Probabilistic Fatigue and Mixed Limit Assessment and Visualization Methods for Airfoils

Abstract

A method for analyzing a hybrid airfoil, the method comprising: generating a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design comprising one of a plurality of hybrid geometries; training a proxy model representing the plurality of simulated hybrid airfoil designs based on natural frequencies, modal forces, and Goodman scaling factors; determining a likelihood of operational failure for each of the plurality of hybrid airfoil designs in response to one or more vibration modes, determining which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint, and generating a hybrid parameter visualization, the hybrid parameter visualization comprising a hybrid design space, wherein the hybrid design space comprises one or more restricted regions indicating hybrid airfoil designs that violate the at least one aeromechanical constraint, and one or more allowed regions indicating hybrid airfoil designs that do not violate the aeromechanical constraint.

Description

[0001] Federally Sponsored Research Statement

[0002] This invention was made with U.S. Government support under Contract No. FA865015D2501 awarded by the Department of the Air Force. The U.S. Government has certain rights in this invention. Technical Field

[0003] The present description relates generally to analysis of airfoil designs, including hybrid airfoils, and more particularly to probabilistic methods for analyzing and modifying airfoil designs. Background Art

[0004] Current methods for evaluating airfoil high-cycle fatigue and airfoil mixed limits are often overly conservative or overly permissive, leading to unnecessary design restrictions in some cases and unacceptable field failure rates in other cases. Therefore, improved methods for analyzing airfoil mixed limits and airfoil high-cycle fatigue are desired to maximize design and repair flexibility while maintaining a high level of airfoil integrity. Summary of the Invention

[0005] Embodiments described herein relate to methods for analyzing and visualizing airfoil hybrid limits dictated by aeromechanical requirements, and methods for probabilistic high-cycle fatigue assessment of turbomachinery airfoils that account for variations in airfoil geometry, system geometry, material strength, analysis methods, and damping. The methods for analyzing high-cycle fatigue on turbomachinery airfoils employ probabilistic techniques to analyze HCF using a single-degree-of-freedom (SDOF) technique utilizing Monte Carlo simulation to generate a percentage distribution of endurance limits (%EL) for each vibration mode of interest, and use this simulation to generate an airfoil HCF model. After running this Monte Carlo simulation, the effects of one or more material property variations are used to provide a realistic probability distribution of HCF failure. This airfoil HCF model can be used to determine which geometric features of the airfoil and surrounding components of the jet engine drive variations in vibration response. In some embodiments, the method can further utilize a Bayesian model calibration framework to provide test data for the airfoil HCF model to better predict fleet-level airfoil HCF.

[0006] Furthermore, to analyze the airfoil blending limits, a proxy model is generated to predict the natural frequencies and vibration responses of the blended airfoil based on one or more blending parameters, such as the depth of the airfoil, the radial position on the airfoil (i.e., the position between the tip of the airfoil and the hub), and the aspect ratio. As used herein, "proxy model" refers to a model of a model and is used in this document to capture other similar terms used in the literature, such as metamodel, response surface model, or simulator. These proxy models are then used to generate these outputs (e.g., natural frequencies and vibration responses) across the entire blending design space. As used herein, "blending design space" refers to the range of physical parameters of the airfoil that can be modified to blend the airfoil to failure. Using the outputs of the proxy model, a blending parameter visualization can be generated that includes a restricted region of the blending design space and an allowed region of the blending design space, where the restricted region is the region of the blending design space that violates one or more aeromechanical constraints, and the allowed region is the region of the blending design space that does not violate one or more aeromechanical constraints. Thus, the allowed region represents feasible parameter changes that can be performed for the blended airfoil during maintenance and repair operations. In other words, the allowed region depicts the feasible design space. In an embodiment, restricted areas are represented by shading in the hybrid parameter visualization, and allowed areas are unshaded in the hybrid parameter visualization. The hybrid parameter visualization enables the user to interactively update constraints or assumptions on design variables and evaluate their impact on the allowable hybrid design space. The hybrid parameter visualization can also be extended to a probabilistic chart that takes into account airfoil geometry, aerodynamic forcing, damping, mis-amplification, and material property variations. These can be used for more accurate reliability assessments and digital twin type applications. These and additional features provided by the embodiments described herein will be more fully understood in view of the detailed description below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The embodiments illustrated in the accompanying drawings are illustrative and exemplary in nature and are not intended to limit the subject matter described herein. The following detailed description of the illustrative embodiments can be understood when read in conjunction with the following drawings, in which:

[0008] Figure 1 schematically depicts a damaged airfoil before and after mixing according to one or more embodiments shown and described herein;

[0009] Figure 2 depicts a flow chart illustrating a method of analyzing and visualizing airfoil mixing limits according to one or more embodiments shown and described herein;

[0010] Figure 3A depicts a single-mode mixing parameter visualization according to one or more embodiments shown and described herein;

[0011] Figure 3B depicts a multimodal mixing parameter visualization according to one or more embodiments shown and described herein;

[0012] Figure 4 depicts a high-level flow chart of a method for analyzing and visualizing airfoil mixing limits according to one or more embodiments shown and described herein;

[0013] Figure 5 Depicts a method according to one or more embodiments shown and described herein. Figure 4 A detailed version of the flowchart;

[0014] Figure 6 depicts a flow chart of a probabilistic method of analyzing high cycle fatigue on an airfoil according to one or more embodiments shown and described herein;

[0015] Figure 7 graphically depicts the probability of an airfoil's response to a vibration stress exceeding the material capabilities of the airfoil according to one or more embodiments shown and described herein;

[0016] Figure 8 depicts an analysis of variance for determining which geographic parameter of an airfoil drives the airfoil's response to vibrational stresses according to one or more embodiments shown and described herein;

[0017] Figure 9 graphically depicts the relative contributions of high cycle fatigue response to different design variables according to one or more embodiments shown and described herein;

[0018] Figure 10 Depicts Bayesian calibrated probability tuning versus traditional regression analysis according to one or more embodiments shown and described herein;

[0019] Figure 11 graphically depicts the resulting durability limit averages using traditional regression analysis and Bayesian calibrated probability tuning according to one or more embodiments shown and described herein;

[0020] Figure 12A depicts a probabilistic mixing parameter visualization according to one or more embodiments shown and described herein; and

[0021] Figure 12B Depicts a method according to one or more embodiments shown and described herein. Figure 12A Grid-point level analysis of probabilistic mixing parameters visualization. DETAILED DESCRIPTION

[0022] During conventional jet engine operation, airfoil damage is common. For integrally bladed rotors (e.g., blisks), it is expensive to discard the entire rotor due to airfoil damage. Instead, airfoils are typically repaired by blending out the damage. However, blending changes the vibration characteristics of the airfoil and can increase the risk of high cycle fatigue (HCK) associated with the airfoil. Therefore, limits are typically set on the area of the airfoil that can be blended in for repair. These blending limits are typically based on conventional engine values rather than HCF calculations and are therefore typically either overly conservative (in which case the blending limits are very strict) or not conservative enough, in which case the likelihood of blended airfoil failure increases.

[0023] Furthermore, the airfoil vibration response is subject to forced variations (from system geometric parameters such as tip clearance, axial clearance, and airfoil geometry variations (driven by manufacturing)). Therefore, the sensitivity of the airfoil response can vary and can be vibration mode specific. Current high cycle fatigue assessment techniques rely on a deterministic design process that only evaluates the nominal design and assigns blanket design limits to account for these variations. However, these deterministic design limits can become overly conservative for vibration modes, where the HCF variations are small and non-conservative in the extreme cases, and the geometric variations cause too much dispersion in the HCF response in the extreme cases. The former leads to over-constrained design requirements that may be difficult to meet or may result in suboptimal aerodynamic designs to meet conservative aeromechanical requirements. The latter may lead to risky designs and unacceptable field failure rates. Therefore, improved methods for analyzing airfoil blending limits and airfoil HCF are needed to maximize design and repair flexibility while maintaining a high level of airfoil integrity.

[0024] Now refer to Figure 1 , depicting the damaged airfoil before and after mixing. Figure 1 As shown, the mixing process smoothes the damage to minimize the possibility of operational failure and malfunction of the hybrid airfoil. Mixing can change one or more parameters of the airfoil, such as local thickness, local width and local radius. Mixing can occur at different radial positions along the airfoil and can reach different depths of the airfoil. These geometric parameters can be modified within the mixing design space, which is a range of physical parameters of the airfoil that can be modified to mix out airfoil damage. Using the method described herein, the limits of the mixing design space can be determined to maximize the potential changes that can be performed during mixing and maximize the performance of the mixed airfoil. Specifically, changes in the physical dimensions of the airfoil during mixing change the natural frequency and vibration response of the airfoil, and the method herein provides an effective and cost-effective way to determine whether the changes in vibration response and natural frequency caused by dimensional changes in a particular airfoil mixture are operationally allowable.

