Papers by Eliz-Mari Lourens
Mechanical Systems and Signal Processing, Feb 1, 2015
In structural dynamics, the forces acting on a structure are often not well known. System inversi... more In structural dynamics, the forces acting on a structure are often not well known. System inversion techniques may be used to estimate these forces from the measured response of the structure. This paper first derives conditions for the invertibility of linear system models that apply to any instantaneous input estimation or joint input-state estimation algorithm. The conditions ensure the identifiability of the dynamic forces and system states, their stability and uniqueness. The present paper considers the specific case of modally reduced order models, which are generally obtained from a physical, finite element model, or from experimental data. It is shown how in this case the conditions can be directly expressed in terms of the modal properties of the structure. A distinction is made between input estimation and joint input-state estimation. Each of the conditions is illustrated by a conceptual example. The practical implementation is discussed for a case study where a sensor network for a footbridge is designed.
CRC Press eBooks, Nov 18, 2016
This paper presents a verification of a state-of-the-art joint input-state estimation algorithm u... more This paper presents a verification of a state-of-the-art joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. A dynamic model of the footbridge is based on a detailed finite element model that is calibrated using a set of experimental modal characteristics. The joint input-state estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation.
Mechanical Systems and Signal Processing, Apr 1, 2019
The dynamic behaviour of long-span bridges is governed by stochastic loads from typically ambient... more The dynamic behaviour of long-span bridges is governed by stochastic loads from typically ambient excitation sources. In real life, these loads cannot be measured directly at full scale. However, inverse methods can be utilised to identify these unknown forces using response measurements together with a numerical model of the relevant structure. This paper presents a case study of full-scale identification of the wave forces on the Bergsøysund bridge, a long-span pontoon bridge that has been monitored since 2013. First, a numerical model of the structure is formed, resulting in a reduced-order state-space model that takes into account the frequency-dependent hydrodynamic mass and damping from the fluid, based on fitting of [.. 1 ]rational transfer functions. Using acceleration data of the structure measured during several events of moderate and strong seas, the wave forces are identified using stochastic-deterministic methods for combined state and input estimation. In addition, a separate frequencydomain assessment of the wave forces is performed, in which the spectral density of the first-order wave forces is constructed from an estimated directional wave field model driven by wave elevation data. When compared in the frequency domain, the force estimates from the two approaches are of comparable magnitude. However, uncertainties in the assumptions and models behind the force estimates from the two approaches still play a significant role.
Data-centric engineering, 2022
Wind turbine towers are subjected to highly varying internal loads, characterized by large uncert... more Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers. As the first large-scale wind farms reach their end-of-lifetime, attention is drawn to the importance of having accurate knowledge on structural reserves that can enable wind farm operators to make reliable decisions about lifetime extension in the future. In this contribution, a methodology for fatigue load monitoring on the basis of a sensor network is proposed and validated. The loads exciting the tower are estimated in conjunction with its dynamic response using a Gaussian process latent force model. Estimates of the full-field strain response can be derived, and therewith fatigue consumption at critical locations in the structure. The results confirm the potential of the proposed methodology for continuous tracking of fatigue life consumption in the structures supporting wind turbine rotors.
Data-Centric Engineering
Wind turbine towers are subjected to highly varying internal loads, characterized by large uncert... more Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dyn...
arXiv (Cornell University), Jul 12, 2022
Virtual sensing techniques have gained traction in applications to the structural health monitori... more Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopilebased offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPLFM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, unknown sources of excitation are modeled as a Gaussian process (GP) and endowed with a structured covariance relationship with response states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch-Tung-Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands. A number of test cases are conducted, where the performance of the GPLFM is evaluated for its sensitivity to varying operational and environmental conditions, to the instrumentation scheme of the turbine, and to the fidelity of the mechanical model. In particular, this paper discusses the capacity of the GPLFM to achieve relatively robust strain predictions under high model uncertainty in the soil-foundation system of the offshore wind turbine by attributing sources of model error to the estimated stochastic input.
A measurement campaign at the Hanko-1 channel marker in the Gulf of Finland is planned in order t... more A measurement campaign at the Hanko-1 channel marker in the Gulf of Finland is planned in order to monitor the forces leading to ice-induced vibrations by means of force identification. It is planned to identify the ice forces using a joint input-state estimation algorithm in conjunction with a modally reduced order model. The methodology is presented together with a finite element model and a detailed analysis that determines the optimal sensor network. The novel approach used to determine the optimal response measurement types and locations ensures the identifiability of the dynamic ice forces from only a limited number of sensors and a selection of vibration modes. The optimal sensor locations are discussed in view of specific challenges posed by the arctic environment. INTRODUCTION Channel markers and lighthouses are examples of structures that occasionally experience iceinduced vibrations. In order to understand the nature of these vibrations, several full-scale and laboratory ...
