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Andrew W Smyth

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Papers by Andrew W Smyth

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

by Eleni Chatzi and Andrew W Smyth

International Journal for …, Jan 1, 2010

This paper investigates the XFEM-GA detection algorithm proposed by Rabinovich et al. on elastost... more This paper investigates the XFEM-GA detection algorithm proposed by Rabinovich et al. on elastostatic problems with different type of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the Extended Finite Element Method (XFEM) as the forward problem and Genetic Algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems. In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular shaped holes. Measurements are obtained from strain sensors which are attached to the surface of the structure at specific locations and provide the target solution to the Genetic Algorithm. The results show convergence robustness and accuracy provided that sufficient number of sensors are employed and sufficiently large flaws are considered.

Application of differential GPS sensing on long-span bridges with accelerometer data fusion

by Eleni Chatzi and Andrew W Smyth

Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty

by Eleni Chatzi and Andrew W Smyth

Structural Safety, Jan 1, 2010

Experimental application and enhancement of the XFEM-GA algorithm for the detection of flaws in structures

by Eleni Chatzi and Andrew W Smyth

Computers & Structures, Jan 1, 2011

The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previo... more The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previously been shown to be very effective in the detection of flaws in structures. By this approach, the XFEM is used to model the forward problem and a GA is used as the optimization scheme, converging to the true flaw. The convergence is obtained by minimizing the error between sensor measurements and data obtained by solving the forward problem.

Nonlinear System Identification: Particle-Based Methods

by Eleni Chatzi and Andrew W Smyth

Encyclopedia of Earthquake Engineering, 2014

Failures Associated with the 2004 Mindulle Typhoon in Taiwan

Geotechnical and Geological Engineering, 2007

On July 2, 2004, a 2000-km southwest air current following the Mindulle Typhoon caused serious da... more On July 2, 2004, a 2000-km southwest air current following the Mindulle Typhoon caused serious damages to infrastructures in Taiwan. The disaster resulted in extensive geological and structural failures, mainly as a result of debris flow. Some of the sites were subjected to types of repeated failures compared to previous typhoons. Some structural failures were attributed to geotechnical failures. It is decided to document and identify causes for some of these major failures triggered by typhoons. The case history showed significant implications to future disaster prevention and management works. New challenges were posed in geotechnical engineering design in encountering rainfall-induced failures.

Benefit-Cost Analysis for Earthquake Mitigation: Evaluating Measures for Apartment Houses in Turkey

In the wake of the 1999 earthquake destruction in Turkey, the urgent need has arisen to evaluate ... more In the wake of the 1999 earthquake destruction in Turkey, the urgent need has arisen to evaluate the benefits of loss mitigation measures that could be undertaken to strengthen the existing housing stock. A cost benefit analysis for the implementation of various seismic retrofitting measures is performed on a common and vulnerable type of apartment building located in Istanbul. The analysis was performed probabilistically, through the development of fragility curves of the structure in its different retrofitted configurations. By incorporating the probabilistic seismic hazard for the region, expected losses were obtained for arbitrary time-horizons. By including realistic cost estimates of the retrofitting schemes and costs of direct losses, one can estimate the benefit of the retrofitting measures in present day values. A sensitivity analysis was performed to determine the effects of varying cost parameters and also the assumed cost of human lives. The analysis implies that, even when considering only direct losses, all of the retrofitting measures considered are very desirable for all but the very shortest time-horizons. The sensitivity analyses conducted suggests that this conclusion is very robust for a wide range of estimates regarding costs of mitigation, discount rates and time-horizons even if no fatalities are associated with the collapse of the building. The methodology developed here can be extended to an entire region by incorporating additional structure types, soil types, retrofitting measures etc. It is hoped that this work can support some of the most urgent decisions and serve as a benchmark for more realistic and targeted cost-benefit analyses

Instructional & Technological Innovations to Attract & Retain Undergraduates to Engineer the Built Environment

International Conference on Engineering Education, Aug 18, 2002

Abstract Columbia University's Departments of Civil Engineering & Engineering Mechanics and... more Abstract Columbia University's Departments of Civil Engineering & Engineering Mechanics and Earth & Environmental Engineering and Center for New Media Teaching and Learning have recently partnered to develop instructional and technological innovations to develop reflective practitioners of engineering that are prepared for the engineering tasks of the 21st century. The partnership has begun a series of initiatives to develop a working prototype, called OPTIMUS, that simulates urban scenarios by integrating a three-dimensional ...

