Hi Mohamad,

actually many methods, a text message would not be sufficient to list them all up. Generally, it can either be a simple linear regression model, which works well if you have temperature measurements that clearly explain the frequency variation, or more "complex" strategies such as dynamic regression, nonlinear regression, neural networks, bayesian inference, etc etc. There are many ways to distinguish the different methods, like supervised or unsupervised learning, static or dynamic models, etc etc. The method you choose, depends on the case study you have. If the data you have is able to explain the frequency variation caused by the environmental effects, most likely the simplest regression method will do the job. On the other hand, if the correlations of the temperature data you have and the identified frequencies look more complicated, or if you don't have thermal data at all, than you need to look for more complex regression and pattern recognition methods. Hard to say which one is the best one. However, they all share a common problem: to train these regression methods, you always need a large data set covering a long period of time in order to catch as many thermal conditions as possible. The one million dollar question here is: how much data you need to train your models? There is no clear answer to this question. If different thermal conditions will happen in the future, it is most likely that your trained regression model could fail. Concerning this latter issue, recently I noticed some papers in the literature that started to tackle this problem. From my perspective, it is a field that still requires a lot of investigation. Hope this post helped a bit. 

If your new inputs show a different pattern,and especially if the new inputs have a different correlation with the new outputs, compared to what observed during the the training period of the model, it is unlikely that the trained model will provide good predictions. Hope this make sense. The question there is: why did the correlation between new input and new output change? because of damage or is it just a normal behavior that was simply not observed during the training period? That is the key distinction to answer.   

So if new inputs do not correlate with the healthy state (trained outputs), doesn't always mean it's damage, maybe it's another healthy state that we haven't considered in training period?

So inputs should simulate the whole structure's behavior during the training period.

To overcome your question, I think we can run an uncertainty analysis on the results to determine the probability of damage occurrence.  

Concerning your first question: yes, it does not always mean you have damage, it could be another healthy state that was not considered in the training period. There is a nice paper, written by a colleague of mine in Sheffield:

Dervilis, 2015, On robust regression analysis as a means of exploring environmental and operational conditions for SHM data, JSV. 

The paper discusses this kind of issues, but there is still a lot of room for research. 

Yes you could run uncertainty analysis, to determine the occurrence of damage, surely it would give you more clues. Personally, I think that damage detection should always be associated with uncertainty analysis. 

This reference ( http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29BE.1943-5592.0000830 ) is related to your question.