Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based 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.

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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.@en

Wind loading is an essential aspect in the design and assessment of long-span bridges, but it is often not well-known and cannot be measured directly. Most structural health monitoring systems can easily measure structural responses at discrete locations using accelerometers. This data can be combined with reduced-order modal models in Kalman filter-based algorithms for an inverse estimation of wind loads and system states. As a further development, this work investigates the incorporation of Gaussian process latent force models (GP-LFMs), which can characterize the evolution of the wind loading. The Hardanger Bridge, a 1310 m long suspension bridge instrumented with a monitoring system for wind and vibrations, is used as a case study. It is shown how the LFMs can be enriched with physical information about the stochastic wind loads using monitoring anemometer data and aerodynamic coefficients from wind tunnel tests. It is found that the estimates of the modal wind loads and modal states obtained from a Kalman filter and Rauch–Tung–Striebel smoother are stable for acceleration output only, thus avoiding the accumulation of errors. The proposed approach demonstrates how physical or environmental data can be injected as valuable information for global monitoring strategies and virtual sensing in bridges.

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An application of inverse force identification of wind loads on bridges is presented. This contribution explores the extension of latent force models (LFMs) in Kalman filters. Specifically, it is shown how LFMs can be enriched with environmental information from wind data in order to realistically reflect the underlying physics behind the wind loads. This is demonstrated in a case study of a long-span suspension bridge equipped with a structural monitoring system, where an extensive data set of 103 time series of 30-minute events is used. The results show that the estimation of modal wind loads and modal response states is stable. Moreover, optimization of LFMs with maximum likelihood methods shows that optimized solutions match well with the actual (measured) wind load conditions. The work elevates the prospects of physics-informed LFMs with interpretable hyperparameters. @en

Fatigue assessment in offshore wind turbine support structures requires the monitoring of strains below the mudline, where the highest bending moments occur. However, direct measurement of these strains is generally impractical. This paper presents the validation of a virtual sensing technique based on the Gaussian process latent force model for dynamic strain monitoring. The dataset, taken from an operating near-shore turbine in the Westermeerwind Park in the Netherlands, provides a unique opportunity for validation of strain estimates at locations below the mudline using strain gauges embedded within the monopile foundation.

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When employing vibration-based damage detection methods for monitoring the structural health of bridges, it is often possible to increase damage feature sensitivity by focusing on local as opposed to global vibrations. This heightened sensitivity, however, comes at a cost: by moving towards the higher frequency ranges and more local behavior, the effects of environmental variability become increasingly pronounced. In an attempt to characterize and quantify the effect of specifically temperature variations on the local vibrations, an extensive long-term monitoring campaign was performed on the Haringvlietbrug, a steel box-girder bridge in the Netherlands. Temperatures were measured on various components of the bridge, including the top and bottom of the asphalt layers. It was found that complex temperature gradients are formed especially in situations where the radiation from the sun strikes the bridge at oblique angles. More importantly, the temperature variations in the asphalt layers were found to strongly impact the natural vibration properties of the bridge in the targeted high-frequency ranges. The obtained results provide valuable indications as to the environmental parameters to monitor when designing vibration-based structural health monitoring systems for local damage detection in bridges.@en

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.

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A vessel's response to waves is dependent on a large number of parameters, some of which are both frequency and direction dependent. To predict vessel response, these parameters are used to construct response amplitude operators (RAOs) that act as transfer functions between the directional wave spectra and the motion spectra of the vessel. In particular situations, however, vessel motions predicted using RAOs calculated with general-purpose radiation-diffraction codes and measured wave spectra are found to deviate from measured vessel responses. To address this problem, a methodology for calibrating RAOs based on measurements of the directional wave spectra and vessel motions is proposed. Use is made of a vector fitting method through which the frequency dependent hydrodynamic properties of the vessel can be approximated by a ratio of two polynomials, thus greatly reducing the number of parameters that need to be calibrated. The reduced set of parameters is subsequently related to previously identified causes of RAO inaccuracy in order to arrive at optimization algorithms for identifying more accurate RAOs from the measurements. It is shown that the RAOs can be improved with accuracy in situations where the discrepancies are caused by imprecise estimates for the vessel's radii of gyration, center of gravity, or viscous damping. When the discrepancies in the RAOs are related to the potential mass, damping and wave forces, however, the problem becomes highly non-convex and it is not possible to find a unique RAO that satisfies the data.

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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.

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Kalman-type filters for coupled input-state estimation can be used to estimate the full-field dynamic response of structures from only a limited set of vibration measurements. The use of these coupled estimators allows for response prediction to be performed in the absence of any knowledge of both the dynamic evolution and spatial distribution of the excitation forces, where often a set of response-driving equivalent forces is identified from the measurements. In this contribution, a rigorous analysis of the concept of equivalent force based response monitoring is performed, with the aim to clearly establish its limitations and ranges of applicability. It is shown that, unlike commonly assumed, the success of this type of response monitoring cannot be related solely to whether the chosen set of equivalent forces satisfy the controllability requirements, but will depend on the bandwith of the excitation forces in combination with the extent/characteristics of the sensor network. Arguments are instantiated using simple numerical examples where a comparison is made between the theoretical assumptions used to derive the filters and the physical situation. Included in the analyses are situations where (a) the applied and equivalent loads are concentrated and collocated, (b) the applied and equivalent loads are concentrated and non-collocated, (c) modal equivalent loads are used to represent concentrated non-moving forces, and (d) modal equivalent loads are used to represent concentrated moving forces. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.

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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.

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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 Bgsøysund 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 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 frequency-domain 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.

