine learning techniques can be applied to identify relationships or patterns between the independent and dependent variables. These identified relationships or patterns can then be extrapolated to predict the future health state of the airfoil using geometric features and lift coefficients that are not present in the historical data set.

[0027] The predicted health state 50 of the airfoil may include the remaining useful life (RUL) 50a and health state (HS) 50b of the airfoil for each mission under nominal detection conditions and fault detection conditions with confidence limits. The RUL 50a may be expressed as the number of mission segments over time. The HS 50b may be issued in the form of one of a plurality of health state categories (e.g., warning, caution, advisory, and nominal). Thus, the dynamics and health state of the airfoil under fault detection conditions may be simulated to generate a comprehensive predicted health state 50 of the airfoil with confidence limits for a given mission.

[0028] For the purposes of this disclosure, an airfoil is defined as a structure designed to manipulate the flow of air, or other gases in certain cases, around an object in order to generate force. The most common application of airfoils is in the design and manufacture of aircraft wings, where the shape of the airfoil allows the aircraft to generate lift, thereby enabling flight. However, airfoils are not limited to aircraft and can be found in other applications such as wind turbines and fans. The specific shape and characteristics of the airfoil may vary depending on the application, with factors such as the expected speed, the size of the aircraft, and the overall mission requirements influencing the design.

[0029] For the purposes of this disclosure, an aircraft is defined as any machine or device capable of atmospheric flight. This includes, but is not limited to, airplanes, helicopters, unmanned aerial vehicles (UAVs, commonly referred to as drones), dirigibles, skiffs, self-propelled aircraft, hovercraft, and intra-atmospheric spacecraft.

[0030] For purposes of this disclosure, lift refers to the aerodynamic force that opposes gravity and enables an airfoil to achieve and maintain flight. This force is typically generated by the flow of air over the airfoil surface. Lift depends primarily on the geometry of the airfoil as well as physics-based characteristics, including the angle of attack, the speed at which the airfoil moves relative to the air around it, and the density of the air. Lift is typically quantified in terms of the lift coefficient, which is a dimensionless number that facilitates comparisons and calculations involving different airfoil shapes and operating conditions.

[0031] Go to Figure 2 , schematically depicting Figure 1An example of the operation of the training function 24 of the neural network model trainer 18 of FIG. The initialization weights and biases 22 may be repeatedly randomized to generate a plurality of randomly initialized weights and biases 22a, 22bb, 22c, 22d, which are used to train an untrained PINN model 26 using the training input data 20 and the training function 24 to generate a plurality of different trained PINN models 28a, 28b, 28c, 28d, respectively, each trained PINN model 28 having a unique configuration of weights and biases 22. The training function 24 may use a back-propagation algorithm to update or adjust the weights and biases 22a-d of the one or more PINN models 28 based on a comparison between the predicted airfoil lift coefficients output by the one or more PINN models 28 and the labels in the training input data 20. The training function 24 may include a loss function to measure the error between the predicted airfoil lift coefficients output by the one or more PINN models 28 and the labels in the training input data 20, so that the measured error may be minimized with each iteration of the back-propagation algorithm. This iterative process of updating or adjusting the weights and biases 22a - d may continue until the output of the predicted airfoil lift coefficient output by the one or more PINN models 28 converges with the labels in the training input data 20 , indicating convergence or minimization of the loss function.

[0032] The adjusted weights and biases 22a-d, each representing a unique configuration of weights and biases, are applied to multiple instantiations of the untrained PINN model 26, thereby creating multiple trained PINN models 28a-d with updated weights and biases 22a-d. In this manner, the neural network model trainer 18 can create multiple trained PINN models 28a-d, each with different weights and biases 22a-d, which can be used to generate a prediction range of airfoil lift coefficients for various perturbed airfoil geometries. Figure 2 Four sets of weights and biases 22a-d and four trained PINN models 28a-d are depicted in FIG. 1 , but the number of weights and biases 22a-d and trained PINN models 28a-d is not particularly limited and may be one or more.

[0033] Figure 3 An example of a fully connected physics-informed neural network 100 as an airfoil lift coefficient prediction model trained using training input data 118 is shown. The physics-informed neural network 100 includes an input layer 102, four fully connected hidden layers 106, 108, 110, 112, and an output layer 114. The hidden layers 106, 108, 110, 112 each include neurons 116, which are shown for simplicity in FIG. Figure 3 Neuron 116 is not shown. Physical notification neural network 100 is Figure 1Example of an untrained PINN model 26.

[0034] The physics-informed neural network 100 receives as input training input data 118 including airfoil geometry features 120, physics-based features 122, and labels 132. The physics-based features 122 may include angle of attack 124, Reynolds number 126, approximate lift coefficient 128, and approximate pressure drag coefficient 130. The label 132 is the true lift coefficient for training purposes.

[0035] The approximate lift coefficient 128 and the approximate pressure-drag coefficient 130 can be simulated using an efficient physics-based method, such as a panel method. The panel method can be used to simulate the airflow around the airfoil by dividing the airfoil into small panels, performing velocity and pressure calculations for each panel, and then using the calculated pressure and velocity information to simulate the lift and drag on the airfoil. Such simulations can be combined with other techniques, such as boundary layer analysis or computational fluid dynamics (CFD) simulations for viscous effects, to increase the accuracy of the simulation. The label 132 for the true lift coefficient can be provided from, for example, a physical experiment, a flight test, a wind tunnel experiment, or a high-fidelity simulator. The physics-informed neural network 100 is configured to receive the nominal geometry of the physical object at the input layer 102. At Figure 2 In the example of , the input layer 102 is configured to receive airfoil geometry features 120 as airfoil xy coordinates, which may represent a vector of current and historical spatial sensor readings of the airfoil geometry.

