Srikanth Akkaram

Gaussian Process Meta-Models for Efficient Probabilistic Design in Complex Engineering Design Spaces

Probabilistic design in complex design spaces is often a computationally expensive and difficult task because of the highly nonlinear and noisy nature of those spaces. Approximate probabilistic methods, such as, First-Order Second-Moments (FOSM) and Point Estimate Method (PEM) have been developed to alleviate the high computational cost issue. However, both methods have difficulty with non-monotonic spaces and FOSM may have convergence problems if noise on the space makes it difficult to calculate accurate numerical partial derivatives. Use of design and Analysis of Computer Experiments (DACE) methods to build polynomial meta-models is a common approach which both smoothes the design space and significantly improves the computational efficiency. However, this type of model is inherently limited by the properties of the polynomial function and its transformations. Therefore, polynomial meta-models may not accurately represent the portion of the design space that is of interest to the engineer. The objective of this paper is to utilize Gaussian Process (GP) techniques to build an alternative meta-model that retains the properties of smoothness and fast execution but has a much higher level of accuracy. If available, this high quality GP model can then be used for fast probabilistic analysis based on a function that much more closely represents the original design space. Achieving the GP goal of a highly accurate meta-model requires a level of mathematics that is much more complex than the mathematics required for regular linear and quadratic response surfaces. Many difficult mathematical issues encountered in the implementation of the Gaussian Process meta-model are addressed in this paper. Several selected examples demonstrate the accuracy of the GP models and efficiency improvements related to probabilistic design.Copyright ?? 2005 by ASME

Challenges in Uncertainty, Calibration, Validation and Predictability of Engineering Analysis Models

Model calibration, validation, prediction and uncertainty quantification have progressed remarkably in the past decade. However, many issues remain. This paper attempts to provide answers to the key questions: 1) how far have we gone? 2) what technical challenges remain? and 3) what are the future directions for this work? Based on a comprehensive literature review from academic, industrial and government research and experience gained at the General Electric (GE) Company, the paper will summarize the advancements of methods and the application of these methods to calibration, validation, prediction and uncertainty quantification. The latest research and application thrusts in the field will emphasize the extension of the Bayesian framework to validation of engineering analysis models. Closing remarks will offer insight into possible technical solutions to the challenges and future research directions.Copyright

Meta Modeling Techniques and Optimal Design of Experiments for Transient Inverse Modeling Applications

The use of model-based simulation in engineering often necessitates the need to estimate model parameters based on physical experiments or field data. This class of problems is referred to as inverse problems in the literature and two significant challenges based on the application of inverse modeling technology to practical engineering problems are (a) computational cost of the inverse solution for complex transient simulation models that needed a long time to execute (b) ability of the instrumentation to shed light on the model parameters being estimated. This paper develops a methodology for the use of transient meta-modeling techniques for data matching applications to address the computational efficiency. The transient meta-models are constructed using the SVD/PCA approach to identify the key transient signature patterns from a dimension reduction perspective. Accuracy of the inverse modeling method with the direct simulation model and the meta-model are compared. The paper concludes with a methodology to optimally design an experiment and collect data to improve the nature of the inverse problem and the confidence with which the model parameters are estimated.Copyright

Reduced Order Clearance Models for Gas Turbine Applications

This paper describes a reduced order model (ROM) developed to predict changes in gas turbine tip clearance – the radial distance between the end of the blade and the stator case. The clearance is estimated by modeling the growth of the sub-components during engine operating conditions. Gas turbine clearances vary significantly during different engine startup and shutdown conditions because of time constant mismatch between interacting sub-components (e.g. rotor and stator). The ROM is developed based on full-fidelity finite element simulation data and can predict the clearance variation as a function of engine thermodynamic conditions. As a result of their real-time execution capability, these models can be used for preliminary design, clearance control, and operational variation studies. The methodology is demonstrated on transient high-pressure compressor stator growth and high-pressure turbine transient clearance data.

Analytical Model to Predict Thermomechanical Relaxation of Shot Peening Induced Residual Stresses

Shot peening is widely used to improve the fatigue life of engine blades and rotors by inducing compressive residual stress on component surfaces. However, the residual stresses can relax due to exposure at high service temperature and mechanical loading. A physics-motivated analytical solution is developed to predict the residual stress relaxation at high temperature and under mechanical loading. In this thermomechanical relaxation model, the plastic strains in the shot peening layer and the substrate are obtained analytically by using linear kinematic hardening material law, and the plastic strain evolution at high temperature is modeled by using a recovery strain term. The final residual stress as a function of time, temperature, and mechanical loading is obtained analytically by combining this recovery strain with equilibrium and compatibility conditions. The whole method can be implemented into Microsoft Excel, and is easy to use and validate. As a special case, an analytical closed-form solution to predict the pure thermal relaxation of a shot peening residual stress is developed. The model predictions agree satisfactorily with published experimental measurements.

