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2023 | Book

Model Validation and Uncertainty Quantification, Volume 3

Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics 2022


About this book

Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the third volume of nine 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:

Uncertainty Quantification and Propagation in Structural DynamicsBayesian Analysis for Real-Time Monitoring and MaintenanceUncertainty in Early Stage DesignQuantification of Model-Form UncertaintiesFusion of Test and AnalysisMVUQ in Action

Table of Contents

1. On Model Validation and Bifurcating Systems: An Experimental Case Study
This chapter demonstrates some of the problems that can arise when validating models of nonlinear bifurcating systems and the approaches that can avoid them. Validation is the process of determining the extent to which a model accurately represents the structure or system of interest. Additional care needs to be taken when attempting to validate models of nonlinear systems because of bifurcations that may occur. These phenomena present a difficulty for validation because if a model does not precisely capture the bifurcation points, then the model’s predictions could be very inaccurate, even if the model is (parametrically) very close to the real system. This situation could lead to a good model being dismissed if data generated close to a bifurcation point were used to validate it. In this chapter, experimental data were gathered from a three-storey shear building structure with a harsh nonlinearity between the top two floors, and bifurcations were observed in the structural response. Two models are constructed here, with parameters estimated using Bayesian system identification: a linear model and a nonlinear model. Selected features and metrics were then used to compare the model predictions to the test data. The results show that an appropriate model could be rejected if an inappropriate validation strategy is employed, purely as a result of slightly misplaced bifurcations. It is demonstrated that discrimination can be improved by taking modelling uncertainties into account as part of the validation process.
Keith Worden, David J. Wagg, Malcolm Scott
Chapter 2. A Comparative Assessment of Online and Offline Bayesian Estimation of Deterioration Model Parameters
Many preventive maintenance schemes for managing structural deterioration rely on stochastic deterioration models. In this context, continuous structural health information can be employed within a Bayesian framework to update the distributions of the time-invariant deterioration model parameters. Bayesian parameter estimation can be performed either in an online or an offline fashion. In this contribution, we investigate different online and offline algorithms implemented for learning the model parameters, and their uncertainty, considering a probabilistic model of fatigue crack growth that is updated with continuous crack monitoring measurements. The numerical investigations provide insights on the performance of the different algorithms in terms of accuracy of the posterior estimates and computational cost.
Antonios Kamariotis, Luca Sardi, Iason Papaioannou, Eleni N. Chatzi, Daniel Straub
Chapter 3. Finite Element Model Updating Using a Shuffled Complex Evolution Markov Chain Algorithm
In this paper, a probabilistic-based evolution Markov chain algorithm is used for updating finite element models. The Bayesian approaches are well-known algorithms used for quantifying uncertainties associated with structural systems and several other engineering domains. In this approach, the unknown parameters and their associated uncertainties are obtained by solving the posterior distribution function, which is difficult to attain analytically due to the complexity of the structural system as well as the size of the updating parameters. Alternatively, Markov chain Monte Carlo (MCMC) algorithms are very popular numerical algorithms used to solve the Bayesian updating problem. These algorithms can approximate the posterior distribution function and obtain the unknown parameters vector and its associated uncertainty. The Metropolis-Hastings (M-H) algorithm, which is the most common MCMC algorithms, is used to obtain a sequence of random samples from a posterior probability distribution. Different approaches are proposed to enhance the performance of the Metropolis-Hastings where M-H depends on a single-chain and random-walk step to propose new samples. The evolutionary-based algorithms are extensively used for complex optimization problems where these algorithms can evolve a population of solutions and keep the fittest solution to the last. In this paper, a population-based Markov chain algorithm is used to approximate the posterior distribution function by drawing new samples using a multi-chain procedure for the Bayesian finite element model updating (FEMU) problem. In this algorithm, the M-H method is combined with the Scuffled Complex Evolution (SCE) strategy to propose new samples where a proposed sample is established through a stochastic move, survival for the fittest procedure, and the complex shuffling process. The proposed SCE-MC algorithm is used for FEMU problems where a real structural system is investigated and the obtained results are compared with other MCMC samplers.
