In recent years, several substructural identification methods have been developed for structural health monitoring. Most of these methods are deterministic, and unknown parameters in the target can ...be identified. However, the uncertainties in the identified results cannot be evaluated. This paper presents a Bayesian probabilistic model updating approach for substructure identification. A new response reconstruction technique is explored and combined with the Bayesian inference method for probabilistic model updating of the target substructure. The large-scale structure was divided into substructures, and the uncertainties in the identified results were evaluated. The stochastic gradient descent method is proposed for estimating the maximum likelihood estimation and maximum a posteriori of the unknown parameters in the target substructure. The posterior distributions of the unknown parameters are estimated using an asymptotic approximation. Numerical studies on a three-span beam structure and experimental studies on an eight-floor steel frame were conducted to verify the accuracy and efficiency of the proposed method. The results show that the estimated results match the actual values, and reasonable standard deviations can be obtained.
The estimation of the posterior probability distribution of unknown parameters remains a challenging issue for model updating with uncertainties. Most current studies are based on stochastic ...simulation techniques. This paper proposes a novel variational Bayesian inference approach to estimate posterior probability distributions by using the vibration responses of civil engineering structures. An adaptive Gaussian process modeling technique is used to represent the “expensive-to-evaluate” likelihood function, and the unknown posterior probability distribution is represented using a Gaussian mixture model. The evidence lower bound (ELBO) and its gradients can be computed analytically using the built Gaussian process and mixture models. The unknown parameters in the Gaussian mixture model can be identified by maximizing the value of ELBO. The stochastic gradient descent method is applied to perform the optimization. Numerical studies on an eight-story shear-type building and a simply supported beam are conducted to verify the accuracy and efficiency of using the proposed approach for probabilistic model updating and damage identification. Experimental studies on a laboratory steel frame structure are also conducted to validate the proposed approach. Results demonstrate that the posterior probability distributions of the unknown structural parameters can be successfully identified, and reliable probabilistic model updating and damage identification can be achieved.
•This paper proposes a novel probabilistic model updating method with variational Bayesian inference.•Approximate Bayesian computation method is conducted to estimate the posterior probability distribution.•The unknown posterior probability distribution is identified by maximizing the value of evidence lower bound (ELBO).
This paper investigates a new probabilistic strategy for Bayesian model updating using incomplete modal data. Direct mode matching between the measured and the predicted modal quantities is not ...required in the updating process, which is realized through model reduction. A Markov chain Monte Carlo technique with adaptive random-walk steps is proposed to draw the samples for model parameter uncertainty quantification. The iterated improved reduced system technique is employed to update the prediction error as well as to calculate the likelihood function in the sampling process. Since modal quantities are used in the model updating, modal identification is first carried out to extract the natural frequencies and mode shapes through the acceleration measurements of the structural system. The proposed algorithm is finally validated by both numerical and experimental examples: a 10-storey building with synthetic data and a 8-storey building with shaking table test data. Results illustrate that the proposed algorithm is effective and robust for parameter uncertainty quantification in probabilistic model updating of buildings.
•A new probabilistic strategy is proposed for Bayesian model updating using incomplete modal data.•Direct mode matching is not required via model reduction.•A MCMC technique with adaptive random-walk steps is proposed for parameter sampling.•The proposed algorithm is successfully verified through numerical and experimental examples.
Continuous monitoring of engineering structures provides a crucial alternative to assess its health condition as well as evaluate its safety throughout the whole service life. To link the field ...measurements to the characteristics of a building, one option is to characterize and update a model, against the measured data, so that it can best describe the behavior and performance of the structure. In this paper, we present a novel computational strategy for Bayesian probabilistic updating of building models with response functions extracted from ambient noise measurements using seismic interferometry. The intrinsic building impulse response functions (IRFs) can be extracted from ambient excitation by deconvolving the motion recorded at different floors with respect to the measured ambient ground motion. The IRF represents the representative building response to an input delta function at the ground floor. The measurements are firstly divided into multiple windows for deconvolution and the IRFs for each window are then averaged to represent the overall building IRFs. A hierarchical Bayesian framework with Laplace priors is proposed for updating the finite element model. A Markov chain Monte Carlo technique with adaptive random-walk steps is employed to sample the model parameters for uncertainty quantification. An illustrative example is studied to validate the effectiveness of the proposed algorithm for temporal monitoring and probabilistic model updating of buildings. The structure considered in this paper is a 21-storey concrete building instrumented with 36 accelerometers at the MIT campus. The methodology described here allows for continuous temporal health monitoring, robust model updating as well as post-earthquake damage detection of buildings.
