Digital Engineering the Test and Modeling Process: Autonomous Methods for Reconciling Test and Model Results
Funded by AFOSR Young Investigator Award
The proposed research focuses on data-driven and deep learning approaches for autonomizing the validation and updating of digital models using Test and Evaluation (T&E) data. The first part of this research will create novel overlapping neural networks that leverage the principle of time reversibility to autonomously repair T&E data with missing data segments. The second portion will produce advanced mathematical techniques for infusing physics into autoencoder neural networks for extracting corresponding universal representations from both test and model results, facilitating the comparison of similar but disparate datasets. The third part will introduce and deploy new generator-discriminator-translator networks by leveraging the power of generative adversarial networks to autonomously update digital model parameters using T&E data. The new deep learning frameworks will be employed on data taken from computer-generated signals, numerical simulations, and experimental measurements.
Understanding the Nonlinear Dynamics Governing Vertical-Lift Vehicles with Variable-speed, Fixed Rotors
Funded by NASA Nebraksa EPSCoR
To meet growing demands for clean and affordable transit options in urban environments, NASA has targeted the creation of revolutionary vertical lift vehicles that introduce a new dimension into transportation. Although implementing electric rotors in such vehicles eliminates air pollution, they do not address the noise pollution produced by them. Furthermore, it is currently unknown how nonlinear interactions arise in the dynamics of VL vehicle and how these interactions affect the performance and noise production of the vehicle. As such, this research will produce a new understanding of the nonlinear dynamics governing VL vehicles with variable speed, fixed rotors. The dynamics of model VL vehicles will be investigated computational and analytically, and these results will be verified through comparable experiments. The resulting research will be disseminated through local and national conferences, a journal publication, and through webinars with NASA collaborators.
Determining the Interactions Between Bolts During Unwanted Loosening
Funded by NSF Nebraska EPSCoR FIRST Award and University of Nebraska-Lincoln Faculty Seed Grant
The loosening of screws and bolts during operation often results in catastrophic failure, as is evidenced by the 2013 Brétigny-sur-Orge train crash in Paris that resulted in seven deaths, 11 serious injuries, and 21 minor injuries. While loosening has been studied since the industrial revolution, mathematical and computational models for loosening have only emerged in the past three decades. Although these attempts have been successful in modeling loosening in a single bolt, they are too computationally expensive to reproduce loosening of multiple bolts at the same time. Consequently, there is a fundamental lack of understanding of loosening when multiple bolts and joints are involved. For example, it is commonly assumed that the loosening of a single bolt is representative of loosening in joints possessing multiple bolts; however, the PI’s preliminary studies have revealed that individual joints can interact with each other to exacerbate or, in some cases, even mitigate loosening. This research project will help the PI generate necessary preliminary data to write a competitive NSF CAREER proposal. The PI and his graduate student will construct and measure the loosening behavior of the joint in the experimental systems consisting of mechanical oscillators connected by bolted lap joints. The resulting measurements will be used to demonstrate the feasibility of modeling the behavior using low-order differential equations. For Research Objective 2, the research team will construct the experimental systems and perform preliminary measurements to demonstrate the connection between surface strains and internal contact area. For the educational component, the PI will participate in two workshops offered by the Online Learning Consortium, focusing on the gamification of education and game-based learning. The first workshop, entitled “Designing Gamified Learning Environments,” focuses on the introduction of game elements into traditional coursework. The second workshop, entitled “Designing Game-based Learning,” focuses on implementing gamification to create a game on a chosen topic. These workshops will provide the PI with the fundamental training needed to achieve Educational Objective 1 of the planned NSF CAREER application.
Detecting the Walking Phases with Raised Oxygen Costs for Targeted Therapy
Funded by University of Nebraska Collaboration Initiative
Increases in oxygen consumption due to aging in combination with reductions in maximal oxygen uptake (e.g., due to COVID) can severely limit walking mobility. Although modern laboratories can measure biomechanical changes with high fidelity, it is currently not possible to pinpoint which phases of the gait cycle cause increased oxygen consumption. This limitation prevents the design of enhanced therapies and assistive devices that target the most expensive phases. Our overall goal is to restore mobility and independence in patients affected by respiratory damage through enhanced therapies and assistive devices that specifically target walking phases with abnormally high oxygen costs. With this data preparation grant, we aim to generate simulation data that is representative of the existing experimental data and identify system identification methods suitable for detecting fluctuations in oxygen cost across the entire gait cycle. Our established method for capturing the oxygen cost of different phases of the walking cycle is based on using wearable robotics to perturb different parts of the gait cycle, leveraging the expertise of PI Malcolm with exoskeletons. The proposed research also relies on Co-PI Moores existing expertise using experimentally measured data to identify and model dynamical systems. As such, this collaboration presents a unique and timely opportunity to employ system identification to diagnose and treat patients with cardiopulmonary impairments, drawing upon the clinical expertise of Co-PI Pipinos. External grant applications will target NIH and NSF and will address the following two research questions: (1) How do oxygen costs vary in different phases of the gait cycle in healthy and pathological patients? (2) How do existing therapies and assistive devices alter oxygen costs in different phases of the walking cycle? The resulting research will produce a new understanding of oxygen costs during walking and lead to the creation of enhanced therapies and assistive devices.