[0036] The physics-based features 122 are cascaded with the latent variables at the middle layer 104. The nodes of the middle layer 104 include a node for the angle of attack 124, a node for the Reynolds number 126, a node for the approximate lift coefficient 128, and a node for the approximate pressure drag coefficient 130. In response, the output layer 114 is configured to output a predicted airfoil lift coefficient 134 based on the input airfoil geometry features 120 and the airfoil physics-based features 122. The output layer 114 includes a single output neuron 136. In some examples, the output neuron 136 includes a sigmoid function. In other examples, the output neuron 136 includes any other suitable type of function.

[0037] The initialized weights and biases 144 of each neuron 116 are randomized before training begins. The weights and biases 142 of each neuron 116 are learned by solving a regression problem, computing a loss function 138 as the mean squared error between the label (true lift coefficient) 132 and the predicted airfoil lift coefficient 134. Based on the computed loss function 138, the weights and biases 142 in the physics-informed neural network 100 are updated by the optimizer 140 until convergence or minimization of the loss function 138. The trained physics-informed neural network 100 is then used to predict the airfoil lift coefficient 134 of airfoils that are not in the training input data 118 by using the airfoil geometric features 120 and the physics-based features 122 of the airfoils.

[0038] In some examples, the physics-informed neural network 100 includes a recurrent neural network. In other examples, the physics-informed neural network 100 can be any other suitable type of machine learning (ML) model, such as a convolutional neural network model.

[0039] Figure 4 Shown as already used Figure 3 1 . The physics-informed neural network 200 includes an input layer 202, four fully connected hidden layers 206, 208, 210, 212, and an output layer 214. The hidden layers 206, 208, 210, 212 each include a neuron 216, which, for simplicity, is represented in FIG. Figure 4 Neuron 216 is not shown. Physical notification neural network 200 is Figure 1 and 2 2. The physics-informed neural network 200 receives input data 218, which includes geometric features 220 of a disturbed airfoil or an unknown airfoil and physics-based features 222. The physics-based features 222 may include an angle of attack 224, a Reynolds number 226, an approximate lift coefficient 228, and an approximate pressure drag coefficient 230. The physics-based features 222 are cascaded with the latent variables at the middle layer 204. In response, the output neuron 236 at the output layer 214 is configured to output a predicted airfoil lift coefficient 234 based on the input airfoil geometric features 220 and the airfoil physics-based features 222.

[0040] Figure 5 A schematic representation of a set of exemplary task-specific requirements 44 is presented. These task-specific requirements 44 are configured to be input to Figure 1The extreme operating condition identifier 46 of the mission specific requirements 44 can be used by the health state assessor 42 to search for and identify reasonable fault detection conditions in various aircraft with different configurations and operating specifications.

[0041] Mission-specific requirements 44 are configured to account for variations that exist across different aircraft models and their corresponding unique application environments. Thus, each set of mission-specific requirements 44 reflects specific operating characteristics and constraints inherent to a particular type of aircraft.

[0042] As an illustration, a first set of specific mission requirements (e.g., first specific mission requirements 44a) are configured for a commercial airliner. These requirements 44a include several parameters, including segment ID 44aa, angle of attack 44ab, Reynolds number 44ac, Mach number 44ad, wing time 44ae, weight or load carrying capacity 44af, and lift requirement 44ag.

[0043] The lift requirement 44ag may indicate the minimum aerodynamic lift that the aircraft needs to maintain for safe operation. The lift requirement 44ag includes several subcomponents, namely a nominal value 44aga, an advisory range 44agb, a warning range 44agc, and a caution range 44agd. The lift requirement 44ag configured for a commercial airliner indicates that high lift generation is required even at lower speeds, which is a significant aspect during phases such as takeoff and landing.

[0044] Similarly, the second mission-specific requirements 44b configured for the supersonic aircraft include a segment ID 44ba, an angle of attack 44bb, a Reynolds number 44bc, a Mach number 44bd, a wing time 44be, a weight or carrying capacity 44bf, and a lift requirement 44bg. The lift requirement 44bg also includes a nominal value 44bga, a recommended range 44bgb, a warning range 44bgc, and a cautious range 44bgd. The lift requirement 44bg configured for the supersonic aircraft may indicate the need to generate moderate lift at low speeds, which simultaneously minimizes aerodynamic drag at high speeds, a feature that is critical for supersonic travel.

[0045] Finally, the third mission-specific requirement 44c configured for the cargo hold includes a segment ID 44ca, an angle of attack 44cb, a Reynolds number 44cc, a Mach number 44cd, a wing time 44ce, a weight or carrying capacity 44cf, and a lift requirement 44cg. The lift requirement 44cg also includes a nominal value 44cga, a recommended range 44cgb, a warning range 44cgc, and a cautious range 44cgd. It is worth noting that in cargo aircraft, the lift requirement 44cg emphasizes the generation of high lift at low speeds. In addition, the weight or carrying capacity 44cf specifies the high structural strength of the airfoil, the requirement to ensure the ability of the airfoil to support heavy payloads, and common scenarios in cargo hold operations. It should be noted that although three mission-specific requirements 44a-c are described here, the number of mission-specific requirements 44 is not particularly limited and can be more than three.

