Unknown Excitation Research Articles

Online identification of time-variant structural parameters under unknown inputs basing on extended Kalman filter

To date, many parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter series methods are attractive in view of the efficient unbiased estimation in recursive manner. However, most of these methods are performed on the premise that the parameters are time-invariant and/or the loadings are known. To circumvent the aforementioned limitations, an online extended Kalman filter with unknown input approach is proposed in this paper for the identification of time-varying parameters and the unknown excitation. A revised observation equation is obtained with the aid of projection matrix. To capture the changes of structural parameters in real time, an online tracking matrix associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of extended Kalman filter, the recursive solution of structural states including the time-variant parameters can be analytically derived. Finally, using the estimated structural states, the unknown inputs are identified by means of least-squares estimation at the same time step. The effectiveness of the proposed approach is validated via linear and nonlinear numerical examples with the consideration of parameters being varied abruptly.

Joint Estimation of Multi-Scale Structural Responses and Unknown Loadings Based on Modal Kalman Filter Without Using Collocated Acceleration Observations

It has been proved that the usage of multi-type observations including global and local information for structural health monitoring (SHM) outperforms that of solo-type measurement. Kalman filter (KF) is a simple but powerful tool for the online state estimation. However, external force is required for the classic KF. Moreover, direct implementation of KF in time domain may be time consuming especially for large structures with many degrees-of-freedoms (DOFs) involved. From these points of view, the idea of modal Kalman filter (MKF) is introduced. An MKF-based approach is then proposed for joint estimation of multi-scale responses and unknown loadings with data fusion of multi-type observations. By using a projection matrix and the selected several modes, a modified observation equation in modal domain is derived. Limited multi-type measurements are fused together for online estimating multi-scale responses of structure at its critical locations. The unknown excitation is simultaneously identified by least squares estimation (LSE). The drift problem of the real time estimation of structural responses and unknown loads is avoided. The effectiveness of the proposed approach is numerically demonstrated via several examples. Results show that the proposed approach is capable of satisfactorily estimating the unmeasured multi-scale responses and identifying the unknown loadings.

A novel constrained UKF method for both updating structural parameters and identifying excitations for nonlinear structures

Finite element-based model updating of civil structures has been attracting increasing attention in structural health assessment and fragility analysis since several decades ago. However, the previously proposed finite element (FE) model updating methods for structures are either primarily limit to linear models under given external excitation or unknown excitation which should satisfy some assumptions. In this regard, this study proposes a novel constrained unscented Kalman filter (UKF) method for both updating structural parameters and identifying unknown external excitations without any assumption for strongly nonlinear structures. The unknown excitation (e.g., ground acceleration) can be preliminarily extracted from the state and measurement equations and then can be estimated by a recursive nonlinear least-square algorithm. To implement the recursive nonlinear least-square algorithm, a combined Matlab-OpenSees recursion platform herein is specially developed. It should be noted that certain constraints are necessary to be imposed on the sigma points to guarantee the propagation of the sigma points at each recursion step when the recursive nonlinear least-square algorithm is running. A three-story three-span steel frame and a three-span continuous reinforced concrete (RC) bridge, as two examples, are investigated for verifying the applicability of the novel constrained UKF method. The parameters which are most sensitive to the dynamic responses of structures are determined for identification. Subsequently, these structural parameters and the unknown excitation (e.g., ground motion) are jointly identified using the novel constrained UKF method based on partially measured noise-contaminated responses. In such a way, the feasibility of the Matlab-OpenSees recursion platform for structural dynamic inverse problems and the effectiveness of the novel constrained UKF for nonlinear model updating of structures are both verified.

Structural Damage Localization under Unknown Seismic Excitation Based on Mahalanobis Squared Distance of Strain Transmissibility Function

Due to the unpredictability of seismic excitation, the data-driven damage identification method, which only depends on the monitoring response data, has a good development prospect in structural health monitoring. In recent years, damage identification methods based on transmissibility function (TF) and Mahalanobis squared distance (MSD) have been widely studied. However, the existing methods are only applicable to damage warning. To overcome this limitation, an improved method for structural damage localization is proposed. Strain TF is used to eliminate the influence of unknown ambient excitation and unknown seismic excitation, which is more sensitive to local damage than traditional TF based on acceleration and displacement data. The MSD of strain TF is employed to construct a novel damage indicator that is used to identify the damage location. Two numerical simulations have been conducted to verify the feasibility of the method for damage localization and good anti-noise performance. In the case of the multi-damage condition, the novel damage indicator is performed to estimate the severity of damage to some extent.

