KEYWORDS: Monte Carlo methods, Probability theory, Performance modeling, Stochastic processes, Error analysis, Buildings, Statistical modeling, Shape analysis, Mathematical modeling, Process modeling, Statistical analysis, Systems modeling
In Bayesian model updating, the likelihood function is commonly formulated by stochastic embedding in which the maximum information entropy probability model of prediction error variances plays an important role and it is Gaussian distribution subject to the first two moments as constraints. The selection of prediction error variances can be formulated as a model class selection problem, which automatically involves a trade-off between the average data-fit of the model class and the information it extracts from the data. Therefore, it is critical for the robustness in the updating of the structural model especially in the presence of modeling errors. To date, three ways of considering prediction error variances have been seem in the literature: 1) setting constant values empirically, 2) estimating them based on the goodness-of-fit of the measured data, and 3) updating them as uncertain parameters by applying Bayes’ Theorem at the model class level. In this paper, the effect of different strategies to deal with the prediction error variances on the model updating performance is investigated explicitly. A six-story shear building model with six uncertain stiffness parameters is employed as an illustrative example. Transitional Markov Chain Monte Carlo is used to draw samples of the posterior probability density function of the structure model parameters as well as the uncertain prediction variances. The different levels of modeling uncertainty and complexity are modeled through three FE models, including a true model, a model with more complexity, and a model with modeling error. Bayesian updating is performed for the three FE models considering the three aforementioned treatments of the prediction error variances. The effect of number of measurements on the model updating performance is also examined in the study. The results are compared based on model class assessment and indicate that updating the prediction error variances as uncertain parameters at the model class level produces more robust results especially when the number of measurement is small.
A data-driven approach for earthquake damage detection and localization in multi-degree of freedom
(MDOF) system subjected to strong ground motion is proposed. The new method is based on the
combination of wavelet analysis and fractal characteristics. The box counting method is employed to
obtain the fractal dimension of the time frequency distribution within the first natural frequency. It is
verified that the proposed fractal dimensions at each DOF of linear system are identical, while the
fractal dimension at the DOFs with nonlinearity will be different from those at the DOFs with linearity.
Therefore, the nonlinearity or weakness of the structure caused by strong ground motion can be
detected and localized through comparing the fractal dimensions at the measured DOFs. The numerical
simulation on a three-bay sixteen-story moment resist frame shows that the aforementioned approach is
capable of detecting and localizing seismic damage.
Compared with the conventional monitoring approach of separately sensing and then compressing the data, compressive
sensing (CS) is a novel data acquisition framework whereby the compression is done during the sampling. If the original
sensed signal would have been sufficiently sparse in terms of some orthogonal basis, the decompression can be done
essentially perfectly up to some critical compression ratio. In structural health monitoring (SHM) systems for civil
structures, novel data compression techniques such as CS are needed to reduce the cost of signal transfer and storage. In
this article, Bayesian compressive sensing (BCS) is investigated for SHM signals. By explicitly quantifying the
uncertainty in the signal reconstruction, the BCS technique exhibits an obvious benefit over the existing regularized
norm-minimization CS. However, current BCS algorithms suffer from a robustness problem; sometimes the
reconstruction errors are large. The source of the problem is that inversion of the compressed signal is a severely ill-posed
problem that often leads to sub-optimal signal representations. To ensure the strong robustness of the signal
reconstruction, even at a high compression ratio, an improved BCS algorithm is proposed which uses stochastic
optimization for the automatic relevance determination approach to reconstructing the underlying signal. Numerical
experiments are used as examples; the improved BCS algorithm demonstrates superior performance than state-of-the-art
BCS reconstruction algorithms.
KEYWORDS: Diagnostics, Compressed sensing, Structural health monitoring, Data storage, Signal processing, Signal detection, Data compression, Interference (communication), Optimization (mathematics), Sensor networks
In structural health monitoring (SHM) systems for civil structures, signal compression is often important to reduce the
cost of data transfer and storage because of the large volumes of data generated from the monitoring system.