In collaboration with Prof. P. Malcolm from the University of Nebraska-Omaha.
Reduced-order Modeling of Bolted Joint Loosening: Torque-Stiffness and Torque Loss Modeling
Funded by UNL UCARE
The purpose of this research is to construct a simple system that reproduces loosening in axial threaded (bolted) joints and allows for the measurement of the instantaneous loss of torque (either directly or by measuring rotation), such that a simplified but physically accurate mathematical model can be determined from the experimental data. We propose to achieve this by coupling two existing harmonic oscillators with an axial threaded joint (using a bolt) and exciting the structure (harmonically and impulsively) to induce loosening in the joint. The response of the oscillators will be measured using accelerometers, and this response will be used to validate the models. A key experimental advancement will be the use of digital image correlation to measure the rotation of the bolt head, which will provide the means to determine the instantaneous loss of torque in a cost-effective manner. More importantly, this will enable us to determine a suitable mathematical model, based on a first-order differential equation, for the instantaneous torque in the joint. The proposed model for the torque will be implemented into the existing models for the oscillators and the resulting system will be simulated and validated through comparisons with the measured response.
Targeted Energy Redirection and Vibration Isolation Through Breaking Dynamic Reciprocity
This research proposes a new approach for targeted vibration isolation based on the breaking of dynamic reciprocity through irreversible nonlinear energy transfers across scales to achieve one-way energy propagation. The research is motivated by a desire to minimize the loss of mechanical energy that arises when vibrations flow uninhibited through a structure (i.e., dissipation that transforms mechanical energy into heat energy). By breaking dynamic reciprocity, preferential energy pathways are introduced into the structure, which may be designed/tuned to manipulate the flow of mechanical energy throughout the structure. This research promotes a new paradigm for achieving extreme vibration isolation and targeted energy redirection by harnessing strongly non-reciprocal dynamics, opening the way for passively controlling the propagation of energy in complex systems. Current research focuses on theoretical and experimental studies in implementing and manipulating preferential energy pathways in multi-floored structures with planned applications to vibrations in aircraft, buildings, and vehicles.
C. Wang, K.J. Moore, “Energy Isolation in a Multi-floor Nonlinear Structure Under Harmonic Excitation,” Nonlinear Dynamics, (submitted on October 6, 2021).
C. Wang, K.J. Moore, “On Nonlinear Energy Flows in Nonlinearly Coupled Oscillators with Comparable Mass,” Nonlinear Dynamics, 103:343-366, 2021. http://dx.doi.org/10.1007/s11071-020-06120-5
Nonlinear Modal Analysis of Big-data Dynamical Systems
Experimental measurements are fundamental for the calibration and validation of computational models. When a model fails to reproduce measurements, engineers must identify and incorporate the missing dynamics to reconcile theoretical prediction and experimental observation. While linear analysis tools are well-established, practicing engineers face significant barriers when studying nonlinear vibrating systems; the reason is that, typically, nonlinearities introduce new dynamical phenomena that have no counterparts in linear settings. Consequently, engineers are often forced to neglect nonlinearity and must rely on linear models instead, resulting in the loss of essential dynamics (e.g., nonlinear resonances) that translates to a cost of approximately $1 trillion per year across all related industries. Therefore, there is a critical need for accessible frameworks for identifying and modeling nonlinear effects directly from measured data. Existing methods focus on applying complex analytical formulations to experimental measurements, which only add to the barriers faced by practicing engineers. Moreover, these methods are developed for small data sets and are not suitable for the large-scale data now acquired in vibration testing. This project aims to help break down these barriers by adopting a data-focused approach to explore the fundamental structure and behavior of nonlinear dynamical systems without relying on any analytical background.
