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2024 | Book

Model Validation and Uncertainty Quantification, Volume 3

Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023


About this book

Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on:

Introduction of Uncertainty Quantification

Uncertainty Quantification in Dynamics

Model Form Uncertainty and Selection incl. Round Robin Challenge

Sensor and Information Fusion

Virtual Sensing, Certification, and Real-Time Monitoring

Surrogate Modeling

Table of Contents

Chapter 1. Introducing a Round-Robin Challenge to Quantify Model Form Uncertainty in Passive and Active Vibration Isolation

The aim is to quantify model form uncertainty in a passive and active vibration isolation system example during a round-robin challenge among IMAC’s Model Validation and Uncertainty Quantification (MVUQ) technical division. In this context, passive means that the vibration isolation only depends on preset inertia, damping, and stiffness properties. Active means that additional controlled forces enhance the vibration isolation. The focus is on studying multiple mathematical models of the same one-mass oscillator system to predict its structural dynamic behavior against a consistent set of experimental data to ensure direct comparability. The models differ in their scope and complexity; the experimental data will be offered to different research groups that are yet to be constituted during this IMAC. The participants are welcome to join the research group and discuss their results in an exclusive IMAC session reserved for round-robin results in the following years.

Roland Platz, Xinyue Xu, Sez Atamturktur
Chapter 2. An Uncertainty-Aware Measure of Model Calibration Flexibility

Physics-based models of structural dynamic systems are needed for various engineering applications, including structural controls and condition monitoring. These models often need to be calibrated against experimental measurements to mitigate uncertainties in poorly known model parameters and account for systemic model errors. In such a calibration campaign, under- or overfitting of a model to measured data may impede obtaining generalizable predictions. The underfitted calibration campaign fails to fully capture the underlying patterns, misses out on opportunities to learn from the measured data, and leads to an inferior predictive capability; while the overfitted calibration campaign may yield a satisfactory goodness-of-fit, it degrades generalizability, and in turn the usefulness of the calibrated model. There is a well-known trade-off between goodness-of-fit to measured data and generalizability in unmeasured settings. In this context, the generalizability of a model calibration campaign denotes the ability of the model to fit alternative datasets. For a given set of available experiments, determining the optimal flexibility of a model calibration campaign is necessary to achieve the maximum possible generalizability. This work presents a generally applicable metric to quantify the flexibility of model calibration that effectively takes these factors into account. We present the computational framework for the metric and demonstrate its application on a polynomial problem.

Xinyue Xu, Yang Yu, Roland Platz, Sez Atamturktur
Chapter 3. Quantifying Model Form Uncertainty in Spring-Mass-Damper Systems

Models built from coupled ordinary differential equations are common in mechanics, chemical kinetics, electrodynamics, and many other fields. A canonical example, in both theory and experiments, is a system of linked spring-mass-dampers. Modeling all interactions between these objects often becomes intractable either due to computational expense or incomplete knowledge of the system. Common reduced models may involve only interactions between a small subset of the spring-mass-dampers. But these simplifications can lead to high model error, rendering the model useless for prediction. In this work, we explore decreasing model error through interpretable model correction: an inadequacy operator augments the reduced model to form an enriched model. We calibrate the enriched model with hierarchical Bayesian inference and validate it with posterior predictive assessments. Physical theory informs the inadequacy operator, which contains terms to capture the effect of the omitted objects on the reduced model. Several analytical and numerical examples are given. Results show that most of the model error can be recovered with a simple time-varying inadequacy operator.

Rileigh Bandy, Rebecca Morrison
Chapter 4. Event Detection Using Floor Vibrations with a Probabilistic Framework

Using floor vibrations has shown potential in human detection for security and human health applications. A key aspect of these methodologies is identifying the event location on the floor. The excitation can be due to a step, a fall, or another type of activity. Wave propagation methodologies used for this purpose face challenges due to wave dispersion, multipath fading, and unknown energy dissipation mechanisms. A new model is proposed using a Bayesian probabilistic framework to identify the location of the excitation to enable human tracking. In the proposed model, combining information from multiple sensors, the amplitude of the acceleration is a function of the distance from the event location to the sensor’s locations, and the unattenuated amplitude, the localization of the event, and the decay rate are represented by random variables. Preliminary results of the probabilistic model were obtained from a ten-impact test bed. The results showed that the model could establish the most likely area of the event location while providing a measure of the uncertainty in the estimation. However, from a probabilistic perspective, the decisions about the localization must be withheld, considering the significant uncertainty in the predicted quantities.