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Numerical predictions of the dynamic response of complex structures are often uncertain due to uncertainties inherited from the assumed load effects. Inverse methods can estimate the true dynamic response of a structure through system inversion, combining measured acceleration data with a system model. This article presents a case study of full-field dynamic response estimation of a long-span floating bridge: the Bergøysund Bridge in Norway. This bridge is instrumented with a network of 14 triaxial accelerometers. The system model consists of 27 vibration modes with natural frequencies below 2 Hz, obtained from a tuned finite element model that takes the fluid-structure interaction with the surrounding water into account. Two methods, a joint input-state estimation algorithm and a dual Kalman filter, are applied to estimate the full-field response of the bridge. The results demonstrate that the displacements and the accelerations can be estimated at unmeasured locations with reasonable accuracy when the wave loads are the dominant source of excitation.

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Kalman-type filters are being increasingly used to estimate the full-field dynamic response of structures from a limited set of vibration measurements. Various coupled input-state and coupled input-state-parameter estimation algorithms have been developed in this context, ranging from an initial formulation for use with linear reduced-order structural systems to alternative filters for dealing with acceleration-only data and recently also nonlinear model descriptions. The use of these algorithms allows for response prediction to be performed in the absence of any knowledge of the excitation forces, where often a set of response-driving equivalent forces is identified from the measurements. Up to now, the success of response estimation based on the identification of equivalent forces has been related only to whether these forces satisfy the so-called controllability requirements. In this contribution, controllability is shown to be an insufficient criterion for guaranteeing the accuracy of response estimates based on equivalent loading. Instead, the need for a new criterion is advocated, which would allow for a proper assessment of the applicability of equivalent force based monitoring to various engineering problems. Concepts are illustrated using simple numerical examples where a comparison is made between the true and assumed noise statistics and the response prediction accuracy for a number of distinct cases. These include situations where (a) the applied and equivalent loads are concentrated and collocated, (b) the applied and equivalent loads are concentrated and non-collocated, and (c) modal equivalent forces are used. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.@en

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. @en

Knowledge of the ambient loads are important for assessing the dynamic behavior of long-span bridges. However, the assumptions in the adopted load models used in the dynamic analysis leads to uncertainties in e.g. reliability assessments. To reduce the uncertainties, full-scale studies of the loads on existing structures can be performed. Recently developed methods for inverse identification can estimate the unknown forces on a structure using a limited set of dynamic response measurements and a numerical model of the structure. In this contribution, a pilot study of full-scale force identification is performed in a practical case study of the Bergsøysund bridge, a pontoon bridge with a floating span of 840 m. A state of the art filtering technique for input estimation is applied to identify the wave forces on the bridge using measured acceleration data. This article also presents a method for frequency-domain reconstruction of the wave forces, based on a parametric wave field model from measured wave elevation data. The obtained force estimates from the two approaches shows a reasonable agreement. The practical use of the identification techniques are reviewed from the viewpoint of this case study and sources of uncertainties are discussed.@en

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.

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The sea ice interaction with a structure may cause system changes and affect the feasibility of common approaches to track modal parameters. In this paper, a covariance-driven stochastic subspace identification method is used to identify the natural frequencies from 190 time series of ice actions against a lighthouse structure. The results are sorted into groups defined by the observed ice conditions and governing ice failure mechanisms during the ice-structure interaction. The identified natural frequencies vary substantially within each individual group and between the groups. Recordings with flexural failures and a north-south ice-drift direction consistently rendered the same identified frequencies, whereas crushing seemed to create large amounts of variability in the identified frequencies. The results show the need for more high-fidelity data to assess whether modern system identification methods can be used to monitor system changes and support decision-making for operations of structures in ice-infested waters, such as offshore wind structures.

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This work reports on experiments that were performed with a freely vibrating cylinder exposed to currents and placed near a plane boundary parallel to the cylinder axis. It is observed that the proximity of the boundary affects the vertical response of the cylinder in two ways: (i) for gaps between 0.75 and 2 diameters (D), the amplitude of oscillation is reduced; (ii) for gaps smaller than 0.75D, the cylinder impacts the boundary, resulting in an increase of amplitudes and frequencies of oscillations as the flow is accelerated. The in-line force acting on the cylinder is also examined, and the dependency of its harmonic components on the flow velocity and distance to the boundary is evaluated. Besides the typical amplification of the mean component inside the lock-in region, it is also observed that as the cylinder is placed closer to the boundary, the harmonic component with the frequency of the vertical oscillations increases, while the component with twice that frequency decreases in similar amount.

Based on the experimental observations, an existing wake-oscillator model for vortex-induced vibrations is enhanced in order to account for the effect of the boundary. The proposed model introduces an effective damper that is activated when the cylinder reaches a certain distance from the boundary, and a damper/spring set representing the rigidity of the boundary and the dissipation of energy due to impact.
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Suspension bridges with very long spans and slender designs are susceptible to large-amplitude dynamic excitation. Monitoring systems installed on bridges can provide measurement data (e.g. accelerations) and therewith valuable information on the true dynamic behaviour. This pilot study examines the possible use of recently developed methods for real-time response estimation at unmeasured locations. The methodology for response estimation is tested in a case study on the Hardanger Bridge, a 1310 m long suspension bridge in Norway, which has a network of twenty accelerometers. Two techniques, a joint input-state estimation algorithm (JIS) and a dual Kalman filter (DKF), are used to estimate the full-field dynamic response using data measured at the bridge and a reduced order structural model. The results show that the DKF is able to estimate accelerations fairly accurately. The JIS estimate, however, suffer from ill-conditioning and consequently show severe errors. Possible reasons for this ill-conditioning are briefly discussed.

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