[0025] Now refer to Figure 2 , depicts a flow chart illustrating an embodiment of a method for analyzing and visualizing the blending limits of an airfoil. The method first includes simulating multiple airfoil designs (e.g., hundreds of simulations or more) having various blending geometries and using these simulations to train a surrogate model of three aeromechanical properties (natural frequency, modal forces, and Goodman scaling factors) as a function of blending parameters. The surrogate model is trained on these properties by designing and analyzing hundreds (or more) of blended airfoils using an autoregressive process (e.g., neural network modeling). Once the surrogate model is trained, the method next includes analyzing the aeromechanical risk (i.e., the probability of operational failure) of any blended airfoil in terms of natural frequency or vibration response (expressed as a percentage of the durability limit) that can be calculated using single degree of freedom (SDOF) equations.

[0026] In practice, this analysis can be performed on many vibration modes. This allows the model to be exercised over the entire mixture design space and facilitates the visualization of the mixture parameters, an example of which is given in Figure 3A and 3B , which visualizes the final design areas where one or more airfoil mixing limits are violated. The method of analyzing and visualizing airfoil mixing limits eliminates the need for a separate, case-specific aeromechanical evaluation (i.e., an MRB evaluation). Instead, the proposed mixture that initially does not meet the requirements can be found on a design space plot to evaluate the acceptability of the proposed mixture. The method of analyzing and visualizing airfoil mixing limits described herein generates physics-based aeromechanical mixing limits compared to previous conventional-based techniques. Additionally, the mixing limits determined using the techniques described herein may be less restrictive than previous techniques, which may increase the number of instances where a less expensive airfoil mixing repair may be achieved rather than a more expensive replacement.

[0027] Now refer to Figure 3A and 3B , showing two example mixing parameter visualizations. Figure 3A depicts the visualization of single-mode mixing parameters, while Figure 3BDepicted is a multi-mode mixing parameter visualization. The mixing parameter visualization is an interactive chart used to visualize the mixing design space in flight using shaded areas that indicate at least one aeromechanical constraint has been violated. Other design variables (damping, mis-amplification, mixing aspect ratio) can be interactively updated along with the output constraints to enable engineers to examine sensitivities and exercise engineering judgment when setting mixing limits. The design spaces of multiple vibration modes can be combined to generate a single chart showing the allowed mixing regions for all vibration modes. In addition, methods for analyzing airfoil mixing, which are constrained by visualizing the airfoil mixing design space, primarily focus on two aeromechanical requirements - natural frequency variation and variation in vibration response within a certain allowable range. In some cases, absolute vibration response can also be considered.

[0028] Now refer to Figure 4 , shows a high-level flow chart of a method for analyzing and visualizing the mixing limit of an airfoil, as well as another example of mixing parameter visualization and schematic airfoil. Figure 4 As shown, the method may first include identifying mixing parameters ("X") and outputs ("Y") to track. Figure 4 In

[0015] , the mixing parameters include the radial position of the mixing location between the tip of the airfoil and the hub (H in the example mixing parameter visualization), the depth of the mixing (D in the example mixing parameter visualization), and the aspect ratio of the mixing, which is the mixing length L divided by the mixing depth D, i.e., L / D. The radial position H, mixing depth D, and mixing length L are all in Figure 4 A schematic airfoil of FIG. 1 is shown. It should be understood that this parameterization is specific to elliptical blends. Other types of blends, such as J-cuts or tip cuts, can be parameterized using a different set of parameters, and blend parameter visualizations can be generated for these different parameter sets.

[0029] The method then includes creating a surrogate model to calculate the output Y as a function of the mixing parameter X. The surrogate model analysis determines the output Y based on the natural frequency, modal force, and Goodman scaling factor of the mixing parameter, including the change in natural frequency (Δf) compared to the original airfoil design, the durability limit (%EL), and the change in durability limit (Δ%EL) compared to the original airfoil design. Additional design variables that can be analyzed by the surrogate model include damping (Q), mis-amplification (Kv), non-uniform blade pitch factor (K nuvs ) and an aero scale factor that extends from the aero condition to the cross (Ps). Next, the method includes setting constraints on the input (ie, the blending parameter X) and the output Y. Example input constraints include a depth constraint D <D max , radial position constraint H>H min and aspect ratio constraints. Example output constraints include %EL < %EL max , Δ%EL<Δ%ELmax and Δf<Δf max These constraints are described in Figure 4 In an example mixing parameter visualization, the shaded area (i.e., restricted area) violates at least one constraint, and the non-shaded area (i.e., allowed area) shows the available mixing space. In operation, the damaged airfoil can be mixed with any mixing parameter within the mixing space to repair the damaged airfoil (i.e., mix the damaged airfoil). In addition, the mixing parameter visualization can be interactive, allowing the user to individually adjust the mixing parameters, additional design variables, input constraints, and output constraints. Figure 5 More details are shown with reference to Figure 4 A method for analyzing and visualizing the mixing limit of airfoils is described.