Yohanna MejiaCruz, Juan M. Caicedo, Zhaoshuo Jiang, Jean M. Franco
Chapter 5. Advancing Model Credibility for Linked Multi-physics Surrogate Models Within a Coupled Digital Engineering Workflow of Nuclear Deterrence Systems

Sandia National Laboratories’ (SNL) digital engineering transformation initiative to accelerate product realization of nuclear deterrence (ND) systems has institutionalized quick turn modeling and simulation solutions. Surrogate modeling, coupled with model-based systems engineering (MBSE) using commercial-off-the-shelf (COTS) tools, moves the start line forward to inform design and requirements. Yet, this paradigm shift poses a large challenge in a high-security environment: quick-turn credibility solutions and verification, validation, and uncertainty quantification (VVUQ) to match the rate at which models are developed.This project demonstrates a model credibility process generating evidence to obtain buy-off from key stakeholders for rapidly developed (<2–3 hours) surrogate models within MATLAB/Simulink that interface with SNL-developed codes and MBSE in an extended integrated digital engineering workflow. The pilot project under the test of this process utilizes legacy higher fidelity and computationally expensive codes to inform mass/stiffness matrices for a structural and aero-dynamics trade study problem that verifies requirements—all on a standard desktop used by the customer vs. need for high-computing power and/or subject matter experts (SMEs).Our technical approach is directed at risk-informed decision-making for design engineers waiting on requirements, up to program leadership making key decisions. The steps include: (1) benchmarking against current VVUQ processes guided by SMEs; (2) uncertainty inventory including source definition, quantification, and mapping (model form, parametric, numerical, and environmental boundary conditions); (3) mapping of uncertainties to modeling activities; and (4) aggregation of evidence to fill gaps identified (e.g., peer review of methodology) or identify risks where additional testing or data may be required. This approach is underpinned by data engineering and configuration management that face need-to-know security challenges creating innovative capability adaptation for national security defense applications.In summary, digital engineering workflows utilizing multi-physics surrogate models integrated with MBSE and data management are the way of the future for SNL—assuming associated credibility evidence, accessibility, and usability advances in parallel. The techniques discussed are an integral step in this process and how these types of models can help inform higher fidelity models, qualification, and beyond.

Sofie W. Schunk, Shane McMurray, Jake A. Gonzales
Chapter 6. Estimating the Effect of Noise on Various ARMA-Based Damage-Sensitive Features

Vibration-based damage-sensitive features (DSFs) are a useful diagnostic tool in condition assessment of structural systems. While many DSFs are designed to be insensitive to random noise, in practice the presence of measurement noise can impede the identification of structural damage. In this study, four DSFs for use with autoregressive moving average (ARMA) models were examined with signal-to-noise ratios (SNR) ranging from 40 to 0.5 dB to evaluate the accuracy of damage estimation for increasing levels of noise. All structural responses were generated from a simulated cantilever beam model. Student t-tests were utilized to compare DSFs between the healthy state and an unknown state. The results indicated that the Cosh spectral distance DSF outperforms the other DSFs for SNRs less than 20 (i.e., greater than 1% of noise added). These results are consistent with prior work that demonstrated the robustness of the Cosh spectral distance as a DSF.

Emmett Lepp, Thomas Matarazzo
Chapter 7. Bayesian Model Updating for System and Damage Identification of Bridges Using Synthetic and Field Test Data

The finite element (FE) models of bridges are vastly used for structural analysis. However, these initial models – developed from as-built drawings – cannot adequately present the real-world bridges due to the inherent modeling uncertainties, irregularities during construction, or aging. The uncertain model parameters can be estimated using Bayesian model updating techniques wherein the initial model is updated using measured responses. The updated finite element model can be used for structural health monitoring and damage diagnosis. This study presents a new framework for operational monitoring and damage diagnosis of bridges through the integration of finite element models with bridge vibration responses and vehicle tracking data using a Bayesian FE model updating method. First, the framework is verified in a simulation environment via synthetic data obtained from a finite element model of the San Roque Canyon Bridge located in Santa Barbara, California. Then, the proposed method is employed using real-world data collected from a pair of full-scale girders at the Turner-Fairbank Highway Research Center in McLean, Virginia. The performance of the employed approach is evaluated through a comparison of the estimated model and previously observed damage in the structure. Taken together, the results demonstrate the capabilities of the proposed framework to diagnose potential damages in real-world bridge structures.

Niloofar Malekghaini, Farid Ghahari, Hamed Ebrahimian, Vinayak Sachidanandam, Eric Ahlberg, Matthew Bowers, Ertugrul Taciroglu
Chapter 8. Static and Dynamic Characterization of a Vibration Decoupling Element Based on a Metamaterial Structure

When targeting vibration isolation, metamaterials do represent very powerful solutions, given the extreme design flexibility that can be introduced. However, dealing with metamaterials ensuring wide bandgaps in vibration stop-band filter configuration is highly challenging. This chapter discusses the static and dynamic characterization of a decoupling mechanical system designed to act as a metamaterial stop-band filter in the 1500–15000 Hz frequency range. The system is produced in PA2200 polyamide powder by exploiting Selecting Laser Sintering technology. The external envelope of the system is a parallelepiped of 4 × $$\times $$ 4 × $$\times $$ 12 cm. Both contact and noncontact vibration approaches have been investigated to properly identify the effective bandwidth of the filter and the eventual structural resonances that might spoil its filtering capabilities in the target frequency range. The experimental data is used to update the linear numerical model exploited for the structure design.

