I am starting to look into a Bayesian inference problem for a dynamic wind turbine model using UQLab. The goal is to calibrate the model parameters for time-dependent model output. I am attaching herewith a figure for easier interpretation of my model response. In my model, I need to incorporate a dynamic response at time-step (t_t) for a simulation run for t_n. This means: the model inputs need to change at t_t than that used to initialize the simulation at t_0. Could someone guide me to any literature where a similar problem was dealt with using the UQLab?
There is only one model. Mathematically: Y =\mathcal{M}(\mathbf{X}_1, t), \quad t \le t_t\ \quad and \quad \mathcal{M}(\mathbf{X}_2, t), \quad t > t_t\ .
So, in this case, the model inputs \mathbf{X}_1 changes to \mathbf{X}_2 at t_t. Having said that, the model parameters \theta (to be calibrated) are meant to have constant values independent of the model inputs.
I would rephrase the mathematical statement then: Y = \mathcal{M}(\mathbf{X}_1(t), \theta), \quad t \le t_t\ \quad and \quad \mathcal{M}(\mathbf{X}_2(t), \theta), \quad t > t_t\ ,
where \mathbf{X}_1 and \mathbf{X}_2 are operating conditions and are time (t) dependent. \theta comprises the vector of model parameters to be calibrated.
So for a given t, \mathbf{X}_1 and \mathbf{X}_2 are known exactly?
In this case I don’t think there is an issue. You can just rewrite your model to depend only on \mathbf{\theta} and let it return a vector of discrete responses at each time step, such that
Yes, for a given t, \mathbf{X}_1 and \mathbf{X}_2 are known.
Yes, that sounds very much correct. Any relevant literature on the same lines that I could refer?