Surrogate Modeling of Manufacturing Variation Effects on Unsteady Interactions in a Transonic Turbine

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Jeffrey M. Brown ◽  
Joseph Beck ◽  
Alexander Kaszynski ◽  
John Clark
Keyword(s):  
Surrogate Model ◽  
Optical Measurement ◽  
Surrogate Modeling ◽  
Point Clouds ◽  
Nearest Neighbor Search ◽  
Model Parameters ◽  
Grid Data ◽  
Reduced Basis ◽  
Small Impact ◽  
Transonic Turbine

This effort develops a surrogate modeling approach for predicting the effects of manufacturing variations on performance and unsteady loading of a transonic turbine. Computational fluid dynamics (CFD) results from a set of 105 as-manufactured turbine blade geometries are used to train and validate the surrogate models. Blade geometry variation is characterized with point clouds gathered from a structured light, optical measurement system and as-measured CFD grids are generated through mesh morphing of the nominal design grid data. Principal component analysis (PCA) of the measured airfoil geometry variations is used to create a reduced basis of independent surrogate model parameters. It is shown that the surrogate model typically captures between 60% and 80% of the CFD predicted variance. Three new approaches are introduced to improve surrogate effectiveness. First, a zonal PCA approach is defined which investigates surrogate accuracy when limiting analysis to key regions of the airfoil. Second, a training point reduction strategy is proposed that is based on the k–d tree nearest neighbor search algorithm and reduces the required training points up to 38% while only having a small impact on accuracy. Finally, an alternate reduction approach uses k-means clustering to effectively select training points and reduces the required training points up to 66% with a small impact on accuracy.

Surrogate Modeling of Manufacturing Variation Effects on Unsteady Interactions in a Transonic Turbine

2018 ◽  
Author(s):  
Jeffrey M. Brown ◽  
Joseph Beck ◽  
Alexander Kaszynski ◽  
John Clark
Keyword(s):  
Surrogate Model ◽  
Optical Measurement ◽  
Surrogate Modeling ◽  
Point Clouds ◽  
Nearest Neighbor Search ◽  
Model Parameters ◽  
Grid Data ◽  
Reduced Basis ◽  
Validation Data ◽  
Transonic Turbine

This effort develops a surrogate modeling approach for predicting the effects of manufacturing variations on blade unsteadiness and performance of a transonic turbine. CFD results from a set of 105 as-manufactured turbine blade geometries are used to train and validate the surrogate models. Blade geometry variation is characterized with point clouds created from a structured light optical measurement system and as-measured CFD grids are generated through mesh morphing of the nominal design grid data. Results from a Reynolds-averaged Navier-Stokes flow solver with the two-equation Wilcox turbulence model are used as training and validation data. Principal Component Analysis (PCA) of the measured airfoil geometry variations is used to create reduced basis of independent surrogate model parameters. Results of the surrogate are compared to the CFD results. It is shown that the surrogate model typically captures between 60% and 80% of the full CFD predicted variance. Three new approaches are introduced to improve the accuracy of the surrogate. A zonal PCA approach is defined which improves surrogate accuracy by focusing on key regions of the airfoil. A training point reduction strategy is proposed that is based on the kd-tree nearest neighbor search algorithm and reduces the required training points by 25%. A second reduction approach uses k-means clustering to effectively select training points from the 105 blade population and is used to reduce the required training points by up to 66%.

How well do we know our models?

2020 ◽  
Author(s):  
Denise Degen ◽  
Karen Veroy ◽  
Mauro Cacace ◽  
Magdalena Scheck-Wenderoth ◽  
Florian Wellmann
Keyword(s):  
Finite Element ◽  
Surrogate Model ◽  
Sensitivity Study ◽  
Reduced Basis Method ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Reduced Basis ◽  
Global Sensitivity ◽  
Sensitivity Studies ◽  
Basis Method