Alessandro Annessi, Valentina Zega, Paolo Chiariotti, Milena Martarelli, Paolo Castellini
Chapter 9. Incorporating Uncertainty in Mechanics-Based Synthetic Data Generation for Deep Learning–Based Structural Monitoring

This chapter presents a hybrid deep-learning methodology for seismic structural monitoring, damage detection, and localization of instrumented buildings. The proposed methodology develops mechanics-based structural models to generate sample response datasets by accounting for the uncertainty of model parameters that can highly affect the estimation of baseline model nonlinear responses. The mechanics-based models are developed considering uncertainties in the stiffness, strength, and geometry of the baseline numerical model’s characteristics and elements. The baseline model is run multiple times with defined assumptions and variations in the selected parameters of the model. The uncertainty of model parameters is evaluated through the design of experiments methodology by employing the central composite design for sampling. A parameter effect analysis is used to assess the significance of the modeling input parameters on the selected structural output response, such as inter-story drifts. The generated sample response dataset is utilized for training a hybrid data-driven model for feature extraction. To select the damage-sensitive features, a convolutional neural network as the main feature extraction body of the network is used. In addition, wavelet packet–based nodal first temporal moments (energies) are also employed to boost the feature extraction power of the network as a complementary body. This data-driven model is designed to use global story-level noise-contaminated response measurements are employed as input for the data-driven model to perform damage detection and localization in a manner consistent with performance-based design criteria. The performance of the proposed methodology is studied in the context of numerical and experimental case studies developed based on the shake table testing of a concentrically braced frame subject to various input ground motion intensities at the E-Defense facility in Miki, Japan. The results show that the proposed methodology provides high accuracy in classifying and localizing various damage patterns.

M. Cheraghzade, M. Roohi
Chapter 10. Aerodynamic Load Estimation in Wind Turbine Drivetrains Using a Bayesian Data Assimilation Approach

This work explores a Bayesian data assimilation approach to estimate the aerodynamic input force on a wind turbine drivetrain. To this end, a high-fidelity wind turbine drivetrain model is created in SIMPACK to generate synthetic data. The NREL 5 MW wind turbine is considered as a case study in this work. The synthetic data include generator rotational speed, generator torque, rotor rotational speed, which are simulated and used as measurement data. A low-fidelity model of the drivetrain is developed for load estimation to accelerate the estimation process. The Bayesian data assimilation approach is employed to integrate synthetic data with the low-fidelity model to estimate aerodynamic input load.

Mohammad Valikhani, Vahid Jahangiri, Hamed Ebrahimian, Sauro Liberatore, Babak Moaveni, Eric Hines
Chapter 11. Rail Roughness Profile Identification from Vibration Data via Mixing of Reduced-Order Train Models and Bayesian Filtering

The increasing demand for mobility worldwide has led to an ever-increasing expansion of railway networks. Such a rapid expansion poses a challenge to guaranteeing quality, reliability, efficiency, and, most importantly, safety of railway infrastructure. Under this perspective, continuous monitoring emerges as a promising alternative to the traditionally adopted visual inspections, or inspections via portable measuring devices, which aim at collecting geometric data for the diagnosis and prognosis of defects in tracks. Recently, railway operators worldwide have adopted the use of dedicated Track Recording Vehicles equipped with optical and inertial sensors to collect data from tracks and assess their condition. Such an approach revolutionized rail condition assessment, introducing a mobile data acquisition platform for track inspection. On the other hand, the deployment of such specialized vehicles requires disruption of regular rail service, which hinders their frequent operation and thus the continuous collection of rail data. This work aims to tackle this limitation by examining an onboard monitoring (OBM) method that hinges on collecting vibration data from in-service trains. The proposed methodology relies on the collection of acceleration data from axle boxes of trains running at normal speeds. Its novelty lies in the usage of realistic train models and the consideration of the dynamic interaction between rails and trains, which is usually simplistically ignored. The adopted train models are reduced so as to decrease the required computational effort. The identification task is based on sequential Bayesian inference for joint input and state estimation, thereby also accounting for uncertainties related to the train model. Estimating the input leads to the identification of the pertinent rail roughness profile, which can subsequently provide information on the existence of isolated defects, for example, welded joints and squats, along the track system. This study is limited to reliable prediction of the dynamics of the train–track system in the vertical direction, but proposes methods and tools of general value.