Various damper forces and dynamic excitation nonparametric identification with a double Chebyshev polynomial using limited fused measurements

By introducting a double Chebyshev polynomial as a general nonparametric model for various nonlinear restorying forces (NRFs) and an updated observation equation, and with the help of an Updated Extended Kalman filter with unknown input (UEKF-UI) algorithm and a data fusion technology, a nonparametric identification approach for both NRFs at multiple locations and excitation for multi-degree-of-freedom (MDOF) lumped mass structures is presented. In order to investigate the generality of the proposed identification method, both numerical and experimental studies on different MDOF structure models equipped with a shape memory alloy (SMA) damper and/or a magnetorheological (MR) damper mimicking different types of nonlinearities that widely exist in practical engineering structures under unknown excitation are carried out. Identification results considering different initial estimation errors and measurement noise show that the NRF provided by different types of dampers at multiple locations, excitation and unmeasured dynamic responses can be identified nonparametrically with acceptable accuracy.

Sensor placement with optimal damage detectability for statistical damage detection

Damage diagnosis based on global structural vibrations critically depends on the sensor layout, in particular when a small number of sensors is used for large structures under unknown excitation. This paper proposes a sensor placement strategy that yields an optimized sensor layout with maximum damage detectability in selected structural components. The optimization criterion is based on the Fisher information, which quantifies the information that the damage-sensitive feature carries on the design parameters of structural components, such as material constants or cross-sectional values. It is evaluated using a finite element model, and considers the statistical uncertainties of the damage-sensitive feature. The methodology is shown for the stochastic subspace-based damage detection method, but can be applied to any damage-sensitive feature whose distribution can be approximated as Gaussian. It is suitable to find the optimal layout for a fixed number of sensors and to choose an appropriate number of sensors. Since the Fisher information is defined component-wise, the sensor layout can be tuned to become more sensitive to damage in local structural components, such as damage hotspots, non-inspectable components, or components that are critical for the safety and serviceability of the structure. For proof of concept, the sensor layout on a laboratory beam is optimized based on numerical simulations, and it is showcased that the optimal sensor layout leads to the highest damage detectability for experimental data.

A substructural and wavelet multiresolution approach for identifying time-varying physical parameters by partial measurements

Currently, most wavelet multiresolution based methods for the identification of time-varying structural physical parameters request the full measurements of all structural responses. All physical parameters including time-varying and time-invariant parameters are expanded by wavelet multiresolution, so it is only applicable to structures with a few degree-of-freedoms. In this paper, based on the substructural identification technique, a novel two-step approach is proposed to identify the time-varying physical parameters of linear structures with more degree-of-freedoms under unknown excitations using only partially measured responses. The whole structure is divided into several substructures. For a substructure concerned, the unknown interaction forces from neighboring structures are treated as ‘additional unknown inputs’ to the substructure, so the identification of complete structure can be transformed to the identification of each substructure with parallel computing in two steps. In the first step, the fading-factor generalized extended Kalman filter under unknown input algorithm is proposed to locate the time-varying physical parameters. In the second step, a synthesized method is developed for the quantitative identification of time-varying physical parameters based on the integration of wavelet multiresolution analysis and the generalized Kalman filter under unknown input. The time-varying structural physical parameters distinguished in the first step are expanded by wavelet multiresolution analysis. Then, the time-invariant physical parameters and the scale coefficients of time-varying physical parameters are identified by performing a nonlinear optimization with an objective function established by the extended Kalman filter under unknown input. Finally, the estimated scale coefficients are used to reconstruct the original time-varying structural physical parameters. Several numerical examples are used to demonstrate the effectiveness of the proposed approach.

Earthquake ground motion estimation for buildings using absolute floor acceleration response data

AbstractEarthquake ground motion information is useful for structural vibration control during earthquakes and post‐earthquake inspections of structural damage. However, in practice, the ground input data on a specific location may not be available because of instrumentation limitations or technical issues. Numerous studies have been devoted to identifying the unknown excitation. Most of these studies required responses in relative coordinates or from systems with direct feedthrough. On the other hand, acceleration monitoring systems in applications measure global responses of buildings, which corresponds to the absolute acceleration of a point on a structure, that is, the measured floor acceleration is the sum of the unknown earthquake‐induced ground motion and acceleration relative to the ground when an earthquake happens. In this study, a ground motion estimation approach was developed based on an extended Kalman filter (EKF) with an embedded Bayesian noise parameter updating technique, which requires a relatively small number of sensors for absolute acceleration measurements. Numerical simulations, a shaking table test, and a real‐world application were performed to demonstrate the applicability and accuracy of the proposed method.