[0046] like Fig. 6A As shown, a third disturbance airfoil geometry 36a is generated with a disturbance scale of ε=1 / 700. Figure 6B As shown, the sixth perturbed airfoil geometry 36b is generated with a perturbation scale of ε=1 / 450, and the ninth perturbed airfoil geometry 36c is generated with a perturbation scale of ε=1 / 300. Note that other methods of simulating airfoil shape degradation may be substituted for the examples herein.

[0047] Fig. 6A and Figure 6B The nominal airfoil geometry 32 and Figure 1 36. These perturbations are represented as modifications to the xy coordinates of the airfoil relative to a Cartesian coordinate system. The leftmost end of each perturbed airfoil geometry 36 presents a small mark or dot, indicating the leading edge point that has undergone a perturbation.

[0048] The degree of perturbation or deformation is represented by the variable ε, which is used as an index to the perturbation scale, indicating the extent to which the original airfoil geometry has been altered. The term "perturbation" in this context is defined as an intentional deviation from the normal or standard airfoil shape, usually introduced in order to simulate the effects of various adverse conditions or faults on the airfoil structure.

[0049] The formation of these disturbed airfoil geometries 36a-c involves a series of system perturbations performed by sequentially applying a series of predetermined failure mechanisms. These mechanisms may include random surface deformation mechanisms, leading edge surface erosion mechanisms, leading edge surface corrosion mechanisms, trailing edge surface erosion mechanisms, trailing edge surface corrosion mechanisms, or combinations thereof. Through these transformations, the nominal airfoil geometry 32 is methodically deformed into a range of disturbed airfoil geometries 36.

[0050] For example, the following leading edge surface erosion mechanism can be used to perturb the leading edge of an airfoil. First, perturb points on the upper and lower surfaces of the leading edge of the airfoil geometry. Second, subtract a randomly generated Δy from the amplitude of each y coordinate using the formula y=y-Δy*sign(y), where sign() is the sign function. Third, scale the increment y using the formula y=y-ε*Δy*sign(y) to adjust the perturbation amount. Repeat the first, second, and third steps for different perturbation scales at different ε values ​​(which may include, for example, 1 / 900, 1 / 800, 1 / 700, 1 / 600, 1 / 500, 1 / 450, 1 / 400, 1 / 350, and 1 / 300).

[0051] Fig. 6A Specifically shown is a third perturbed airfoil geometry 36a which has been generated using a perturbation scale defined by ε = 1 / 700. This indicates that the perturbation has been performed at a relatively fine scale, implying a minor adjustment to the standard nominal airfoil geometry.

[0052] Go to Figure 6B , two additional perturbed airfoil geometries 36b, 36c are shown, respectively. Here, the sixth perturbed airfoil geometry 36b has been generated with a perturbation scale of ε=1 / 450, while the ninth perturbed airfoil geometry 36c has been generated with a perturbation scale of ε=1 / 300. These values ​​represent larger scale perturbations, indicating more significant deformations of the airfoil geometry.

[0053] It should be noted that while the present disclosure provides certain specific techniques for simulating airfoil shape degradation, the principles outlined are not limited to these examples. Alternative methods capable of producing similar simulations of airfoil shape disturbances or degradation are within the scope of the present invention and may be used instead of or in conjunction with the methods described herein.

[0054] Figure 7 Shown by Figure 1 One or more trained PINN models 28 or Figure 4 An example of a predicted airfoil lift coefficient 38 generated by the trained physics-informed neural network 200 for a nominal airfoil geometry. The predicted airfoil lift coefficient 38 is plotted against various angles of attack. The grey area is the uncertainty region indicating the range between the minimum and maximum predicted airfoil lift coefficient 38, and the black dashed line is the average of the predicted values.

[0055] FIG. 8A to FIG. 8I An example of a predicted airfoil lift coefficient 38 is shown, which may be given by Figure 1 One or more trained PINN models 28 or Figure 4The trained physics-informed neural network 200 is generated for various perturbed airfoil geometries. Fig. 8A An example of the predicted airfoil lift coefficient 38 plotted for various angles of attack for a first perturbed airfoil geometry generated at a perturbation scale of ε=1 / 950 is shown. Figure 8B An example of a predicted airfoil lift coefficient 38 plotted for various angles of attack for a second perturbed airfoil geometry that has been generated at a perturbation scale of ε=1 / 800 is shown. Figure 8C An example of the predicted airfoil lift coefficient 38 plotted for various angles of attack for a third perturbed airfoil geometry generated at a perturbation scale of ε=1 / 700 is shown. Fig.8D An example of predicted airfoil lift coefficient 38 plotted for various angles of attack for a fourth perturbed airfoil geometry that has been generated at a perturbation scale of ε=1 / 600 is shown. Fig. 8E An example of a predicted airfoil lift coefficient 38 plotted for various angles of attack for a fifth perturbation airfoil geometry that has been generated at a perturbation scale of ε=1 / 500 is shown. FIG. 8A to FIG. 8I An example of predicted airfoil lift coefficient 38 plotted for various angles of attack for a sixth perturbation airfoil geometry that has been generated at a perturbation scale of ε=1 / 450 is shown. Figure 8G An example of the predicted airfoil lift coefficient 38 plotted for various angles of attack for a seventh perturbation airfoil geometry that has been generated at a perturbation scale of ε=1 / 400 is shown. Figure 8H An example of predicted airfoil lift coefficient 38 plotted for various angles of attack for an eighth perturbation airfoil geometry that has been generated at a perturbation scale of ε=1 / 350 is shown. Fig.8I An example of predicted airfoil lift coefficient 38 plotted for various angles of attack for a ninth perturbation airfoil geometry that has been generated at a perturbation scale of ε=1 / 300 is shown.