Marwan Sherri, Ilyes Boulkaibet, Tshilidzi Marwala, Michael I. Friswell
4. On the Dynamic Virtualization of a 3D-Printed Scaled Wind Turbine Blade
Innovative production techniques, such as 3D printing of metals, require attention both in the production and in the post-production phase. In fact, such manufacturing processes introduce higher margins of uncertainty compared to more canonical processes. As a consequence, they require an increased effort to succeed in delivering representations for the so-called dynamic virtualization process. Virtualization encompasses the ensemble of activities that are aimed at formulating the virtual model of a given structure and subsequently validating and updating this model in order to guarantee a realistic and accurate response prediction in a broad range of operating conditions. This chapter explores the main challenges related to the mentioned limitations, in the context of a down-scaled industrially relevant case study: a 3D-printed scaled titanium Wind Turbine (WT) blade. The scaled blade has been the object of a complete virtualization process: from the design by means of conventional WT blade tests, up to its “Digital-Twin” establishment, where we exploit state-of-the-art Virtual Sensing (VS) techniques, due to their intrinsic capability of “enriching” the high-fidelity model’s predictions with information extracted from test data.
Heorhi Brzhezinski, Silvia Vettori, Emilio Di Lorenzo, Bart Peeters, Eleni Chatzi, Francesco Cosco
Chapter 5. Wavelet Energy Features for Damage Identification: Sensitivity to Measurement Uncertainties
In vibration-based structural parameter identification, wavelet transformation has been widely used for extraction of damage pertinent data for onward identification of structural parameters or the occurrence of anomalies. Among wavelet-based techniques, the use of wavelet packet node energy (WPNE) as damage-sensitive features has attracted much research interest in more recent years. WPNE features contain detailed information which can be highly sensitive to local damages. However, most of the existing studies in the literature on using wavelet energy-based features have been numerical and involved idealised assumptions such as perfect and identical excitations among different tests. This paper presents an investigation into the tolerance of a wavelet packet energy with neural network approach to uncertainties in the input excitations and measurement noises. WPNEs are extracted from vibration signals from impact tests as feature proxies and a back-propagation neural network is used for classification. The method is firstly applied on a beam model using finite element simulations, in which variation in the excitations and measurement noises are incorporated to investigate the susceptibility of the approach to such uncertainties. Subsequently, the method is applied to the experimental data from the laboratory test of a steel beam. The results from both the numerical simulations and the experimental verification demonstrate that the wavelet energy with neural network approach to detecting structural changes is workable, and given a reasonably controlled impact test, it is possible to identify the initiation of damage with good accuracy.
Xiaobang Zhang, Yong Lu
Chapter 6. Advanced Meta-Modelling Techniques and Sensitivity Analysis for Rotordynamics in an Uncertain Context
It is essential to predict accurately the critical speeds and associated vibration amplitudes of rotating machineries to ensure a correct design to limit noise nuisance and fatigue failure. However, numerous uncertainties are present, due to environmental variations or manufacturing tolerances, e.g. and must be taken into consideration in the design stage to limit their impact on the system dynamics. These uncertainties are usually modelled with a probability law, and the dynamic response becomes stochastic. On the other side, during the design stage, a few key parameters, often called design parameters, are identified and tuned to ensure a robust conception of the rotor w.r.t. the uncertain model parameters. In this context, one must tackle a high-dimension parametric problem but numerous parameters of different nature. The efficiency of an advanced meta-modelling technique that couple polynomial chaos expansion and kriging is demonstrated here. The kriging efficiency is improved by introducing physical properties of the rotor. A finite element model of a rotor subjected to nine uncertain parameters is studied. The hybrid surrogate model gives a direct access to the Sobol indices, exploited to conduct an extensive sensitivity analysis.