A novel unknown-input and single-output approach to extract vibration patterns via a roving continuous random excitation

Operating deflection shape analysis allows investigating the dynamic behaviour of a structure during operation. It normally requires simultaneous, multi-point measurements to capture the response from an unknown excitation source (unknown-input and multiple-output), which can complicate its usage for structures without ease of access. A novel vibration pattern testing method is proposed based on a roving continuous random excitation employing a small robotic Hexbug device and a single-point measurement. The Hexbug introduces a random excitation in consecutive locations while roaming over the structure. The resulting multi-modal, time and location dependent response of the system is captured in a single location, and then analysed with a newly developed method based on empirical wavelet transform, multiscale morphological filtering and optimization to extract the excited vibration patterns. The efficiency of the proposed method is experimentally demonstrated on a free–free and a cantilevered beam with comparison to mode shapes extracted by hammer test. The validation highlights its ability to extract several vibration patterns from a long slender structure with good accuracy and robustness, with the general ability to expand the usability of an operating deflecting shape analysis.

A Generalized Identification of Joint Structural State and Unknown Inputs Using Data Fusion MKF-UI

The classical Kalman filter (KF) can estimate the structural state online in real time. However, the classical KF presupposes that external excitations are known. The existing methods of Kalman filter with unknown inputs (KF-UI) have limitations that require observing the acceleration response at the excitation point or assuming the unknown force. To surmount the above defects, an innovative modal Kalman filter with unknown inputs (MKF-UI) is proposed in this paper. Modal transformation and modal truncation are used to reduce the dimensionality of the structural state, and the accelerations at the excitation positions do not need to observe. Besides, the proposed MKF-UI does not require the assumption of unknown external excitation. Therefore, the proposed approach is suitable for the generalized identification of dynamic structural states and unknown loadings. The effectiveness and feasibility of the proposed identification approach are ascertained by some numerical simulation examples.

Identification of linear and nonlinear flutter derivatives of bridge decks by unscented Kalman filter approach from free vibration or stochastic buffeting response

This study presents an unscented Kalman filter (UKF) approach for identification of linear or nonlinear flutter derivatives (FDs) of bridge decks from free vibration or buffeting response time history. The nonlinear FDs, which are dependent on torsional vibration amplitude, are represented in polynomial functions of torsional displacement. The augmented state variables of the two degrees of freedom (2DOF) bridge deck system, which include bridge deck motions and unknown FDs, are estimated simultaneously with the UKF approach based on response measurement data. Firstly, the steady-state vortex-induced vibration and flutter of a streamlined bridge deck section are used to illustrate the performance of UKF approach in extracting nonlinear FDs. The equivalent linear FDs are also identified from the same response data which reveals the deficiency of the linear model. Secondly, the stochastic buffeting responses of the bridge deck contributed from two modal responses with linear FDs are generated, and the performance of UKF approach with unknown excitations is examined. It is pointed out that the buffeting response must be separated into two modal response components, such that the unknown buffeting force excitations can be modeled as white noise processes, and the UKF approach offers satisfactory identification of FDs.

Modal analysis of slow varying non-stationary vibration by model updating with Schur complement

This paper proposes a new algorithm for the online monitoring of slow varying modal parameters in vibrating structures subjected to unknown excitations. In this method, an Auto-Regressive (AR) model will be applied in a Short-Time Sliding Window (STSW) on measured signals. The model parameters will be determined and updated through the order and time obtained from the previous computational window. The recursive multivariable least-squares method is utilized in conjunction with the Schur complement method to find solutions. Numerical simulations of the gradual changing system acted by the random excitations and sinusoidal force are presented. Finally, the modal parameters for the multichannel data measured on an experimental steel plate emerging from the water are identified and compared with those obtained with the analytical method and Short-Time Fourier Transform (STFT), providing a powerful means of validating the proposed method.

Unsupervised Damage Detection for Offshore Jacket Wind Turbine Foundations Based on an Autoencoder Neural Network.

Structural health monitoring for offshore wind turbine foundations is paramount to the further development of offshore fixed wind farms. At present time there are a limited number of foundation designs, the jacket type being the preferred one in large water depths. In this work, a jacket-type foundation damage diagnosis strategy is stated. Normally, most or all the available data are of regular operation, thus methods that focus on the data leading to failures end up using only a small subset of the available data. Furthermore, when there is no historical precedent of a type of fault, those methods cannot be used. In addition, offshore wind turbines work under a wide variety of environmental conditions and regions of operation involving unknown input excitation given by the wind and waves. Taking into account the aforementioned difficulties, the stated strategy in this work is based on an autoencoder neural network model and its contribution is two-fold: (i) the proposed strategy is based only on healthy data, and (ii) it works under different operating and environmental conditions based only on the output vibration data gathered by accelerometer sensors. The proposed strategy has been tested through experimental laboratory tests on a scaled model.

