River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6 Dario Di Maio Javad Baqersad Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA
The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research
River Publishers Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6 Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 Dario Di Maio • Javad Baqersad Editors
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-4380-016-3 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Preface Rotating Machinery, Optical Methods & Scanning LDV Methods represents one of the nine volumes of technical papers presented at the 39th IMAC, A Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics and held on February 8–11, 2021. The full proceedings also include volumes on Nonlinear Structures & Systems; Dynamics of Civil Structures; Model Validation and Uncertainty Quantification; Dynamic Substructures; Special Topics in Structural Dynamics & Experimental Techniques; Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing; Topics in Modal Analysis & Parameter Identification; and Data Science in Engineering. Each collection presents early findings from experimental and computational investigations on an important area within structural dynamics. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Flint, MI, USA Javad Baqersad Enschede, Overijssel, The Netherlands D. DiMaio v
Contents 1 WaveAR: A Real-Time Sensor-Based Augmented Reality Implementation for Operating Deflection Shapes .............................................................................................. 1 Daniel Herfert and Kai Henning 2 Full-Field 3D Mode Shape Measurement Using the Multiview Spectral Optical Flow Imaging Method ............................................................................................... 9 Domen Gorjup, Janko Slavicˇ, and Miha Boltežar 3 Stereophotogrammetry Camera Pose Optimization....................................................... 13 Bryan L. Witt, J. Justin Wilbanks, Brian C. Owens, and Daniel P. Rohe 4 Simplified Finite Element Models of Pyramidal Truss Sandwich Panels with Welded Joints for Dynamic Analysis and Their Experimental Validation ............................................... 39 Ke Yuan and Weidong Zhu 5 Operational Modal Analysis of Rotating Structures Under Ambient Excitation Using Tracking Continuously Scanning Laser Doppler Vibrometry............................................ 51 L. F. Lyu and W. D. Zhu 6 Delamination Detection in Fiber Metal Laminates Using Ultrasonic Wavefield Imaging............. 59 Casey Gardner, Young Ko, Michael Koutoumbas, Eric Flynn, Ian Cummings, and Phil Cornwell 7 One-Dimensional Convolutional Neural Networks for Real-Time Damage Detection of Rotating Machinery ........................................................................................ 73 Onur Avci, Osama Abdeljaber, Serkan Kiranyaz, Sadok Sassi, Abdelrahman Ibrahim, and Moncef Gabbouj 8 A Practical Guide to Motion Magnification ................................................................ 85 Sean Collier and Tyler Dare 9 Squeeze Film Damper Experimental and Numerical Correlation: Test Setup Description and Parameter Identification of Dry System............................................................... 93 Jason Cook, Jay Basinger, Thomas Hazelwood, Claire Luttrell, Blake Van Hoy, and Adolfo Delgado 10 Full-Field Modal Analysis by Using Digital Image Correlation Technique............................. 105 Davide Mastrodicasa, Emilio Di Lorenzo, Simone Manzato, Bart Peeters, and Patrick Guillaume 11 Validating Complex Models Accurately and Without Contact Using Scanning Laser Doppler Vibrometry (SLDV) ........................................................................................... 113 Jerome Eichenberger and Joerg Sauer 12 Effect of Different Test Setup Configurations on the Identification of Modal Parameters from Digital Image Correlation.............................................................................. 125 L. Marchetti, D. Mastrodicasa, E. Di Lorenzo, S. Manzato, L. Bregant, B. Peeters, and P. Lava 13 WaveImage – Order ODS for Rotating Machineries ...................................................... 135 Matthias Urban, Daniel Herfert, and Maik Gollnick vii
viii Contents 14 Multi-Level Damage Detection Using Octree Partitioning Algorithm................................... 143 Mehrdad S. Dizaji and Zhu Mao 15 Photogrammetry-Based Experimental Modal Analysis for Plate Structures........................... 147 J. S. Kim and Y. F. Xu 16 An Optical Mode Shape-Based Damage Detection Using Convolutional Neural Networks........... 157 Celso T. do Cabo and Zhu Mao 17 Full-Field 3D Experimental Modal Analysis from Dynamic Point Clouds Measured Using a Time-of-Flight Imager ...................................................................................... 163 Moisés Silva, Andre Green, John Morales, Peter Meyerhofer, Yongchao Yang, Eloi Figueiredo, and David Mascareñas 18 Application of a U-Net Convolutional Neural Network to Ultrasonic Wavefield Measurements for Defect Characterization .................................................................................. 167 Joshua D. Eckels, Isabel F. Fernandez, Kelly Ho, Nikolaos Dervilis, Erica M. Jacobson, and Adam J. Wachtor 19 Application of the RASTAR Method to Continuous Scanning LDV Measurements................... 183 D. Di Maio and S. Bruinsma