[0056] 9A to 9E An additional example of a predicted airfoil lift coefficient 38 is shown, which may be given by Figure 1 One or more trained PINN models 28 or Figure 4 The trained physics informed neural network 200 is generated for various disturbance airfoil geometries and angles of attack. 9A to 9E In the example of FIG. 3 , the predicted airfoil lift coefficient 38 is plotted for various disturbance scales for a given angle of attack, assuming a Reynolds number of 1,000,000. The gray area is the uncertainty region indicating the range between the minimum and maximum predicted airfoil lift coefficient 38, and the black dashed line is the average of the predicted values. It should be noted that the uncertainty bounds generally increase in tandem with increasing disturbance scales, possibly indicating unstable and unpredictable aerodynamic forces.

[0057] Fig.9A Four different graphs are shown, each representing the predicted airfoil lift coefficient 38 versus the varying scale of the perturbation of the airfoil geometry. The graphs are specifically generated for four different angles of attack (i.e., 20 degrees, -18 degrees, -16 degrees, and -14 degrees), with each angle of attack corresponding to a separate graph. Fig. 9B Four different graphs are shown, each representing the predicted airfoil lift coefficient 38 versus the varying scale of the perturbation of the airfoil geometry. The graphs are specifically generated for four different angles of attack (i.e., -12, -10, -9, and -6 degrees), with each angle of attack corresponding to a separate graph. Fig. 9C Four different graphs are shown, each representing the predicted airfoil lift coefficient 38 associated with varying scales of disturbances in the airfoil geometry. These graphs are specifically generated for four different angles of attack (i.e., 4 degrees, 2 degrees, 0 degrees, and 2 degrees), with each angle of attack corresponding to a separate graph. Fig.9D Four different graphs are shown, each representing the predicted airfoil lift coefficient 38 associated with varying scales of disturbances in the airfoil geometry. These graphs are specifically generated for four different angles of attack, namely 4, 6, 8 and 10 degrees, with each angle of attack corresponding to a separate graph. Fig.9E Four different graphs are shown, each representing the predicted airfoil lift coefficient 38 versus the varying scale of the perturbation of the airfoil geometry. The graphs are specifically generated for four different angles of attack (i.e., 12 degrees, 14 degrees, 16 degrees, and 18 degrees), with each angle of attack corresponding to a separate graph.

[0058] Fig.10 A first computerized method 300 for generating a predicted health state of an airfoil is shown. The following description of the first computerized method 300 refers to the above description and is incorporated herein by reference. Figures 1 to 9E It should be understood that the first computerized method 300 can also be performed in other contexts using other suitable hardware and software components.

[0059] At step 302, training input data including geometric features and physics-based features of an airfoil is received. At step 304, weights and biases of one or more PINN models are randomly initialized so that a unique configuration of weights and biases is applied to each of the one or more PINN models. At step 306, one or more PINN models are trained using the training input data and the randomly initialized weights and biases to learn the lift coefficient of the airfoil, thereby generating one or more trained PINN models. At step 308, an input of a nominal airfoil geometry of the airfoil is received. At step 310, the nominal airfoil geometry is perturbed to generate a perturbed airfoil geometry. At step 312, the perturbed airfoil geometry is input into one or more trained PINN models to generate a corresponding predicted airfoil lift coefficient of the perturbed airfoil geometry. At step 314 , a predicted health state of the airfoil is generated based on the predicted airfoil lift coefficient of the perturbed airfoil geometry, thereby utilizing physics-informed machine learning to efficiently generate airfoil predictions.

[0060] Fig.11 A second computerized method 400 for training a physically informed neural network for generating a predicted airfoil lift coefficient is shown. The following description of the second computerized method 400 refers to the method described above and in Figures 1 to 9E It should be understood that the second computerized method 400 can also be performed in other contexts using other suitable hardware and software components.

[0061] At step 402, training input data including airfoil geometry features, physics-based features, and labels are received as input. At step 404, airfoil geometry features are received at an input layer. At step 406, physics-based features are cascaded at an intermediate layer. At step 408, a predicted airfoil lift coefficient is output based on the airfoil geometry features and the physics-based features. At step 410, a loss function of the error between the measured labels and the predicted airfoil lift coefficient is calculated. At step 412, the weights and biases of the PINN are iteratively updated based on the calculated loss function until convergence or minimization of the loss function.

[0062] Fig.12 A third computerized method 500 is shown, which is a leading edge surface erosion mechanism for disturbing airfoil geometry. The following description of the third computerized method 500 refers to the above description and in Figures 1 to 9E It should be understood that the third computerized method 500 can also be performed in other contexts using other suitable hardware and software components.

[0063] At step 502, points on the upper and lower surfaces of the leading edge of the airfoil geometry are perturbed. At step 504, a randomly generated increment y is subtracted from the magnitude of each y coordinate using the formula y=y-Δy*sign(y), where sign() is a sign function. At step 506, the increment y is scaled to tune the perturbation amount using the formula y=y-ε*Δy*sign(y). At step 508, steps 502, 504, and 506 are repeated for different perturbation scales for different ε values, which may include, for example, 1 / 900, 1 / 800, 1 / 700, 1 / 600, 1 / 500, 1 / 450, 1 / 400, 1 / 350, and 1 / 300.