Evaluating Earthquake Retrofitting Measures For Schools: A Demonstration Of Cost-Benefit Analysis

Based on a cost-benefit approach for evaluating seismic mitigation options for apartment building... more Based on a cost-benefit approach for evaluating seismic mitigation options for apartment buildings in Istanbul, Turkey, this paper presents a demonstration study for a hypothetical vulnerable school building. A probabilistic cost-benefit analysis provides a useful framework for assessing seismic mitigation measures, taking into consideration limited resources and social costs. The hypothetical school is analysed over a variety of time-horizons to determine the break-even point for investments for several seismic retrofitting options. * Negative values (unshaded) indicate economically undesirable choices for the given time-horizon, while positive values (shaded) indicate economically desirable choices.

On the observability and identifiability of nonlinear structural and mechanical systems

Structural Control and Health Monitoring, 2014

ABSTRACT The question of a priori observability of a dynamic system, that is, whether the states ... more ABSTRACT The question of a priori observability of a dynamic system, that is, whether the states of a system can be identified given a particular set of measured quantities is of utmost importance in multiple disciplines including biology, economics, and engineering. More often than not, some of the parameters of the system need to be identified, and thus the issue of identifiability, that is, whether the measurements result in unique or finite solutions for the values of the parameters, is of interest. Identifiability arises in conjunction with the question of observability, when the notion of states may be augmented to include both the actual state variables of the dynamic system and its parameters. This results in the formulation of a nonlinear augmented system even though the dynamic equations of motion of the original system might be linear.In this work, three methods for the observability and identifiability of nonlinear dynamic systems are considered. More specifically, for a system whose state and measurement equations are analytic, the geometric Observability Rank Condition, which is based on Lie derivatives may be used. If the equations are rational, algebraic methods are also available. These include the algebraic observability methods and the algebraic identifiability algorithms which determine the finiteness or uniqueness of the solutions for the parameters. The aforementioned methods are used to study the observability and identifiability of suitable problems in civil engineering and highlight the connections between them and the corresponding concepts. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Experimental Validation of the Dual Kalman Filter for Online and Real-Time State and Input Estimation

Conference Proceedings of the Society for Experimental Mechanics Series, 2015

In this study, a novel dual implementation of the Kalman filter is proposed for simultaneous esti... more In this study, a novel dual implementation of the Kalman filter is proposed for simultaneous estimation of the states and input of structures via acceleration measurements. In practice, the uncertainties stemming from the absence of information on the input force, model inaccuracy and measurement errors render the state estimation a challenging task and the research to achieve a robust solution is still in progress. Via the use of numerical simulation, it was shown that the proposed method outperforms the existing techniques in terms of robustness and accuracy of displacement and velocity estimations [8]. The efficacy of the proposed method is validated using the data obtained from a shake table experiment on a laboratory test structure. The measured accelerations of the floors of the structure are fed into the filter, and the estimated time histories of the displacement estimates are cross-compared to the true time histories obtained from the displacement sensors.

Nonlinear System Identification: Particle-Based Methods

Encyclopedia of Earthquake Engineering, 2014

Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty

Structural Safety, 2010

... The state space formulation incorporates a Bouc–Wen type hysteretic model properly modified w... more

The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing

Structural Control and Health Monitoring, 2009

The use of heterogeneous, non-collocated measurements for non-linear structural system identifica... more The use of heterogeneous, non-collocated measurements for non-linear structural system identification is explored herein. In particular, this paper considers the example of sensor heterogeneity arising from the fact that both acceleration and displacement are measured at various locations of the structural system. The availability of non-collocated data might often arise in the identification of systems where the displacement data may be provided through Global Positioning Systems (GPS). The well known Extended Kalman Filter (EKF) is often used to deal with nonlinear system identification. However, as suggested in [1], the EKF is not effective in the case of highly nonlinear problems. Instead, two techniques are examined herein, the Unscented Kalman Filter method (UKF), proposed by Julier and Uhlman, and the Particle Filter method, also known as Sequential Monte Carlo method (SMC). The two methods are compared and their efficiency is evaluated through the example of a three degree of freedom system, involving a Bouc Wen hysteretic component, where the availability of displacement and acceleration measurements for different DOFs is assumed.