<p>In Geosciences, we face the challenge of characterizing uncertainties to provide reliable predictions of the earth surface to allow, for instance, a sustainable and renewable energy management. In order, to address the uncertainties we need a good understanding of our geological models and their associated subsurface processes.</p><p>Therefore, the essential pre-step for uncertainty analyses are sensitivity studies. Sensitivity studies aim at determining the most influencing model parameters. Hence, we require them to significantly reduce the parameter space to avoid unfeasibly large compute times.</p><p>We distinguish two types of sensitivity analyses: local and global studies. In contrast, to the local sensitivity study, the global one accounts for parameter correlations. That is the reason, why we employ in this work a global sensitivity study. Unfortunately, global sensitivity studies have the disadvantage that they are computationally extremely demanding. Hence, they are prohibitive even for state-of-the-art finite element simulations.</p><p>For this reason, we construct a surrogate model by employing the reduced basis method. The reduced basis method is a model order reduction technique that aims at significantly reducing the spatial and temporal degrees of freedom of, for instance, finite element solves. In contrast to other surrogate models, we obtain a surrogate model that preserves the physics and is not restricted to the observation space. As we will show, the reduced basis method leads to a speed-up of five to six orders of magnitude with respect to our original problem while retaining an accuracy higher than the measurement accuracy.</p><p>In this work, we elaborate on the advantages of global sensitivity studies in comparison to local ones. We use several case studies, from large-scale European sedimentary basins to demonstrate how the global sensitivity studies are used to learn about the influence of transient, such as paleoclimate effects, and stationary effects. We also demonstrate how the results can be used in further analyses, such as deterministic and stochastic model calibrations. Furthermore, we show how we can use the analyses to learn about the subsurface processes and to identify model short comes.</p>

The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine

2017 ◽  
Author(s):  
John P. Clark ◽  
Joseph A. Beck ◽  
Alex A. Kaszynski ◽  
Angela Still ◽  
Ron-Ho Ni
Keyword(s):  
Fourier Transforms ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Region Of Interest ◽  
Navier Stokes ◽  
Analysis Tool ◽  
Grid Data ◽  
Discrete Fourier Transforms ◽  
Numerical Predictions ◽  
Transonic Turbine

This effort focuses on the comparison of unsteadiness due to as-measured turbine blades in a transonic turbine to that obtained with blueprint geometries via computational fluid dynamics (CFD). A Reynolds-averaged Navier-Stokes flow solver with the two-equation Wilcox turbulence model is used as the numerical analysis tool for comparison between the blueprint geometries and as-manufactured geometries obtained from a structured light optical measurement system. The nominal turbine CFD grid data defined for analysis of the blueprint blade was geometrically modified to reflect as-manufactured turbine blades using an established mesh metamorphosis algorithm. The approach uses a modified neural network to iteratively update the source mesh to the target mesh. In this case the source is the interior CFD surface grid while the target is the surface blade geometry obtained from the optical scanner. Nodes interior to the CFD surface were updated using a modified iterative spring analogy to avoid grid corruption when matching as-manufactured part geometry. This approach avoids the tedious manual approach of regenerating the CFD grid and does not rely on geometry obtained from Coordinate Measurement Machine (CMM) sections, but rather a point cloud representing the entirety of the turbine blade. Surface pressure traces and the discrete Fourier transforms thereof from numerical predictions of as-measured geometries are then compared both to blueprint predictions and to experimental measurements. The importance of incorporating as-measured geometries in analyses to explain deviations between numerical predictions of blueprint geometries and experimental results is readily apparent. Further analysis of every casting produced in the creation of the test turbine yields variations that one can expect in both aero-performance and unsteady loading as a consequence of manufacturing tolerances. Finally, the use of measured airfoil geometries to reduce the unsteady load on a target blade in a region of interest is successfully demonstrated.

scholarly journals An Investigation of Surrogate Models for Efficient Performance-Based Decoding of 3D Point Clouds

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
James D. Cunningham ◽  
Timothy W. Simpson ◽  
Conrad S. Tucker
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Surrogate Model ◽  
Surrogate Modeling ◽  
Point Clouds ◽  
Absolute Error ◽  
3D Models ◽  
Test Case ◽  
3D Point Clouds ◽  
Comparable Accuracy

Abstract This work investigates surrogate modeling techniques for learning to approximate a computationally expensive function evaluation of 3D models. While in the past, 3D point clouds have been a data format that is too high dimensional for surrogate modeling, by leveraging advances in 3D object autoencoding neural networks, these point clouds can be mapped to a one-dimensional latent space. This leads to the fundamental research question: what surrogate modeling technique is most suitable for learning relationships between the 3D geometric features of the objects captured in the encoded latent vector and the physical phenomena captured in the evaluation software? Radial basis functions (RBFs), Kriging, and shallow 1D analogs of popular deep 2D image classification neural networks are investigated in this work. We find the nonintuitive result that departing from neural networks to decode latent representations of 3D objects into performance predictions is far more efficient than using a neural network decoder. In test cases using datasets of aircraft and watercraft 3D models, the non-neural network surrogate models achieve comparable accuracy to the neural network models. We find that an RBF surrogate model is able to approximate the lift and drag coefficients of 234 aircraft models with a mean absolute error of 1.97 × 10−3 and trains in only 3 seconds. Furthermore, the RBF surrogate model is able to rank a set of designs with an average percentile error of less than 8%. In comparison, a 1D ResNet achieves an average absolute error of 1.35 × 103 in 38 min for the same test case. We validate the comparable accuracy of the four techniques through a test case involving 214 3D watercraft models, but we also find that the distribution of the performance values of the data, in particular the presence of many outliers, has a significant negative impact on accuracy. These results contradict a common perception of neural networks as an efficient “one-size-fits-all” solution for learning black-box functions and suggests that even within systems that utilize multiple neural networks, potentially more efficient alternatives should be considered for each network in the system. Depending on the required accuracy of the application, this surrogate modeling approach could be used to approximate an expensive simulation software, or if the tolerance for error is low, it serves as a first pass which can narrow down the number of candidate designs to be analyzed more thoroughly.