[0064] The above-described system and method for assessing the health of an airfoil utilizes a physics-informed neural network for efficient aerodynamic analysis to generate an efficient and accurate prediction of the remaining useful life of the airfoil. By using a physics-informed neural network, the lift coefficient of the airfoil can be inferred without performing expensive numerical simulations (such as CFD). The inferred airfoil lift coefficient can then be used for impending failure simulations of aerodynamic analysis of damaged airfoils to efficiently and accurately generate a predicted health report of the airfoil for different missions.

[0065] The methods and processes described herein may be bound to a computing system of one or more computing devices. In particular, such methods and processes may be implemented as an executable computer application, a network accessible computing service, an application programming interface (API), a library, or a combination of the above and / or other computing resources.

[0066] Fig.13 Schematically illustrated is a simplified representation of a computing system 600 configured to provide any or all of the computing functionality described herein. The computing system 600 may take the form of one or more network accessible devices, server computers, mobile computing devices, Internet of Things (IoT) devices, embedded computing devices, vehicle computing systems, SAR systems, vehicle guidance systems, and / or other computing devices.

[0067] The computing system 600 includes a logic subsystem 602 and a storage subsystem 604. The computing system 600 may optionally include a display subsystem 606, an input subsystem 608, a communication subsystem 610, and / or other subsystems not shown in the figure. Fig.13 Other subsystems shown in .

[0068] The logic subsystem 602 includes one or more physical devices configured to execute instructions. For example, the logic subsystem may be configured to execute instructions as part of one or more applications, services, or other logical structures. The logic subsystem may include one or more hardware processors configured to execute software instructions. Additionally or alternatively, the logic subsystem may include one or more hardware or firmware devices configured to execute hardware or firmware instructions. The processor of the logic subsystem may be single-core or multi-core, and the instructions executed thereon may be configured for sequential, parallel, and / or distributed processing. The various components of the logic subsystem may optionally be distributed in two or more separate devices, which may be remotely located and / or configured for coordinated processing. Various aspects of the logic subsystem may be virtualized and executed by a remotely accessible networked computing device configured in a cloud computing configuration.

[0069] The storage subsystem 604 includes one or more physical devices configured to temporarily and / or permanently hold computer information such as data and instructions that can be executed by the logic subsystem. When the storage subsystem includes two or more devices, the devices can be collocated and / or remotely located. The storage subsystem 604 can include volatile, non-volatile, dynamic, static, read / write, read-only, random access, sequential access, location addressable, file addressable, and / or content addressable devices. The storage subsystem 604 can include removable and / or built-in devices. When the logic subsystem executes instructions, the state of the storage subsystem 604 can be converted-for example, to hold different data.

[0070] Aspects of logic subsystem 602 and storage subsystem 604 may be integrated together into one or more hardware logic components. For example, such hardware logic components may include programmable and application specific integrated circuits (PASIC / ASIC), programmable and application specific standard products (PSS / ASSP), systems on chips (SOC), and complex programmable logic devices (CPLD).

[0071] The logic subsystem 602 and the storage subsystem 604 can collaborate to instantiate one or more logic machines. As used herein, the term "machine" is used to collectively refer to a combination of hardware, firmware, software, instructions, and / or any other components that collaborate to provide computer functions. In other words, a "machine" is never an abstract idea and always has a tangible form. A machine can be instantiated by a single computing device, or a machine can include two or more subcomponents instantiated by two or more different computing devices. In some embodiments, a machine includes a local component (e.g., a software application executed by a computer processor) that collaborates with a remote component (e.g., a cloud computing service provided by a server computer network). The software and / or other instructions that give a particular machine its functionality can optionally be stored as one or more unexecuted modules on one or more suitable storage devices.

[0072] When included, the display subsystem 606 can be used to present a visual representation of the data maintained by the storage subsystem 604. The visual representation can take the form of a graphical user interface (GUI). The display subsystem 606 may include one or more display devices utilizing almost any type of technology. In some implementations, the display subsystem may include one or more virtual, augmented, or mixed reality displays.

[0073] When included, the input subsystem 608 may include one or more input devices or interface with one or more input devices. The input device may include a sensor device or a user input device. Examples of user input devices include a keyboard, a mouse, a touch screen, or a game controller. In some embodiments, the input subsystem may include or interface with selected natural user input (NUI) components. Such components may be integrated or peripheral, and the conversion and / or processing of input actions may be processed on-board or off-board. Example NUI components may include microphones for voice and / or speech recognition; infrared, color, stereo and / or depth cameras for machine vision and / or gesture recognition; head trackers, eye trackers, accelerometers and / or gyroscopes for motion detection and / or intent recognition.

[0074] When included, the communication subsystem 610 can be configured to communicatively couple the computing system 600 with one or more other computing devices. The communication subsystem 610 can include wired and / or wireless communication devices compatible with one or more different communication protocols. The communication subsystem can be configured to communicate via a personal, local area network, and / or wide area network.

[0075] Furthermore, the present disclosure includes configurations according to the following clauses.

[0076] Clause 1. A computing system comprising: a processor; and a memory storing executable instructions that, when executed by the processor, cause the processor to perform: an impending fault simulator, the impending fault simulator being configured to: receive an input of a nominal airfoil geometry of an airfoil, simulate an impending fault in the airfoil by perturbing the nominal airfoil geometry to generate a disturbed airfoil geometry, and input the disturbed airfoil geometry into one or more physically informed neural network (PINN) models to generate a corresponding predicted airfoil lift coefficient for the disturbed airfoil geometry; and a health state assessor, the health state assessor being configured to generate a predicted health state of the airfoil based on the predicted airfoil lift coefficient for the disturbed airfoil geometry, thereby utilizing physically informed machine learning to efficiently generate airfoil predictions.