Charikleia D. Stoura, Konstantinos E. Tatsis, Eleni N. Chatzi
Chapter 12. Optimal Sensor Placement for Developing Reliable Digital Twins of Structures

Sensor networks are mounted on structures to collect information for addressing a number of important but competing tasks involved in building a reliable digital twin from the collected data. These monitoring tasks include (1) modal identification under low vibration measurements assuming that the system can behave linearly, (2) physics-based model selection and model parameter estimation under various vibration levels activating nonlinear mechanisms at subsystem levels, (3) virtual sensing and response reconstruction over the whole body of the structure using the information from the limited number of sensors, and finally (4) structural health monitoring and damage identification (location and severity). Optimal sensor configuration (OSC) designs (type, number and location of sensors) have been developed in the past to address individual tasks, making assumptions about the loads, models and environmental conditions. However, the sensor network should be designed to collect data that are informative for all tasks simultaneously. In addition, the OSC design should be made robust to modelling, loading and environmental uncertainties. Cost issues related to budget availability for implementing and maintaining a sensor configuration should also be considered in the sensor network design. In this work, a multi-objective OSC framework based on utility functions that are built from information theoretic measures and cost considerations is presented for accounting simultaneously for the aforementioned tasks and thus using cost-effective information extracted from the physical sensing system for developing reliable digital twins. The Kullback-Liebler divergence is used to quantify the information gain from a sensor network, and heuristic algorithms to solve the multi-objective optimization problem are proposed.

Tulay Ercan, Costas Papadimitriou
Chapter 13. DataSEA: Mature, Modern Data Management Enabling Sustainable Data Strategy

We present DataSEA, a mature data management platform that emphasizes the role of metadata in contextualizing and finding data through an extended evidentiary cycle and complements existing report-oriented documentation practices to produce sustainable, long-lived data strategy.

Justin Wu, Stephen C. Jackson
Chapter 14. Optimal Sensor Placement Considering Operational Sensor Failures for Structural Health Monitoring Applications

A structural health monitoring (SHM) system acquires sensor measurements from which a structural state can be inferred. An updated understanding of the structural state is crucial in making appropriate maintenance decisions over the life cycle of the structure. However, the inferred structural state may be incorrect if the sensing system that initiates the SHM workflow is unreliable. The operational and environmental conditions that these sensors can face, in addition to normal manufacturing defects, result in varying functionality at different monitoring locations, at different times. Therefore, it is important to account for sensor reliability in the optimal sensor design process for the SHM system at the outset. In this chapter, we propose an optimal sensor design framework that accounts for the time-dependent reliability of the sensor network over the life cycle of the structure. The targeted objective function (Bayes risk) must consider the consequence of unreliable measurements over time, uncertainties in loading, sensor readings, and bias. This makes the Bayes risk a multidimensional integral with a non-linear integrand. The algorithm deploys the Bayesian optimization technique in tandem with univariate dimensional reduction and Gaussian-Hermite numerical approximation of the Bayes risk that catalyzes efficient numerical implementation of an otherwise computationally exhaustive process. We consider monitoring of a miter gate as the demonstration example and focus on the inference of an unknown and uncertain state-parameter(s) (i.e., damage from the loss of contact between the gate and wall, the “gap”) from the acquired sensor data.

Mayank Chadha, Yichao Yang, Zhen Hu, Michael D. Todd
Chapter 15. Sequential Harmonic Component Tracking for Underdetermined Blind Source Separation in a Multitarget Tracking Framework

Smart factories are composed of heterogeneous cyber-physical systems. In light of their complexity and the lack of transparency in their design, monitoring the health of these machines in real time is made possible by the use of nonintrusive sensors. Such sensors produce mixed signals capturing component-specific signatures. Retrieving the activation statuses of the components (over the different operating modes of a machine) is essential for estimating their associated performance indicators. This is a special case of underdetermined blind source separation (UBSS), yet a sensor fusion perspective is adopted in this chapter. A harmonic component detector produces observations in the time-frequency (TF) domain, inherently entailing noise-induced false alarms. The main contribution of this chapter consists of a clutter-resilient multiharmonic component tracking algorithm, based on the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter. Additionally, this chapter presents a track association algorithm adapting the results obtained in the multitarget tracking framework for unsupervised multilabel classification. The combination of the two algorithms mitigates typical difficulties encountered in traditional UBSS problems, such as nonstationary and partially coupled mode decomposition. The performance of the proposed technique is assessed on synthetic data.