[0030] Now refer to Figure 6 , a flow chart of a probabilistic method for analyzing high cycle fatigue on an airfoil is shown. The method first includes generating hundreds of simulated airfoils with varying geometries representing various manufactured airfoils (i.e., airfoils with various size combinations), and then generating training data for prestress modes, modal forces, and Goodman scaling factors. The simulated airfoil designs and training data can be generated using Monte Carlo simulation. Secondly, a surrogate model can be trained based on three scalar parameters: natural frequency, modal force, and Goodman scaling factor. Once the surrogate model is trained, a durability limit (%EL) distribution can be generated using Monte Carlo analysis based on the dimensional characteristics of the simulated airfoils, a range of the three scaling factors, and a range of additional inputs such as damping, non-uniform blade spacing, mis-amplification, and pressure scaling. Once the durability limit distribution is generated, the probability of exceeding the material capability of the airfoil is determined probabilistically, taking into account the effects of material property variations, to generate a probability distribution of HCF failure. The durability limit distribution can be used to generate an airfoil HCF model to determine how different material property variations affect vibration stresses. This probabilistic evaluation can address the over- and under-constraint issues of design requirements that may arise when using deterministic design limits by performing the evaluation on a vibration mode-specific basis and calculating the probability of failure for each vibration mode of interest.

[0031] Designing airfoils based on probabilistic evaluations helps to manufacture better performing airfoils while requiring fewer design iterations to develop an early understanding of the impact of design decisions on component failure rates. In addition, the probabilistic approach described in this paper for analyzing high cycle fatigue on airfoils is based on an SDOF forced response model that captures the effects of airfoil and system geometry variations through only three scalar parameters: natural frequency, modal force, and Goodman scaling factor. This allows for the establishment of simplified workflows that are well suited for use in industrial environments within time-constrained design cycles and can reduce design cycle times due to fewer redesigns driven by fewer restrictive requirements. Probabilistic techniques result in fewer design practice deviations than previous deterministic techniques. Design practice deviations typically require separate analysis, reducing manufacturing efficiency. Probabilistic techniques also reduce the number of individual case-specific aeromechanical evaluations (i.e., MRB evaluations). In addition, the variance analysis of airfoil responses facilitated by the method described in this paper increases the understanding of the key geometric parameters that drive response variations, which can improve airfoil design. In other words, the airfoil HCF model can be used to determine which geometric features of the airfoil and surrounding components of the jet engine drive changes in the vibration response, thereby forming a better understanding of what geometric features drive failure rates and a more precise understanding of geometric tolerances, which can lead to less restrictive aeromechanical requirements and more optimized airfoils. Indeed, the probabilistic method of analyzing high cycle fatigue on an airfoil can further include manufacturing the airfoil, the airfoil including an airfoil geometry having a probability of high cycle fatigue failure below a failure threshold, wherein the failure threshold is based on a threshold durability limit of the airfoil geometry.

[0032] Now refer to Figure 7 , illustrates the probability of an airfoil's response to vibration stresses that exceed the material capabilities of the airfoil. Figure 7 The distribution of the vibration response of the airfoil as a function of the -3 sigma material capability is plotted. The probability distribution of the material HCF capability is also plotted on the same graph. This can be constructed from a material fatigue test database that records the variation in material capability. The quantity of interest is the vibration response of the airfoil over time. Figure 7 The equation shown calculates the probability of the material capability. The probability that the airfoil vibration response exceeds the material capability can be used to determine and set the threshold durability limit for the airfoil geometry.