[0077] Clause 2. A computing system according to clause 1, wherein the processor further executes a model trainer configured to train the one or more PINN models to learn the lift coefficient of the airfoil using training input data including geometric features and physics-based features of the airfoil.

[0078] Clause 3. The computing system of clause 2, wherein the physics-based characteristic comprises at least one selected from the group consisting of angle of attack, Reynolds number, simulated lift coefficient, and simulated pressure drag coefficient.

[0079] Clause 4. A computing system according to clause 2 or 3, wherein the model trainer randomly initializes weights and biases of one or more PINN models so as to apply a unique configuration of weights and biases to each of the one or more PINN models.

[0080] Clause 5. A computing system according to any one of clauses 2 to 4, wherein the model trainer uses the training input data and randomly initialized weights and biases to train the one or more PINN models via a loss function that measures the error between the predicted airfoil lift coefficient and the true lift coefficient, wherein the loss function is minimized over iterative updates of the weights and biases.

[0081] Clause 6. The computing system of any one of Clauses 2 to 5, wherein the true lift coefficient is provided from at least one selected from the group consisting of: physical experiments, flight tests, wind tunnel experiments, and high-fidelity simulators.

[0082] Clause 7. A computing system according to any one of clauses 1 to 6, wherein the impending failure simulator is configured to generate the disturbed airfoil geometry by using at least one mechanism selected from the group consisting of a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface corrosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface corrosion mechanism, and combinations thereof.

[0083] Clause 8. The computing system of any of Clauses 1 to 7, wherein the impending failure simulator is configured to quantify uncertainty regions of the predicted airfoil lift coefficient at different operating dimensions.

[0084] Clause 9. The computing system of any of Clauses 1 to 8, wherein the health state assessor is configured to generate the predicted health state of the airfoil for each of a plurality of mission-specific requirements.

[0085] Clause 10. A computing system according to any one of clauses 1 to 9, wherein the health state assessor includes an extreme operating condition identifier, which is configured to use a fault detection strategy to search for reasonable fault detection conditions, and use the reasonable fault detection conditions to simulate an impending failure and generate the predicted health state of the airfoil for each of the multiple mission-specific requirements.

[0086] Clause 11. The computing system of any one of clauses 1 to 10, wherein the predicted health state of the airfoil includes a remaining useful life for each of the plurality of mission-specific requirements, the predicted health state for each of the plurality of mission-specific requirements having a confidence limit.

[0087] Clause 12. The computing system of any of Clauses 1 to 11, wherein the predicted health state of the airfoil further comprises one of a plurality of health state categories.

[0088] Clause 13. A method, the method comprising: receiving an input of a nominal airfoil geometry of an airfoil; simulating an impending failure in the airfoil by perturbing the nominal airfoil geometry to generate a disturbed airfoil geometry; and inputting the disturbed airfoil geometry into one or more physically informed neural network (PINN) models to generate a corresponding predicted airfoil lift coefficient for the disturbed airfoil geometry; and generating a predicted health state of the airfoil based on the predicted airfoil lift coefficient for the disturbed airfoil geometry, thereby effectively generating the predicted health state of the airfoil using the one or more PINN models.

[0089] Clause 14. The method of clause 13, further comprising: training the one or more PINN models to learn a lift coefficient of the airfoil using training input data comprising geometric features and physics-based features of the airfoil.

[0090] Clause 15. The method of clause 14, wherein the physics-based characteristic comprises at least one selected from the group consisting of angle of attack, Reynolds number, simulated lift coefficient, and simulated pressure drag coefficient.

[0091] Clause 16. The method of clause 14 or 15, wherein the disturbed airfoil geometry is generated by using at least one mechanism selected from the group consisting of a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface erosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface erosion mechanism, and combinations thereof.

[0092] Clause 17. The method of any of clauses 14 to 16, wherein the uncertainty region of the predicted airfoil lift coefficient is quantified at different operational dimensions.

[0093] Clause 18. The method of any of Clauses 14 to 17, wherein the predicted health state of the airfoil is generated for each of a plurality of mission-specific requirements.

[0094] Clause 19. The method of clause 18, wherein a fault detection strategy is used to search for reasonable fault detection conditions, and the reasonable fault detection conditions are used to simulate an impending failure and generate a predicted health state of the airfoil for each of a plurality of mission-specific requirements.

[0095] Clause 20. A computing system, the system comprising: a processor; and a memory storing executable instructions, the executable instructions, when executed by the processor, causing the processor to perform: receiving an input of a nominal airfoil geometry of an airfoil, simulating an impending failure in the airfoil by perturbing the nominal airfoil geometry to generate a disturbed airfoil geometry, and generating a corresponding predicted airfoil lift coefficient for the disturbed airfoil geometry; and generating a predicted health state for the airfoil based on the predicted airfoil lift coefficient for the disturbed airfoil geometry, wherein the disturbed airfoil geometry is generated by using at least one mechanism selected from the group of: a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface erosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface erosion mechanism, and combinations thereof.

[0096] It should be understood that "and / or" as used herein refers to a logical disjunction operation, so A and / or B has the following truth table.