Substructural identification with weighted global iteration considering unknown interfacial forces and external excitation

Many of available substructural identification (SSI) methods are performed with the interface forces and/or the external excitation being available. However, the prior knowledge of these two forces is not always possible. Therefore, an extended Kalman filter-based substructural identification with unknown interface forces (EKF-SSI-UIF) approach is proposed in this paper for simultaneously identifying the parameters and interface forces of the concerned substructure as well as the unknown excitation applied to it. A projection matrix is introduced, and then a modified observation equation is obtained. The recursive solution for the extended substructural states is analytically derived. Data fusion technique is employed to avoid the so-called low-frequency drift in the estimated quantities. Moreover, to assure the convergence and stability of the identified results, a weighted global iteration procedure is introduced. The effectiveness of the proposed approach is numerically demonstrated via several linear substructures and a substructure with local nonlinearity.

Nuclear Data Sheets for A=123

Experimental nuclear structure and decay data are evaluated for all of 15 known nuclides of mass 123 (Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, I, Xe, Cs, Ba, La, Ce). For each nuclide, detailed evaluated spectroscopic information is presented in each reaction and decay, and the best values combining all available data are recommended for level properties, γ and β radiations, and other spectroscopic properties. No excited states have been identified in 123Ru, 123Rh and 123Pd. For 123Ag, the long-predicted 1/2−β-emitting isomer has been identified at 60-keV by 2019Ch24 recently, resolving unknown excitation energies in the level scheme that was previously available only from isomeric decays of two isomers (202 ns and 393 ns) with the position and spin-parity of the former remaining unknown. Significant discrepancies exist between data on high-spin sequences based on 11/2(−) isomer in 123Cd (2002Hw01 and 2016Re05), which needs to be resolved with further experimental investigation. In 123Cs, the 114-ns isomer as the πg9/2 bandhead proposed at 231.6+x by 2000Gi12 has been resolved by 2004Si26 and 2004Si27 to be the 328-keV level that is proposed by 2000Gi12 as a separate level. Excited states in 123La and 123Ce have only been studied via (HI, xnγ) reactions, with their base levels and thus excitation energies remaining unknown. The β− decay schemes for daughter nuclide 123Cd, 123In and 123Sn and the ε decay schemes for 123Xe, 123Cs and 123Ba are considered incomplete due to large gaps between the highest observed excited levels and the Q-values. 123Sn, 123Sb, 123Te and 123I are the most extensively studied nuclides via various reactions and decays. This work supersedes earlier full evaluations of A=123 by 2004Oh11, 1993Oh12, 1980Ta02 and 1972Au10.

State-Input System Identification of Tall Buildings under Unknown Seismic Excitations Based on Modal Kalman Filter with Unknown Input

The seismic safety evaluation of tall building structures is necessary, but the multidegree-of-freedom feature of tall buildings increases the difficulty of joint identification of structural states, structural parameters, and unknown seismic excitations. Therefore, the state-input-system identification of tall buildings under unknown seismic excitations is the focus of this paper. To avoid the complex work of establishing a structural motion equation in absolute coordinate system, the simple structural motion equation in relative coordinates is directly adopted, but the measured absolute accelerations are used to establish the observation equation. In this way, the establishment of approximate assumptions is avoided, and direct feedback is not reflected in the observation equation. Also, the modal expansion technique is adopted to reduce the dimension of the motion equations and the size of the structural state to be identified. Different from the previous methods based on modal Kalman filtering, the unknown seismic excitation is treated as an unknown input instead of unknown modal forces in this paper, so the dimension of unknown forces in the identification process is not increased. When structural parameters of tall buildings are known, the generalized modal Kalman filtering with unknown input (GMKF-UI) proposed by the authors can simultaneously identify structural states and unknown seismic excitations by observing partial absolute acceleration responses. When extended to the case of unknown structural parameters, a generalized modal extended Kalman filtering with unknown input (GMEKF-UI) is proposed in this paper to simultaneously identify structural states, the unknown seismic inputs, and tall building systems using only partial absolute acceleration responses. Two numerical examples are used to verify the effectiveness of the proposed method.

Structural Damage Classification in a Jacket-Type Wind-Turbine Foundation Using Principal Component Analysis and Extreme Gradient Boosting.