E. Denimal, J.-J. Sinou
Chapter 7. Variational Filter for Predictive Modeling of Structural Systems
Bayesian inference offers a distinct advantage in predictive structural modeling as it quantifies the inherent epistemic uncertainties that arise due to observations of the system which are both finite in length and limited in representative behavioral information. Current research interest in the field of predictive structural modeling has emphasized analytical and sampling approaches to Bayesian inference, which have the respective advantages of either computational speed or inference accuracy. Recent work in optimization-based inference approaches have created new opportunities to balance these advantages and generate flexible, efficient, and scalable filters for joint parameter-state identification of complex nonlinear structural systems. These techniques, commonly referred to as variational inference, infer the hidden states of a system by attempting to match the true posterior and to a parameterized distribution. In this study we build on the theory of automatic differentiation variational inference to introduce a novel approach to variational filtering for the identification of complex structural systems. We evaluate our method using experimental observations from a nonlinear energy sink device subject to base excitation. Comparison between identification performed using our approach and the unscented Kalman filter reveals the utility of the variational filtering technique in terms of both flexibility in the stochastic model and robustness of the method to poor specification of prior uncertainty.
Alana Lund, Ilias Bilionis, Shirley J. Dyke
Chapter 8. Optimal Sensor Configuration Design for Virtual Sensing in a Wind Turbine Blade Using Information Theory
Optimal sensor placement (OSP) strategies in complex engineering systems aim to maximize the information gain from data by optimizing the location, type and number of the sensors or the actuators. It is used as a guide for assessing the structural condition, detecting damages and supporting the decision-making regarding structural health, safety and performance. In this work, a Bayesian optimal experimental design framework is used to optimize the type, location and number of sensors in composite wind turbine blades (WTB) excited by wind loads. The framework is based on a modal expansion technique for virtual sensing under output-only vibration measurements and on information theory for quantifying the information contained in a sensor configuration. The optimal sensor configuration optimizes a utility function associated with the expected Kullback-Leibler divergence (KL-div) between the prior and posterior distribution of the predictions at the virtual sensing (Ercan and Papadimitriou, Sensors 21:3400, 2021). The design variables include the location, type and number of sensors.
Tulay Ercan, Konstantinos Tatsis, Victor Flores Terrazas, Eleni Chatzi, Costas Papadimitriou
Chapter 9. Probability Bounds Analysis Applied to Multi-purpose Crew Vehicle Nonlinearity
The Multi-purpose Crew Vehicle (MPCV) Program Orion finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The hybrid parametric variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second-order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value or an interval of response values at a specific probability.
Daniel C. Kammer, Paul Blelloch, Joel Sills
10. A Physics-Based Reduction with Monitoring Data Assimilation for Adaptive Representations in Structural Systems
Digital twin representations have become an indispensable tool for delivering data-informed virtualizations of operating systems, especially in structural health monitoring applications. In this context, challenges arise when the response often shifts beyond regular operating conditions due to extreme events such as earthquakes or structural damage. Our work proposes a reduced order modeling for adaptive digital twins, for systems undergoing damage, condition deterioration, or experiencing stochastic excitation. Our approach initiates by featuring a projection-based reduced order model (ROM), relying on proper orthogonal decomposition (POD) and local subspaces to form a low-cost surrogate of the parametrized high-fidelity system that retains a physical connotation. However, extreme events induce loading conditions and model states that challenge the accuracy of such representations. To this end, we propose adopting the derived ROM as a forward simulator and adapt the projection basis on-the-fly during operation via a Gaussian processes regressor (GPR) scheme. During operation, the ROM framework receives response monitoring information from a sparse number of nodes. It employs a suitable condition indicator to highlight the potential low precision of the initial surrogate. Subsequently, the GPR-based scheme utilizes the monitoring input to reconstruct the current deformed configuration of the whole system in an online manner. In turn, this approximation serves as a damaged mode that enriches the projection-based ROM and enables online adaptivity. This coupling yields a ROM equipped with critical features for health monitoring applications such as (near) real-time basis refinement, signaling potentially irreversible consequences, and estimation of the uncertainty in the enrichment mode and the adapted ROM prediction.
