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

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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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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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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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

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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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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The Norwegian Public Roads Administration is reviewing the possibility of using floating bridges as fjord crossings. The dynamic behaviour of very long floating bridges with novel designs are prone to uncertainties. Studying the dynamic behaviour of existing bridges is valuable for understanding the in-situ performance. We present a case study of the Bergsøysund Bridge, a 840 m long floating pontoon bridge located in Norway. An extensive monitoring system is installed on the bridge, including a network of accelerometers. A finite element model of the bridge is established. Using the measured acceleration output and recently developed Kalman filter based methods (a joint input-state (JIS) estimation algorithm and a dual Kalman filter (DKF)), we estimate accelerations at unmeasured locations. It is shown that the estimated response from the DKF agrees well with direct reference measurements. For the JIS, numerical instabilities in the estimates occur due to ill-conditioning of the matrices used in the system inversion.@en

Knowledge of excitation loads on bridges are important for reliable design. Load models are however prone to uncertainties. Force identification using dynamic response measured on full-scale structures can be used to reduce the
uncertainty. In this contribution, numerical simulations are performed to examine the feasibility of force identification on the floating pontoon Bergsoysund Bridge. We present a practical case study in which wave excitation forces and motion
induced forces are estimated using only acceleration output. The sensor network considered represents the monitoring system currently installed on the bridge. A reduced order model with 26 modes is used to represent the structure in the identification. Wave force time series are generated by Monte Carlo simulations, and the acceleration response is obtained from a frequency domain solution of the equations of motion. The generated acceleration data is polluted with noise and subsequently used for identification. The results show that a joint input-state estimation algorithm is able to adequately identify a subset of hydrodynamic forces acting on the pontoons in the presence of both measurement and model errors. The translational forces are identified with a larger accuracy than the moments. Lastly, considerations and improvements for an analysis with experimental field data are presented.@en