Chapter 1 WaveAR: A Real-Time Sensor-Based Augmented Reality Implementation for Operating Deflection Shapes Daniel Herfert and Kai Henning Abstract We present WaveAR, the first sensor-based augmented reality system for structural dynamic measurements of operating deflection shapes. WaveAR offers a significant simplification of the configuration effort of vibration sensor measurements by an automatically sensor tracking coupled by an efficient 3D scan generation of the structure. AR markers are used for sensor tracking which are placed on the sensor. This allows the determination of the sensor pose relative to the scanned structure. For this purpose the vibration sensors must be covered with AR markers. This allows a universal easy application also for existing sensor equipment. For 3D scanning and sensor tracking, a low-cost stereo depth camera is used. Because the AR application should be independent from data acquisition hardware, we have implemented a universal HTTP Rest-API interface for data acquisition connection. Through this, it is also supported to use wireless sensors. Based on this configuration, a real-time visualization in the form of an augmented reality application of the operating deflection shapes can be performed under real operating conditions. This enables the user to view the measurement from different perspectives by moving the camera around the object to be examined. Keywords Augmented reality · Data acquisition · Operating deflection shapes · Sensor pose tracking · 3D scanning 1.1 Introduction At the current state of technology, the performance of a vibration analysis for construction, evaluation, or dynamic optimization of structures or buildings requires a lot of time and human resources. Especially when using many sensors and complex structures from a geometrical point of view, a large amount of time has to be planned for the whole measuring process. The structural dynamic validation of the measurement, especially the evaluation of the mode or operational deflection shapes, is currently performed after the measurements. Thus, errors within the measurement process can only be detected afterward. The use of applications for real-time visualization in the form of an augmented reality (AR) representation is an essential point of interaction between the digital and analog worlds in the industrial environment in the age of Industry 4.0. Currently, these systems are used primarily for maintenance tasks, as digital manuals in service and maintenance, in plant and production planning, in training and further education, and in marketing, as well as at exhibitions. In most cases the systems are used as pure visualization and there is no consideration of other sensors. The use of AR systems in combination with other sensors offers an even more realistic interaction between the user and the digital application. The real-time visualization of essential sensor information at the scene of the event and always in relation to the structure under investigation are significant advantages of these systems. These advantages would also be very useful for the field of structural dynamics within the construction phase of new structures, as well as in the optimization phase of existing structures which would allow a direct interaction with the structure. Thus the vibration response of the structure could be visualized directly during operation. Again, this procedure would significantly reduce the time needed to perform vibration analyses and would also allow direct analyses in real operation of the structure. In the context of this publication, the AR system was applied to the modal analysis of a car rim and a steel plate. In addition to the results, the significant time savings in carrying out the measurement should be shown. D. Herfert ( ) · K. Henning Department of Structural Dynamics/Pattern Recognition, Society for the Advancement of Applied Computer Science, Berlin, Germany e-mail: herfert@gfai.de; henning@gfai.de © The Society for Experimental Mechanics, Inc. 2022 D. Di Maio, J. Baqersad (eds.), Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-76335-0_1 1
2 D. Herfert and K. Henning 1.2 Background In the field of structural dynamics, ever increasing demands are made on a realistic visualization of the natural and operational modes of vibration. This visualization is necessary to enable an optimal comparability with simulation results and is necessary to implement an even more precise analysis. The improved visualization possibilities of 3D animations, especially of computer games and movies, lead to higher and higher demands also on engineering software. Currently, all forms of visualization as defined in the reality-virtuality continuum [1] are available, from a purely virtual vibration animation to a vibration animation in the real environment (see Fig. 1.1). In contrast to real-time visualization applications, these are only available after the measurement is complete. Therefore, a direct interaction with the structure during operation is not possible for the user. To achieve these realistic representations, three things are necessary: 1. 3D reconstruction with high resolution and texture of the structure under investigation. 2. High measurement resolution, so that in the best case, one measurement point can be assigned to each point in the triangle mesh. 3. Textures from the real environment to project the results of the vibration analysis on the real background. Currently, AR applications are technically only possible with electromechanical sensors. The optical methods for vibration measurement are currently not applicable for AR applications. For high-speed cameras, a real-time data stream via Ethernet is not feasible due to the large amount of data. With multipoint vibrometers, visualization or analysis of the measured data is also only possible after the measurement. The biggest disadvantages of electromechanical sensors are the significantly higher configuration effort, the measurement resolution, and the difficult surface measurement in comparison to optical methods. Thus, a fundamental aim of this work is to minimize these disadvantages compared to the optical sensors. 1.3 Technical Implementation The aim of the work was the development of software components to accelerate and simplify the measurement chain for vibration analysis of mechanical structures by means of electromechanical sensors. To achieve this aim, three software components were created that can be used autonomously or in combination (see Fig. 1.2). Fig. 1.1 Overview of all structural dynamic representation forms (reality, augmented reality, virtual reality, virtuality), created with the WaveImage software (gfai tech GmbH)