Romain Delabeye, Martin Ghienne, Jean-Luc Dion
Chapter 16. Physics-Based Corrosion Reliability Analysis of Miter Gates Using Multi-scale Simulations and Adaptive Surrogate Modeling

Corrosion-induced crack initiation is primarily simulated in the meso-scale. Such physics-based simulation usually is computationally very expensive. It is computationally even more challenging, or impossible, if the meso-scale simulation model is coupled with macro-scale structural analysis for reliability analysis. This chapter breaks the computational barrier and makes it possible to perform physics-based corrosion reliability analysis of large structures using localized meso-scale simulations, by developing a novel adaptive surrogate modeling framework. A global surrogate model is first constructed at the macro-scale level to enable for the propagation of various input uncertainty sources, such as water levels and gap damage, to uncertainty of the stress response of the structure. After that, a local surrogate model is constructed to predict the local failure probability of any given location by accounting for uncertainty sources presented in both the macro- and meso-scale analysis models. To guarantee the accuracy of the local surrogate model and reduce the required number of meso-scale phase-field (PF) simulations for corrosion reliability analysis, an adaptive surrogate modeling method is proposed based on importance sampling (IS) and active learning to adaptively refine the surrogate model in critical regions. Corrosion reliability analysis of a miter gate structure is employed to demonstrate the efficacy of the proposed method. The result shows that the proposed framework can efficiently and accurately generate a failure probability map for a large structure like miter gate based on computationally expensive meso-scale PF simulations.

Guofeng Qian, Zhen Hu, Michael D. Todd
Chapter 17. Adaptive Randomized Sketching for Dynamic Nonsmooth Optimization

Dynamic optimization problems arise in many applications, including optimal flow control, full waveform inversion, and medical imaging, where they are plagued by significant computational challenges. For example, memory is often a limiting factor on the size of problems one can solve since the evaluation of derivatives requires the entire state trajectory. Additionally, many applications employ nonsmooth regularizers such as the L 1 $$L^1$$ -norm or the total variation as well as auxiliary constraints on the optimization variables. In this chapter, we introduce a novel trust-region algorithm for minimizing the sum of a smooth, nonconvex function and a nonsmooth, convex function that addresses these two challenges. Our algorithm employs randomized sketching to store a compressed version of the state trajectory for use in derivative computations. By allowing the trust-region algorithm to adaptively learn the rank of the state sketch, we arrive at a provably convergent method with near optimal memory requirements. We demonstrate the efficacy of our method on a parabolic PDE-constrained optimization problem with measure-valued control variables.

Robert J. Baraldi, Evelyn Herberg, Drew P. Kouri, Harbir Antil
Chapter 18. Predicting Nonlinear Structural Dynamic Response of ODE Systems Using Constrained Gaussian Process Regression

Identification and characterization of a nonlinear structural dynamic system often involve inferring unknown parameters from experimental data. Compared to its linear counterparts, nonlinear systems include additional parameters related to the restoring force, making identifiability more challenging. In this chapter, we propose to augment linear structural dynamic models with empirically inferred state-dependent parameters to predict the responses of nonlinear structural dynamic models. Specifically, we represent the state-dependent parameter by a constrained Gaussian process regression (cGP). In addition to computational efficiencies, the use of cGP to constrain the model from uncertainty by incorporating prior knowledge is intended to enhance extrapolation performance. To demonstrate the feasibility and effectiveness of the proposed approach, we focus on a simple ordinary differential equations (ODEs) case study and impose the monotonicity constraint on a state-dependent parameter to highlight the impact of prior knowledge on predictive performance.

Yishuang Wang, Yang Yu, Xinyue Xu, Sez Atamturktur
Chapter 19. Probabilistic Model Updating for Structural Health Monitoring Using a Likelihood-Free Bayesian Inference Method

Bayesian inference has received considerable attention and is an accredited framework in structural health monitoring (SHM) to evaluate structural integrity. In Bayesian inference, structural parameters are estimated as probability density distributions (PDF) using measurements, and associated uncertainty is then naturally quantified. However, the likelihood function as a crucial component in Bayesian inference is usually analytically intractable due to model complexity. Furthermore, solving the likelihood function is computationally demanding. This study investigates a novel likelihood-free and computationally efficient Bayesian inference method, for probabilistic damage detection through model updating in SHM. The method is based on normalizing flow and conditional invertible neutral network (cINN) and is called BayesFlow. It consists of a training phase and an inference phase. In the training phase, a summary and a cINN are trained simultaneously given synthetic data. The summary network targets on automatically learning the most useful features from raw data for damage detection rather than handcrafted ones. The cINN aims to learn the posterior distribution of model parameters by sampling a Gaussian latent distribution and using the trained inverse function. Based on the summary network and cINN, Bayesian inference can be performed efficiently without evaluating any likelihood function in the inference phase. The performance of the BayesFlow is verified with a benchmark example, an 18-story steel frame. Results show that BayesFlow provides more accurate damage identification with less measurement data and lower uncertainties compared to traditional sampling-based Bayesian inference method.