This paper presents a verification of a state-of-the-art joint input-state estimation algorithm u... more This paper presents a verification of a state-of-the-art joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. A dynamic model of the footbridge is based on a detailed finite element model that is calibrated using a set of experimental modal characteristics. The joint input-state estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is...
This paper presents a validation of a recently developed joi nt input-state estimation algorithm ... more This paper presents a validation of a recently developed joi nt input-state estimation algorithm for force identification and response estimation in structural dynam ics, using data obtained from in situ experiments on a footbridge. First, the algorithm is used to identi fy two impact forces applied to the bridge deck. Next, the algorithm is used to extrapolate measured ac celerations due to wind loading to unmeasured locations in the structure. The dynamic model of th e ootbridge used in the system inversion is obtained from a detailed finite element model, that is cali br ted using a set of experimental modal characteristics. The quality of the estimated forces and ac celerations is assessed by comparison with the corresponding measured quantities. In both cases, a ver y good overall agreement is obtained.
Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017
The evaluation of fatigue damage accumulation on wind turbine support structures under operationa... more The evaluation of fatigue damage accumulation on wind turbine support structures under operational conditions is heavily influenced by a number of uncertainties. These uncertainties may, firstly, be attributed to the highly variable and complex environmental loads, and secondly, to the unavoidable modelling errors which mainly originate from the inherent randomness in both material properties and fatigue resistance of structural components. It is therefore essential that assessment of fatigue life is carried out within a probabilistic framework; one that accounts for the stochastic nature of the phenomenon. The present study proposes a strategy for real-time reliability prediction of accumulated fatigue damage on wind turbine support structures by taking into account the above-mentioned uncertainties. To this end, the availability of structural monitoring information for the identification of the global response on wind-turbine support structures is exploited in order to address the discrepancies between actual and predicted damage accumulation. This is carried through utilization of an augmented version of the Kalman filter, which is capable of jointly estimating the response and the unknown inputs of the structure while relying on a limited number of noisy observations and a presumably uncertain model of the real system. A fixed-lag smoother is further deployed for the attenuation of the estimation error in an on-line mode and the smoothed stochastic estimates of the response are propagated over the model at the level of stresses. The accumulated damage along with the corresponding reliability level is finally predicted using a stochastic nonstationary fatigue damage model. The proposed scheme is demonstrated via implementation on the NREL 5.0 MW wind turbine under different operational conditions, on the basis of dummy vibration data generated via the FAST software. 76
Life-Cycle of Engineering Systems, 2016
Quasi-periodic loading resulting from waves and a rotationally sampled wind field often leads to ... more Quasi-periodic loading resulting from waves and a rotationally sampled wind field often leads to fatiguedriven designs for offshore wind turbine support structures. The uncertainty on wind and wave loading, together with large modelling uncertainties, lead to large discrepancies between the observed and predicted dynamic behaviour of these structures. Among many recent-developed techniques for monitoring of true fatigue damage development, two promising Kalman-type filters are compared, namely the recently proposed Dual Kalman filter (DKF) and the Gillijns and De Moor filter (GDF). The filters are applied to synthetic vibration data in order to predict the global response of a lattice support structure assuming large modelling uncertainties and no knowledge of the input forces. A critical assessment of both filters with regard to requirements on the available data and tuning of the filter parameters is presented.
Mechanical Systems and Signal Processing, 2021
This paper presents a general framework for estimating the state and unknown inputs at the level ... more This paper presents a general framework for estimating the state and unknown inputs at the level of a system subdomain using a limited number of output measurements, enabling thus the component-based vibration monitoring or control and providing a novel approach to model updating and hybrid testing applications. Under the premise that the system subdomain dynamics are driven by the unknown (i) externally applied inputs and (ii) interface forces, with the latter representing the unmodeled system components, the problem of output-only response prediction at the substructure level can be tailored to a Bayesian input-state estimation context. As such, the solution is recursively obtained by fusing a Reduced Order Model (ROM) of the structural subdomain of interest with the available response measurements via a Bayesian filter. The proposed framework is without loss of generality established on the basis of fixed-and free-interface domain decomposition methods and verified by means of three simulated Wind Turbine (WT) structure applications of increasing complexity. The performance is assessed in terms of the achieved accuracy on the estimated unknown quantities.
Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015), 2019
The traditional wind load assessment for long-span bridges rely on assumed models for the wind fi... more The traditional wind load assessment for long-span bridges rely on assumed models for the wind field and aerodynamic coefficients from wind tunnel tests, which usually introduces some uncertainties. It is therefore desired to develop tools that can utilize full-scale vibration response data from existing bridges in order to study the wind loading in detail for in-situ conditions. This paper presents a novel case study of inverse identification of dynamic wind loads on the 1310 m long Hardanger bridge, a suspension bridge equipped with a network of accelerometers. The identification method used is an extented Kalman-type filter for joint input, state, and parameter estimation. A system model considering the still-air modes in addition to a quasi-steady submodel for the self-excited forces of the bridge is presente. The coefficients for self-excited lift and pitching moment are considered unknown and are jointly estimated with the buffeting forces. 4421 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.