1 WaveAR: A Real-Time Sensor-Based Augmented Reality Implementation for Operating Deflection Shapes 3 Fig. 1.2 Overview of all software and hardware components used to implement the data acquisition system for measurement configuration and realistic AR visualization 1.3.1 Acceleration and Simplification of the Measurement Configuration for Electromechanical Sensors New concepts were implemented to improve the measurement configuration. These include an efficient 3D reconstruction, an automatic optical marker tracking of the vibration sensors, and the automatic assignment of the sensor poses to the triangular mesh of the structure under investigation. These work steps simplify the currently manually performed procedure for the configuration of the measurement setup in many ways. Furthermore, this feature can be applied to existing data acquisition systems. To carry out the extension, only Arco markers have to be printed out and attached to the sensors. The Intel Real Sense D455 stereo camera has to be purchased and connected to a USB 3.0 port of the mobile measurement computer. With this hardware and the software WaveAR, the entire measurement configuration required to create the geometry and to assign the sensors to the geometry is possible. The created geometry and the corresponding sensor assignment can also be exported and used autonomously with external software components. But it can also be used as a measurement configuration for the following AR animation. 1.3.2 Universal Data Acquisition Interface Furthermore, the transfer of the results to existing data acquisition systems is essential in order to ensure a wide applicability. Besides the use of existing sensors, the integration of already existing data acquisition hardware plays a special role. This is essential for the later user, because in most applications the data acquisition hardware has the highest costs for measuring equipment. Therefore a standardized software development kit in C++called DAQIO SDK was developed. This SDK contains all functions for the implementation of the DAQIO network protocol. With this SDK any data acquisition device can communicate with the visualization component in the future. This should standardize the communication of DAQ devices. Communication is understood to be the transfer of measurement data as well as the control. DAQIO provides a communication protocol for the data acquisition interface. With the SDK DAQ devices can be extended with the DAQIO protocol. The DAQIO protocol was implemented as a network protocol, so that the data acquisition device can be used via Ethernet or WLAN or as a local host on the measuring computer. Real-time visualization in the form of an AR application is only possible through wireless data transfer. This network protocol can also be used independently and represents an independent innovation.
4 D. Herfert and K. Henning Fig. 1.3 Mobile measuring case for structural dynamics A mobile measuring case was developed for the AR application. This allows a complete structural dynamic measurement even outdoors without wired connection. The transfer of the measurement data from the acquisition unit to the visualization application is done via WLAN and with the DAQIO SDK. The mobile measuring case (see Fig. 1.3) is used for both indoor and outdoor measurements. For outdoor measurements it has a protected cable inlet and also works with closed lid. Therefore it is dust and water protected. The measuring case called WaveCase consists of three separate components. The first component is a CompactDAQ package from National Instruments with up to 32 channels and a sampling rate per channel of 50 kHz. Eight measurement cards can be integrated into this housing. The possible measurement cards include various types of sensors and do not only cover the field of structural dynamics. Therefore this measurement case could be used for other applications with other sensors. The entire data acquisition system but also the visualization was designed in a modular way, so that the whole system would be transferable to other sensor data and thus could be used in other application areas. The second component includes a commercially available tablet and is used to set up the server which is used to control the data acquisition device, synchronize data acquisition, store the measurement data locally, preprocess the measurement data, and transfer the measurement data to data acquisition clients. The third component includes a high-performance rechargeable battery, which allows a minimum measurement time of 48 h. This battery supplies both the data acquisition device and the tablet and is easily replaceable. In addition, the measuring case offers storage space for the sensors and their cables and a Bluetooth keyboard and mouse for easier operation of the tablet. 1.3.3 Real-Time Visualization in the Form of an AR Application The software WaveAR is the world’s first AR application for structural dynamics (see Fig. 1.4). This form of real-time visualization enables for the first time a vibration animation by means of a color map, embedded in the video image. The color map is determined by means of current sensor values. In order to be able to assign sensor values to pixels or points of the geometry which were not measured, an interpolation [2] was implemented. This type of interpolation originally comes from the field of computer vision and is first used in the field of structural dynamics. This allows a much more realistic surface measurement even with electromechanical sensors. By the computer-aided extension of the perception of reality in the form of an AR application, the operating deflection shapes can be shown directly in reality. This component requires the previously described components of the measurement configuration and universal data acquisition interface for the execution and therefore cannot be used independently.