•A novel computational strategy is proposed for continuous monitoring of buildings.•The travel waves are extracted from ambient noises using seismic interferometry.•The wave velocity, frequencies, mode shapes and damping ratios can be directly estimated from the extracted waves.•The building model is characterized using a hierarchical Bayesian inference framework.•The parameter uncertainties are quantified using a Markov chain Monte Carlo technique.
Summary
Finite element (FE) model updating is essential to improve the reliability of physical model‐based approaches in structural engineering applications. The surrogate model is considered an ...alternative to time‐consuming iterative FE analyses in performing the updating procedure. This paper presents a Bayesian neural network (BNN) as the surrogate model for probabilistic FE model updating using the measured modal data. The BNN involves high computational efficiency by introducing the approximate Gaussian inference of the posterior distribution. In practice, the modal data are usually incomplete because of the measurement noise and limited sensors. The developed BNN exploits the nonlinear relationship between the selected parameters and incomplete modal data. As opposed to the traditional surrogate‐based approach, the proposed framework uses the modal data as inputs and structural parameters to be updated as outputs. It enables uncertainty quantification of the estimated structural parameters efficiently. In particular, an adaptive sampling strategy is established to shrink the searching space of optimal updating parameters based on the truncated Gaussian distribution. Numerical examples are conducted to demonstrate the effectiveness of the presented approach. Then it is applied to the laboratory and experimental structures using the measured data. Results indicate that the proposed framework is accurate and efficient for parameter uncertainty quantification in structural model updating.
Summary
We present a computational methodology for structural identification and damage detection via linking the concepts of seismic interferometry and Bayesian inference. A deconvolution‐based ...seismic interferometry approach is employed to obtain the waveforms that represent the impulse response functions with respect to a reference excitation source. Using the deconvolved waveforms, we study the following two different damage detection methods that utilize shear wave velocity variations: the arrival picking method and the stretching method. We show that variations in the shear wave velocities can be used for qualitative damage detection and that velocity reduction is more evident for more severely damaged states. Second, a hierarchical Bayesian inference framework is used to update a finite element model by minimizing the gap between the predicted and the extracted time histories of the impulse response functions. Through comparison of the model parameter distributions of the damaged structure with the updated baseline model, we demonstrate that damage localization and quantification are possible. The performance of the proposed approach is verified through two shake table test structures. Results indicate that the proposed framework is promising for monitoring structural systems, which allows for noninvasive determination of structural parameters.
Simplifications and theoretical assumptions are usually incorporated into the numerical modeling of structures. However, these assumptions may reduce the accuracy of the simulation results. This ...problem has led to the development of model-updating techniques to minimize the error between the experimental response and the modeled structure by updating its parameters based on the observed data. Structural numerical models are typically constructed using a deterministic approach, whereby a single best-estimated value of each structural parameter is obtained. However, structural models are often complex and involve many uncertain variables, where a unique solution that captures all the variability is not possible. Updating techniques using Bayesian Inference (BI) have been developed to quantify parametric uncertainty in analytical models. This paper presents the implementation of the BI in the parametric updating of a five-story building model and the quantification of its associated uncertainty. The Bayesian framework is implemented to update the model parameters and calculate the covariance matrix of the output parameters based on the experimental information provided by modal frequencies and mode shapes. The main advantage of this approach is that the uncertainty in the experimental data is considered by defining the likelihood function as a multivariate normal distribution, leading to a better representation of the actual building behavior. The results showed that this Bayesian model-updating approach effectively allows a statistically rigorous update of the model parameters, characterizing the uncertainty and increasing confidence in the model’s predictions, which is particularly useful in engineering applications where model accuracy is critical.
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