Particle filter scheme with mutation for the estimation of time-invariant parameters in structural health monitoring applications

Structural Control and Health Monitoring, 2012

In this study, a novel method is presented for non-linear, non-Gaussian online state and paramete... more In this study, a novel method is presented for non-linear, non-Gaussian online state and parameter identification, developed for use in structural health monitoring (SHM) problems. The algorithm consists of a particle filter (PF) that combines the use of the standard PF with mutation operators. The algorithm aims at alleviating the sample impoverishment problem, which is a well-known limitation of the standard PF, yielding it inefficient for demanding non-linear identification problems. To overcome this hurdle, we introduce here an alternative approach, influenced by the principles of evolutionary computation. After the standard PF steps are performed to a point where the sample diversity drops below some threshold, the unfit particles are replaced by either the fittest particles or the current weighted estimate of the state. Next, the time-invariant components of the particles are mutated under some mutation probability, and the new sample is then propagated to the next time step. This process is well suited for joint state and parameter estimation problems, as is usually the case in SHM techniques. As a result, the loss of diversity associated with the standard PF is overcome, and the new PF with mutation is shown to outperform the standard PF and the unscented Kalman filter for the case of high process noise. The method is validated through an established benchmark problem found in the literature, lying outside of the structural identification concept, and a previously referenced 3DOF structural system with hysteresis elaborating the SHM aspect.

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

International Journal for Numerical Methods in Engineering, 2009

This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed... more

Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures

Computers & Structures, 2011

The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previo... more The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previously been shown to be very effective in the detection of flaws in structures. By this approach, the XFEM is used to model the forward problem and a GA is used as the optimization scheme, converging to the true flaw. The convergence is obtained by minimizing the error

Uncertainty quantification for joint input-state estimation in structural dynamics

This paper presents a novel approach for quantification of the estimation uncertainty on the resu... more This paper presents a novel approach for quantification of the estimation uncertainty on the results obtained from joint input-state estimation in structural dynamics. The uncertainty accounted for originates from measurement errors and unknown stochastic excitation, that is acting on the structure besides the forces that are to be identified. The uncertainty quantification approach is applied for a joint input-state estimation algorithm that is used for force identification and response estimation in structural dynamics. The approach can, however, be extended to other force and state estimation algorithms. The uncertainty on the estimated quantities can be used to design a sensor network and to determine the optimal noise statistics that are applied for joint input-state estimation. The uncertainty quantification approach is verified using numerical simulations.

Symmetry properties of natural frequency and mode shape sensitivities in symmetric structures

Mechanical Systems and Signal Processing, 2020

When updating a finite element (FE) model to match the measured properties of its corresponding s... more When updating a finite element (FE) model to match the measured properties of its corresponding structure, the sensitivities of FE model outputs to parameter changes are of significant interest. These sensitivities form the core of sensitivity-based model updating algorithms, but they are also used for developing reduced parametrizations, such as in subset selection and clustering. In this work, the sensitivities of natural frequencies and mode shapes are studied for structures having at least one plane of reflectional symmetry. It is first shown that the mode shapes of these structures are either symmetric and anti-symmetric, which is used to prove that natural frequency sensitivities are equal for symmetric parameters. Conversely, mode shape sensitivities are shown to be unequal for symmetric parameters, as measured by cosine distance. These topics are explored with a small numerical example, where it is noted that mode shape sensitivities for symmetric parameters exhibit similar properties to asymmetric parameters.

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Structural Control and Health Monitoring, 2020

Model updating is used to reduce error between measured structural responses and corresponding fi... more Model updating is used to reduce error between measured structural responses and corresponding finite element (FE) model outputs, which allows accurate prediction of structural behavior in future analyses. In this work, reduced-order parametrizations of an underlying FE model are developed from singular value decomposition (SVD) of the sensitivity matrix, thereby improving efficiency and posedness in model updating. A deterministic error minimization scheme is combined with asymptotic Bayesian inference to provide optimal regularization with estimates for model evidence and parameter efficiency. Natural frequencies and mode shapes are targeted for updating in a small-scale example with simulated data and a full-scale example with real data. In both cases, SVD-based parametrization is shown to have as-good or better results than subset selection with very strong results on the full-scale model, as assessed by Bayes factor.

