918 research outputs found
Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters
This study presents a spectral method for fatigue damage evaluation of linear structures with uncertain-but-bounded parameters subjected to the stationary multi-correlated Gaussian random excitation. The first step of the proposed method is to model uncertain parameters by introducing interval theory. Within the framework of interval analysis, the approximate expressions of the bounds of spectral moments of generic response are obtained by the improved interval analysis via the Extra Unitary Interval and Interval Rational Series Expansion. Based on the cumulative damage theory and the Tovo-Benasciutti method, the lower and upper bounds of expected fatigue damage rate are accurately evaluated by properly combining the bounds of the spectral parameters of the power density spectral function of stress of critical points. Finally, a numerical example concerning a truss under random excitation is used to illustrate the accuracy and efficiency of the proposed method by comparing with the vertex method
Random vibration analysis for coupled vehicle-track systems with uncertain parameters
Purpose
β The purpose of this paper is to present a new random vibration-based assessment method for coupled vehicle-track systems with uncertain parameters when subjected to random track irregularity.
Design/methodology/approach
β The uncertain parameters of vehicle are described as bounded random variables. The track is regarded as an infinite periodic structure, and the dynamic equations of the coupled vehicle-track system, under mixed physical coordinates and symplectic dual coordinates, are established through wheel-rail coupling relationships. The random track irregularities at the wheel-rail contact points are converted to a series of deterministic harmonic excitations with phase lag by using the pseudo excitation method. Based on the polynomial chaos expansion of the pseudo response, a chaos expanded pseudo equation is derived, leading to the combined hybrid pseudo excitation method-polynomial chaos expansion method.
Findings
β The impact of uncertainty propagation on the random vibration analysis is assessed efficiently. According to GB5599-85, the reliability analysis for the stability index is implemented, which can grade the comfort level by the probability. Comparing to the deterministic analysis, it turns out that neglect of the parameter uncertainty will lead to potentially risky analysis results.
Originality/value
β The proposed method is compared with Monte Carlo simulations, achieving good agreement. It is an effective means for random vibration analysis of uncertain coupled vehicle-track systems and has good engineering practicality
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Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures
In recent years different inerter - based vibration absorbers (IVAs) emerged for the earthquake protection of building structures coupling viscous and tuned - mass dampers with an inerter device . In the three most popular IVAs the inerter is functioning either as a motion amplifier [tuned - viscous - mass - damper (TVMD) configuration], mass amplifier [tuned - mass - damper - inerter (T MDI) configuration], or mass substitute [tuned - inerter - damper (TID) configuration]. Previous work has shown that through proper tuning , IVAs achieve enhanced earthquake - induced vibration suppression and/or weight reduction compared to conventional dampers/absorbers , but at the expense of increased control forces exerted from the IVA to the host building structure . These potentially large forces are typically not accounted for by current IVA tuning approaches. In this regard, a multi-objective IVA design approach is herein developed to identify the compromise between the competing objectives of (i) suppressing earthquake-induced vibrations in buildings, and (ii) avoiding development of excessive IVA (control) forces, while, simultaneously, assessing the appropriateness of different modeling assumptions for practical design of IVAs for earthquake engineering applications . The potential of the approach to pinpoint Pareto optimal IVA designs against the above objectives is illustrated for different IVA placements along the height of a benchmark 9-storey steel frame structure. Objective (i) is quantified according to current performanc e-based seismic design trends using first-passage reliability criteria associated with the probability of exceeding pre-specified thresholds of storey drifts and/or floor accelerations being the engineering demand parameters (EDPs) of interest . A variant, simpler, formulation is also considered using as performance quantification the sum of EDPs variances in accordance to traditional tuning methods for dynamic vibration absorbers. Objective (ii) is quantified through the variance of the IVA force. It is found that reduction of IVA control force of up to 3 times can be achieved with insignificant deterioration of building performance com pared to the extreme Pareto optimal IVA design targeting maximum vibration suppression , while TID and TMDI a chieve practically the same building performance and significantly outperform the TVMD. Moreover, it is shown that the simpler variant formulation may provide significantly suboptimal reliability performance . Lastly, it is verified that the efficacy of optimal IVA designs for stationary conditions is maintained for non-stationary stochastic excitation model capturing typical evolutionary features of earthquake excitations
Uncertainty modelling in power spectrum estimation of environmental processes
For efficient reliability analysis of buildings and structures, robust load models are required in stochastic dynamics, which can be estimated in particular from environmental processes, such as earthquakes or wind loads. To determine the response behaviour of a dynamic system under such loads, the power spectral density (PSD) function is a widely used tool for identifying the frequency components and corresponding amplitudes of environmental processes. Since the real data records required for this purpose are often subject to aleatory and epistemic uncertainties, and the PSD estimation process itself can induce further uncertainties, a rigorous quantification of these is essential, as otherwise a highly inaccurate load model could be generated which may yield in misleading simulation results. A system behaviour that is actually catastrophic can thus be shifted into an acceptable range, classifying the system as safe even though it is exposed to a high risk of damage or collapse. To address these issues, alternative loading models are proposed using probabilistic and non-deterministic models, that are able to efficiently account for these uncertainties and to model the loadings accordingly. Various methods are used in the generation of these load models, which are selected in particular according to the characteristic of the data and the number of available records.