Data-driven Identification of Nonlinear Dynamical Systems
System identification concerns the development of mathematical models using the measured output of a system to a given input. Methods for the identification of linear vibrating systems are well-established, whereas the identification of nonlinear systems has evolved into a flourishing field of research. However, these techniques are typically developed using small data sets acquired using discrete sensors and, as such, do not remain cost-effective when scaled to big data systems. Recently, data-driven methods have emerged as the frontrunner for resolving this issue, but, so far, have only been demonstrated using small data sets. Thus, this research focuses on the development of a scalable nonlinear system identification (NSI) methodology applicable to big data systems through the merger of existing NSI techniques and data-driven methods such as dynamic mode decomposition and machine learning. The first phase of this research focuses on the investigation of existing tools and the development of new ones using large datasets from video-based measurements of nonlinear dynamical systems. The second phase focuses on the development of the framework to handle big data systems and applications to turbulent fluid flows.
Non-reciprocal Energy Guiding Using Common Mechanical Connections
Mechanical joints are present in nearly every engineered structure, introduce significant nonlinearity into the governing physics through mechanisms such as hysteresis and micro-impacts, and can break symmetry when design appropriately. Previous studies demonstrated that the combination of asymmetry and nonlinearity results in the loss of reciprocity (a classical physical law that requires acoustic waves to propagate identically in both forward and reverse directions), such that uni-directional wave scattering can be realized. However, these studies focus on non-reciprocal lattices where the nonlinearity is introduced by transverse deflection in steel wires, resulting in hardening stiffness nonlinearity. Thus, this research will investigate the viability of common mechanical joints, which introduce both softening and hardening stiffness nonlinearity and nonlinear damping, for breaking reciprocity and creating mechanisms for controlling the propagation of energy. The first phase of this research investigates the effects of mechanical joints on reciprocity in otherwise linear structures using established reduced-order models (e.g., Iwan elements) followed by experimental verifications. The second phase focuses on the use of mechanical joints for controlling the propagation of energy through built-up structures. The third phase explores the construction of a robust, broadband energy absorber using mechanical joints as the primary nonlinearity.
Characteristic Nonlinear System Identification: A Data-Driven Approach for Local Nonlinear Attachments
This research introduces the characteristic nonlinear system identification (CNSI) procedure, which is a novel, data-driven approach for modeling the dynamics of local, nonlinear attachments. The CNSI method is unique in that it requires no prior knowledge of the linear or nonlinear dynamics of the primary structure or the attachment. Instead, the procedure relies entirely on the measured response of the attachment and its connection points (such that the relative motion can be computed), the mass of the attachment, and a model for its dynamics. The method is applied in two phases: first, the measured response is post-processed to obtain characteristic displacements and velocities (comparable to instantaneous amplitudes), and instantaneous frequency and damping curves based on the relative motion. Second, the analyst proposes a model for the dynamics of the attachment and performs a systematic identification of the unknown parameters in the model using the post-processed data from the previous phase. The result is a reduced-order model for the nonlinear physics governing the response of the attachment that incorporates both nonlinear stiffness and damping models.
- K.J. Moore, “Characteristic Nonlinear System Identiﬁcation: A Data-driven Approach for Local Nonlinear Attachments,” Mechanical Systems and Signal Processing, 131:335-347, 2019. http://dx.doi.org/10.1016/j.ymssp.2019.05.066
- A. Singh, K.J. Moore, “Characteristic Nonlinear System Identiﬁcation of Clearance Nonlinearities in Local Attachments,” Nonlinear Dynamics, 102:1667-1684, 2020. http://dx.doi.org/10.1007/s11071-020-06004-8
- A. Singh, K.J. Moore, “Identiﬁcation of Multiple Local Nonlinear Attachments Using a Single Measurement,” Journal of Sound and Vibration, 513:116410, 2021. http://dx.doi.org/10.1016/j.jsv.2021.116410
(a) Instrumented LO-NES system with the flexures, wires, NES, LO and applied force indicated by the arrow. (b) Instrumented Wing-NES system with a zoomed-in view of the NES.
(a) Comparison of the frequency-displacement plots with the instantaneous frequency computed using the experimental measurements and the identified model for the LO-NES and Wing-NES systems. (b) Comparison of the response for the NES in the LO-NES system and comparison of the response for the NES in the Wing-NES system.