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

by Eleni Chatzi and Andrew W Smyth

International Journal for …, Jan 1, 2010

This paper investigates the XFEM-GA detection algorithm proposed by Rabinovich et al. on elastost... more This paper investigates the XFEM-GA detection algorithm proposed by Rabinovich et al. on elastostatic problems with different type of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the Extended Finite Element Method (XFEM) as the forward problem and Genetic Algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems. In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular shaped holes. Measurements are obtained from strain sensors which are attached to the surface of the structure at specific locations and provide the target solution to the Genetic Algorithm. The results show convergence robustness and accuracy provided that sufficient number of sensors are employed and sufficiently large flaws are considered.

Application of differential GPS sensing on long-span bridges with accelerometer data fusion

by Eleni Chatzi and Andrew W Smyth

Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty

by Eleni Chatzi and Andrew W Smyth

Structural Safety, Jan 1, 2010

Experimental application and enhancement of the XFEM-GA algorithm for the detection of flaws in structures

by Eleni Chatzi and Andrew W Smyth

Computers & Structures, Jan 1, 2011

The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previo... more The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previously been shown to be very effective in the detection of flaws in structures. By this approach, the XFEM is used to model the forward problem and a GA is used as the optimization scheme, converging to the true flaw. The convergence is obtained by minimizing the error between sensor measurements and data obtained by solving the forward problem.

Nonlinear System Identification: Particle-Based Methods

by Eleni Chatzi and Andrew W Smyth

Encyclopedia of Earthquake Engineering, 2014

Failures Associated with the 2004 Mindulle Typhoon in Taiwan

Geotechnical and Geological Engineering, 2007

On July 2, 2004, a 2000-km southwest air current following the Mindulle Typhoon caused serious da... more On July 2, 2004, a 2000-km southwest air current following the Mindulle Typhoon caused serious damages to infrastructures in Taiwan. The disaster resulted in extensive geological and structural failures, mainly as a result of debris flow. Some of the sites were subjected to types of repeated failures compared to previous typhoons. Some structural failures were attributed to geotechnical failures. It is decided to document and identify causes for some of these major failures triggered by typhoons. The case history showed significant implications to future disaster prevention and management works. New challenges were posed in geotechnical engineering design in encountering rainfall-induced failures.

Benefit-Cost Analysis for Earthquake Mitigation: Evaluating Measures for Apartment Houses in Turkey

In the wake of the 1999 earthquake destruction in Turkey, the urgent need has arisen to evaluate ... more In the wake of the 1999 earthquake destruction in Turkey, the urgent need has arisen to evaluate the benefits of loss mitigation measures that could be undertaken to strengthen the existing housing stock. A cost benefit analysis for the implementation of various seismic retrofitting measures is performed on a common and vulnerable type of apartment building located in Istanbul. The analysis was performed probabilistically, through the development of fragility curves of the structure in its different retrofitted configurations. By incorporating the probabilistic seismic hazard for the region, expected losses were obtained for arbitrary time-horizons. By including realistic cost estimates of the retrofitting schemes and costs of direct losses, one can estimate the benefit of the retrofitting measures in present day values. A sensitivity analysis was performed to determine the effects of varying cost parameters and also the assumed cost of human lives. The analysis implies that, even when considering only direct losses, all of the retrofitting measures considered are very desirable for all but the very shortest time-horizons. The sensitivity analyses conducted suggests that this conclusion is very robust for a wide range of estimates regarding costs of mitigation, discount rates and time-horizons even if no fatalities are associated with the collapse of the building. The methodology developed here can be extended to an entire region by incorporating additional structure types, soil types, retrofitting measures etc. It is hoped that this work can support some of the most urgent decisions and serve as a benchmark for more realistic and targeted cost-benefit analyses

Instructional & Technological Innovations to Attract & Retain Undergraduates to Engineer the Built Environment

International Conference on Engineering Education, Aug 18, 2002

Abstract Columbia University's Departments of Civil Engineering & Engineering Mechanics and... more Abstract Columbia University's Departments of Civil Engineering & Engineering Mechanics and Earth & Environmental Engineering and Center for New Media Teaching and Learning have recently partnered to develop instructional and technological innovations to develop reflective practitioners of engineering that are prepared for the engineering tasks of the 21st century. The partnership has begun a series of initiatives to develop a working prototype, called OPTIMUS, that simulates urban scenarios by integrating a three-dimensional ...