In case multiple data records are available, reliable statistical information can be extracted from a set of similar PSD functions that differ, for instance, only slightly in shape and peak frequency. Based on these statistics, a PSD function model is derived utilising subjective probabilities to capture the epistemic uncertainties and represent this information effectively. The spectral densities are characterised as random variables instead of employing discrete values, and thus the PSD function itself represents a non-stationary random process comprising a range of possible valid PSD functions for a given data set.
If only a limited amount of data records is available, it is not possible to derive such reliable statistical information. Therefore, an interval-based approach is proposed that determines only an upper and lower bound and does not rely on any distribution within these bounds. A set of discrete-valued PSD functions is transformed into an interval-valued PSD function by optimising the weights of pre-derived basis functions from a Radial Basis Function Network such that they compose an upper and lower bound that encompasses the data set. Therefore, a range of possible values and system responses are identified rather than discrete values, which are able to quantify the epistemic uncertainties.
When generating such a load model using real data records, the problem can arise that the individual records exhibit a high spectral variance in the frequency domain and therefore differ too much from each other, although they appear to be similar in the time domain. A load model derived from these data may not cover the entire spectral range and is therefore not representative. The data are therefore grouped according to their similarity using the Bhattacharyya distance and k-means algorithm, which may generate two or more load models from the entire data set. These can be applied separately to the structure under investigation, leading to more accurate simulation results. This approach can also be used to estimate the spectral similarity of individual data sets in the frequency domain, which is particularly relevant for the load models mentioned above.
If the uncertainties are modelled directly in the time signal, it can be a challenging task to transform them efficiently into the frequency domain. Such a signal may consist only of reliable bounds in which the actual signal lies. A method is presented that can automatically propagate this interval uncertainty through the discrete Fourier transform, obtaining the exact bounds on the Fourier amplitude and an estimate of the PSD function. The method allows such an interval signal to be propagated without making assumptions about the dependence and distribution of the error over the time steps.
These novel representations of load models are able to quantify epistemic uncertainties inherent in real data records and induced due to the PSD estimation process. The strengths and advantages of these approaches in practice are demonstrated by means of several numerical examples concentrated in the field of stochastic dynamics.FΓΌr eine effiziente ZuverlΓ€ssigkeitsanalyse von GebΓ€uden und Strukturen sind robuste Belastungsmodelle in der stochastischen Dynamik erforderlich, die insbesondere aus Umweltprozessen wie Erdbeben oder Windlasten geschΓ€tzt werden kΓΆnnen. Um das Antwortverhalten eines dynamischen Systems unter solchen Belastungen zu bestimmen, ist die Funktion der Leistungsspektraldichte (PSD) ein weit verbreitetes Werkzeug zur Identifizierung der Frequenzkomponenten und der entsprechenden Amplituden von Umweltprozessen. Da die zu diesem Zweck benΓΆtigten realen DatensΓ€tze hΓ€ufig mit aleatorischen und epistemischen Unsicherheiten behaftet sind und der PSD-SchΓ€tzprozess selbst weitere Unsicherheiten induzieren kann, ist eine strenge Quantifizierung dieser Unsicherheiten unerlΓ€sslich, da andernfalls ein sehr ungenaues Belastungsmodell erzeugt werden kΓΆnnte, das zu fehlerhaften Simulationsergebnissen fΓΌhren kann. Ein eigentlich katastrophales Systemverhalten kann so in einen akzeptablen Bereich verschoben werden, so dass das System als sicher eingestuft wird, obwohl es einem hohen Risiko der BeschΓ€digung oder des Zusammenbruchs ausgesetzt ist. Um diese Probleme anzugehen, werden alternative Belastungsmodelle vorgeschlagen, die probabilistische und nicht-deterministische Modelle verwenden, welche in der Lage sind, diese Unsicherheiten effizient zu berΓΌcksichtigen und die Belastungen entsprechend zu modellieren. Bei der Erstellung dieser Lastmodelle werden verschiedene Methoden verwendet, die insbesondere nach dem Charakter der Daten und der Anzahl der verfΓΌgbaren DatensΓ€tze ausgewΓ€hlt werden.