Konstantinos Vlachas, Konstantinos Tatsis, Carianne Martinez, Eleni Chatzi
11. Comprehensive Testing Environment to Evaluate Approaches in Uncertainty Quantification for Passive and Active Vibration Isolation
This contribution introduces a one-mass oscillator subject to passive and active vibration isolation. In this context, passive means that the vibration isolation behavior only depends on preset inertia, damping, and stiffness properties. Active means that additional controlled forces change and adapt the damping properties to enhance the vibration isolation behavior. The purpose of the system is, eventually, to assess diverse measures in quantifying model form uncertainty of various mathematical models of the passive and active vibration isolation configuration in a consistent and comparable way. On the one hand, the one-mass oscillator is simple enough to be modeled analytically to establish a reference model. With its realization as an experimental test environment, it also allows more complex models such as a two-mass oscillator, which is still modeled analytically, and numerical finite and multi-body modeling. The test environment guarantees a consistent and comparable discussion about different approaches to quantify model form uncertainty in an uppermost comprehensive and extended way. First, the author derives the mathematical model for numerical simulation and explains the real test environment. An impulse excites the mass, and the mass responds with vibrations, given by velocity and acceleration responses. Second, preliminary studies for different passive and active damping cases identify the differences between numerical and experimental outcomes from simulation and test. The contribution closes with an invitation to continue and extend the work by a round robin within IMAC’s Model Validation and Uncertainty Quantification MVUQ community.
Roland Platz
Chapter 12. An Optimal Sensor Network Design Framework for Structural Health Monitoring Using Value of Information
A structural health monitoring (SHM) system is essentially an information-gathering mechanism. The information accumulated via an SHM system is crucial in making appropriate maintenance decisions over the life cycle of the structure. An SHM system is feasible if it leads to a greater expected reward (by making data and risk-informed decisions) than the intrinsic cost (or investment risk) of the information-acquiring mechanism incurred over the lifespan of the structure. In short, the value of information acquired through a feasible SHM system manifest into net positive expected cost savings over the life cycle of the structure. Traditionally, the cost-benefit analysis of an SHM system is carried out through pre-posterior decision analysis that helps one evaluate the benefit of an information-gathering mechanism using the expected value of information (EVoI) metric. EVoI is a differential measure and can be mathematically expressed as a difference between the expected reward and investment risk. Therefore, by definition, EVoI fails to capture the compounded savings over the life cycle of the structure (since it quantifies absolute savings). Unlike EVoI, we quantify the economic advantage of installing an SHM system for inference of the structural state by using a normalized expected-reward (benefit of using an SHM system) to investment-risk (cost of SHM over the life cycle) ratio metric (also called a risk-adjusted reward in short) as the objective function to quantify the value of information (VOI). 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 loss of contact between gate and wall, the “gap”) from the acquired sensor data. This paper proposes a sensor optimization framework that maximizes the net expected compounded savings achieved as a result of making SHM system-acquired data-informed life cycle management decisions. We also inspect the impact of various risk intensities of decision-makers on the optimal sensor design.
Mayank Chadha, Zhen Hu, Charles R. Farrar, Michael D. Todd
Chapter 13. Uncertainty Effects on Bike Spoke Wheel Modal Behaviour
In bicycles, one of the components which mostly influences the global system dynamics is the wheel-tyre subsystem. In this paper, the modal behaviour of a bike spoke wheel is numerically and experimentally investigated focusing on the characterisation of the spoke pretension effect, role of boundary conditions and parameter uncertainties.
A linearised parametric finite element model (FEM) is developed with the open-source code LUPOS in Matlab® environment. A detailed description of the model which includes several components, i.e. rim, hub, spokes and hub gears, is given. The FEM model is based on a reduced set of key nodes belonging to the wheel cross section profile, material and geometrical characteristic assignment and automated meshing procedure, allowing reduced computational effort and high model accuracy.
Experimental modal analysis is conducted on the wheel, and critical issues in the pole identification are highlighted, due to the high modal density given by the spokes and uncertainties. A further numerical investigation based on a variational approach is applied to investigate the role of system uncertainties on the modal parameters. The analysis shows that the identification issues are mainly related to spoke pretension, cross contact and boundary conditions. Moreover, the spoke pretension uncertainty induces a mistuning in the structure and the corresponding loss of axial symmetry. The fine model updating of the preliminary model is then achieved optimising geometrical and material properties of the components as well spoke pretension.