Evaluating Earthquake Retrofitting Measures For Schools: A Demonstration Of Cost-Benefit Analysis

Based on a cost-benefit approach for evaluating seismic mitigation options for apartment building... more Based on a cost-benefit approach for evaluating seismic mitigation options for apartment buildings in Istanbul, Turkey, this paper presents a demonstration study for a hypothetical vulnerable school building. A probabilistic cost-benefit analysis provides a useful framework for assessing seismic mitigation measures, taking into consideration limited resources and social costs. The hypothetical school is analysed over a variety of time-horizons to determine the break-even point for investments for several seismic retrofitting options. * Negative values (unshaded) indicate economically undesirable choices for the given time-horizon, while positive values (shaded) indicate economically desirable choices.

On the observability and identifiability of nonlinear structural and mechanical systems

Structural Control and Health Monitoring, 2014

ABSTRACT The question of a priori observability of a dynamic system, that is, whether the states ... more ABSTRACT The question of a priori observability of a dynamic system, that is, whether the states of a system can be identified given a particular set of measured quantities is of utmost importance in multiple disciplines including biology, economics, and engineering. More often than not, some of the parameters of the system need to be identified, and thus the issue of identifiability, that is, whether the measurements result in unique or finite solutions for the values of the parameters, is of interest. Identifiability arises in conjunction with the question of observability, when the notion of states may be augmented to include both the actual state variables of the dynamic system and its parameters. This results in the formulation of a nonlinear augmented system even though the dynamic equations of motion of the original system might be linear.In this work, three methods for the observability and identifiability of nonlinear dynamic systems are considered. More specifically, for a system whose state and measurement equations are analytic, the geometric Observability Rank Condition, which is based on Lie derivatives may be used. If the equations are rational, algebraic methods are also available. These include the algebraic observability methods and the algebraic identifiability algorithms which determine the finiteness or uniqueness of the solutions for the parameters. The aforementioned methods are used to study the observability and identifiability of suitable problems in civil engineering and highlight the connections between them and the corresponding concepts. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Experimental Validation of the Dual Kalman Filter for Online and Real-Time State and Input Estimation

Conference Proceedings of the Society for Experimental Mechanics Series, 2015

In this study, a novel dual implementation of the Kalman filter is proposed for simultaneous esti... more In this study, a novel dual implementation of the Kalman filter is proposed for simultaneous estimation of the states and input of structures via acceleration measurements. In practice, the uncertainties stemming from the absence of information on the input force, model inaccuracy and measurement errors render the state estimation a challenging task and the research to achieve a robust solution is still in progress. Via the use of numerical simulation, it was shown that the proposed method outperforms the existing techniques in terms of robustness and accuracy of displacement and velocity estimations [8]. The efficacy of the proposed method is validated using the data obtained from a shake table experiment on a laboratory test structure. The measured accelerations of the floors of the structure are fed into the filter, and the estimated time histories of the displacement estimates are cross-compared to the true time histories obtained from the displacement sensors.

Nonlinear System Identification: Particle-Based Methods

Encyclopedia of Earthquake Engineering, 2014

Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty

Structural Safety, 2010

... The state space formulation incorporates a Bouc–Wen type hysteretic model properly modified w... more

The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing

Structural Control and Health Monitoring, 2009

The use of heterogeneous, non-collocated measurements for non-linear structural system identifica... more The use of heterogeneous, non-collocated measurements for non-linear structural system identification is explored herein. In particular, this paper considers the example of sensor heterogeneity arising from the fact that both acceleration and displacement are measured at various locations of the structural system. The availability of non-collocated data might often arise in the identification of systems where the displacement data may be provided through Global Positioning Systems (GPS). The well known Extended Kalman Filter (EKF) is often used to deal with nonlinear system identification. However, as suggested in [1], the EKF is not effective in the case of highly nonlinear problems. Instead, two techniques are examined herein, the Unscented Kalman Filter method (UKF), proposed by Julier and Uhlman, and the Particle Filter method, also known as Sequential Monte Carlo method (SMC). The two methods are compared and their efficiency is evaluated through the example of a three degree of freedom system, involving a Bouc Wen hysteretic component, where the availability of displacement and acceleration measurements for different DOFs is assumed.