Analytical Derivatives Technology for Parametric Shape Design and Analysis in Structural Applications

The ability to perform and evaluate the effect of shape changes on the stress, modal and thermal response of components is an important ingredient in the ‘design’ of aircraft engine components. The classical design of experiments (DOE) based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters [1]. Since the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity analysis based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE) based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation [2,3] to compute the Taylor series or its Pade equivalent for finite element based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.Copyright

Modeling Thermo-Mechanical Relaxation of Shot Peening Induced Residual Stresses During Engine Operation

Shot peening is widely used to improve the fatigue life of engine blades and rotors by inducing compressive residual stress. However, the residual stresses can relax due to exposure at high service temperature and mechanical loading. A physics-motivated analytical solution was developed to predict the residual stress relaxation at high temperature and under mechanical loading. In this thermo-mechanical relaxation model, the plastic strains in shot peening layer and substrate are obtained analytically by using linear kinematic hardening materials law, and then the plastic strain evolution at high temperature is modeled by using a recovery strain term. The final stress as a function of time, temperature and mechanical loading is obtained analytically by combining this recovery strain with equilibrium and compatibility conditions. The whole method can be implemented into Microsoft (MS) Excel, and is easy to use and validate. As a special case, an analytical closed-form solution to predict pure thermal relaxation of shot peening residual stress is developed. The model predictions agree satisfactorily with published experimental data.Copyright

Inverse Modeling Techniques for Application to Engine Transient Performance Data Matching

A framework demonstrating the application of inverse modeling technology for engine performance data matching is presented. Transient aero-thermodynamic cycle models are used to simulate engine performance and control characteristics over the entire flight envelope. These models are used not only for engine design and certification but also to provide performance guarantees to the customer and for engine diagnostics. Therefore, it is extremely important that these models are able to accurately predict the performance metrics of interest. Accuracy of these models can be improved by fine-tuning model parameters so that the model output best matches the flight test data. The performance of an aircraft engine is fine tuned from several sensor observations, e.g. exhaust gas temperature, fuel flow, and fan speed. These observations vary with parameters like power level, core speed and operating conditions like altitude, inlet conditions (temperature and pressure), and Mach number, and are used in conjunction with a transient performance simulation model to assess engine performance. This is normally achieved through an iterative manual approach that requires a lot of expert judgment. Simulating transient performance characteristics often requires an engineer to estimate model parameters by matching model response to engine sensor data. Such an estimation problem can be posed using inverse modeling technology. One of the main challenges in the application of inverse modeling for parameter estimation is that the problem can be ill-posed that leads to instability and non-uniqueness of the solution. The inverse method employed here for parameter estimation provides a solution for both well-posed and ill-posed problems. Sensitivity analysis can be used to better pose the data-matching problem. Singular value decomposition (SVD) technique is used to address the ill-posed nature of the inverse problem, which is solved as a finite dimensional non-linear optimization problem. Typically, the transient response is highly nonlinear and it may not be possible to match the whole transient simultaneously. This paper extends the framework on transient inverse modeling developed in [1] for engine transient performance applications. Variable weighting mechanism allows providing different weights to different sensors. This helps in better control on data matching, identify drift in parameter values over time, and point towards incorrect modeling assumptions. The application of the inverse methodology is demonstrated on a single spool non-afterburning engine and a commercial aviation engine model.Copyright

Inverse Modeling Technology For Transient Engine Performance Data Matching

The paper develops a framework for application of inverse modeling techniques to develop accurate simulation models for aircraft engine performance characteristics. Typically, the performance of an aircraft engine is fine tuned from several sensor observations, e.g. exhaust gas temperature, fuel flow and fan speed. These observations vary with parameters like power level, core speed and operating conditions like ambient temperature, pressure and MACH number, and are used in conjunction with a transient performance simulation model to assess engine performance. Transient aero-thermodynamic cycle models have been developed to simulate engine performance and control characteristics over the entire flight envelope. Accuracy of these models can be improved by fine-tuning model parameters so that the model output best matches the flight test data. The application of inverse modeling for parameter estimation for transient data matching is challenging for two reasons. Firstly, the problem can be ill posed leading to instability and non-uniqueness of the solution. The Singular Value Decomposition (SVD) technique employed in this paper for parameter estimation provides a solution for both well-posed and ill-posed inverse problems, which is solved as a finite dimensional non-linear optimization problem [1]. Secondly, the transient response of an engine is highly non-linear and it may not be possible to match the entire transient regime accurately with a given set of model parameters. The transient weighting capability developed in this paper overcomes this difficulty by doing selective data matching over a specified region of interest. The application of the inverse methodology is demonstrated on a single spool non-afterburning engine and other aviation engine models.

Fretting Fatigue Modeling and Repair Evaluation for Generator Rotors

Generator Rotor Tooth Cracks have been recently observed on some long service generator rotors. The purpose of this paper is to document the root cause analysis as well as a repair methodology that was developed in support of one of these cracked units. The paper discusses the development of a finite element model to understand the operating modes and failure mechanisms that caused the initiation of these cracks. The results of the analysis agreed very well with field observations on cracked units and with some limited repair options that have been successfully used in the past. An experimental fretting fatigue testing program is currently underway to substantiate and extend the results reported in this paper.Copyright