scholarly journals Data-Driven Model Updating of an Offshore Wind Jacket Substructure

2021 ◽  
Author(s):  
Dawid Augustyn ◽  
Martin Dalgaard Ulriksen
Keyword(s):  
Parameter Estimation ◽  
Model Updating ◽  
Offshore Wind ◽  
Modal Parameters ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Modal Parameter ◽  
In Situ Data ◽  
Non Linear ◽  
Updating Procedure

The present paper provides a model updating application study concerning the jacket substructure of an o?shore wind turbine. Theupdating is resolved in a sensitivity-based parameter estimation setting, where a cost function expressing the discrepancy betweenexperimentally obtained modal parameters and model-predicted ones is minimized. The modal parameters of the physical systemare estimated through stochastic subspace identification (SSI) applied to vibration data captured for idling and operational states ofthe turbine. From a theoretical outset, the identification approach relies on the system being linear and time-invariant (LTI) and theinput white noise random processes; criteria which are violated in this application due to sources such as operational variability, theturbine controller, and non-linear damping. Consequently, particular attention is given to assess the feasibility of extracting modalparameters through SSI under the prevailing conditions and subsequently using these parameters for model updating. On this basis,it is deemed necessary to disregard the operational turbine states—which severely promote non-linear and time-variant structuralbehaviour and, as such, imprecise parameter estimation results—and conduct the model updating based on modal parametersextracted solely from the idling state. The uncertainties associated with the modal parameter estimates and the model parameters tobe updated are outlined and included in the updating procedure using weighting matrices in the sensitivity-based formulation. Byconducting the model updating based on in-situ data harvested from the jacket substructure during idling conditions, the maximumeigenfrequency deviation between the experimental estimates and the model-predicted ones is reduced from 30% to 1%.

Influence of farm, parity, season and litter size on the lactation curve parameters of white British dairy goats

1993 ◽  
Vol 57 (1) ◽  
pp. 99-104 ◽  
Author(s):  
J. C. Williams
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Litter Size ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Dairy Goats ◽  
Lactation Curve ◽  
Non Linear ◽  
Research Institute

AbstractThe following goat lactation model was fitted (using non-linear regression) to 407 lactations from five commercial goat dairies and one Research Institute goat herd: y = A exp (B(l + n'/2)n' + Cn' 2 - 1·01/n) where y = daily yield in kg; n = day of lactation (post parturition); and n' = (n -150)1100.Influence of farm, parity and season on the parameter estimates for 376 individual lactations was studied, using multiple linear regression. The models adopted were of the form: A = 1·366 + 1·122 × parity - 0·137 × parity2; ln(-B) = - 1·711 + 0·107 × parity + 0·512 season one; C = 0·037, with a standard deviation for A of 0·658, for ln(-B) of 0·636 and for C of 0·127.Influence of litter size on parameters was investigated for the Research Institute herd. There was no evidence of an effect on any of the model parameters.

scholarly journals How Can Spatially Distributed Uncertainties Be Included in FEA and in Parameter Estimation for Model Updating?

2003 ◽  
Vol 10 (1) ◽  
pp. 15-25 ◽  
Author(s):  
M.W. Zehn ◽  
A. Saitov
Keyword(s):  
Parameter Estimation ◽  
Model Updating ◽  
A Priori ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Fe Model ◽  
Weighting Matrix ◽  
Spatially Distributed ◽  
Updating Procedure ◽  
Parameter Estimation Methods

Owing to manufacturing composite materials and others show considerable uncertainties in wall-thickness, fluctuations in material properties and other parameter, which are spatially distributed over the structure. These uncertainties have a random character and can therefore not being reduced by some kind of mesh refinement within the FE model. What we need is a suitable statistical approach to describe the parameter changing that holds for the statistics of the process and the correlation between the parameter spatially distributed over the structure. The paper presents a solution for a spatial correlated simulation of parameter distribution owing to the manufacturing process or other causes that is suitable to be included in the FEA. The parameter estimation methods used in updating algorithms for FE-models, depend on the choice of a priori to be determined weighting matrices. The weighting matrices are in most cases assumed by engineering judgement of the analyst carrying out the updating procedure and his assessment of uncertainty of parameters chosen and measured and calculated results. With the statistical description of the spatial distribution at hand, we can calculate a parameter weighting matrix for a Baysian estimator. Furthermore, it can be shown in principle that with model updating it is possible to improve the probabilistic parameter distribution itself.

