Process Compensated Resonance Testing Modeling for Damage Evolution and Uncertainty Quantification

Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation method that measures and analyzes the resonance frequencies of a component for material state characterization, defect detection and process monitoring. PCRT inspections of gas turbine engine components have demonstrated the sensitivity of resonance frequencies to manufacturing defects and in-service thermal and mechanical damage. Prior work on PCRT modeling has developed forward modeling and model inversion techniques that simulate the effects of geometry variation, material property variation, and damage on Mar-M-247 nickel-based superalloy samples. Finite element method (FEM) forward model simulations predicted the effects of variation in geometry, material properties and damage on resonance frequencies. Model inversion used measured resonance frequencies to characterize the material state of components. Parallel work developed a process for uncertainty quantification (UQ) in PCRT models and measurements. The UQ process evaluated the propagation of uncertainty from various sources, identified the most significant uncertainty sources, and enabled uncertainty mitigation to improve model and measurement accuracy. Current efforts have expanded on those developments in several areas. One-factor-at-a-time (OFAT) forward model simulations were conducted on cylindrical dog bone coupons made from Mar-M-247. The simulations predicted the resonance frequency response to variation in geometry, elastic properties, crystallographic orientation, creep strain and cracking. The OFAT studies were followed by forward model Monte Carlo simulations that predicted the effects of multiple, concurrent sources of variation and damage on resonance frequencies, allowing characterization of virtual populations and quantification of uncertainty propagation. The Monte Carlo simulation design points were used to demonstrate the generation of a virtual database of components for training PCRT inspection applications, or “sorting modules.” Virtual database training sets can potentially overcome the limitations imposed by the availability of components and material states for training sets based on physical examples. Forward modeling tools and techniques were applied to titanium to simulate the effects of material variation, damage, and crystallographic texture. Forward modeling was also applied to more complex geometries, including a notional turbine blade, to demonstrate the application of modeling tools to shapes representative of gas turbine engine components. Model inversion tools and techniques have also advanced under the current effort. Prior inversion methods relied on iterative fitting to polynomial expressions for simple geometries and bulk material properties. Current efforts have demonstrated FEM-based model inversion which allows characterization of complex shapes and material states. FEM-based design spaces were generated, model inversion was carried out for surrogate modeled resonance spectra, and inversion performance was evaluated. Analysis of PCRT modeling results led to the development of automated resonance mode matching tools based on the calculation of modal assurance criteria (MAC) values, mode shape displacement metrics and Hungarian Algorithm sorting methods

Model-based Probe State Estimation and Crack Inverse Methods Addressing Eddy Current Probe Variability

Recent work on model-based inverse methods with eddy current inspections of surface breaking discontinuities has shown some sizing error due to variability in probes with the same design specifications [1]. This is an important challenge for model-based inversion crack sizing techniques, to be robust to the varying characteristics of eddy current probes found in the field [1-2]. In this paper, a model-based calibration process is introduced that estimates the state of the probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both tangential and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the gain/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with good agreement within +/- 2.5 degrees. The RMS error was found to be significantly reduced by fitting the probe state and, in many instances, probe state estimation addresses the previously un-modelled characteristics (model error) with real probe inversion studies. Additional studies are presented comparing the size of the calibration notch and the quality of the calibration fit, where calibrating with too small or too large a notch can produce poorer inversion results. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Because of the dimensionality of this problem, simulations were made at a limited set of select flaw sizes with varying length, depth and width, and an interpolation scheme was used to address the effect of the probe state at intermediate solution points. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states

Model-based Probe State Estimation and Crack Inverse Methods Addressing Eddy Current Probe Variability

Recent work on model-based inverse methods with eddy current inspections of surface breaking discontinuities has shown some sizing error due to variability in probes with the same design specifications [1]. This is an important challenge for model-based inversion crack sizing techniques, to be robust to the varying characteristics of eddy current probes found in the field [1-2]. In this paper, a model-based calibration process is introduced that estimates the state of the probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both tangential and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the gain/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with good agreement within +/- 2.5 degrees. The RMS error was found to be significantly reduced by fitting the probe state and, in many instances, probe state estimation addresses the previously un-modelled characteristics (model error) with real probe inversion studies. Additional studies are presented comparing the size of the calibration notch and the quality of the calibration fit, where calibrating with too small or too large a notch can produce poorer inversion results. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Because of the dimensionality of this problem, simulations were made at a limited set of select flaw sizes with varying length, depth and width, and an interpolation scheme was used to address the effect of the probe state at intermediate solution points. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states.</p

Process Compensated Resonance Testing Modeling for Damage Evolution and Uncertainty Quantification

Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation method that measures and analyzes the resonance frequencies of a component for material state characterization, defect detection and process monitoring. PCRT inspections of gas turbine engine components have demonstrated the sensitivity of resonance frequencies to manufacturing defects and in-service thermal and mechanical damage. Prior work on PCRT modeling has developed forward modeling and model inversion techniques that simulate the effects of geometry variation, material property variation, and damage on Mar-M-247 nickel-based superalloy samples. Finite element method (FEM) forward model simulations predicted the effects of variation in geometry, material properties and damage on resonance frequencies. Model inversion used measured resonance frequencies to characterize the material state of components. Parallel work developed a process for uncertainty quantification (UQ) in PCRT models and measurements. The UQ process evaluated the propagation of uncertainty from various sources, identified the most significant uncertainty sources, and enabled uncertainty mitigation to improve model and measurement accuracy. Current efforts have expanded on those developments in several areas. One-factor-at-a-time (OFAT) forward model simulations were conducted on cylindrical dog bone coupons made from Mar-M-247. The simulations predicted the resonance frequency response to variation in geometry, elastic properties, crystallographic orientation, creep strain and cracking. The OFAT studies were followed by forward model Monte Carlo simulations that predicted the effects of multiple, concurrent sources of variation and damage on resonance frequencies, allowing characterization of virtual populations and quantification of uncertainty propagation. The Monte Carlo simulation design points were used to demonstrate the generation of a virtual database of components for training PCRT inspection applications, or “sorting modules.” Virtual database training sets can potentially overcome the limitations imposed by the availability of components and material states for training sets based on physical examples. Forward modeling tools and techniques were applied to titanium to simulate the effects of material variation, damage, and crystallographic texture. Forward modeling was also applied to more complex geometries, including a notional turbine blade, to demonstrate the application of modeling tools to shapes representative of gas turbine engine components. Model inversion tools and techniques have also advanced under the current effort. Prior inversion methods relied on iterative fitting to polynomial expressions for simple geometries and bulk material properties. Current efforts have demonstrated FEM-based model inversion which allows characterization of complex shapes and material states. FEM-based design spaces were generated, model inversion was carried out for surrogate modeled resonance spectra, and inversion performance was evaluated. Analysis of PCRT modeling results led to the development of automated resonance mode matching tools based on the calculation of modal assurance criteria (MAC) values, mode shape displacement metrics and Hungarian Algorithm sorting methods.</p