[0033] Figure 8 Depicted is an analysis of variance used to determine which geographic parameter of an airfoil drives the airfoil's response to vibration stresses. This calibration model can then be used to provide a blisk-specific reliability estimate when fed into the blisk's measured airfoil geometry. This blisk-specific estimate can be aggregated across the fleet to obtain a fleet-level (e.g., global) reliability estimate for the component. Additionally, Figure 9An example of the relative contribution of high cycle fatigue response to different design variables is shown. Figure 9 As shown, certain design variables may have a disproportionate impact on high cycle fatigue response. Using the method described herein, these disproportionately impacting design variables can be identified, thereby facilitating improved airfoil designs.

[0034] A common problem faced when predicting the vibration response of airfoils is the disconnect between analytical predictions and the responses observed during maneuvering or engine testing. In these cases, the analytical model becomes useless after testing and the test responses are used directly to validate the component. However, this approach assumes that the tested part is representative of all manufactured parts, which may not be true. Again, referencing Figure 8 , the Bayesian model calibration method can use test data to help calibrate the uncertain parameters in the physics-based model described in this paper and fill the gaps in the physics-based model by providing a difference model (which bridges the gap between the observed data and the calibrated model). The Bayesian model calibration method provides test data for the probabilistic airfoil HCF model to better predict fleet-level airfoil HCF. These calibrated predictions can be used for more accurate reliability assessments and digital twin applications. Without being limited by theory, a digital twin is a digital replica of a physical entity. That is, a digital twin is a digital version of a machine (also called an "asset"). Once created, a digital twin can be used to represent a machine in a digital representation of a real-world system. A digital twin is created so that it computationally reflects the behavior of the corresponding machine. In addition, a digital twin can reflect the state of a machine within a larger system. For example, sensors can be placed on a machine (e.g., an airfoil) to capture real-time (or near real-time) data from a physical object to relay it back to a remote digital twin. The digital twin can then make any necessary changes to maintain its correspondence with the twin asset, providing operational instructions, diagnostics, insights into internal physical dynamics that cannot be measured, and insights into efficiency and reliability.

[0035] Figure 10 Depicts a comparison of Bayesian calibrated probability tuning and traditional regression analysis, Figure 11 The results of traditional regression analysis ( Figure 11 in the title "Uncalibrated Model") and Bayesian Calibrated Probability Tuning ( Figure 11 The average value of the durability limit is obtained from the calibration model. Figure 11 The average durability limits of their respective models and the actual test average values of the durability limits are shown. Figure 11 As shown, Bayesian calibrated probability tuning generates modeled average durability limits (e.g., "calibrated model mean") that are closer to the test mean than the modeled durability limits generated using traditional regression analysis (titled "uncalibrated model mean").

[0036] Now refer to Figure 12A and 12B In some embodiments, the probabilistic techniques used to analyze high cycle fatigue on airfoils described above may also be incorporated into the method of generating mixing parameter visualizations of mixing limits. Figure 12A Depicted is a probabilistic mixing parameter visualization. The probabilistic mixing parameter visualization can account for variations in damping, mis-amplification factors, airfoil geometry, aerodynamic forcing, and material properties. The probabilistic design space is represented by the probability of exceeding each aeromechanical constraint and the combined probability of reaching the mixing limit. Figure 12B A grid point level analysis of the probabilistic mixing parameter visualization is shown. This allows the user to view a detailed breakdown of the probability of exceeding the mixing limit for each parameter point on the probabilistic mixing parameter visualization.

[0037] Each method described herein can be implemented on a computer system comprising at least a processor and a non-transitory computer-readable medium including programming instructions stored thereon that can be executed by the processor. In addition, any component can be implemented in a single computer system, distributed across multiple computer systems, or using cloud computing resources. Some non-limiting examples of computer systems include laptops, desktops, smartphone devices, tablets, PCs, cloud computing platforms, etc. Various cloud computing platforms are known by product names, including but not limited to Amazon Web Services, Google Cloud Services, Microsoft Azure, and IBM Bluemix. The technology described herein can be implemented using computer-readable instructions stored on a non-transitory computer-readable medium, such that when executed by a processor, the computer-readable instructions cause the processor to perform any function described in the disclosed embodiments. A person of ordinary skill in the art will understand which computer systems, processors, or memories can be used for the disclosed embodiments.

