290 K. Worden et al. oracle is equipped with a model of the structure of interest, which is the candidate mirror and also has facilities for carrying out physical testing on the structure. The interrogator is allowed to present the oracle with a set of schedules eC W fromsome given context, and the oracle is required to return either the test responses of the structure rC W, or simulations from the model mC W. 8 If the interrogator is unable to decide which option the oracle has taken in any case, then the model in question is a Turing-mirror or T-mirror. While this may seem like nothing more than an amusing digression, there is the possibility that the work over the years in terms of implementing the Turing test could be used in order to derive rigorous methods of testing mirrors. This is enough of basic definitions for now; in the next section, the potential uses of the technology are explored via a number of example cases. 34.3 Examples 34.3.1 A Simple Example: Context Change One of the simpler problems one can imagine in the context of mirrors, is how to analyse the performance of a given model, when asked to make predictions outside its original context C. This problem is interesting because it can be made to include the case of extrapolation, although that will not be discussed in great detail here. Extrapolation for a data-based or hybrid model occurs, when the model MhC(Dtr) is used to make predictions outside the range of data encompassed by the training set Dtr. Even if the model MhC(Dtr) is an -mirror on schedules in the training set, this may not hold if the model extrapolates. One simple way to make the problem of context change encompass the problem of extrapolation, would be to extend the definition of context C, so that it not only specifies the variables under investigation, but also the ranges of those variables encountered in training data. This example will consider a different problem, where a model MC is required to make predictions on different variables to its context C. Suppose the model is modified in order to predict in a context C , with the new model denoted M C . Furthermore, assume that there are no training or test data available for the context C . The interesting question is: Given that a model MC is an -mirror for the context C; following modification to M C , is the new model an -mirror for C for any , and if so, what is the minimum value of for which this holds? (Note that, with the extended definition of context discussed above, this is the extrapolation problem if M=M ). Consider a simple example. Suppose one has constructed a Finite Element (FE) model MC, of a cantilever beam (as in Fig. 34.2). The model has been validated on test data measured as the displacement responses yi(t) at points i = 1, 3, 5, so that the predictive context is {y1,y3,y5}. Suppose that MC has been established as an -mirror on the context C. Now, further suppose that one wishes to make predictions of the response at points 2, 3 and 4, so the predictive context for C is Fig. 34.2 Simple FE model for illustrating context change 5 6 4 3 2 1 8Clearly, there are subtleties. For example, if the necessary test programme in a given case were to take 10 days, while running the model would only take 10 h, the oracle would only return the results after the greater time.
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