Experimental Non-Linear Model Updating Applied in Cylindrical Journal Bearings

2001 ◽  
Author(s):  
Katia Lucchesi Cavalca ◽  
Sérgio Junichi Idehara ◽  
Franco Giuseppe Dedini ◽  
Robson Pederiva
Keyword(s):  
Linear Model ◽  
Model Updating ◽  
Optimization Method ◽  
Model Parameters ◽  
Numeric Model ◽  
Rotating Systems ◽  
Non Linear ◽  
Symmetric Rotor ◽  
Set Up ◽  
Experimental Values

Abstract The present paper proposes the use of non linear model updating applying unrestricted optimization method, in order to obtain a methodology, which allows the calibration of mathematical models in rotating systems. An experimental set up for this purpose consists of a symmetric rotor, on a rigid foundation supported by two hidrodynamic cylindrical bearings and with a central disk of considerable mass, working as na unbalancing excitation force. Once the numeric and experimental values are obtained, error vectors are defined, which are the minimization parameters, through the variation of the numeric model parameters. The method presented satisfactory results, as it was able to calibrate the mathematical model, and then to obtain reliable responses for the physical system studied. The research also presents a contribution for the rotating machine desing area as it presents a relatively simple methodology on the updating and revalidation of computacional models for machines and structures.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

Simultaneous Dynamics-Based Visual Inspection Using Modal Parameter Estimation

2011 ◽  
Vol 23 (1) ◽  
pp. 180-195 ◽  
Author(s):  
Hua Yang ◽  
◽  
Takeshi Takaki ◽  
Idaku Ishii
Keyword(s):  
Parameter Estimation ◽  
Real Time ◽  
Visual Inspection ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Parameter ◽  
Resonant Frequencies ◽  
Modal Parameter Estimation ◽  
Non Destructive

In this study, we introduce the concept of dynamicsbased visual inspection with High-Frame-Rate (HFR) video analysis as a novel non-destructive active sensing method for verifying dynamic properties of a vibrating object. The HFR video is used for determining the structural dynamic properties of an object, such as its resonant frequencies and mode shapes, which can be estimated as modal parameters by modal analysis only when the object is excited. By improving and implementing a fast output-only modal parameter estimation algorithm on a real-time 2000-fps vision platform, the modal parameters of an excited object are simultaneously estimated as its input-invariant dynamic properties for dynamics-based visual inspection evenwhen the objects undergo different excitation conditions. Our simultaneous 2000-fps visual inspection system can facilitate non-destructive and longterm monitoring of the structures of beam-shaped objects vibrating at dozens or hundreds of hertz, and it can detect small changes in the dynamic properties of these objects caused by internal defects such as fatigue cracks in real time, even when their static appearances are similar. To demonstrate the performance of the proposed 2000-fps simultaneous dynamics-based visual inspection approach, the resonant frequencies and mode shapes for beam-shaped cantilevers with different artificial cracks and weights, excited by human finger tapping, were estimated in real time.

scholarly journals Operational Modal Identification of Time-Varying Structures via a Vector Multistage Recursive Approach in Hybrid Time and Frequency Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Si-Da Zhou ◽  
Li Liu ◽  
Wu Yang ◽  
Zhi-Sai Ma
Keyword(s):  
Parameter Estimation ◽  
Frequency Domain ◽  
Real Time ◽  
Time Estimation ◽  
Recursive Estimation ◽  
Modal Parameters ◽  
Time Varying ◽  
Modal Parameter ◽  
Structural Dynamic ◽  
Modal Parameter Estimation

Real-time estimation of modal parameters of time-varying structures can conduct an obvious contribution to some specific applications in structural dynamic area, such as health monitoring, damage detection, and vibration control; the recursive algorithm of modal parameter estimation supplies one of fundamentals for acquiring modal parameters in real-time. This paper presents a vector multistage recursive method of modal parameter estimation for time-varying structures in hybrid time and frequency domain, including stages of recursive estimation of time-dependent power spectra, frozen-time modal parameter estimation, recursive modal validation, and continuous-time estimation of modal parameters. An experimental example validates the proposed method finally.

Computational Modal Analysis of Half Scale Generic Business Jet Substructures

2020 ◽  
Author(s):  
Chris B. Lam ◽  
Chris K. Mechefske
Keyword(s):  
Model Updating ◽  
Primary Objective ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Widespread Application ◽  
Aircraft Fuselage ◽  
Business Jet ◽  
Updating Procedure ◽  
Skin Panels ◽  
Future Work

Abstract The primary objective of this work was to determine the modal parameters of two substructures of a half scale generic business jet model with pre-stressed skin panels. The effect that pre-stiffened skin panels has on the modal parameters of an aircraft fuselage subsection is not well documented in the literature. First, bending pre-stress on stiffened plates was empirically determined to increase stiffness without changing mode shapes. Second, preliminary finite element models of the substructures determined that the effect of skin pre-stress was significant in one of the two substructures. Finally, an updating technique to account for stiffening effects was proposed and validated to be effectively used in the substructure, improving computational results across all metrics. It is recommended that the model updating procedure developed in this work be used to model skin pre-stress for aircraft fuselage substructures. The improved accuracy of the updated computational model should be of significant interest to the aerospace industry. Future work can be performed to further develop the model updating technique introduced in this work to allow for widespread application.