Journal of Wind Engineering and Industrial Aerodynamics, 2020
The traditional wind load assessment for long-span bridges relies on assumed models for the wind ... more The traditional wind load assessment for long-span bridges relies on assumed models for the wind field and aerodynamic coefficients from wind tunnel tests, which usually introduce some uncertainties. Recent studies have shown that large deviations can exist between the predicted and observed wind-induced dynamic response of suspension bridges. In studies of the dynamical behavior of bridges, inverse force identification methods can therefore be an interesting tool in the assessment of possible uncertainties involved in the modeling of wind loads. This paper presents a novel case study of the identification of the dynamic wind loads on the 1310 m long Hardanger bridge, a suspension bridge equipped with a monitoring system for wind and vibrations. The modal wind loads are identified from acceleration data using an algorithm for model-based joint input and state estimation. Several data sets with different wind conditions are presented. The wind loads are studied in the time and frequency domains and are compared to the mean velocity and turbulence characteristics of the wind.
Journal of Civil Structural Health Monitoring, 2018
Structural health monitoring (SHM) seeks to assess the condition or behaviour of the structure fr... more Structural health monitoring (SHM) seeks to assess the condition or behaviour of the structure from measurement data, which for long-span bridges typically are wind velocities and/or structural vibrations. However, in the assessment of the wind-induced response effects, models for the actual loads must be adopted, which introduces uncertainties. An alternative is to apply model-based inverse methods that consider the input forces unknown, and estimate these forces jointly together with the system states using limited vibration data. This article presents a case study of implementing Kalman-type inverse methods to a long-span suspension bridge in complex terrain, with the objective of estimating the full-field response. Previous studies have shown the local wind field is complicated, leading to uncertain load effects. We discuss the key challenges faced in the use of the methodology for the long-span bridges and present the results for a six hour storm event. The analysis show that the dynamic response contribution from the 14 lowermost bridge modes (up to 3 rad/s or 0.5 Hz) can be reconstructed with decent accuracy. The estimated response magnitude differs from the predicted response from design specifications, pointing to initial load model uncertainties that can be reduced to give greater confidence in the assessment of wind-induced fatigue, wind-resistant performance or other response effects.
Mechanical Systems and Signal Processing, 2019
The dynamic behaviour of long-span bridges is governed by stochastic loads from typically ambient... more The dynamic behaviour of long-span bridges is governed by stochastic loads from typically ambient excitation sources. In real life, these loads cannot be measured directly at full scale. However, inverse methods can be utilised to identify these unknown forces using response measurements together with a numerical model of the relevant structure. This paper presents a case study of full-scale identification of the wave forces on the Bergsøysund bridge, a long-span pontoon bridge that has been monitored since 2013. First, a numerical model of the structure is formed, resulting in a reduced-order state-space model that takes into account the frequency-dependent hydrodynamic mass and damping from the fluid, based on fitting of [.. 1 ]rational transfer functions. Using acceleration data of the structure measured during several events of moderate and strong seas, the wave forces are identified using stochastic-deterministic methods for combined state and input estimation. In addition, a separate frequencydomain assessment of the wave forces is performed, in which the spectral density of the first-order wave forces is constructed from an estimated directional wave field model driven by wave elevation data. When compared in the frequency domain, the force estimates from the two approaches are of comparable magnitude. However, uncertainties in the assumptions and models behind the force estimates from the two approaches still play a significant role.
Procedia Engineering, 2017
The problem of level ice interacting with compliant structures is addressed, where the ice loads ... more The problem of level ice interacting with compliant structures is addressed, where the ice loads can depend on the dynamical behavior of the structures. We are interested in a special type of ice-induced vibration, known as frequency lock-in, and characterized by having the dominant frequency of the ice forces near a natural frequency of the structure. It is shown that accurate estimates of the model parameters for the well-known Määttänen's model for ice-induced vibrations can be obtained from measurements of the structural vibrations and the ice velocity. Määttänen's model uses a state-dependent piecewise nonlinear function for the ice crushing strength, which leads to nonlinear negative damping in the equations of motion of the considered structure. The identification is achieved by means of an Unscented Kalman Filter using simulated noisy measurements of the structural behavior.
Mechanical Systems and Signal Processing, 2016
This paper presents a verification of a joint input-state estimation algorithm using data obtaine... more This paper presents a verification of a joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. The estimation of the input and the system states is performed in a minimum-variance unbiased way, based on a limited number of response measurements and a system model. A dynamic model of the footbridge is obtained using a detailed finite element model that is updated using a set of experimental modal characteristics. The joint inputstate estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation.
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Papers by Eliz-Mari Lourens