Wenn mehrere DatensΓ€tze verfΓΌgbar sind, kΓΆnnen zuverlΓ€ssige statistische Informationen aus einer Reihe Γ€hnlicher PSD-Funktionen extrahiert werden, die sich z.B. nur geringfΓΌgig in Form und Spitzenfrequenz unterscheiden. Auf der Grundlage dieser Statistiken wird ein Modell der PSD-Funktion abgeleitet, das subjektive Wahrscheinlichkeiten verwendet, um die epistemischen Unsicherheiten zu erfassen und diese Informationen effektiv darzustellen. Die spektralen Leistungsdichten werden als Zufallsvariablen charakterisiert, anstatt diskrete Werte zu verwenden, somit stellt die PSD-Funktion selbst einen nicht-stationΓ€ren Zufallsprozess dar, der einen Bereich mΓΆglicher gΓΌltiger PSD-Funktionen fΓΌr einen gegebenen Datensatz umfasst.
Wenn nur eine begrenzte Anzahl von DatensΓ€tzen zur VerfΓΌgung steht, ist es nicht mΓΆglich, solche zuverlΓ€ssigen statistischen Informationen abzuleiten. Daher wird ein intervallbasierter Ansatz vorgeschlagen, der nur eine obere und untere Grenze bestimmt und sich nicht auf eine Verteilung innerhalb dieser Grenzen stΓΌtzt. Ein Satz von diskret wertigen PSD-Funktionen wird in eine intervallwertige PSD-Funktion umgewandelt, indem die Gewichte von vorab abgeleiteten Basisfunktionen aus einem Radialbasisfunktionsnetz so optimiert werden, dass sie eine obere und untere Grenze bilden, die den Datensatz umfassen. Damit wird ein Bereich mΓΆglicher Werte und Systemreaktionen anstelle diskreter Werte ermittelt, welche in der Lage sind, epistemische Unsicherheiten zu erfassen.
Bei der Erstellung eines solchen Lastmodells aus realen DatensΓ€tzen kann das Problem auftreten, dass die einzelnen DatensΓ€tze eine hohe spektrale Varianz im Frequenzbereich aufweisen und sich daher zu stark voneinander unterscheiden, obwohl sie im Zeitbereich Γ€hnlich erscheinen. Ein aus diesen Daten abgeleitetes Lastmodell deckt mΓΆglicherweise nicht den gesamten Spektralbereich ab und ist daher nicht reprΓ€sentativ. Die Daten werden daher mit Hilfe der Bhattacharyya-Distanz und des k-means-Algorithmus nach ihrer Γhnlichkeit gruppiert, wodurch zwei oder mehr Belastungsmodelle aus dem gesamten Datensatz erzeugt werden kΓΆnnen. Diese kΓΆnnen separat auf die zu untersuchende Struktur angewandt werden, was zu genaueren Simulationsergebnissen fΓΌhrt. Dieser Ansatz kann auch zur SchΓ€tzung der spektralen Γhnlichkeit einzelner DatensΓ€tze im Frequenzbereich verwendet werden, was fΓΌr die oben genannten Lastmodelle besonders relevant ist.
Wenn die Unsicherheiten direkt im Zeitsignal modelliert werden, kann es eine schwierige Aufgabe sein, sie effizient in den Frequenzbereich zu transformieren. Ein solches Signal kann mΓΆglicherweise nur aus zuverlΓ€ssigen Grenzen bestehen, in denen das tatsΓ€chliche Signal liegt. Es wird eine Methode vorgestellt, mit der diese Intervallunsicherheit automatisch durch die diskrete Fourier Transformation propagiert werden kann, um die exakten Grenzen der Fourier-Amplitude und der SchΓ€tzung der PSD-Funktion zu erhalten. Die Methode ermΓΆglicht es, ein solches Intervallsignal zu propagieren, ohne Annahmen ΓΌber die AbhΓ€ngigkeit und Verteilung des Fehlers ΓΌber die Zeitschritte zu treffen.
