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The computation of thresholds are formulated also as an optimization problem, which can be solved by using LMIs.
When compared to the most common strategies in the literature, the suggested approach: (i) under suitable conditions, guarantees false alarms are avoided; (ii) unlike residual-based architectures, does not require the computation of thresholds to declare faults; (iii) has applicability to a wide class of plants.
The postulate κ → ∗ ( N + 1 ) = [ κ N ∗ ( N + 1 ), κ ∗ → ( N ) ] helps to reduce complexity for computation of thresholds significantly.
This new formulation involves two problems: (1) the approximation of posterior probabilities on each level and (2) the computation of thresholds on these probabilities to make a decision.
Flow chart for SA algorithm for computation of thresholds has been shown in Figure 3. Numerical results for the optimization process using SA algorithm are discussed in Section 8. Figure 3 Flow chart for implementation of SA for optimization of thresholds.
Our procedure for the computation of thresholds for the likelihood ratio test statistics makes our proposal quite computationally intensive but in the current climate this presents little difficulty.
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Since the latter method allows for direct computation of the thresholds for all traits, whereas the simulation required significant computing time for each trait, we used the thresholds obtained using the effective number of markers.
It allows the explicit computation of adaptive thresholds ensuring a guaranteed robustness with respect to structured and bounded disturbances which can be not only additive but also multiplicative.
The computation of such thresholds depends on the nature of the task for the dialogue system under study and how "emotional" the interactions can be.
For the computation of significant thresholds, 10,000 simulations were used under the null hypothesis (no QTL) for each trait and LG.
Table 3 Computation of the threshold frontier for switching on/off one carrier assuming with two traffics 1: Define λ TH =∅.
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