Damage classification is an important topic in the development of structural health monitoring systems. When applied to wind-turbine foundations, it provides information about the state of the structure, helps in maintenance, and prevents catastrophic failures. A data-driven pattern-recognition methodology for structural damage classification was developed in this study. The proposed methodology involves several stages: (1) data acquisition, (2) data arrangement, (3) data normalization through the mean-centered unitary group-scaling method, (4) linear feature extraction, (5) classification using the extreme gradient boosting machine learning classifier, and (6) validation applying a 5-fold cross-validation technique. The linear feature extraction capabilities of principal component analysis are employed; the original data of 58,008 features is reduced to only 21 features. The methodology is validated with an experimental test performed in a small-scale wind-turbine foundation structure that simulates the perturbation effects caused by wind and marine waves by applying an unknown white noise signal excitation to the structure. A vibration-response methodology is selected for collecting accelerometer data from both the healthy structure and the structure subjected to four different damage scenarios. The datasets are satisfactorily classified, with performance measures over after using the proposed damage classification methodology.

Beam‐Driven Electron Cyclotron Harmonic Waves in Earth's Magnetotail

AbstractAlthough electron cyclotron harmonic (ECH) waves are the primary contributor to plasma sheet electron scattering loss, experimental verification of their most widely accepted excitation mechanism, loss‐cone instability, has been lacking for decades. Using 10 years of time history of events and macroscale interactions during substorms satellite observations, we investigate ECH wave properties near dipolarization fronts, the predominant source of such waves. To our surprise we find that more than 30% of observed ECH waves have moderately oblique (∼70°) wave normal angles (WNA), much less than the ∼85° expected from classical loss‐cone instability. These moderately oblique WNA ECH waves carry a strong field‐aligned electric field that is used to identify them. They are often observed with cold, dense electrons that exhibit enhanced parallel flux at a few hundred eV energy, which suggests that low‐energy counterstreaming beams (likely of ionospheric origin) might be their free energy source. By solving the linear dispersion relation for parameters representative of such plasma sheet electron distributions, we confirm that ECH waves at WNA ∼ 70° can indeed be driven unstable by such beams. Our work reveals a previously unknown excitation mechanism for ECH waves and exposes the need for quantifying the conditions for and relative importance of beam‐driven waves compared to those excited by the loss‐cone instability in Earth's plasma sheet.

Identification of model‐free hysteretic forces of magnetorheological dampers embedded in buildings under unknown excitations using incomplete structural responses

Magnetorheological (MR) damper is efficient to mitigate vibration of the structure subject to severe excitations. The identification of nonlinear characteristics of MR damper has attracted increasing attention. However, it is still challenging to identify model-free hysteresis of MR dampers embedded in structures using only incomplete measurements of structural responses under unknown excitations. In this paper, an identification technique is proposed for this tough task, namely, nonparametric identification of MR nonlinear restoring forces in building structures under unknown excitations. The proposed technique involves identifications in two stages. In the first stage, the identification of linear parameters of bare structure and MR dampers under low-level unknown excitations is conducted based on the generalized extended Kalman filter with unknown input (GEKF-UI) by the authors. In the second stage, the hysteretic forces of MR dampers are proposed to be treated as “unknown fictitious forces” to the corresponding linear bare structure identified in the first stage. The generalized Kalman filter with unknown inputs (GKF-UI) by the authors is adopted to identify all unknown inputs including the “unknown fictitious forces” originated from MR dampers. To demonstrate the proposed technique, some numerical examples are used to identify model-free hysteresis of single or multi MR dampers with different nonlinear restoring force models in shear frames under unknown external force excitations or unknown seismic excitations, respectively. Furthermore, experimental testing of the identification of model-free MR damper in a multi-story shear frame under unknown external excitation is conducted.

Weighted Transmissibility Assurance Criterion for Structural Damage Detection

Transmissibility function (TF) is a useful damage indicator for effective structural damage detection (SDD) under unknown external excitations. However, TF is not sensitive enough to structural damage under measurement noise. To improve the sensitivity of this indicator, a common model reduction technique, that is, the system equivalent reduction expansion process (SEREP) was first adopted to obtain reduced element stiffness matrices in the initial analytical finite-element model of a structure; this was used to weight the TFs in this study. Then, inspired by the cosine similarity measure, a novel damage indicator, called the weighted transmissibility assurance criterion (WTAC), was proposed for evaluating structural states. The effectiveness of the proposed damage indicator, WTAC, was first studied by a six-story frame in numerical simulations. The results showed that the TF weighted by the reduced element stiffness matrices improved the signal-to-noise ratio of the TF, and the proposed WTAC detected changes in structural states under noise. Moreover, further experimental studies on an aluminum alloy frame were conducted in order to assess the proposed WTAC. The results indicated that the proposed WTAC may provide a potential tool for effective SDD with strong robustness and stability for long-term monitoring on site.