Component-Scaled Signal Reconstruction for Enhanced Noise Filtration
This research introduced a new procedure for signal denoising based on linear combinations of intrinsic mode functions extracted using empirical mode decomposition. The method employed the standard empirical mode decomposition, with no enhancements to address mode mixing, to decompose the signals into functions. We leveraged the problem of mode mixing by constructing an optimal linear combination of the intrinsic to enhance the removal of noise. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the resulting denoised signal. The previous research thrust focused on the implementation of full-field displacement response of entire structures generated using digital image correlation.
- A. Singh, K.J. Moore, “Component-Scaled Signal Reconstruction for Enhanced Noise Filtration,” Journal of Vibration and Control, (in press; accepted on September 17, 2021).
Reduced-order Modeling of Bolted Joint Loosening: Interactions between Multiple Joints in Axial Rods
Funded in part by an Othmer Fellowship
Maintaining preload in bolted joints is critical for the safe and efficient operation of nearly all built-up structures. Dynamic loss of preload during operation occurs when sufficient shear force is applied to the joint such that slip is induced in at least the threads if not the entire bolt. Such shear forces are often realized when the joint is subjected to sustained vibrations, resulting in loosening over relatively long periods of time, or extreme shock loading where loosening occurs over fractions of a second. Modeling of joint loosening often focuses on complex analytical approaches or high-fidelity simulations using finite element models, and neither approach is able to simulate the interactions that arise between multiple bolts and joints during loosening. This research implements a recently developed reduced-order model for loosening in axial joints to investigate the interactions that arise between multiple joints including how these interactions affect loosening.
Research on Wave Interaction in Stacked Concrete Slabs
Funded by Air Force Office of Scientific Research through the Summer Faculty Fellowship Program
During a sled test, it is customary to stack concrete targets to create thick layers for warhead penetration tests. It has been observed that upon impact there is visible and immediate tensile damage on the concrete which is not present for single slabs. Further, the penetration resistance per linear foot appears to be much less if the thickness is comprised of stacked slabs vs nontouching slabs of the same total thickness. Research is needed on the phenomenon and perhaps wave interaction of penetration of warheads through slabs that are touching.
Targeted Vibration Isolation of Airline Interior Cabins from External Disturbances
Funded by UNL UCARE
This research focuses on dynamically isolating the interior cabin of an airplane from external disturbances by breaking dynamic reciprocity to achieve one-way distribution of energy in the system. Specifically, the cabin will be coupled to the exterior wall using strongly nonlinear springs with no linear stiffness component such that energy is allowed to flow from the cabin to the exterior, but energy will not be able to flow from the exterior into the cabin. The benefit of this design is that the cabin can be safely isolated from external disturbances, such as turbulence, which will improve passenger comfort and safety. We will investigate the targeted vibration isolation of the interior cabin theoretically and analytically using two numerical models: first, a highly reduced-order model composed of discrete oscillators representing the wings and fuselage, and, second, a finite element model of an already existing experimental model airplane. Both models will be numerically simulated using MATLAB and the analytical governing equations of motion for external disturbances such as gusts and turbulence, and the data will be analyzed to determine the best combination of parameters to ensure that the interior cabin is isolated from the exterior. A representative experimental system will be constructed and measured for impulsive and harmonic excitation to validate the computational study. The results will be published in a full-length journal article following the completion of the experiments.
Design of Nonlinear Vibration Absorbers to Enhance Aeroelastic Performance of High-aspect-ratio Wings in Commercial Aircraft
Funded by a UNO NASA EPSCoR Grant
If commercial airliners are to meet growing demands for increased performance and reduced environmental impact, they must adopt a significantly more efficient structural design. One promising approach that NASA is pursuing to enhance aerodynamic performance is using high-aspect-ratio (HAR) designs for the wing. However, the performance increases that HAR wings can provide are often offset by significant increases in the amplitude of dangerous vibrations that the wing experiences during flight. This research will develop a broadband vibration mitigation strategy for HAR wings by determining the effectiveness of single and multiple nonlinear vibration absorbers under realistic excitation. The absorbers will be studied experimentally for a half-airplane model provided by NASA and a full-airplane model created from NASA’s model. The resulting research will be disseminated through local and national conferences, a journal publication, and through webinars with NASA collaborators.