The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
John P. Clark ◽  
Joseph A. Beck ◽  
Alex A. Kaszynski ◽  
Angela Still ◽  
Ron-Ho Ni
Keyword(s):  
Fourier Transforms ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Region Of Interest ◽  
Navier Stokes ◽  
Analysis Tool ◽  
Grid Data ◽  
Discrete Fourier Transforms ◽  
Numerical Predictions ◽  
Transonic Turbine

This effort focuses on the comparison of unsteadiness due to as-measured turbine blades in a transonic turbine to that obtained with blueprint geometries via computational fluid dynamics (CFD). A Reynolds-averaged Navier–Stokes flow solver with the two-equation Wilcox turbulence model is used as the numerical analysis tool for comparison between the blueprint geometries and as-manufactured geometries obtained from a structured light optical measurement system. The nominal turbine CFD grid data defined for analysis of the blueprint blade were geometrically modified to reflect as-manufactured turbine blades using an established mesh metamorphosis algorithm. The approach uses a modified neural network to iteratively update the source mesh to the target mesh. In this case, the source is the interior CFD surface grid while the target is the surface blade geometry obtained from the optical scanner. Nodes interior to the CFD surface were updated using a modified iterative spring analogy to avoid grid corruption when matching as-manufactured part geometry. This approach avoids the tedious manual approach of regenerating the CFD grid and does not rely on geometry obtained from coordinate measurement machine (CMM) sections, but rather a point cloud representing the entirety of the turbine blade. Surface pressure traces and the discrete Fourier transforms (DFT) thereof from numerical predictions of as-measured geometries are then compared both to blueprint predictions and to experimental measurements. The importance of incorporating as-measured geometries in analyses to explain deviations between numerical predictions of blueprint geometries and experimental results is readily apparent. Further analysis of every casting produced in the creation of the test turbine yields variations that one can expect in both aero-performance and unsteady loading as a consequence of manufacturing tolerances. Finally, the use of measured airfoil geometries to reduce the unsteady load on a target blade in a region of interest is successfully demonstrated.

Robotic motion compensation for bone movement, using ultrasound images

2015 ◽  
Vol 42 (5) ◽  
pp. 466-474 ◽  
Author(s):  
P.M.B. Torres ◽  
P. J. S. Gonçalves ◽  
J.M.M. Martins
Keyword(s):  
Motion Compensation ◽  
Optical Measurement ◽  
Three Dimensional ◽  
Point Clouds ◽  
Robotic System ◽  
Ultrasound Images ◽  
Bone Drilling ◽  
Content Type ◽  
3D Point Clouds ◽  
Robotic Motion

Purpose – The purpose of this paper is to present a robotic motion compensation system, using ultrasound images, to assist orthopedic surgery. The robotic system can compensate for femur movements during bone drilling procedures. Although it may have other applications, the system was thought to be used in hip resurfacing (HR) prosthesis surgery to implant the initial guide tool. The system requires no fiducial markers implanted in the patient, by using only non-invasive ultrasound images. Design/methodology/approach – The femur location in the operating room is obtained by processing ultrasound (USA) and computer tomography (CT) images, obtained, respectively, in the intra-operative and pre-operative scenarios. During surgery, the bone position and orientation is obtained by registration of USA and CT three-dimensional (3D) point clouds, using an optical measurement system and also passive markers attached to the USA probe and to the drill. The system description, image processing, calibration procedures and results with simulated and real experiments are presented and described to illustrate the system in operation. Findings – The robotic system can compensate for femur movements, during bone drilling procedures. In most experiments, the update was always validated, with errors of 2 mm/4°. Originality/value – The navigation system is based entirely on the information extracted from images obtained from CT pre-operatively and USA intra-operatively. Contrary to current surgical systems, it does not use any type of implant in the bone to track the femur movements.