Jice Zeng, Michael D. Todd, Zhen Hu
Chapter 20. Deep Learning for Image Segmentation and Subsurface Damage Detection Based on Full-Field Surface Strains

Damage detection plays a key role in estimating the health of the structure. Accurate damage detection allows judging the reduced capacity of the structure and further retrofitting the damage. Error in damage detection may have catastrophic consequences, especially when the damage is subsurface that may accumulate over time. In this study, a deep convolutional neural network (CNN) based on full-field strain measurements is developed to localize subsurface damage. The dataset is prepared artificially by finite element simulation of rectangular metal bars having subsurface damage of varied length, size, depth, and direction of propagation. For the trained network, the Intersection of Union score is found to be 0.72 for both training and testing set. This implies that the model can localize the subsurface damage and can be further explored for applications in nondestructive testing. For continuously generated strain maps, applications in dynamics systems to study damage initiation and propagation can be studied for dynamic loading.

Ashish Pal, Wei Meng, Satish Nagarajaiah
Chapter 21. A Spatio-Temporal Model for Response and Distributed Wave Load Estimation on Offshore Wind Turbines

Sequential Bayesian inference schemes show tremendous potential for online information extraction from sparsely instrumented, uncertain dynamical systems. Within this context, notable paradigms are the tasks of state, input-state, and joint input-state-parameter estimation. A problem that has been scarcely studied in this context is the concurrent estimation of dynamic states and distributed loads on the basis of output-only (response) measurements. Examples of particular practical interest include the estimation of wind pressure on wind turbine blades, high-rise buildings and bridges, as well as wave loading in offshore structures. In such cases, the sensing of distributed inputs is heavily constrained by the instrumentation cost and the oftentimes limited access for sensor deployment. To tackle this challenge, this contribution investigates the fusion of Gaussian process regression (GPR) models with physics-based system representations for the recursive state and distributed wave load estimation on monopile offshore wind turbines. In particular, the distributed excitation is modeled with a GPR, which enables the implementation of a spatio-temporal filtering for the input process, while the system dynamics are represented by a physics-based model, which is in turn tailored to a recursive Bayesian scheme for the solution of the state estimation problem. The proposed approach is assessed in terms of a simulated case study on the finite element model of an offshore wind turbine.

Karin L. Yu, Konstantinos E. Tatsis, Vasilis K. Dertimanis, Eleni N. Chatzi, Andrew W. Smyth
Chapter 22. Identification of Axial Forces in Structural Rod Members Under Compression by a Modal Approach

The identification of axial forces in structural members by means of identified modal parameters has been the subject of numerous studies in the last decade. In most cases, the estimation of tensile forces is considered. However, only a very few publications also address the identification of compressive axial forces. One problem in modal testing of compression members is the control of the boundary conditions that have also an important influence on the dynamic behavior of the system. In this contribution, an experimental study is presented that shows how the modal behavior of a steel rod in a compression test changes with an increasing axial compression loading.

Volkmar Zabel, Mena Abdelnour
Chapter 23. Digital Twin Output Functions and Statistical Performance Metrics for Engineering Dynamic Applications

One of the most common uses of digital twins is to provide information to a user to aid in the decision-making process. The process a digital twin undertakes to generate information can be considered a digital twin output function. These can involve predictive simulations, historical trends, and other types of analysis using the data gathered directly from the physical twin and the models contained within the digital twin. Because of this dependency on model simulations and gathered data, the concept of trust is highly relevant to the development of digital twins. To evaluate the trust of a digital twin, specifically the quantitative aspects, the calculation of uncertainty and performance metrics is vital. This chapter considers how performance metrics can be used to compare the output functions of a digital twin to the measured quantities of interest in the physical twin, and thus provide additional information to establish trust in the digital twin that aids in decision-making. This approach will be demonstrated using an engineering dynamics example related to vibration testing.

Matthew S. Bonney, David Wagg
Chapter 24. Next-Generation Non-contact Strain-Sensing Method Using Strain-Sensing Smart Skin (S4) for Static and Dynamic Measurement

In this study, the next-generation non-contact strain-sensing method with the Strain-Sensing Smart Skin (S4), based on measuring strain-induced shifts in the emission near-infrared fluorescence spectra of single-walled carbon nanotubes (SWCNTs) embedded in a thin film (S4) on the surface of the specimen is presented. S4 is a direct sensing method. In the existing material and structural testing, strain mapping is performed using Digital Image Correlation (DIC), which is an indirect method that compares images of undeformed and deformed configurations to calculate strain maps. The results of the finite element method (FEM) analysis, measured S4, and DIC strain maps are presented. For static loading, the raster-scanned strain maps generated from S4 demonstrate more accurate strain maps (especially hotspots and stress/strain concentration areas with steep strain gradients), than DIC, when tested on acrylic specimens. Further, strain maps obtained from finite element analysis matched more closely with S4 as compared to DIC, demonstrating the superior quality of static strain mapping using S4. For dynamic loading, the single point S4 measurement also agreed well with the strain gauge at 3 Hz. The reference-free direct strain-sensing capability of S4 during static and dynamic loading presented in this study demonstrates the significant potential of the novel method as a promising next-generation strain measurement technology for field applications of structural non-destructive evaluation and structural health monitoring.

