This is a theoretical study of the consistency properties of Bayesian inference using mixtures of logistic regression models. When standard logistic regression models are combined in a mixtures-of-experts setup, a flexible model is formed to model the relationship between a binary (yes-no) response y and a vector of predictors x. Bayesian inference conditional on the observed data can then be used for regression and classification. This letter gives conditions on choosing the number of experts (i.e., number of mixing components) k or choosing a prior distribution for k, so that Bayesian inference is consistent, in the sense of often approximating the underlying true relationship between y and x. The resulting classification rule is also consistent, in the sense of having near-optimal performance in classification. We show these desirable consistency properties with a nonstochastic k growing slowly with the sample size n of the observed data, or with a random k that takes large values with nonzero but small probabilities.

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Summary Online model updating in hybrid simulation (HS) can represent an effective technique to reduce modeling errors of parts numerically simulated, that is, numerical substructures, especially when only a few critical components of a large system can be tested, that is, physical substructures. As a result, in an enhanced HS with online model updating, parameters of constitutive relationship can be identified based on experimental data provided by physical substructures and updated in numerical substructures. This paper proposes a novel method to identify constitutive parameters of concrete laws with unscented Kalman filter (UKF). In order to implement UKF, parts of the source codes of the OpenSEES software were modified to compute estimated measurements. Prior to experimental HS, a parametric study of UKF constitutive law parameters was conducted. As a result, the effectiveness of the UKF combined with OpenSEES was validated through numerical simulations, a monotonic loading test on a concrete column and real‐time HSs of a reinforced concrete frame run with both standard and model‐updating techniques based on UKF.

Summary Hybrid simulation is a powerful and cost‐effective simulation technique to evaluate structural dynamic performance. However, it is sometimes rather difficult to guarantee all the boundaries on the physical substructures, especially when the boundary conditions are very complex, due to limited laboratory resources. Lacking of boundary conditions is bound to change the stress state of the structure and eventually result in an inaccurate evaluation of structural performance. A model updating‐based online numerical simulation method is proposed in this paper to tackle the problem of incomplete boundary conditions. In the proposed method, 2 sets of finite element models with the same constitutive model are set up for the overall analysis of the whole structure and the constitutive model parameter estimation of the physical substructure, respectively. The boundary conditions are naturally satisfied because the response is calculated from the overall structural model, and the accuracy is improved as the material constitutive parameters are updated. The effectiveness of the proposed method is validated via numerical simulations and actual hybrid tests on a RC frame structure, and the results show that the negative effect of incomplete boundary conditions is almost eliminated and the accuracy of hybrid simulation is very much improved.

To improve the experimental accuracy and stability of shaking table substructure testing (STST), an explicit central difference method (CDM) and a three-variable control method (TVCM) with velocity positive feedback (VPF) are proposed in this study. First, the explicit CDM is presented for obtaining an improved control accuracy of the boundary conditions between the numerical and experimental substructures of STST. Compared with the traditional CDM, the proposed method can provide explicit control targets for displacement, velocity, and acceleration. Furthermore, a TVCM-VPF is proposed to improve the control stability and accuracy for loading the explicit control targets of displacement, velocity, and acceleration. The effectiveness of the proposed methods is validated by experiments on a three-story frame structure with a tuned liquid damper loaded on an old shaking table originally designed with the traditional displacement control mode. The experimental results show that the proposed explicit CDM works well, and the response rate and control accuracy of the shaking table are significantly improved with the contribution of the TVCM-VPF compared with those of the traditional proportional integral derivative (PID) controller. This indicates the advantage of the proposed TVCM-VPF over the traditional PID for STST. A comparison between the traditional shaking table test and STST shows that when the latter is based on the TVCM-VPF, it exhibits an excellent performance in terms of the stability and accuracy of displacement and an acceptable performance in terms of the acceleration accuracy.