Diese neuartigen Darstellungen von Lastmodellen sind in der Lage, epistemische Unsicherheiten zu quantifizieren, die in realen DatensΓ€tzen enthalten sind und durch den PSD-SchΓ€tzprozess induziert werden. Die StΓ€rken und Vorteile dieser AnsΓ€tze in der Praxis werden anhand mehrerer numerischer Beispiele aus dem Bereich der stochastischen Dynamik demonstriert
Solving Coupled Differential Equation Groups Using PINO-CDE
As a fundamental mathmatical tool in many engineering disciplines, coupled
differential equation groups are being widely used to model complex structures
containing multiple physical quantities. Engineers constantly adjust structural
parameters at the design stage, which requires a highly efficient solver. The
rise of deep learning technologies has offered new perspectives on this task.
Unfortunately, existing black-box models suffer from poor accuracy and
robustness, while the advanced methodologies of single-output operator
regression cannot deal with multiple quantities simultaneously. To address
these challenges, we propose PINO-CDE, a deep learning framework for solving
coupled differential equation groups (CDEs) along with an equation
normalization algorithm for performance enhancing. Based on the theory of
physics-informed neural operator (PINO), PINO-CDE uses a single network for all
quantities in a CDEs, instead of training dozens, or even hundreds of networks
as in the existing literature. We demonstrate the flexibility and feasibility
of PINO-CDE for one toy example and two engineering applications: vehicle-track
coupled dynamics (VTCD) and reliability assessment for a four-storey building
(uncertainty propagation). The performance of VTCD indicates that PINO-CDE
outperforms existing software and deep learning-based methods in terms of
efficiency and precision, respectively. For the uncertainty propagation task,
PINO-CDE provides higher-resolution results in less than a quarter of the time
incurred when using the probability density evolution method (PDEM). This
framework integrates engineering dynamics and deep learning technologies and
may reveal a new concept for CDEs solving and uncertainty propagation
Response statistics and failure probability determination of nonlinear stochastic structural dynamical systems
Novel approximation techniques are proposed for the analysis and evaluation of nonlinear dynamical systems in the field of stochastic dynamics. Efficient determination of response statistics and reliability estimates for nonlinear systems remains challenging, especially those with singular matrices or endowed with fractional derivative elements. This thesis addresses the challenges of three main topics.
The first topic relates to the determination of response statistics of multi-degree-of-freedom nonlinear systems with singular matrices subject to combined deterministic and stochastic excitations. Notably, singular matrices can appear in the governing equations of motion of engineering systems for various reasons, such as due to a redundant coordinates modeling or due to modeling with additional constraint equations. Moreover, it is common for nonlinear systems to experience both stochastic and deterministic excitations simultaneously.
In this context, first, a novel solution framework is developed for determining the response of such systems subject to combined deterministic and stochastic excitation of the stationary kind. This is achieved by using the harmonic balance method and the generalized statistical linearization method. An over-determined system of equations is generated and solved by resorting to generalized matrix inverse theory.
Subsequently, the developed framework is appropriately extended to systems subject to a mixture of deterministic and stochastic excitations of the non-stationary kind. The generalized statistical linearization method is used to handle the nonlinear subsystem subject to non-stationary stochastic excitation, which, in conjunction with a state space formulation, forms a matrix differential equation governing the stochastic response. Then, the developed equations are solved
by numerical methods.
The accuracy for the proposed techniques has been demonstrated by considering nonlinear structural systems with redundant coordinates modeling, as well as a piezoelectric vibration energy harvesting device have been employed in the relevant application part.
The second topic relates to code-compliant stochastic dynamic analysis of nonlinear structural systems with fractional derivative elements. First, a novel approximation method is proposed to efficiently determine the peak response of nonlinear structural systems with fractional derivative elements subject to excitation compatible with a given seismic design spectrum. The proposed methods involve deriving an excitation evolutionary power spectrum that matches the design
spectrum in a stochastic sense. The peak response is approximated by utilizing equivalent linear elements, in conjunction with code-compliant design spectra, hopefully rendering it favorable to engineers of practice. Nonlinear structural systems endowed with fractional derivative terms in the governing equations of motion have been considered. A particular attribute pertains to utilizing localized time-dependent equivalent linear elements, which is superior to classical
approaches utilizing standard time-invariant statistical linearization method.
Then, the approximation method is extended to perform stochastic incremental dynamical analysis for nonlinear structural systems with fractional derivative elements exposed to stochastic excitations aligned with contemporary aseismic codes. The proposed method is achieved by resorting to the combination of stochastic averaging and statistical linearization methods, resulting in an efficient and comprehensive way to obtain the response displacement probability density function. A stochastic incremental dynamical analysis surface is generated instead of the traditional curves, leading to a reliable higher order statistics of the system response.