Wei Meng, Ashish Pal, Sergei M. Bachilo, R. Bruce Weisman, Satish Nagarajaiah
Chapter 25. Online Structural Model Updating for Ship Structures Considering Impact and Fatigue Damage

Naval ship structures (i.e., supports, hull, driving machinery, etc.) have various damage states that develop on short-term (i.e., impact) and long-term (i.e., fatigue) time scales. An up-to-date digital twin of ship structures that can deliver condition assessment in real time would empower a real-time decision-making framework to undertake informed response management. Together, the digital twin and decision-maker will increase ship engagement survivability during combat events and reduce the severity of long-term fatigue effects. A core challenge in digital twin development is the advancement of reliable methodologies that distinguish the short-term and long-term damage states. Furthermore, these methodologies must effectively assimilate large amounts of data into physics-based or data-driven prognostics models while operating on the naval structure’s resource-constrained computing environments and considering stringent real-time latency constraints. This work details the experimental validation of a specially designed multievent model updating framework that meets strict real-time latency constraints while operating on a system with limited computational resources. The proposed methodology tracks both impact and fatigue structural damage using a particle swarm that represents numerical models with varying input parameters, given set constraints for latency and computational resources. Experimental validation of the proposed methodology is undertaken using data collected from a structural testbed designed to provide responses representative of a ship subjected to fatigue and impact, considering a predetermined wave loading. Results demonstrate that a physics-based model of the structure can be updated in real time while distinguishing between plastic deformation caused by impact and continuous fatigue crack growth. Latency effects, resource-constrained accuracy, and parameter optimization of the proposed system are quantified and further discussed in this work.

Jason Smith, Austin R. J. Downey, Ben Grisso, Alysson Mondoro, Sourav Banerjee
Chapter 26. Detuning Optimization of Nonlinear Mistuned Bladed Disks Using a Probabilistic Learning Tool

This chapter deals with the detuning optimization of a mistuned bladed disk in the presence of geometrical nonlinearities. A full data basis is constructed by using a finite element model of a bladed disk with cyclic order 12, which allows all the possible detuning configurations to be computed. It is then proposed to reformulate the combinatorial optimization problem in a probabilistic framework using and adapting the recent probabilistic learning on manifolds (PLoM) tool to the detuning context. The available full data basis is used in order to validate the proposed method.

Evangéline Capiez-Lernout, Christian Soize
Chapter 27. Model-Based Inspection Planning for Large-Scale Structures Using Unmanned Aerial Vehicles

This chapter proposes a model-based inspection planning framework for damage diagnostics and maintenance optimization of large-scale deteriorating structures. An objective function is constructed using the definition of cost per unit time (CPUT) based on the three key parameters of unmanned aerial vehicle (UAV) inspection: inspection distance, inspection interval, and crack limit for repair action. To accelerate the process of optimizing the expensive-to-evaluate function, a Bayesian optimization is employed which improves the time and computational efficiency. The results demonstrate that the proposed method is able to efficiently determine the optimal parameters of UAV inspection parameters and continuously update the information model.

Zihan Wu, Jice Zeng, Zhen Hu, Michael D. Todd
Chapter 28. The Effect of Temporal Correlations on State Estimation Through Variational Bayesian Inference

Effective health monitoring in dynamic systems hinges on the proper estimation of the system’s state. As one of the most powerful methods of state estimation, variational Bayesian inference provides a flexible framework for making probabilistic inference about the state of a system. This method approximates the latent variables’ posteriors by minimizing the evidence lower bound (ELBO) loss function, which is an estimate of the information lost by approximating the true posterior with the selected variational family. This chapter focuses on the flexibility of the variational family and investigates the effect of considering dependency between the latent variables on the quality of posteriors, with respect to applications in structural health monitoring. The most common assumption made for the variational family is mean-field Gaussian, restricting the posterior’s space by independent Gaussian distributions. As this space does not realistically represent the relation between the dynamic system’s parameters, in this study, temporal correlations are added to the family’s covariance matrix structure. To evaluate the effect of the temporal off-diagonal covariance matrix on the performance of the inference, a numerical simulation of a linear single-degree-of-freedom system is utilized. The results of employing this covariance structure in the variational family are discussed from the accuracy, robustness, and computational cost standpoints. The findings show that for this linear system, the estimates of the parameters would not be meaningfully enhanced by adding the temporal dependency to the mean-field structure of the variational family.