E. Bonisoli, A. D. Vella, S. Venturini
Chapter 14. Probabilistic Assessment of Footfall Vibration
As one of the serviceability limit states of structural design, excessive vibration has attracted more attention in recent years, with the design trend moving toward lighter and more slender structures. Footfall vibration contains high uncertainties in nature, with significant variations in walker weight, walking speeds, and dynamic load factor. Since conservative designs can often lead to significant cost premiums, this study focuses on the stochastic assessment of footfall vibration of on a composite steel floor to better understand the variation in performance of various design factors and better inform the ultimate decision-makers. To close the knowledge gap between academia and industry in this area, San Francisco State University and the University of South Carolina partnered with Arup through an NSF-funded Research Experience for Undergraduates (REU) program. A composite steel structure was modeled to resemble a typical office bay. The model was developed and analyzed in Oasys GSA. Monte Carlo simulation was used to quantify the probability of exceeding certain common vibration criteria. The results of this study would provide actionable guidance to stakeholders to weigh the benefits and costs between performance targets.
Chase Hibbard, Karly J. Vial, Aliz Fischer, Nick Sherrow-Groves, Jean M. Franco Lozada, Juan Caicedo, Zhaoshuo Jiang
Chapter 15. Digital Twinning of Modeling for Offshore Wind Turbine Drivetrain Monitoring: A Numerical Study
Failures in wind turbine drivetrain system including gearbox, bearings, and generator accounts for more than 60% of total wind turbine downtime. In this study, a mechanics-based digital twin technology is proposed to update drivetrain models parameters using measured data and predict the mechanics-based demand in drivetrain components. With the proposed mechanics-based digital twin, the alternations in the structural model parameters can be monitored and identified for damage diagnosis purposes. The proposed technology is implemented on a numerical torsional model of a wind turbine drivetrain system to update the drivetrain model using simulated data and predict the mechanics-based demand in drivetrain components. Implementation of this approach is used to update the failure models and estimate the remaining useful life of drivetrain components including gears and shafts.
Vahid Jahangiri, Mohammad Valikhani, Hamed Ebrahimian, Sauro Liberatore, Babak Moaveni, Eric Hines
Chapter 16. Prediction of Footbridge Vibrations and Their Dependence on Pedestrian Loads
Prediction of structural vibrations due to vertical loads generated by pedestrians is an assignment that many engineers involved with footbridge design have encountered. Often, the problem matter is not ultimate limit-state-requirements, but concern is on serviceability-limit-state requirements in the form of potential excessive structural vibrations. The nature of human locomotion dictates that the action of pedestrians on footbridges is random. This also has the effect that the footbridge vibrational response is random and potentially depends on a set of walking parameters (pacing speed, load amplifications factors, pedestrian weight, etc.) and the stochastic nature of these parameters. The paper will address issues of predicting footbridge vibrations in this context, taking offset in artificial footbridges. Monte Carlo simulations and Newmark time integration will be employed for determining footbridge vibrations.
Lars Pedersen, Christian Frier
17. Combining Simulation and Experiment for Acoustic-Load Identification
Bayesian inference is a technique that researchers have recently employed to solve inverse problems in structural dynamics and acoustics. More specifically, this technique can identify the spatial correlation of a distributed set of pressure loads generated during vibroacoustic testing. In this context, Bayesian inference augments the experimenter’s prior knowledge of the acoustic field prior to testing with vibration measurements at several locations on the test article to update these pressure correlations. One method to incorporate prior knowledge is to use a theoretical form of the correlations; however, theoretical forms only exist for a few special cases, e.g., a diffuse field or uncorrelated pressures. For more complex loading scenarios, such as those arising in a direct-field acoustic test, utilizing one of these theoretical priors may not be able to accurately reproduce the acoustic loading generated during the experiment. As such, this work leverages the pressure correlations generated from an acoustic simulation as the Bayesian prior to increase the accuracy of the inference for complex loading scenarios.
Garrett K. Lopp, Ryan Schultz
Model Validation and Uncertainty Quantification, Volume 3
Zhu Mao
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