[0038] The computer network may include one or more of a personal area network, a local area network, a grid computing network, a wide area network, a cellular network, a satellite network, the Internet, a virtual network in a cloud computing environment, and / or any combination thereof. Suitable local area networks can utilize wired Ethernet, wireless technologies such as wireless fidelity (Wi-Fi), and / or virtual network resources in a cloud computing environment. Suitable personal area networks can utilize wireless technologies such as IrDA, Bluetooth, wireless USB, Z-Wave, ZigBee, and / or other near-field communication protocols. Suitable personal area networks can utilize wired computer buses such as USB, serial ATA, eSATA, and FireWire. Suitable cellular networks include, but are not limited to, technologies such as LTE, WiMAX, UMTS, CDMA, and GSM. Thus, one or more computer networks can be used as wireless access points to access one or more servers implementing the processes described herein.

[0039] In addition, the computing system may include a modeling component that is configured to generate one or more custom probability distributions using one or more models. The model may include a quantitative model, a statistical model, a simulation model, a machine learning model, or an artificial intelligence model. According to some embodiments, the modeling component uses one or more machine learning models trained according to historical operational data to generate a custom probability distribution. The machine learning model may include, but is not limited to, a neural network, linear regression, logistic regression, a decision tree, an SVM (support vector machine), a naive Bayesian, kNN, K-means, a random forest, a dimensionality reduction algorithm, or a gradient boosting algorithm, and may adopt a learning type, including but not limited to supervised learning, unsupervised learning, reinforcement learning, semi-supervised learning, self-supervised learning, multiple instance learning, inductive learning, deductive reasoning, transductive learning, multi-task learning, active learning, online learning, transfer learning, or ensemble learning.

[0040] Each custom probability distribution may correspond to a variable used to simulate or analyze an airfoil design and vibration response. A simulation component may be implemented in a computing system. The simulation component is configured to simulate the airfoil vibration response using the custom probability distribution. The simulation component may use a multivariable model to identify and characterize the interactions between various parameters and operating components. Using the multivariable model, the simulation component can describe not only the behavior of the parameters and operating components, but also the complex interactions between the parameters and operating components.

[0041] It should now be understood that the embodiments described herein relate to methods for analyzing and visualizing airfoil mixing limits dictated by aeromechanical requirements and methods for probabilistic high cycle fatigue assessment of turbomachinery airfoils that account for variations in airfoil geometry, system geometry, material strength, analysis methods, and damping. While particular embodiments have been shown and described herein, it should be understood that various other changes and modifications may be made without departing from the spirit and scope of the claimed subject matter.

[0042] Further aspects of the invention are provided by the subject matter of the following clauses:

[0043] 1. A method for analyzing a hybrid airfoil, the method comprising: generating, using a computing system, a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design comprising one of a plurality of hybrid geometries; training, using the computing system, a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; determining, using the computing system, a likelihood of operational failure of each of the plurality of hybrid airfoil designs in response to one or more vibration modes; determining, using the computing system, which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint; generating, using the computing system, a hybrid parameter visualization comprising a hybrid design space, wherein the hybrid design space comprises one or more restricted regions indicating hybrid airfoil designs that violate at least one aeromechanical constraint and one or more allowed regions indicating hybrid airfoil designs that do not violate the aeromechanical constraint; and providing, via the computing system, the hybrid parameter visualization to an external system for blending a damaged airfoil.

[0044] 2. The method of any preceding clause, further comprising blending the damaged airfoil based on simulated hybrid airfoil designs located in the one or more allowed regions of the hybrid design space.

[0045] 3. The method of any preceding clause, wherein the hybrid design space comprises at least two hybrid parameters.

[0046] 4. The method of any preceding clause, wherein a first mixing parameter comprises a radial position of the mixing between a tip of the mixing airfoil and a hub.

[0047] 5. The method of any preceding clause, wherein the mixing parameter visualization is interactive such that the at least one aero-mechanical constraint and the at least two mixing parameters are adjustable.

[0048] 6. The method of any preceding clause, wherein determining which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint is a probabilistic determination, and the hybrid design space of the hybrid parameter visualization includes a probabilistically restricted region and a probabilistically allowed region.

[0049] 7. The method of any preceding clause, wherein the plurality of simulated hybrid airfoil designs are generated using Monte Carlo simulation.

[0050] 8. The method of any preceding clause, wherein said proxy model representing said plurality of simulated hybrid airfoil designs is further trained based on damping, misamplification, non-uniform blade spacing factor, and an aeronautical scaling factor expanded from aeronautical conditions to crossover.

[0051] 9. The method of any preceding clause, wherein the at least one aeromechanical constraint is based on a change in natural frequency compared to an original airfoil design, a durability limit, and a change in the durability limit compared to the original airfoil design.