Compressive sensing is a novel data compressing method whereby one does not measure the entire signal directly but
rather a set of related ("projected") measurements. The length of the required compressive-sensing measurements is
typically much smaller than the original signal, therefore increasing the efficiency of data transfer and storage. Recently,
a Bayesian formalism has also been employed for optimal compressive sensing, which adopts the ideas in the relevance
vector machine (RVM) as a decompression tool, such as the automatic relevance determination prior (ARD). Recently
publications illustrate the benefits of using the Bayesian compressive sensing (BCS) method. However, none of these
publications have investigated the robustness of the BCS method. We show that the usual RVM optimization algorithm
lacks robustness when the number of measurements is a lot less than the length of the signals because it can produce sub-optimal
signal representations; as a result, BCS is not robust when high compression efficiency is required. This induces
a tradeoff between efficiently compressing data and accurately decompressing it. Based on a study of the robustness of
the BCS method, diagnostic tools are proposed to investigate whether the compressed representation of the signal is
optimal. With reliable diagnostics, the performance of the BCS method can be monitored effectively. The numerical
results show that it is a powerful tool to examine the correctness of reconstruction results without knowing the original
signal.
The presence of noise greatly affects the effectiveness and robustness of structural damage detection methods. In this
study, a new damage detection method for beam structures is presented, utilizing time, frequency and space domain
information effectively. Local free vibrations of both undamaged and damaged signals are firstly extracted utilizing the
Natural Excitation Technique (NExT). Then the signals are decomposed into the low frequency region and high
frequency region by the wavelet packet transform (WPT). The Higuchi's fractal dimension (HFD) is applied to measure
the complexity of new local signals, which combine the low frequency component of undamaged signals and high
frequency component of damaged signals. Damage can be localized by the peak value of Katz's fractal dimension (KFD) analyzing the spatial curve of the calculated HFD values along the structure. For validation, the numerical studies of a simple supported beam were conducted. The results demonstrate that the method is capable of localizing single and multiple damage of various severity accurately. Furthermore, it is found that the proposed damage index is directly connected to damage severity. And the results of tests under heavy noise reveal strong robustness of the proposed method.
This paper presents a novel approach to detect structural damage combining non-negative matrix factorization (NMF)
and relevance vector machine (RVM). Firstly, the time history of acceleration signal are decomposed using the wavelet
packet transform to extract wavelet packet node energy as the damage feature, and construct a non-negative matrix using
the wavelet packet node energy index of all time history of acceleration data measured by multiple accelerometers
installed on the different locations of structure. Secondly, for increasing the damage detection accuracy, the dimension of
the feature non-negative matrix is reduced by NMF techniques and new representation of this matrix is obtained. Lastly,
RVM, a powerful tool for classification and regression, is used to detect the location of potential damage from the
reduced damage feature matrix. Numerical study on the Binzhou Yellow River Highway Bridge is carried out to illustrate the ability of the proposed method in damage detection.
KEYWORDS: Fractal analysis, Image information entropy, Sensors, Optical simulations, Signal processing, Computer simulations, Beam shaping, Damage detection, Finite element methods, Signal to noise ratio
Fractal geometry has been widely used to describe irregular phenomena such as damage in the structure as a new
mathematical tool. However, most of structural damage identification methods based on fractal theory have the drawback
of being sensitive to noise which restricts their practical application. A new high noise robustness damage identification
method based on fractal dimension and Shannon entropy is presented in this paper. The damage index was deduced from
the Katz's fractal dimensions of certain sampling points with arithmetic of Shannon entropy. The selection of the number
of sampling points for calculating the proposed damage index is also studied in this paper and it can be regarded as a
trade-off between the peak value generated by the damage and the stability of the curve of the proposed damage index.
As a validation, the proposed method is applied to detect damage in simply supported beams by numerical and
experimental study. The successful detection of the damage in the beam demonstrates that the method is capable of
estimating the location of the damage. And tests with measurement noise in simulated and the laboratory tested beams
demonstrate the strong robustness of the method under the influence of noise with appropriate number of sampling
interval for calculating the proposed damage index.
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