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Publications & Standards

Read Vibrant’s publications, white papers and ASTM Standards to keep you up-to-date on the latest with PCRT.

Validation of Model-Trained Process Compensated Resonance Testing Inspection for Creep Deformation – A Model – Assisted Probability of Detection Study

A model-assisted probability of detection (MAPOD) validation of Process Compensated Resonance Testing (PCRT) inspection for creep deformation is presented. The PCRT inspection was trained entirely with resonance data from PCRT forward models that predicted the effect of creep deformation on resonance frequencies. The MAPOD validation was conducted with a combination of physical validation specimens and modeled specimens. The modeled specimens included simulations of the effects of uncertainty inherent in the measurement of physical samples. The results validated PCRT forward modeling accuracy for creep deformation, and accurate PCRT classification of acceptable and unacceptable levels of creep.

Validation of Process Compensated Resonance Testing (PCRT) Sorting Modules Trained with Modeled Data

Process Compensated Resonance Testing (PCRT) combines the collection of broadband resonance data with advanced pattern recognition to produce a fast, accurate, and automated non-destructive inspection for aerospace, automotive, and power generation components. To create a PCRT targeted defect inspection (Sorting Module) the resonance spectra of statistically significant populations of characterized acceptable and unacceptable parts are needed to train PCRT algorithms to recognize the frequency patterns that indicate defects in the midst of normal, acceptable material and geometry variations. In cases where a sufficient number of parts are not available, spectra from physical part populations can be supplemented with ‘virtual’ spectra generated with PCRT forward models. Previous work investigated the creation of model-trained sorting modules for the detection of creep deformation and crystal orientation for coupon and turbine blade geometries made from single crystal Ni-based [...]

Process Compensated Resonance Testing (PCRT) Inversion for Material Characterization and Digital Twin Calibration

The Digital Twin paradigm is based on the idea that a component’s serviceable life and performance can be better predicted and monitored by creating a faithful virtual counterpart of a real component, which in turn leads to improvements in end-product safety and cost. Such a model requires accurate inputs for the initial material state of the part as well as in-service loads and damage states throughout its service life. The resonance frequencies of a part correlate to a part’s material state and damage state. Similarly, changes in resonance frequencies correlate to changes in the part’s material state resulting from in-service loads and damage. Process Compensated Resonance Testing (PCRT) leverages these physical relationships to perform nondestructive evaluation (NDE) and material characterization using the measured resonance frequencies of a component. Prior work has established techniques for modeling the effects of material property variation, crystal orientation, and damage [...]

Detection of Microtexture Regions in Titanium Turbine Engine Disks using Process Compensated Resonance Testing: A Modeling Study

Titanium alloys used by the aerospace industry, like Ti-64 or Ti-6242, with Microtexture Regions (MTR’s) have been shown to exhibit significantly reduced dwell fatigue lifetimes. Over the last several decades, these titanium alloys have been used for critical components such as turbine engine disks, which are then susceptible to failure well below their expected service life. Current Nondestructive Inspection (NDE) methods are time consuming and can miss MTR’s. Process Compensated Resonance Testing (PCRT) is a fast and accurate full-body NDE method that has been proposed for the detection of MTR’s in titanium turbine engine disks. PCRT excites a part’s resonance frequencies and correlates the resonance spectrum to the part’s material and/or damage state. Turbine engine disks with MTR’s will have different resonance spectra than fully isotropic disks. Both the MTR’s geometric parameters (i.e. size, location, and orientation) and the microstructural parameters (i.e. degree of [...]

Uncertainty Quantification of Resonant Ultrasound Spectroscopy for Material Property and Single Crystal Orientation Estimation on a Complex Part

A case study is presented evaluating uncertainty in Resonance Ultrasound Spectroscopy (RUS) inversion for a single crystal (SX) Ni-based superalloy Mar-M247 cylindrical dog-bone specimens. A number of surrogate models were developed with FEM model solutions, using different sampling schemes (regular grid, Monte Carlo sampling, Latin Hyper-cube sampling) and model approaches, N-dimensional cubic spline interpolation and Kriging. Repeated studies were used to quantify the well-posedness of the inversion problem, and the uncertainty was assessed in material property and crystallographic orientation estimates given typical geometric dimension variability in aerospace components. Surrogate model quality was found to be an important factor in inversion results when the model more closely represents the test data. One important discovery was when the model matches well with test data, a Kriging surrogate model using un-sorted Latin Hypercube sampled data performed as well as the best [...]