[0052] 10. The method of any preceding clause, wherein the hybrid parameter visualization comprises the hybrid design space for a single vibration mode.

[0053] 11. The method of any preceding clause, wherein the hybrid parameter visualization comprises the hybrid design space for a plurality of vibration modes.

[0054] 12. A method for analyzing high cycle fatigue of an airfoil, the method comprising: generating, using a computing system, a plurality of simulated airfoil designs, each simulated airfoil design including one of a plurality of airfoil geometries; training, using the computing system, a proxy model representing the plurality of simulated airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; generating, using the computing system, a probability distribution for a likelihood of high cycle fatigue failure for each of the plurality of airfoil designs in response to one or more vibration modes; determining, using the computing system, a relative influence of each of a plurality of geometric parameters of the plurality of airfoil geometries on the high cycle fatigue of the plurality of airfoil designs; and providing, by the computing system, data corresponding to the relative influence to an external device for use in manufacturing an airfoil.

[0055] 13. The method of any preceding clause, further comprising manufacturing the airfoil, the airfoil comprising an airfoil geometry having a probability of high cycle fatigue failure below a failure threshold.

[0056] 14. The method of any preceding clause, wherein the failure threshold is based on a threshold durability limit of the airfoil geometry.

[0057] 15. The method of any preceding clause, wherein the plurality of simulated hybrid airfoil designs are generated using Monte Carlo simulation.

[0058] 16. The method of any preceding clause, wherein said proxy model representing said plurality of simulated hybrid airfoil designs is further trained based on damping, misamplification, non-uniform blade spacing factor, and an aero scaling factor expanded from aero conditions to crossover.

[0059] 17. The method of any preceding clause, further comprising calibrating the probability distribution of likelihood of high cycle fatigue failure using Bayesian calibrated probability tuning.

[0060] 18. The method of any preceding clause, wherein the likelihood of high cycle fatigue failure is based on the durability limit of the airfoil geometry.

[0061] 19. A system comprising: a processor; and a non-transitory processor-readable storage medium including one or more programming instructions thereon that, when executed, cause the processor to: generate a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design including one of a plurality of hybrid geometries; train a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; determine a likelihood of operational failure of each of the plurality of hybrid airfoil designs in response to one or more vibration modes; determine which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint; generate a hybrid parameter visualization comprising a hybrid design space, wherein the hybrid design space includes one or more restricted regions indicating hybrid airfoil designs that violate at least one aeromechanical constraint and one or more allowed regions indicating hybrid airfoil designs that do not violate the aeromechanical constraint; and provide the hybrid parameter visualization to an external system for blending a damaged airfoil.

[0062] 20. A system comprising: a processor; and a non-transitory processor-readable storage medium including one or more programming instructions thereon, the programming instructions, when executed, causing the processor to: generate a plurality of simulated airfoil designs, each simulated airfoil design including one of a plurality of airfoil geometries; train a proxy model representing the plurality of simulated airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; generate a probability distribution for the likelihood of high cycle fatigue failure of each of the plurality of hybrid airfoil designs in response to one or more vibration modes; determine a relative effect of each of a plurality of geometric parameters of the plurality of airfoil geometries on the high cycle fatigue of the plurality of airfoil designs; and provide data corresponding to the relative effects to an external device for use in manufacturing airfoils.

Claims

1. A method for analyzing a hybrid airfoil, characterized in that: The method comprises: generating, using a computing system, a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design including one of a plurality of hybrid geometries; using the computing system, training a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; determining, using the computing system, a likelihood of operational failure for each of the plurality of simulated hybrid airfoil designs in response to one or more vibration modes; determining, using the computing system, which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint; generating, using the computing system, a hybrid parameter visualization comprising a hybrid design space, wherein the hybrid design space comprises one or more restricted regions indicating simulated hybrid airfoil designs that violate at least one aero-mechanical constraint and one or more allowed regions indicating simulated hybrid airfoil designs that do not violate the aero-mechanical constraint; and The mixing parameter visualization is provided to an external system by the computing system for mixing the damaged airfoil.

2. The method according to claim 1, characterized in that Further comprising blending the damaged airfoil based on a simulated hybrid airfoil design located in the one or more allowable regions of the hybrid design space.

3. The method according to claim 1, characterized in that in, The hybrid design space includes at least two hybrid parameters.

4. The method according to claim 3, characterized in that in, A first mixing parameter includes a radial position of the mixture between a tip of the mixing airfoil and a hub.