1 WaveAR: A Real-Time Sensor-Based Augmented Reality Implementation for Operating Deflection Shapes 5 Fig. 1.4 Software user interface for time operating deflection shapes and visualization of a steel plate with WaveCase and Intel Real Sense D455 camera. The transfer of the measured values is done via Wi-Fi 1.4 Measurement Setup The analysis of the system was carried out in the form of a modal analysis. The vibration response of a car rim and a steel plate to a selective force excitation was investigated to conduct the experimental modal analysis. For this purpose, a car rim and a steel plate were mounted freely suspended in an aluminum frame. The car rim and the steel plate were excited by an automated modal hammer (WaveHitMAX, gfai tech GmbH) [3] on a fixed position. This modal hammer offers the advantage of automated repetitions of single hit excitation with a defined and constant force amplitude. Equipped with a force sensor (PCB type 208C03), a plastic tip, and an additional mass of 60 g, a repeatable excitation of 500 N has been achieved in order to obtain the best signal-to-noise ratio at all measurement points. The response of the car rim into z direction to the impact excitation was measured with five accelerometers (MMF KS943B.100). A series of three measurements with same input were carried out, each with five measuring points. First one part of the outer radius of the rim, then the second part of the outer radius, and then inner radius of the rim were measured. Due to the complete reproducibility of the excitation, the three measurements were combined into one measurement. The response of the steel plate only in z direction to the impact excitation was measured with five accelerometers (MMF KS943B.100). 1.5 Analysis At the beginning of the two measurements, the automatic optical measurement configuration was performed with the support of the WaveAR system. For this purpose, five ArUco markers were glued to the inserted sensors. Another ArUco marker was used to position the box in which the 3D scan takes place. Furthermore, the Intel Real Sense D455 camera was connected to the USB 3.0 port. After that, the settings were made on the DAQ software. Among other things, this includes setting the sampling rate, the assignment between the marker ID and the associated channel of the DAQ device. After that, the test object was scanned (see Fig. 1.5). It should be noted that there is no post-processing of the 3D scan. If there are even higher demands on the visualization, an automated post-processing of the 3D scan would be possible. However, this would have no influence on the structural dynamic properties. After scanning, the ArUco markers are then scanned to determine the relative pose of the sensors to the scanned structure. To scan the sensors, each sensor must appear in the camera image. If the user agrees with the determined sensor pose, it can be selected and continue with the scan of the next sensor pose afterward. If all sensors are to be determined with once, they all can be confirmed together (see Fig. 1.6). To optimize the pose determination, an extended Kalman filter has been implemented, which can also compensate the pose if the sensor is not currently in the image. After the pose determination is finished by the user, the automatic assignment of
6 D. Herfert and K. Henning Fig. 1.5 3D scans with software WaveAR with Intel Real Sense D455 camera of a car rim (left) and steel plate (right) without mesh post-processing Fig. 1.6 Sensor pose detection with optical markers of a car rim (left) and steel plate (right) the sensors to the 3D scan and the precalculation of the significant parameters of the interpolation for the later AR application are performed. After the assignment is completed, the sensors were connected to the DAQ device of the WaveCase, and the impulse hammer was positioned at the test object. Then the measurement was started, allowing real-time visualization in the form of an AR application (see Fig. 1.4). The sensor values are transmitted wirelessly from the WaveCase to the AR computer. To validate the data, both measurements were exported and analyzed with the software WaveImage [4]. For this purpose the experimental modal analysis component of the software WaveImage (gfai tech GmbH) was used to extract the eigenfrequencies and mode shapes using the Complex Mode Indicator Function AI (CMIF-AI) algorithm [5]. In Fig. 1.7 the CMIF-AI results and in Table 1.1 all detected eigenfrequencies are shown. For the car rim, ten and for the steel plate eight different modes could be identified. The Modal Assurance Criterion (MAC) matrix (see Fig. 1.8) is used to validate the linear independence of the detected modes. In both measurements there is a dependency only between mode 2 and mode 5. Otherwise there are no significant dependencies between modes. This indicates that the measurement was performed correctly. In Fig. 1.9 one mode shape per investigated object is presented. The mode shapes look quite realistic without a big effort for the geometry creation. Both measurements were feasible under 1 h, including the measurement setup, measurement configuration, data acquisition, and modal analysis by the WaveImage software. Without the WaveAR system, we would have needed much longer for the structural dynamic measurement of complex structures, such as the car rim. 1.6 Conclusion In summary, this work has created a first research proposal on the following topics in the field of structural dynamics: 1. Automatic optical measurement configuration for structural dynamics for electromagnetic sensors. 2. Implementation of a universal data acquisition interface. 3. Real-time visualization in form of an AR application for electromagnetic sensors.