Particle filter scheme with mutation for the estimation of time-invariant parameters in structural health monitoring applications

Structural Control and Health Monitoring, 2012

In this study, a novel method is presented for non-linear, non-Gaussian online state and paramete... more In this study, a novel method is presented for non-linear, non-Gaussian online state and parameter identification, developed for use in structural health monitoring (SHM) problems. The algorithm consists of a particle filter (PF) that combines the use of the standard PF with mutation operators. The algorithm aims at alleviating the sample impoverishment problem, which is a well-known limitation of the standard PF, yielding it inefficient for demanding non-linear identification problems. To overcome this hurdle, we introduce here an alternative approach, influenced by the principles of evolutionary computation. After the standard PF steps are performed to a point where the sample diversity drops below some threshold, the unfit particles are replaced by either the fittest particles or the current weighted estimate of the state. Next, the time-invariant components of the particles are mutated under some mutation probability, and the new sample is then propagated to the next time step. This process is well suited for joint state and parameter estimation problems, as is usually the case in SHM techniques. As a result, the loss of diversity associated with the standard PF is overcome, and the new PF with mutation is shown to outperform the standard PF and the unscented Kalman filter for the case of high process noise. The method is validated through an established benchmark problem found in the literature, lying outside of the structural identification concept, and a previously referenced 3DOF structural system with hysteresis elaborating the SHM aspect.

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

International Journal for Numerical Methods in Engineering, 2009

This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed... more

Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures

Computers & Structures, 2011

The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previo... more The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previously been shown to be very effective in the detection of flaws in structures. By this approach, the XFEM is used to model the forward problem and a GA is used as the optimization scheme, converging to the true flaw. The convergence is obtained by minimizing the error

Uncertainty quantification for joint input-state estimation in structural dynamics

This paper presents a novel approach for quantification of the estimation uncertainty on the resu... more This paper presents a novel approach for quantification of the estimation uncertainty on the results obtained from joint input-state estimation in structural dynamics. The uncertainty accounted for originates from measurement errors and unknown stochastic excitation, that is acting on the structure besides the forces that are to be identified. The uncertainty quantification approach is applied for a joint input-state estimation algorithm that is used for force identification and response estimation in structural dynamics. The approach can, however, be extended to other force and state estimation algorithms. The uncertainty on the estimated quantities can be used to design a sensor network and to determine the optimal noise statistics that are applied for joint input-state estimation. The uncertainty quantification approach is verified using numerical simulations.

Symmetry properties of natural frequency and mode shape sensitivities in symmetric structures

Mechanical Systems and Signal Processing, 2020

When updating a finite element (FE) model to match the measured properties of its corresponding s... more When updating a finite element (FE) model to match the measured properties of its corresponding structure, the sensitivities of FE model outputs to parameter changes are of significant interest. These sensitivities form the core of sensitivity-based model updating algorithms, but they are also used for developing reduced parametrizations, such as in subset selection and clustering. In this work, the sensitivities of natural frequencies and mode shapes are studied for structures having at least one plane of reflectional symmetry. It is first shown that the mode shapes of these structures are either symmetric and anti-symmetric, which is used to prove that natural frequency sensitivities are equal for symmetric parameters. Conversely, mode shape sensitivities are shown to be unequal for symmetric parameters, as measured by cosine distance. These topics are explored with a small numerical example, where it is noted that mode shape sensitivities for symmetric parameters exhibit similar properties to asymmetric parameters.

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Structural Control and Health Monitoring, 2020

Model updating is used to reduce error between measured structural responses and corresponding fi... more Model updating is used to reduce error between measured structural responses and corresponding finite element (FE) model outputs, which allows accurate prediction of structural behavior in future analyses. In this work, reduced-order parametrizations of an underlying FE model are developed from singular value decomposition (SVD) of the sensitivity matrix, thereby improving efficiency and posedness in model updating. A deterministic error minimization scheme is combined with asymptotic Bayesian inference to provide optimal regularization with estimates for model evidence and parameter efficiency. Natural frequencies and mode shapes are targeted for updating in a small-scale example with simulated data and a full-scale example with real data. In both cases, SVD-based parametrization is shown to have as-good or better results than subset selection with very strong results on the full-scale model, as assessed by Bayes factor.