Continuous updating gmm
06-Oct-2019 09:54, measures the distance between m and zero).The properties of the resulting estimator will depend on the particular choice of the norm function, and therefore the theory of GMM considers an entire family of norms, defined as also asymptotically efficient.Consistency is a statistical property of an estimator stating that, having a sufficient number of observations, the estimator will converge in probability to the true value of parameter: The second condition here (so-called Global identification condition) is often particularly hard to verify.There exist simpler necessary but not sufficient conditions, which may be used to detect non-identification problem: Asymptotic normality is a useful property, as it allows us to construct confidence bands for the estimator, and conduct different tests.When the number of moment conditions is greater than the dimension of the parameter vector θ, the model is said to be over-identified.Over-identification allows us to check whether the model's moment conditions match the data well or not.Abstract : Damage monitoring under time-varying structural boundary condition is one of the most difficult tasks in piezoelectric transducers (PZTs) and Lamb wave based SHM methods for engineering applications.Because the structural boundary changes such as variations in the tightness of bolts between structures can lead to false monitoring result even the structure is in health state.
The significant statistic indicates that one or more of our instruments are not valid (assuming that the model is otherwise correctly specified).gmm’s numerical derivative routines are very accurate, so most of the time you do not need to spend time taking analytic derivatives.This paper proposes a Lamb wave based on-line continuous updating Gaussian Mixture Model (GMM) to study the problem.Based on the baseline GMM constructed by features of Lamb wave signals in structural health state, an on-line continuous updating GMM is studied to learn the dynamic changes of Lamb wave monitoring signals without any prior knowledge of damage patterns.The KullbackÐLeibler (KL) divergence is used as a degradation index to estimate the structural damage by measuring the difference between the baseline GMM and the on-line GMM.
The proposed method is validated on an aircraft steel beam.
However, if speed is of the essence or if you plan to fit the same model repeatedly, analytic derivatives can be a boon.