1 WaveAR: A Real-Time Sensor-Based Augmented Reality Implementation for Operating Deflection Shapes 7 Fig. 1.7 Complex Mode Indicator Function AI (CMIF AI) of a car rim (left) and steel plate (right) Table 1.1 Eigenfrequencies with the corresponding mode number of the car rim and the steel plate Mode number EMA frequency RIM (Hz) EMA frequency steel plate (Hz) 1 388 163 2 741 203 3 1215 278 4 1703 323 5 2175 350 6 2597 442 7 2690 528 8 2935 563 9 3163 10 3223 Fig. 1.8 Modal Assurance Criterion (MAC) matrix of the ten measured modes of car rim (left) and eight measured modes of steel plate (right) With the current state of the work, an essential basis for the implementation of a cost-effective data acquisition system in the form of an AR application has been created. The possibilities for integration into existing data acquisition hardware and the low additional acquisition costs allow the current status to be used directly in applications in research and industry. Based on the achieved results, further steps of the measurement can be integrated into the system, but also existing methods can be improved and validated on new measurement applications. All in all, this system offers a new kind of interaction and assistance during and before the measurement, which does not exist in this form at this time. In addition, the measurement
8 D. Herfert and K. Henning Fig. 1.9 Three different views from the third mode (1215 Hz) of car rim. Seventh mode (528 Hz) of steel plate without texture time can be significantly reduced with this system, and less expert knowledge is also required to perform the measurement. To protect the innovation, a detailed patent search and a patent application based on it were prepared and submitted. The patent was granted with the name “Method and System for Structural Dynamic Analysis” on September 5, 2019 (Germany patent no. DE102018103333, 2019). References 1. Milgram, P.: A taxonomy of mixed reality visual displays. IEICE Trans. Inf. Syst. 77(12), 1321–1329 (1994) 2. Herfert, D., Heimann, J., Henning, K.: Automatic interpolation for the animation of unmeasured nodes with differential geometric methods. In: Rotating Machinery, Optical Methods & Scanning LDV Methods, vol. 6, pp. 53–59. Springer International Publishing, Cham (2021) 3. Product Page of the WaveImageMAX. https://wave-hit.com/ 4. Product Page of the WaveImage Software. https://wave-image.com/?lang=en 5. Gollnick, M., Herfert, D., Heimann, J.: 9. Automatic modal parameter identification with methods of artificial intelligence. In: Topics in modal analysis & testing, vol. 8. Springer International Publishing, Cham (2021)
Chapter 2 Full-Field 3D Mode Shape Measurement Using the Multiview Spectral Optical Flow Imaging Method Domen Gorjup, Janko Slavicˇ, and Miha Boltežar Abstract In some modal testing applications, image-based techniques offer compelling advantages compared to conventional sensors, particularly in cases where mass loading is problematic or a high spatial resolution is required. Still, the limited field of view of the well-established stereo DIC method can be a limiting factor in some measurements. By employing the principles of multi-view imaging, this constraint can be alleviated. For linear, time-invariant structures, multi-view triangulation can be performed in the frequency domain. The measurement field of view can in this way be arbitrarily extended using only a single moving camera imaging system. By using the simplified optical flow method in the displacement spectra identification step, a still-frame camera can be used for image acquisition, considerably lowering the complexity and cost of the imaging system. In this work, the spectral optical flow imaging and frequency-domain multi-view triangulation approaches are combined in an effort to identify mode shapes of a simple three-dimensional structure. The aim is to develop a robust and cost-effective single still-frame camera-based modal testing method. Keywords Single camera · Multiview · Full-field measurement · Frequency-domain triangulation · Spectral optical flow imaging 2.1 Introduction Image-based displacement measurement methods offer a viable alternative to traditional vibration measurement techniques, owing their appeal mainly to the high spatial resolution and the non-contacting nature of the measurement, especially important in cases where mass loading may impede the use of conventional transducers [1]. Due to an inherent limitation of 2D imaging systems, only the planar kinematics of the observed surface can be measured from a single camera point of view. With the introduction of stereo measurement methods (e.g., 3D Digital Image Correlation, DIC), this limitation is eliminated, but the field of view of the stereo camera pair remains limited to a single observed viewpoint [2]. Utilizing the principles of multi-view imaging [3], the field of view of an image-based vibration measurement can be extended for objects of arbitrary geometry. These methods extract spatial information from simultaneously acquired highspeed video frames of the observed process using triangulation. Alternatively, the mode shape data, captured by a moving stereo pair of high-speed cameras, can be used to extend the field of view of the measurement with a process called surface stitching [2]. When using these multi-view methods, possible distortions in the optical systems and time-synchronization errors with using multiple cameras can negatively affect the accuracy of the multi-view measurement [4]. This is the main motivation behind the so-called single-camera multi-view measurement methods. Using only a single digital camera, the complexity and cost of an imaging system are lowered. Single-camera multi-view systems however usually require additional light-splitting elements such as mirror adapters or prisms to project multiple views of the observed object on a single image sensor, sometimes resulting in lower spatial resolution [5]. The recently proposed method of frequency-domain triangulation for spatial vibration measurement offers an alternative single-camera measurement option [6]. Frequency-domain images of small harmonic motion can be used to reconstruct 3D deflection shapes of a linear, time-invariant mechanical structure under stationary excitation while arbitrarily extending the field-of-view of the measurement using only a single, moving image camera, preserving the full-field resolution of the result. D. Gorjup ( ) · J. Slavicˇ · M. Boltežar Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia e-mail: domen.gorjup@fs.uni-lj.si; janko.slavic@fs.uni-lj.si; miha.boltezar@fs.uni-lj.si © The Society for Experimental Mechanics, Inc. 2022 D. Di Maio, J. Baqersad (eds.), Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-76335-0_2 9