Part-to-Itself Model Inversion in Process Compensated Resonance Testing

Process Compensated Resonance Testing (PCRT) is a non-destructive evaluation (NDE) method involving the collection and analysis of a part’s resonance spectrum to characterize its material or damage state. Prior work used the finite element method (FEM) to develop forward modeling and model inversion techniques. In many cases, the inversion problem can become confounded by multiple parameters having similar effects on a part’s resonance frequencies. To reduce the influence of confounding parameters and isolate the change in a part (e.g. creep), a part-to-itself (PTI) approach can be taken. A PTI approach involves inverting only the change in resonance frequencies from the before and after states of a part. This approach reduces the possible inversion parameters to only those which change in response to in-service loads and damage mechanisms. To evaluate the effectiveness of using a PTI inversion approach, creep strain and material properties were estimated in virtual and real [...]

Process Compensated Resonance Testing Modeling for Damage Evolution and Uncertainty Quantification

Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation (NDE) method based on the fundamentals of Resonant Ultrasound Spectroscopy (RUS). PCRT is used for material characterization, defect detection, process control and life monitoring of critical gas turbine engine and aircraft components. Forward modeling and model inversion for PCRT have the potential to greatly increase the method’s material characterization capability while reducing its dependence on compiling a large population of physical resonance measurements. This paper presents progress on forward modeling studies for damage mechanisms and defects in common to structural materials for gas turbine engines. Finite element method (FEM) models of single crystal (SX) Ni-based superalloy Mar-M247 dog bones and Ti-6Al-4V cylindrical bars were created, and FEM modal analyses calculated the resonance frequencies for the samples in their baseline condition. Then the frequency effects of superalloy creep [...]

Process Compensated Resonance Testing Models for Quantification of Creep Damage in Single Crystal Nickel-Based Superalloys

Process compensated resonant testing (PCRT) is a full body nondestructive evaluation (NDE) method that measures the resonance frequencies of a part and correlates them to the part’s material state, structural integrity, or damage state. This paper describes the quantification of creep damage in a virtual part population via the correlation of PCRT parameters to creep strain using inversion methods and vibrational pattern recognition (VIPR) analysis. Modeled populations were created using the finite element method (FEM) for single crystal (SX) nickel-based superalloy dogbone and turbine engine airfoil geometries. The modeled populations include nominal variation in crystallographic orientation, geometric dimensions, and material properties. Modeled populations also include parts with variable levels of creep strain, allowing for NDE sensitivity studies. FEM model inversion tools quantified creep strain and distinguished it from other variations in the part populations. Resonant [...]

Resonance Ultrasound Spectroscopy Forward Modeling and Inverse Characterization of Nickel-based Superalloys

The objective of this paper is to investigate Resonance Ultrasound Spectroscopy (RUS) measurement models to more precisely connect changes in the resonance frequencies of nickel-based super-alloy material to the macro/microscopic state. RUS models using analytical solutions and the finite element method (FEM) were developed to address varying elastic properties, grain structures and creep. Experimental studies were performed investigating the effect of exposure to high temperatures and stress for varying part shape and three grain structure classes: single crystals, directionally-solidified and polycrystalline structures. Inversion using both traditional analytical models was enhanced in order to simultaneously estimate varying material properties and changes in part geometry due to creep. Inversion using surrogate models from FEM simulations was also developed, addressing varying crystal orientation and complex geometries. Results are presented comparing the forward model trends [...]

Uncertainty Quantification in Modeling and Measuring Components with Resonant Ultrasound Spectroscopy

This report presents the motivation, background, methods and results of a Phase II Small Business Innovation Research (SBIR) project that continued the development and application of an uncertainty quantification (UQ) process for models and measurements made with Process Compensated Resonance Testing (PCRT). Resonant Ultrasound Spectroscopy (RUS) is a nondestructive evaluation (NDE) method which can be used for material characterization, defect detection, process control and life monitoring for critical components in gas turbine engines, aircraft and other systems. Accurate forward and inverse modeling for RUS requires a proper accounting of the propagation of uncertainty due to the model and measurement sources. A process for quantifying the propagation of uncertainty to RUS frequency results for models and measurements was developed. Epistemic and aleatory sources of uncertainty were identified for forward model parameters, forward model material property and geometry inputs, [...]


  • U.S. Patent 10481104, 10718723 for Utilizing RI of in-service parts
  • U.S. Patent 9157788, 10067094 for Part evaluation system/method using both resonances and surface vibration data
  • U.S. Patent 8903675 for Acoustic system and method for NDT of a part through frequency sweeps
  • U.S. Patent 9228981 for Resonance Inspection-based surface defect system/method
  • U.S. Patent 9335300 for SAW mode-based surface defect method
  • U.S. Patent 9927403 for Resonance inspection sorting module array
  • U.S. Patent 10295510 for Part evaluation based upon system natural frequency
  • U.S. Patent 9074927 for Methods for non-destructively evaluating a joined component
  • U.S. Patent 9228980 for Non-destructive evaluation methods for aerospace components
  • U.S. Patent 10746704 for PCRT for process control

ASTM Standards

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