Legislación para el cercado de las semillas

First, to combine the approaches proposed in Chapter 4 and 6 for this present case, a 3-dimensional matrix Tm,d,b is introduced. Each column of Tm,d,b contains a set of

unique identical IIR-LRNNs, and each page of Tm,d,b starting from the second page

contains a set of corresponding bootstrapped network of the first page. The proposed algorithm for computing robust quantity of interest from the networks in Tm,d,b are

reported in the following steps:

Step 1: Construct a set V of optimal IIR-LRNN architectures from DBARC.

Step 3: Construct a 3-dimensional array Tm,d,b, where the first page of the 3-dimensional

matrix is identical to matrix Am,d in Chapter 6.

Step 4: Compute the posterior probability of the IIR-LRNN in the first page.

Step 5: Provide point estimate of the quantity of interest Q in the first page of the matrix.

Step 6: Compute robust estimate ˆQd

robust, ˆQ d

robust, ˆQ d

robust of the quantity of interest ˆQ

based on approach in Chapter 6.

Step 7: Check if the stopping criterion is met for increasing the number of M . If met, proceed to the next step, else, return to Step 2 and add another row M = M +1. The stopping criterion used in this present algorithm is the area a between the lower and upper confidence bound as defined in Equation ??, and convergence is met when the tolerance T ≤ 1 × 10−4) is achieved.

Step 8: Generate next page B = 2 in Tm,d,b corresponding to the bootstrap networks

of the networks in the first page. Repeat step 4-6 for each subsequent page generated.

Step 9: Compute Bootstrap Bias Corrected (BBC) point estimate along the pages in Tm,d,b based on approach in Chapter 4.

Step 10: Check if stopping criterion is met for the number of bootstrap IIR-LRNNs to be constructed. If met go to next step, else, go back to step 8 and generate additional page B = B + 1 of bootstrap IIR-LRNNs. Note that one stopping criterion is used for all the bootstrapped models along the pages of Tm,d,b, such

that if any network within the array meets the criterion first, the remaining networks automatically adopts the criterion.

Step 11: Compute ˆQBBC, robust, ˆQ_{BBC, robust}, ˆQBBC, robust such that:

QBBC, robust = 1 M M X m=1 ˆ QBBC, robust, m (8.2) ˆ Q

BBC, robust, ˆQBBC, robust are propagated via vertex method.

Subsequently, it is obvious that the training of the models and calculation of the point estimates Qm,d,b in Tm,d,b is computationally expensive. However, thanks to

the advancements in high performance computing, such as the parallel computation support in modern devices like NVIDIA GPUs, the training of the IIR-LRNNs in Tm,d,b and the estimates Qm,d,b is fast.

Analysis

Using the same experimental settings and model architecture discovered in the pre- vious case (Case 2), the algorithm converged after M = 35 and B = 100 iterations respectively.

Results

The result obtained from the above analysis is shown in Figure 8.10. From the results in Figure 8.10, it is clearly seen that the width of the confidence bounds from this present approach (Case 3) is narrower compared to that shown in Figure 8.8 (Case 2). Similarly, the expected robust estimates shown in Figure 8.10 closely matches to their respective target values compared to the results shown in Figure 8.8. Clearly, the reason for these low bias and variance in the robust prediction of the blind case is the fact that all the sources of uncertainty affecting a models prediction have been considered. Thus, it is been concluded that the proposed strategy in this present case is sufficient for an adequate quantification of model uncertainty.

Figure 8.10: Blind Case Data Set Prediction from Robust IIR-LRNN. Top Figure, Break Level Prediction for 75% Break Size. Middle Figure, Break Level Prediction for 50% Break Size. Bottom Figure, Break Level Prediction for 160% Break Size.

8.3

Chapter Summary

In this chapter, FF-ANNs and IIR-LRNNs have been integrated into the approaches proposed in this thesis. Theses models are being compared in the task for monitoring and diagnosing a nuclear reactor based on real-time data collected from plant sensors. The models developed here carries out early detection and identifies break sizes that might affect the operation of the reactor, which might lead to core damage. In all the cases considered, IIR-LRNNs have demonstrated to outperform FF-ANNs in terms of predictive capability. In particular, the difference in the performances of the two models is much more evident in the estimation of the confidence intervals, as IIR- LRNNs always produces tighter confidence bounds compared to FF-ANNs. On the other hand, the computational time required for training the ensemble of IIR-LRNNs is much more larger than that of FF-ANNs due to the number of recurrent layers. However, with the recent advances in computational power, parallelization approaches can be adopted to reduce the computational time by a huge order of magnitude.

Chapter 9

Uncertainty Analysis of Spectral

Correction Schemes in

High-Energy Environments

In this chapter, surrogate models for correcting dose underestimation are proposed. In particular, the proposed models are used for correcting the readings of conventional neutron dose meters used in high energy En > 10M eV environments. Subsequently,

the approaches developed in this thesis is adopted to the proposed models in order to quantify the model uncertainties.