10 D. Gorjup et al. To extend the feasibility of high-speed imaging methods for measuring high frequency, as well as reduce the complexity and cost of high-speed imaging systems, various approaches to extending the frequency range of image-based measurement have been researched [7]. The Spectral Optical Flow Imaging (SOFI) method [8] has recently been used in a multi-view configuration to measure 3D operating deflection shapes (ODSs) of a vibrating specimen using a still-frame digital camera [9], with the frequency range of the measurement limited only by the frequency of a harmonically controlled light source. In this paper, the possibility of using deflection shape images, obtained by the single-camera multi-view SOFI method, together with the excitation spectra, measured using a single force transducer, in a frequency-domain triangulation procedure to measure full-field 3D mode shapes of a mechanical structure is explored. 2.2 Theoretical Background A method of measuring 3D ODSs using a single, moving still-frame camera is presented in [9]. Multiple images of the ODSs of a vibrating structure at selected frequencies of interest are acquired from various viewpoints using SOFI. Spatial operating deflection shapes X(ω) of a linear, time-invariant structure are reconstructed from frequency-domain images of the observed u(ω) =Δu(ω) +u REF = 1 w P ΔU(ω) +U REF (2.1) spatial motion ΔU(ω), reconstructed from image data by frequency-domain triangulation of ODS images u(ω): X(ω) =U(ω) −U REF (2.2) where wis the perspective scaling factor, assumed to be constant for small harmonic displacements ΔU[6]. By adding a force transducer between the shaker and the structure in the measurement chain, as illustrated in Fig. 2.1, the excitation spectra can also be measured, and the frequency-response functions H(ω) can be computed for all the points, observed in the full-field optical measurement at the selected measurement frequencies. The mode shapes Ψ(ω) can then be obtained, e.g., by using the least-squares frequency-domain (LSFD) method [10]. 2.3 Preliminary Experiment A concave steel object, composed of three 1-mm-thick 120 ×120 mm sheet metal planes, bent and welded along one edge was mounted onto an electrodynamic shaker through a PCB 208C01 force transducer. A single PCB SN 53358 accelerometer was mounted onto the object, in the middle of one of the three planes, facing away from the camera. The accelerometer was Fig. 2.1 Multi-view SOFI with frequency-domain triangulation for mode shape identification
2 Full-Field 3D Mode Shape Measurement Using the Multiview Spectral Optical Flow Imaging Method 11 Fig. 2.2 Measured accelerance FRF of the observed object Fig. 2.3 Mode shapes, measured in the preliminary experiment used to measure the FRF of the object in the 10–2000 Hz frequency band using sine-sweep excitation. It remained mounted to the object throughout the whole measurement process. Using the measured FRF, shown in Fig. 2.2, five measurement frequencies, corresponding to distinct resonant peaks, were selected for further analysis using multi-view SOFI. A high contrast speckle pattern was applied to the object’s three visible faces. The SOFI images were obtained at each selected frequency using a Basler Ace still-frame monochrome camera with a resolution of 4096 × 3000 pixels, with exposure period set to 2 s. The LED light source was controlled simultaneously with the shaker excitation, force, and image acquisition triggering, by external signals, generated using a single National Instruments 9263 output module. The process was repeated six times at each frequency, rotating the object on the shaker by approximately 60◦ between each measurement, to obtain six distinct views of the process. The multi-view system was calibrated using the perspective N-point algorithm [3]. A regular grid of 100×100 points was projected from the 3D model of the specimen onto each of the three visible faces in every view. A rectangular region of 175 ×175 pixels with the grid node in the center was analyzed using the multi-view SOFI method [9], to obtain the spatial response at each selected point for every measurement frequency. The resulting 3D ODS were used together with the force measurement to compute the full-field FRF values at the measurement frequencies. These were used to finally compute the 3D mode shapes of the observed object using the LSFD method. The results are shown in Fig. 2.3. 2.4 Conclusions Although further analysis of the obtained results is required, the results of the preliminary experiment approximate the expected mode shapes of the observed object well, confirming the potential for future applications of the proposed method to 3D mode shape measurement. Multi-view SOFI enables single still-frame camera measurements of spatial mode shapes for linear, time-invariant mechanical structures by utilizing the properties of a stationary mechanical process to facilitate full-field 3D measurements without the need for precise time-synchronization of multiple video sequences, with the only additional equipment required being a controlled light source. The multi-view SOFI method measures the response of a vibrating specimen directly in the frequency domain, significantly reducing the amount of the acquired data and the postprocessing times, compared to existing full-field spatial measurement methods.