A Rational Design Approach to Gaussian Process Modeling for Variable Fidelity Models

2011 ◽  
Author(s):  
Roxanne A. Moore ◽  
David A. Romero ◽  
Christiaan J. J. Paredis
Keyword(s):  
Gaussian Process ◽  
Surrogate Model ◽  
Rational Design ◽  
Sequential Sampling ◽  
Accurate Determination ◽  
Surrogate Modeling ◽  
Sampling Strategy ◽  
New Approach ◽  
Variable Fidelity ◽  
The Cost

Computer models and simulations are essential system design tools that allow for improved decision making and cost reductions during all phases of the design process. However, the most accurate models tend to be computationally expensive and can therefore only be used sporadically. Consequently, designers are often forced to choose between exploring many design alternatives with less accurate, inexpensive models and evaluating fewer alternatives with the most accurate models. To achieve both broad exploration of the design space and accurate determination of the best alternatives, surrogate modeling and variable accuracy modeling are gaining in popularity. A surrogate model is a mathematically tractable approximation of a more expensive model based on a limited sampling of that model. Variable accuracy modeling involves a collection of different models of the same system with different accuracies and computational costs. We hypothesize that designers can determine the best solutions more efficiently using surrogate and variable accuracy models. This hypothesis is based on the observation that very poor solutions can be eliminated inexpensively by using only less accurate models. The most accurate models are then reserved for discerning the best solution from the set of good solutions. In this paper, a new approach for global optimization is introduced, which uses variable accuracy models in conjuction with a kriging surrogate model and a sequential sampling strategy based on a Value of Information (VOI) metric. There are two main contributions. The first is a novel surrogate modeling method that accommodates data from any number of different models of varying accuracy and cost. The proposed surrogate model is Gaussian process-based, much like classic kriging modeling approaches. However, in this new approach, the error between the model output and the unknown truth (the real world process) is explicitly accounted for. When variable accuracy data is used, the resulting response surface does not interpolate the data points but provides an approximate fit giving the most weight to the most accurate data. The second contribution is a new method for sequential sampling. Information from the current surrogate model is combined with the underlying variable accuracy models’ cost and accuracy to determine where best to sample next using the VOI metric. This metric is used to mathematically determine where next to sample and with which model. In this manner, the cost of further analysis is explicitly taken into account during the optimization process.

Discrepancy Prediction in Dynamical System Models Under Untested Input Histories

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Kyle Neal ◽  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Jon Zumberge
Keyword(s):  
Dynamical System ◽  
Simulation Model ◽  
Model Prediction ◽  
Surrogate Model ◽  
Surrogate Modeling ◽  
Model Bias ◽  
Time Step ◽  
System Models ◽  
Input Time ◽  
Dynamical System Models

This paper presents a probabilistic framework for discrepancy prediction in dynamical system models under untested input time histories, based on information gained from validation experiments. Two surrogate modeling-based methods, namely observation surrogate and bias surrogate, are developed to predict the bias of a dynamical system simulation model under untested input time history. In the first method, a surrogate model is built for the observed experimental output, and the model bias for the untested input is obtained by comparing the output of the observation surrogate with the output of the physics-based model. The second method constructs a surrogate model for the bias in terms of the inputs in the conducted experiments. The bias surrogate model is then used to correct the simulation model prediction at each time-step under a predictor–corrector scheme to predict the model bias under untested conditions. A neural network-based surrogate modeling technique is employed to implement the proposed methodology. The bias prediction result is reported in a probabilistic manner, in order to account for the uncertainty of the surrogate model prediction. An air cycle machine case study is used to demonstrate the effectiveness of the proposed bias prediction framework.

Digital Measurement and its Error Analysis for the Machining Free-Form Surface

2014 ◽  
Vol 664 ◽  
pp. 263-267
Author(s):  
Feng Lu ◽  
Ning Li ◽  
Xiao Fei Zhang
Keyword(s):  
Laser Scanning ◽  
Optical Measurement ◽  
Three Dimensional ◽  
Point Clouds ◽  
Free Form ◽  
Digital Measurement ◽  
Machining Errors ◽  
Three Dimensional Measurement ◽  
Free Form Surface ◽  
Free Form Surfaces

To deal with the lack of accurate and efficient inspection methods in complex free-form surfaces, three-dimensional measurement method based on the optical measurement and computer image processing technology was proposed. It adopted laser scanning technology to get point clouds of free-form surface. Used rapid measurement software to inspect precision of point cloud& CAD model. What could be the cause of machining errors was analyzed. 3D deviation inspection of complex surfaces was applied by an artifact. Detected the machining error of an important section, and outputted test report. This research provides a convenient and swift method for the inspection of free-form surface and processing quality control.

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