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Recently, based on negentropy of squared envelope (SE) and of squared envelope spectrum (SES), extensions of spectral kurtosis, the infograms including the SE infogram and the SES infogram, were proposed to detect impulsive and cyclostationary transients. Moreover, they have abilities to detect transients in the cases, where impulsive noises exist or relaxation times of repetitive transients are lower than their repetition rate. Nevertheless, the infograms are fast filtering algorithms and cannot achieve optimal filtering for bearing fault feature identification. This paper aims to extend the infograms to novel Bayesian inference based optimal wavelet filtering for bearing fault feature identification. The innovations of this paper are summarized as follows. Firstly, a state space model of wavelet parameters is presented. Here, wavelet parameters are the states of the state space model. Monotonically increasing guess negentropy measurements are constructed. Secondly, either the SE infogram or the SES infogram is employed to initialize the state space model. Then, considering Gaussian disturbance on wavelet parameters, wavelet parameters are assumed to follow a joint Gaussian distribution. Thirdly, spherical cubature integration based Bayesian inference is introduced to iteratively establish posterior wavelet parameters distributions. At last, optimal wavelet parameters are determined from the posterior wavelet parameters distributions so as to conduct optimal wavelet filtering. Two instance studies including simulated and experimental bearing fault data were investigated to illustrate how the proposed Bayesian inference method works. The results show that the proposed Bayesian inference method is convergent and provides more fault signatures than the infogram. [ABSTRACT FROM AUTHOR]

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, the tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in several ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter – the 'L-kernel' – is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid the implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimal L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65% and 70%. Python code and code tests accompanying this manuscript are available through the Github repository https://github.com/plgreenLIRU/SMC_approx_optL. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]