Lastly, the problem of the first excursion probability of nonlinear dynamic systems subject to imprecisely defined stochastic Gaussian loads is considered. This involves solving a nested double-loop problem, generally intractable without resorting to surrogate modeling schemes. To overcome these challenges, this thesis first proposes a generalized operator norm framework based on statistical linearization method. Its efficiency is achieved by breaking the double loop and determining the values of the epistemic uncertain parameters that produce bounds
on the probability of failure a priori. The proposed framework can significantly reduce the computational burden and provide a reliable estimate of the probability of failure
Machine Learning Aided Stochastic Elastoplastic and Damage Analysis of Functionally Graded Structures
The elastoplastic and damage analyses, which serve as key indicators for the nonlinear performances of engineering structures, have been extensively investigated during the past decades. However, with the development of advanced composite material, such as the functionally graded material (FGM), the nonlinear behaviour evaluations of such advantageous materials still remain tough challenges. Moreover, despite of the assumption that structural system parameters are widely adopted as deterministic, it is already illustrated that the inevitable and mercurial uncertainties of these system properties inherently associate with the concerned structural models and nonlinear analysis process. The existence of such fluctuations potentially affects the actual elastoplastic and damage behaviours of the FGM structures, which leads to the inadequacy between the approximation results with the actual structural safety conditions. Consequently, it is requisite to establish a robust stochastic nonlinear analysis framework complied with the requirements of modern composite engineering practices.
In this dissertation, a novel uncertain nonlinear analysis framework, namely the machine leaning aided stochastic elastoplastic and damage analysis framework, is presented herein for FGM structures. The proposed approach is a favorable alternative to determine structural reliability when full-scale testing is not achievable, thus leading to significant eliminations of manpower and computational efforts spent in practical engineering applications. Within the developed framework, a novel extended support vector regression (X-SVR) with Dirichlet feature mapping approach is introduced and then incorporated for the subsequent uncertainty quantification. By successfully establishing the governing relationship between the uncertain system parameters and any concerned structural output, a comprehensive probabilistic profile including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs) of the structural output can be effectively established through a sampling scheme.
Consequently, by adopting the machine learning aided stochastic elastoplastic and damage analysis framework into real-life engineering application, the advantages of the next generation uncertainty quantification analysis can be highlighted, and appreciable contributions can be delivered to both structural safety evaluation and structural design fields
Ambient vibration testing, system identification and model updating of a multiple-span elevated bridge
Peer reviewedPreprin
Stochastic System Design and Applications to Stochastically Robust Structural Control
The knowledge about a planned system in engineering design applications is never
complete. Often, a probabilistic quantification of the uncertainty arising from this missing
information is warranted in order to efficiently incorporate our partial knowledge about the
system and its environment into their respective models. In this framework, the design
objective is typically related to the expected value of a system performance measure, such
as reliability or expected life-cycle cost. This system design process is called stochastic
system design and the associated design optimization problem stochastic optimization. In
this thesis general stochastic system design problems are discussed. Application of this
design approach to the specific field of structural control is considered for developing a
robust-to-uncertainties nonlinear controller synthesis methodology.
Initially problems that involve relatively simple models are discussed. Analytical
approximations, motivated by the simplicity of the models adopted, are discussed for
evaluating the system performance and efficiently performing the stochastic optimization.
Special focus is given in this setting on the design of control laws for linear structural
systems with probabilistic model uncertainty, under stationary stochastic excitation. The
analysis then shifts to complex systems, involving nonlinear models with high-dimensional
uncertainties. To address this complexity in the model description stochastic simulation is
suggested for evaluating the performance objectives. This simulation-based approach
addresses adequately all important characteristics of the system but makes the associated
design optimization challenging. A novel algorithm, called Stochastic Subset Optimization
(SSO), is developed for efficiently exploring the sensitivity of the objective function to the
design variables and iteratively identifying a subset of the original design space that has
v i
high plausibility of containing the optimal design variables. An efficient two-stage
framework for the stochastic optimization is then discussed combining SSO with some
other stochastic search algorithm. Topics related to the combination of the two different
stages for overall enhanced efficiency of the optimization process are discussed.
Applications to general structural design problems as well as structural control problems
are finally considered. The design objectives in these problems are the reliability of the
system and the life-cycle cost. For the latter case, instead of approximating the damages
from future earthquakes in terms of the reliability of the structure, as typically performed in
past research efforts, an accurate methodology is presented for estimating this cost; this
methodology uses the nonlinear response of the structure under a given excitation to
estimate the damages in a detailed, component level
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