12 D. Gorjup et al. References 1. Helfrick, M.N., Niezrecki, C., Avitabile, P., Schmidt, T.: 3D digital image correlation methods for full-field vibration measurement. Mech. Syst. Signal Process. 25(3), 917–927 (2011). https://doi.org/10.1016/j.ymssp.2010.08.013 2. Patil, K., Srivastava, V., Baqersad, J.: A multi-view optical technique to obtain mode shapes of structures. Measurement. 122, 358–367 (2018). https://doi.org/10.1016/j.measurement.2018.02.059 3. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, New York, NY (2003) 4. Yu, L., Pan, B.: Single-camera stereo-digital image correlation with a four-mirror adapter: Optimized design and validation. Opt. Lasers Eng. 87, 120–128 (2016). https://doi.org/10.1016/j.optlaseng.2016.03.014 5. Durand-Texte, T., Simonetto, E., Durand, S., Melon, M., Moulet, M.-H.: Vibration measurement using a pseudo-stereo system, target tracking and vision methods. Mech. Syst. Signal Process. 118, 30–40 (2019). https://doi.org/10.1016/j.ymssp.2018.08.049 6. Gorjup, D., Slavicˇ, J., Boltežar, M.: Frequency domain triangulation for full-field 3D operating-deflection-shape identification. Mech. Syst. Signal Process. 133, 106287 (2019). https://doi.org/10.1016/j.ymssp.2019.106287 7. Barone, S., Neri, P., Paoli, A., Razionale, A.V.: Low-frame-rate single camera system for 3D full-field high-frequency vibration measurements. Mech. Syst. Signal Process. 123, 143–152 (2019). https://doi.org/10.1016/J.YMSSP.2019.01.016 8. Javh, J., Slavicˇ, J., Boltežar, M.: Measuring full-field displacement spectral components using photographs taken with a DSLR camera via an analogue Fourier integral. Mech. Syst. Signal Process. 100, 17–27 (2018). https://doi.org/10.1016/j.ymssp.2017.07.024 9. Gorjup, D., Slavicˇ, J., Babnik, A., Boltežar, M.: Still-camera multiview Spectral Optical Flow Imaging for 3D operating-deflection-shape identification. Mech. Syst. Signal Process. (2021). https://doi.org/10.1016/j.ymssp.2020.107456 10. Verboven, P.: Frequency-Domain System Identification for Modal Analysis, Ph.D. Thesis. Department of Mechanical Engineering, Vrije Universiteit Brussel, Brussels, Belgium (2002)
Chapter 3 Stereophotogrammetry Camera Pose Optimization Bryan L. Witt, J. Justin Wilbanks, Brian C. Owens, and Daniel P. Rohe Abstract Stereophotogrammetry makes use of calibrated camera pairs to obtain three-dimensional information from twodimensional images. The accuracy of the extracted measurements is extremely dependent on the selection and setup of the camera system. For a given test object and desired viewing orientation, there is no one “correct” stereo camera setup, but rather a range of potential setups with some approaching an optimal system with respect to maximizing the measurement resolution. The open-ended nature of this test design exercise is compounded by equipment availability and the fact that many of the setup parameters have dependent characteristics, e.g., changing focal distance will affect stand-off distance, field of view, and image projection, among others. This work describes a planning tool that utilizes projective and Euclidian geometry to iteratively estimate optimal camera poses for available equipment, determines the most efficient image size, and also performs checks for lens diffraction, minimum focal distance, and adequate depth of field. Integrating a finite element model with these calculations further extends planning capabilities by allowing (1) an accurate definition of the volume to be imaged and (2) the ability to estimate response displacements in pixels due to an arbitrary excitation applied to the test object. This latter capability is critical for pre-test determination of the chosen camera setup’s ability to successfully extract three-dimensional measurements. The theory and workflow are presented along with an experimental demonstration. Keywords Stereo · Photogrammetry · Test planning · Camera pose · Displacement estimation 3.1 Introduction Photogrammetry is well established as a diagnostic capability for quasi-static displacement and strain measurements as well as large-scale (integer pixel) motion tracking [1–4]. Optical measurement techniques have many benefits, such as being non-contact and very fast to field. Photogrammetry’s use in structural dynamics, where higher frequency displacements are typically sub-pixel, is gaining popularity as camera technology and bespoke data processing methods are established [5–8]. A recent study [9] demonstrated that carefully constructed experimental modal tests using DIC can directly extract modal information from displacements as small as 0.001 pixel. The resolution of any optical system is dependent of the field of view (FOV); optimizing the number of pixels across an imaged area of interest (AOI) is critical for measuring sub-pixel displacements. However, because there are an endless number of practical considerations for each unique optical test (e.g., camera sensor selection, lenses available, physical space around the test object, etc.), there is no single truly “optimized” configuration. Typically, the practitioner must rely solely on Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the US government. B. L.Witt ( ) · D. P. Rohe Experimental Structural Dynamics Department, Sandia National Laboratories, Albuquerque, NM, USA e-mail: blwitt@sandia.gov; dprohe@sandia.gov J. J. Wilbanks · B. C. Owens Analytical Structural Dynamics Department, Sandia National Laboratories, Albuquerque, NM, USA e-mail: jjwilba@sandia.gov; bcowens@sandia.gov © The Society for Experimental Mechanics, Inc. 2022 D. Di Maio, J. Baqersad (eds.), Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-76335-0_3 13