[0097] A B A and / or B T T T T F T F T T F F F

[0098] Those of ordinary skill in the art will appreciate without undue experimentation that the configurations and / or methods described herein are exemplary in nature, and these specific implementations or examples should not be considered restrictive, as many variations are possible. The specific routines or methods described herein may represent one or more of any number of processing strategies. Therefore, the various actions shown and / or described may be performed in the order shown and / or described, in other orders, in parallel or omitted. Likewise, the order of the above process may be changed.

[0099] The subject matter of the present disclosure includes all novel and nonobvious combinations and subcombinations of the various processes, systems and configurations, and other features, functions, acts, and / or properties disclosed herein, as well as any and all equivalents thereof. Parts List:

[0100] Computing system 10

[0101] Processor 12

[0102] Memory 14

[0103] Executable instruction 16

[0104] Neural Network Model Trainer 18

[0105] Training input data 20

[0106] Weights and Biases 22

[0107] Weights and biases 22a, 22b, 22c, 22d

[0108] Training function 24

[0109] Physically Informed Neural Network (PINN) Model 26

[0110] Trained PINN model 28

[0111] Different trained PINN models 28a, 28b, 28c, 28d of impending fault simulators 30

[0112] Nominal airfoil geometry 32

[0113] Prescribed airfoil deformer 34

[0114] Perturbation Airfoil Geometry 36

[0115] Airfoil geometry 36a

[0116] Airfoil geometry 36b

[0117] Ninth perturbation airfoil geometry 36c

[0118] Predicted airfoil lift coefficient 38

[0119] Airfoil lift coefficient database 40

[0120] Health Status Evaluator 42

[0121] Mission Specific Requirements44

[0122] First Task Specific Requirement 44a

[0123] Segment ID 44aa

[0124] Angle of attack 44ab

[0125] Reynolds number 44ac

[0126] Mach number 44ad

[0127] Wing Time 44ae

[0128] Carrying capacity 44af

[0129] Lift requirement 44ag

[0130] Second Task Specific Requirement 44b

[0131] Segment ID 44ba

[0132] Angle of attack 44bb

[0133] Reynolds number 44bc

[0134] Mach 44bd

[0135] Wing Time 44be

[0136] Carrying capacity 44bf

[0137] Lift requirement 44bg

[0138] Third Task Specific Requirement 44c

[0139] Segment ID 44ca

[0140] Angle of attack 44cb

[0141] Reynolds number 44cc

[0142] Mach number 44cd

[0143] Wing Time 44ce

[0144] Carrying capacity 44cf

[0145] Lift requirement 44cg

[0146] Extreme operating condition identifier 46

[0147] Health Status Estimator 48

[0148] Predicted health status 50

[0149] Remaining useful life (RUL) 50a

[0150] Health status (HS) 5b

[0151] Fully Connected Physics-Informed Neural Networks 100

[0152] Input layer 102

[0153] Middle layer 104

[0154] Four fully connected hidden layers 106, 108, 110, 112

[0155] Output layer 114

[0156] Neuron 116

[0157] Training input data 118

[0158] Airfoil geometry 120

[0159] Physics-based features 122

[0160] Angle of attack 124

[0161] Reynolds number 126

[0162] Approximate lift coefficient 128

[0163] Approximate pressure drag coefficient 130

[0164] True lift coefficient 132

[0165] Predicted airfoil lift coefficient 134

[0166] Single output neuron 136

[0167] Loss Function 138

[0168] Optimizer 140

[0169] Deviation 142

[0170] Deviation 144

[0171] Fully trained physics-informed neural network 200

[0172] Input layer 202

[0173] Middle layer 204

[0174] Four fully connected hidden layers 206, 208, 210, 212

[0175] Output layer 214

[0176] Neuron 216

[0177] Input data 218

[0178] Geometric features 220

[0179] Physics-based features 222

[0180] Angle of attack 224

[0181] Reynolds number 226

[0182] Approximate lift coefficient 228

[0183] Approximate pressure drag coefficient 230

[0184] Predicting the lift coefficient of an airfoil 234

[0185] Output neuron 236

[0186] First Computerized Method 300

[0187] Step 302

[0188] Step 304

[0189] Step 306

[0190] Step 308

[0191] Step 310

[0192] Step 312

[0193] Step 314

[0194] Second Computerized Method 400

[0195] Step 402

[0196] Step 404

[0197] Step 406

[0198] Step 408

[0199] Step 410

[0200] Step 412

[0201] Third Computerized Method 500

[0202] Step 502

[0203] Step 504

[0204] Step 506

[0205] Step 508

[0206] Computing system 600

[0207] Logic Subsystem 602

[0208] Storage subsystem 604

[0209] Display subsystem 606

[0210] Input Subsystem 608

[0211] Communication subsystem 610

Claims

1. A computing system (10), comprising: Processor (12); A memory (14) storing executable instructions (16) which, when executed by the processor (12), cause the processor (12) to perform: An impending failure simulator (30), the impending failure simulator being configured to: receiving an input of a nominal airfoil geometry (32) of the airfoil, simulating an impending failure in the airfoil by perturbing the nominal airfoil geometry (32) to generate a perturbed airfoil geometry (36), and inputting the disturbed airfoil geometry (36) into one or more physics-informed neural network models (28) to generate a corresponding predicted airfoil lift coefficient (38) for the disturbed airfoil geometry (36); as well as A health state assessor (42) is configured to generate a predicted health state (50) of the airfoil based on the predicted airfoil lift coefficient (38) of the disturbed airfoil geometry (36), thereby utilizing physics-informed machine learning to efficiently generate airfoil predictions.