Impact of Accelerometer Placement on Modal Extraction of Offshore Wind Structures

2020 ◽  
Author(s):  
M. Richmond ◽  
S. Siedler ◽  
M. Häckell ◽  
U. Smolka ◽  
A. Kolios
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Sensor Placement ◽  
Element Model ◽  
Offshore Wind ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Optimal Sensor Placement ◽  
Permanent Campaign

Abstract The modal parameters extracted from a structure by accelerometers can be used for damage assessment as well as model updating. To extract modal parameters from a structure, it is important to place accelerometers at locations with high modal displacements. Sensor placement can be restricted by practical considerations, and installation might be conducted more based on engineering judgement rather than analysis. This leads to the question of how important the optimal sensor placement is, and if fewer sensors suffice to extract the modal parameters. In this work, an offshore wind substation (OSS) from the Wikinger offshore wind farm (owned by Iberdrola) is instrumented with 12, 3-axis accelerometers. This sensor setup consists of 6 sensors in a permanent campaign where sensors were placed based purely on engineering judgement, as well as 6 sensors in a temporary campaign, placed based on a placement analysis. An optimal sensor placement study was conducted using a finite element model of the structure in the software package FEMtools, resulting in optimal layouts. The temporary campaign sensors were placed such that they, in combination with the permanent campaign, can be used to complete the proposed layouts. Samples for each setup are processed using the software ARTeMIS modal to extract the mode shapes and natural frequencies through the Stochastic Subspace Identification (SSI) technique. The frequencies found by this approach are then clustered together using a k-means algorithm for a comparison within clusters. The modal assurance criterion (MAC) values are calculated for each result and compared to the finite element model from which the optimal sensor placement study was conducted. This is to match mode shapes between the two and thus determine the importance of off diagonal MAC elements in the sensor optimization process. MAC values are also calculated relative to a cluster-averaged set of eigenvectors to determine how they vary over the 1.5 months. The results show that for all sensor layouts, the three lower frequency modes are consistently identified. The most optimized sensor layout, consisting of only 3 sensors, was able to distinguish an additional, higher frequency mode which was never identified in the 6-sensor permanent layout. However, the reduced sensor layout shows slightly more scatter in the results than the 6-sensor layout. There is a higher signal to noise ratio in the temporary campaign which results in scatter. We conclude that with an optimized placement of accelerometers, more modes can be identified and distinguished. However, off diagonal elements in the original MAC matrix, as well as loss of sensor degrees of freedom, can result in additional scatter in the measurements. Some of these findings can be extended to other offshore jacket structures, such as those of wind turbines, in that it gives a better understanding of the consequence of an optimal sensor placement study.

scholarly journals A non-linear neural network technique for updating of river flow forecasts

2001 ◽  
Vol 5 (4) ◽  
pp. 577-598 ◽  
Author(s):  
A. Y. Shamseldin ◽  
K. M. O’Connor
Keyword(s):  
Neural Network ◽  
Soil Moisture ◽  
River Flow ◽  
Model Updating ◽  
Ar Model ◽  
Soil Moisture Accounting ◽  
Non Linear ◽  
Auto Regressive ◽  
Input Model ◽  
Updating Procedure

Abstract. A non-linear Auto-Regressive Exogenous-input model (NARXM) river flow forecasting output-updating procedure is presented. This updating procedure is based on the structure of a multi-layer neural network. The NARXM-neural network updating procedure is tested using the daily discharge forecasts of the soil moisture accounting and routing (SMAR) conceptual model operating on five catchments having different climatic conditions. The performance of the NARXM-neural network updating procedure is compared with that of the linear Auto-Regressive Exogenous-input (ARXM) model updating procedure, the latter being a generalisation of the widely used Auto-Regressive (AR) model forecast error updating procedure. The results of the comparison indicate that the NARXM procedure performs better than the ARXM procedure. Keywords: Auto-Regressive Exogenous-input model, neural network, output-updating procedure, soil moisture accounting and routing (SMAR) model

Interpretation of Simulation Studies for Efficient Estimation of Population Pharmacokinetic Parameters

1993 ◽  
Vol 27 (9) ◽  
pp. 1034-1039 ◽  
Author(s):  
Ene I. Ette ◽  
Andrew W. Kelman ◽  
Catherine A. Howie ◽  
Brian Whiting
Keyword(s):  
Parameter Estimation ◽  
Efficient Estimation ◽  
Experimental Unit ◽  
Pharmacokinetic Parameters ◽  
Population Pharmacokinetic ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Good Precision ◽  
Simulation Studies ◽  
Individual Parameter

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (Φ) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The Φ approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the Φ for individual parameter estimation and the overall Φ for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.

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