Motahareh Mirfarah, Alana Lund, Shirley J. Dyke
Chapter 29. On the Selection and Validation of Component Damage Models for Prediction of Damage-State Behavior of a Truss Bridge

Structural health monitoring has seen significant progress in recent decades and offers major potential benefits in terms of life-cycle management of engineering infrastructure compared to traditional monitoring and maintenance methods. However, many challenges remain, including the lack of availability of sufficient damage-state data from structures of interest on which to validate physics-based models, which can be used to simulate the behavior of structures in their damaged conditions. This can potentially be avoided by validating the damage models at the components or subassemblies where damage would be expected to be found. It is hypothesized that the uncertainty quantified at the component level can then be propagated to the assembly level, thereby avoiding the requirement for damage-state data from the assembly.This chapter presents an investigation of the process described above, where component-level damage-state data is used to select and validate predictive damage models of the struts of a truss bridge, which are then built into an assembly model using dynamic substructuring. The validated assembly-level damage predictions are then compared to a test dataset covering a range of damage conditions in the assembly, and the candidate component-level damage models are compared against each other in terms of accuracy of fit to the test data.

James Wilson, Paul Gardner, Graeme Manson, Robert J. Barthorpe
Chapter 30. Surrogate Aerodynamics Modeling Applied to Surrogate Structural Dynamical Systems

Surrogate modeling can be used to rapidly develop and test a complex system whose broad characteristics can be simplified to answer specific questions. In turn, the inputs to these systems can also be converted into surrogates that represent real test scenarios, all of which drive the design process. The driver is to accelerate product realization by means of digital engineering practices.Our team at Sandia National Laboratories has developed a workflow that combines aerodynamic and structural surrogate models to analyze the effects of broad component parameters on the primary modes of a system. Given a desired preliminary design, a surrogate model is created which can be used to obtain mode shapes and frequencies that, ideally through proper modeling and understanding, are representative of the full system. Furthermore, our team has developed a range of surrogate structural dynamics models in the interest of a “ground-up” approach, wherein the simpler models are used to inform each subsequent, more complex iteration.An aerodynamic model is also created from the expected conditions the structure will be subjected to. Power spectral density (PSD) is extracted and converted into pressure data and further into forces applied to the structure, providing the capability to fully analyze the modal behavior of the system via the interfacing of surrogate models. An additional challenge addressed is a quick-turn model credibility process to match the speed at which these surrogate models are developed.The surrogates facilitate rapid simulation and design changes, significantly cutting the time and computing power required to obtain modal and test information compared to high-fidelity alternatives.

Jonathan R. Smith
Chapter 31. Footbridge Vibration Predictions and Interaction with Walking Load Model Decisions

Vibrations in footbridges generated by pedestrians are a matter of concern, typically because there is the risk that vibration thresholds may exceed resulting in an unacceptable serviceability-limit-state.There are challenges involved with predicting vibration levels at the design stage as the engineer in charge of predictions needs to make a number of choices for his calculations, for instance, regarding the load model for the pedestrians and the adjoining parameters (walking parameters). Through sensitivity studies employing artificial footbridges, the chapter will investigate the impact selected choices will have on the outcome of bridge vibration response predictions. In the chapter, a stochastic representation of the load will be considered, and hence the response calculations will end up in a stochastic representation of footbridge response.The way to arrive at stochastic representations of bridge response will be by employing Newmark time integration and Monte Carlo simulations. The action in focus is the vertical load by pedestrians, and likewise, it will be the vertical footbridge response that is focused on.

Lars Pedersen, Christian Frier
Chapter 32. Assembling Uncertainty Effects on the Dynamic Response of Nominally Identical Motorbike Components

The chassis and swingarm are the main components of the motorbike frame. The dynamic response of these components strongly influences the frame flexibility and consequently the motorbike dynamics. However, there may be variability in nominally identical manufactured components. The uncertainty may arise from many sources including geometric tolerances, material properties, and variability in the manufacturing and assembling process, for example, adhesive bonding of hollow parts. The presence of uncertainties can significantly alter motorbike component dynamic response and modal properties, and thus their overall performance during a racing competition. Therefore, competitive riders test several components during the racing weekend to find the specific motorbike frame with which they are more comfortable.In this chapter, experimental modal analyses have been carried out on the flexible components of a motorbike frame. The experimental campaign results have demonstrated significative differences in frequency response functions, natural frequencies and damping of motorbike components. Modal assurance criterion and other indexes have been used to compare mode shapes of the seemingly identical components and to assess possible crossing and veering phenomena, due to uncertainty.

Elvio Bonisoli, Luca Dimauro, Simone Venturini, Lorenzo Peroni
33. Correction to: Assembling Uncertainty Effects on the Dynamic Response of Nominally Identical Motorbike Components
Elvio Bonisoli, Luca Dimauro, Simone Venturini, Lorenzo Peroni
Model Validation and Uncertainty Quantification, Volume 3
Roland Platz
Garrison Flynn
Kyle Neal
Scott Ouellette
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