2. The computing system (10) of claim 1, wherein: The processor (12) also executes a model trainer (18) configured to train the one or more physics-informed neural network models (26) to learn a lift coefficient of the airfoil using training input data (118) including geometric features (120) and physics-based features (122) of the airfoil.

3. The computing system (10) of claim 2, wherein: The physics-based characteristic (122) includes at least one selected from the group consisting of: angle of attack (124), Reynolds number (126), simulated lift coefficient (128), and simulated pressure drag coefficient (130).

4. The computing system (10) of claim 2, wherein: The model trainer (18) randomly initializes the weights and biases (22) of the one or more physics-informed neural network models (26) so as to apply a unique configuration of weights and biases (22) to each of the one or more physics-informed neural network models (26).

5. The computing system (10) of claim 4, wherein: The model trainer (18) uses the training input data (118) and randomly initialized weights and biases (22) to train the one or more physically informed neural network models (26) via a loss function (138) that measures the error between the predicted airfoil lift coefficient (38) and the true lift coefficient (132), the loss function (138) being minimized during iterative updating of the weights and biases (22).

6. The computing system (10) of claim 5, wherein: The true lift coefficient (132) is provided from at least one selected from the group consisting of: physical experiments, flight tests, wind tunnel experiments, and high-fidelity simulators.

7. The computing system (10) of claim 1, wherein: The impending fault simulator (30) is configured to generate the disturbed airfoil geometry (36) by using at least one mechanism selected from the group consisting of: a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface corrosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface corrosion mechanism, and combinations thereof.

8. The computing system (10) of claim 1, wherein: The impending fault simulator (30) is configured to quantify uncertainty regions of the predicted airfoil lift coefficient (38) at different operating dimensions.

9. The computing system (10) of claim 1, wherein: The state of health evaluator (42) is configured to generate the predicted state of health (50) of the airfoil for each of a plurality of mission-specific requirements (44).

10. The computing system (10) of claim 9, wherein: The health state assessor (42) includes an extreme operating condition identifier (46) configured to use a fault detection strategy to search for reasonable fault detection conditions and use the reasonable fault detection conditions to simulate an impending fault and generate the predicted health state (50) of the airfoil for each of the plurality of mission-specific requirements (44).

11. The computing system (10) of claim 10, wherein: The predicted health state (50) of the airfoil includes a remaining useful life (50a) for each of the plurality of mission-specific requirements (44), the predicted health state (50) for each of the plurality of mission-specific requirements (44) having a confidence limit.

12. The computing system (10) of claim 11, wherein: The predicted health state (50) of the airfoil also includes a health state category among a plurality of health state categories.

13. A method (300), comprising: receiving an input of a nominal airfoil geometry (32) of the airfoil, simulating an impending failure in the airfoil by perturbing the nominal airfoil geometry (32) to generate a perturbed airfoil geometry (36), inputting the disturbed airfoil geometry (36) into one or more physics-informed neural network models (28) to generate a corresponding predicted airfoil lift coefficient (38) for the disturbed airfoil geometry (36); as well as A predicted health state (50) of the airfoil is generated based on the predicted airfoil lift coefficient (38) of the disturbed airfoil geometry (36), thereby utilizing the one or more physics-informed neural network models (26) to effectively generate the predicted health state (50) of the airfoil.

14. The method according to claim 13, further comprising: The one or more physics-informed neural network models (26) are trained using training input data (118) including geometric features (120) and physics-based features (122) of the airfoil to learn a lift coefficient of the airfoil.

15. The method according to claim 14, wherein: The physics-based characteristic (122) includes at least one selected from the group consisting of: angle of attack (124), Reynolds number (126), simulated lift coefficient (128), and simulated pressure drag coefficient (130).

16. The method according to claim 13, wherein: The disturbed airfoil geometry (36) is generated by using at least one mechanism selected from the group consisting of a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface corrosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface corrosion mechanism, and combinations thereof.

17. The method according to claim 13, wherein: The uncertainty region of the predicted airfoil lift coefficient (38) is quantified at different operational dimensions.

18. The method according to claim 13, wherein: The predicted health state (50) of the airfoil is generated for each of a plurality of mission-specific requirements (44).

19. The method according to claim 18, wherein: A fault detection strategy is used to search for plausible fault detection conditions, the plausible fault detection conditions are used to simulate an impending fault, and the predicted health state (50) of the airfoil is generated for each of the plurality of mission-specific requirements (44).

20. A computing system (10), the computing system comprising: Processor (12); A memory (14) storing executable instructions (16) which, when executed by the processor (12), cause the processor (12) to perform: receiving an input of a nominal airfoil geometry (32) of the airfoil, simulating an impending failure in the airfoil by perturbing the nominal airfoil geometry (32) to generate a perturbed airfoil geometry (36), generating a corresponding predicted airfoil lift coefficient (38) for the disturbed airfoil geometry (36); as well as A predicted health state (50) of the airfoil is generated based on the predicted airfoil lift coefficient (38) of the disturbed airfoil geometry (36), wherein The disturbed airfoil geometry (36) is generated using at least one mechanism selected from the group consisting of a random surface deformation mechanism, a leading edge surface erosion mechanism, a leading edge surface corrosion mechanism, a trailing edge surface erosion mechanism, a trailing edge surface corrosion mechanism, and combinations thereof.

Images