Manipulating Nonlinear Absorbers to Enhance Vibration Suppression in Ultra-high-aspect-ratio Wings
Funded by a UNO NASA Spacegrant
Growing public demand to reduce the environmental impact of commercial airliners requires that the industry increase overall airliner efficiency and performance. However, the design of commercial airliners has stalled for decades, with no changes to their overall shape. One approach targeted by NASA is to enhance the aerodynamic performance of current aircraft designs using ultra-high-aspect-ratio (UHAR) wings. While increasing the aspect ratio of wings enhances aerodynamical performance, this increase often significantly increases the amplitude of vibration that the wings experience during flight. Furthermore, due to the increased length of UHAR wings, vibrations with dangerous amplitudes are likely to occur at multiple frequencies compared to single frequencies in traditional wings. Accordingly, there is a critical need to develop vibration absorption solutions for UHAR wings capable of simultaneously suppressing vibrations at multiple frequencies. Without meeting this need, UHAR wings are unlikely to be installed on existing aircraft or those planned for construction in the next decades, greatly extending the current environmental impact of commercial airliners.
Nonlinear System Identification of Airplane Stores
This research investigates the effects of local nonlinear stores on the global dynamics of a model airplane. The stores are constructed and installed on the wings of the plane such that, when locked, they only contribute as “mass effects” to the plane and, when unlocked, they participate nonlinearly in the dynamics. The system is studied experimentally in three configurations: both stores locked (the baseline linear system), one store unlocked and both stores unlocked. The measured responses reveal that the unlocked stores drastically impact the participation of the first and second modes despite being local attachments. The global effects of the unlocked stores are further investigated by projecting the measured responses of each configuration onto the linear modes of the plane with both stores locked (computed using an updated finite element model). The projections are used to compute the instantaneous total energy in each mode, which reveals that the first and second modes decay at significantly faster rates compared to the linear baseline system when only one store is unlocked. However, when both stores are unlocked, the first mode decays at an increased rate, whereas the second mode reproduces the response of the linear baseline system. The results suggest that, when both stores are unlocked, they interfere constructively and destructively with respect to the first and second modes, and this hypothesis is tested by studying the nonlinear forces induced by the stores on the plane.
This research was conducted in collaboration with professors Alexander Vakakis and Larry Bergman at the University of Illinois.
J.D.E. Dalisay, K.J. Moore, L.A. Bergman, A.F. Vakakis, “Local nonlinear stores induce global modal interactions in the steady-state dynamics of a model airplane,” Journal of Sound and Vibration, 500:116020, 2021. http://dx.doi.org/10.1016/j.jsv.2021.116020
J.D.E. Dalisay, K.J. Moore, L.A. Bergman, A.F. Vakakis, “Effects of Nonlinear Stores on the Dynamics of a Computational Model Airplane,” Journal of Aircraft, 57(5):938-957, 2020. http://dx.doi.org/10.2514/1.C035736
Multi-harmonic Vibration Mitigation Through the Exploitation of Structural Instability
Funded by UNL UCARE, John Woollam Scholar, and William D. Pierson Scholarship
This research will introduce a new vibration mitigation approach capable of combatting unwanted vibrations at multiple frequencies using a single nonlinear absorber equipped with a Bunyan-Tawfick spring. This spring is unique in that its force-deflection curve consists of regimes of linear, zero-stiffness, and strongly nonlinear behavior that correspond to changes in how the spring deforms. The benefit of such a complex force-deflection curve is that it causes a simple oscillator to resonate at multiple frequencies. Thus, we hypothesize that an absorber with a Bunyan-Tawfick spring will effectively mitigate vibrations at multiple frequencies. We will determine the effectiveness of this absorber by computationally and experimentally implementing it onto a model airplane wing. The springs will be additively manufactured out of rubber and will be tested in multiple combinations to determine the best setup. The academic year research will focus on the theoretical and computational study of the absorber whereas the focus of the summer term will be on experimentally reproducing the theoretical result.
Estimation of Contact Areas in Bolted Lap Joints Through External Strain Measurements
Funded by UNL UCARE
This research focuses on estimating contact areas inside the interfaces of bolted lap joints by measuring the strains on the external surfaces induced by tightening the bolt. The research will be performed in series starting with a computational investigation using finite element models and concluding with experimental measurements of comparable systems. The finite element models will allow for high-fidelity predictions of the external strains while maintaining control of the loading conditions in the bolt. The finite element models will be used to determine the levels of strains induced by tightening a bolt, how these levels vary with bolt tension, and how the contact area in the interface correlates with the strains. The experimental investigation will focus on employing high-speed digital image correlation to measure the surface strains surrounding the bolt hole as the bolt is tightened using a digital torque wrench. The experimental measurements will be validated against the strains predicted by the finite element models, such that the resulting contact areas in the experimental systems can be estimated based on the external strains. The results will be published in a full-length journal article following the completion of the experiments.