5. The method according to claim 3, characterized in that in, The mixing parameter visualization is interactive such that the at least one aeromechanical constraint and the at least two mixing parameters are adjustable.

6. The method according to claim 1, characterized in that in, Determining which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint is a probabilistic determination, and the hybrid design space of the hybrid parameter visualization includes a probabilistically restricted region and a probabilistically allowed region.

7. The method according to claim 1, characterized in that in, The plurality of simulated hybrid airfoil designs are generated using Monte Carlo simulation.

8. The method according to claim 1, characterized in that in, The proxy model representing the plurality of simulated hybrid airfoil designs is further trained based on damping, misamplification, a non-uniform blade spacing factor, and an aeronautical scaling factor expanded from aeronautical conditions to crossover.

9. The method according to claim 1, characterized in that in, The at least one aeromechanical constraint is based on a change in natural frequency compared to an original airfoil design, a durability limit, and a change in the durability limit compared to the original airfoil design.

10. The method according to claim 1, characterized in that in, The hybrid parameter visualization includes the hybrid design space for a single vibration mode.

11. The method according to claim 1, wherein in, The hybrid parameter visualization includes the hybrid design space for a plurality of vibration modes.

12. A method for analyzing high cycle fatigue of an airfoil, characterized in that: The method comprises: generating, using a computing system, a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design including one of a plurality of airfoil geometries; using the computing system, training a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; generating, using the computing system, a probability distribution of likelihood of high cycle fatigue failure for each of the plurality of simulated hybrid airfoil designs in response to one or more vibration modes; determining, using the computing system, a relative effect of each of a plurality of geometric parameters of the plurality of airfoil geometries on high cycle fatigue of the plurality of simulated hybrid airfoil designs; and Data corresponding to the relative influence is provided by the computing system to an external device for use in manufacturing an airfoil.

13. The method according to claim 12, characterized in that Further included is manufacturing the airfoil, the airfoil comprising an airfoil geometry having a probability of high cycle fatigue failure below a failure threshold.

14. The method according to claim 13, characterized in that in, The failure threshold is based on a threshold durability limit of the airfoil geometry.

15. The method according to claim 12, characterized in that in, The plurality of simulated hybrid airfoil designs are generated using Monte Carlo simulation.

16. The method according to claim 12, characterized in that in, The proxy model representing the plurality of simulated hybrid airfoil designs is further trained based on damping, misamplification, a non-uniform blade spacing factor, and an aeronautical scaling factor expanded from aeronautical conditions to crossover.

17. The method according to claim 12, wherein: Further comprising calibrating the probability distribution of likelihood of high cycle fatigue failure using Bayesian calibrated probability tuning.

18. The method according to claim 12, characterized in that in, The likelihood of high cycle fatigue failure is based on the durability limit of the airfoil geometry.

19. A system, characterized in that: include: processor; and A non-transitory processor-readable storage medium including one or more programming instructions thereon that, when executed, cause the processor to: generating a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design including one of a plurality of hybrid geometries; training a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; determining a likelihood of operational failure for each of the plurality of simulated hybrid airfoil designs in response to one or more vibration modes; determining which of the plurality of simulated hybrid airfoil designs violates at least one aeromechanical constraint; generating a hybrid parameter visualization comprising a hybrid design space, wherein the hybrid design space comprises one or more restricted regions indicating simulated hybrid airfoil designs that violate at least one aero-mechanical constraint and one or more allowed regions indicating simulated hybrid airfoil designs that do not violate the aero-mechanical constraint; and The mixing parameter visualization is provided to an external system for mixing the damaged airfoil.

20. A system, characterized in that: include: processor; and A non-transitory processor-readable storage medium including one or more programming instructions thereon that, when executed, cause the processor to: generating a plurality of simulated hybrid airfoil designs, each simulated hybrid airfoil design including one of a plurality of airfoil geometries; training a proxy model representing the plurality of simulated hybrid airfoil designs based on at least one of natural frequencies, modal forces, and Goodman scaling factors; generating a probability distribution of likelihood of high cycle fatigue failure for each of the plurality of simulated hybrid airfoil designs in response to one or more vibration modes; determining a relative effect of each of a plurality of geometric parameters of the plurality of airfoil geometries on the high cycle fatigue of the plurality of simulated hybrid airfoil designs; and Data corresponding to the relative influence is provided to an external device for use in manufacturing the airfoil.

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