14 B. L. Witt et al. their experience to select cameras and lenses and then determine their best pose in a stereo rig. Pose is defined here as the physical location and orientation of the cameras in space relative to each other as well as the test object. It is entirely conceivable to set up a stereo system, collect and download images, and post-process the data only to find that the displacements of the test object never overcame the noise floor of the optical system. This work presents a photogrammetry pre-test planning workflow that will inform the selection of camera/lens pairs and the stereo poses that approximate their optimal setup in terms of measurement resolution. This process also considers lens minimum focus distances and depth of field (DOF) requirements and checks for lens diffraction limitations. Finally, we use a finite element model (FEM) and the pose optimization results to determine what points in a bounding volume will be visible to both cameras and estimate their respective displacement amplitudes on a mode-by-mode basis for a given excitation. The modal displacement estimates can be directly correlated to the known (or estimated) noise floor of the camera system, easily identifying which modes may or may not be observable by the optical system. Armed with the information from the test planning workflow, the practitioner can easily iterate on the test setup (equipment, AOI, pose, excitation, etc.) to have the best opportunity to obtain the measurements of interest and meet the test objectives. The following section provides background information on general stereo camera setups, including the coordinate systems which are utilized and a brief coverage of 3D–2D projective transformations. Section 3.3 presents the iterative pose optimization routine and demonstrates output results relative to an actual test. Section 3.4 provides a stand-alone FEM analysis to determine visible nodes and estimate displacements, using the final results from Sect. 3.3 as input. The reader is cautioned that these two sections use different variable definitions. The final section discusses conclusions and future work under consideration. 3.2 General Stereophotogrammetry Setup The test planning workflow described in this work can be applied to a 2D photogrammetry using a single camera. However, a single camera test is usually much easier to setup and iterate upon; in this work we will focus on the more complex stereo camera setup utilizing two cameras for 3D photogrammetry measurements. Consider a test article in 3D space which is defined in an arbitrary “world” Cartesian coordinate system, Ow, as depicted in Fig. 3.1. It is usually extremely convenient to let the world coordinate system match that of the FEM global coordinate system, as is done in this work. Two cameras, denoted Camera 0 and Camera 1, are positioned such that their optical axes are pointed in the direction of the test article and have local coordinate systems Oi where i indicates the camera index 0 or 1, respectively. The baseline (BL) is the line formed between the origin points of Oi and lies on the same plane containing all points along both optical axes, zi. The camera rig is a fourth coordinate system, Or, and is defined at the center of the baseline, oriented such that xr points from Camera 0 to Camera 1 and yr is normal to the plane containing the baseline and optical axes. Finally, the image planes are located at the focal distance fi along the optical axis zi. Ideally, the image center would lie on the optical axis zi such that (cx, cy)i =(0, 0); typically there are slight offsets, but this is a reasonable approximation for Fig. 3.1 Stereophotogrammetry setup
3 Stereophotogrammetry Camera Pose Optimization 15 a planning tool. By convention, the integer pixel indexing in each image space is defined such that (u, v)i =(0, 0) is in the upper left corner as shown in Fig. 3.1. As part of a stereophotogrammetry test, a camera calibration is performed prior to data collection, which establishes both the intrinsic and extrinsic parameters of the camera system. In the test planning workflow, we do not have equipment setup to perform a calibration, but the form of the results elucidates the parameters needed for planning purposes. The intrinsic parameters formKi and comprise the optical center (cx, cy)i, the focal lengths (fx, fy)i, and a skew termq that is the tangent of the angle between the image axes. The extrinsic parameters form[R|T]ir and comprise the rotation matrix and translation vector that transforms 3D coordinates X(in homogeneous coordinates) fromOr to Oi. Thus, Eq. (3.1) describes the projective transform between a 3D point in the rig coordinate system to 2D pixels uin the image frame. The uresults are also in homogeneous coordinates and should be divided by the homogeneous scalar a to obtain final pixel values. The form of this projection will be used throughout the process. ui =Ki[R|T]irXr ⎡ ⎣ au av a ⎤ ⎦i = ⎡ ⎣ fx q cx 0 fy cy 0 0 1 ⎤ ⎦ i ⎡ ⎣ rxx rxy rxz tx ryx ryy ryz ty rzx rzy rzz tz ⎤ ⎦ ir ⎡ ⎢⎢ ⎣ X Y Z 1 ⎤ ⎥⎥ ⎦r (3.1) 3.3 Stereo Pose Optimization An overview of the workflow is provided in Fig. 3.2. At a high level, the process is divided into four main segments: input, setup, pose estimation, and pose validation. The following section will elaborate on each segment, providing necessary details for those interested in recreating the tool in a programming language of choice. 3.3.1 User Inputs First, specifications regarding the available imaging hardware are gathered. Specifically, the following information must be compiled: • Camera sensor specifications: – Full image size (sx, sy) (pixels) – Pixel size, (mm) • Camera orientation (landscape or portrait; see Sect. 3.3.3) • Camera stand orientation (horizontal or vertical; see Sect. 3.3.3) • A list of lenses available and their properties: – Make and model – Nominal focal length f (mm) – Minimum focal distance, smin (mm) – Aperture f -stop values, N(minimum and maximum) With the exception of the above hardware specifications, all of the other user inputs presuppose a knowledge of the planning process and will be described in detail in the following sections: • Physical size or coordinates of a bounding box that encloses the surfaces to be imaged • Bounding box margin • Euler angles that describe the viewing orientation (i.e., how to “look at” test object) • Space available around the part – Acceptable range for standoff distance (SOD) – Acceptable range for camera baseline (BL) – Acceptable range for camera perpendicular distance (PD)
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