Optimization loops

Return to step 1 and update HRAT if on outer optimization loop over HRAT is considered. 

Remark 1 The above statement corresponds to the simultaneous consideration of all steps shown in Figure 8.20, including the optimization loop of the HRAT. We do not decompose based on the artificial pinch-point which provides the minimum utility loads required, but instead allow for the appropriate trade-offs between the operating cost (i.e., utility loads) and the investment cost (i.e., cost of heat exchangers) to be determined. Since the target of minimum utility cost is not used as heuristic to determine the utility loads with the LP transshipment model, but the utility loads are treated as unknown variables, then the above problem statement eliminates the last part of decomposition imposed in the simultaneous matches-network optimization presented in section 8.5.1. 

Remark 2 In Figure 8.20 we have discussed the optimization loop of HRAT. Specifying a value of H RAT allows the calculation of the minimum utility loads using the LP transshipment model, The optimization loop of HRAT had to be introduced so as to determine the optimal value of HRAT that gives the trade-off of operating and investment cost. Note, however, that in the approach of this section, in which we perform no decomposition at all, we do not specify the H RAT, but we treat the hot and cold utility loads as explicit unknown optimization variables. As a result, there is no need for the optimization loop of HRAT since we will determine directly the utility loads. 

Window sizes have been picked empirically, but the window size seems to determine the frequency spectrum of the loop splice click . If the window size is made small, then sub-optimal loops tend to have a large low frequency thump. If the window size is made large, remaining artifacts will be high frequency clicks. 

Fig. 17. An incremental approach to the design of a four-helix bundle protein (Ho and DeGrado, 1987). (a) The sequence of a peptide is first optimized for forming a very stable tetramer of a helices. The stability of the tetramer can be assessed from the dissociation constant for the cooperative monomer-to-tetramer equilibrium, (b) Two optimized helical sequences are then connected in a head-to-tail manner by a single loop. The loop sequence can be optimized by evaluating a series of alternate designs, (c) Finally, the entire four-helix bundle structure can be constructed from four optimized helices and three optimized loops.

The decreased affinity of TFl for T-DNA is correlated with reduced bending, suggesting that the substitution of hmU for T might affect deformability. Binding to hmU-containing loop-constructs was therefore compared to results obtained with T-containing DNA. Most loop-placements diminish the affinity of TFl for hmU-DNA. For DNA with optimal placement of 4-nt loops (9 bp separation), the affinity is identical to that of perfect hmU-duplex ( 3 nM). Remarkably, the discrimination between hmU and T essentially disappears with the optimal loop separation. Since site-specific flexure qualitatively and quantitatively substitutes for hmU-preference, we propose that hmU-content and loops offer the same or similar contributions to complex formation (10). 

The algorithm in Fig. 7.27 is characterized by two optimization loops. The inner loop describes the operating parameter optimization based on the strategies introduced before. When for one set-up (e.g. one column length) the optimized operating parameters have been found, a new set-up (e.g. another column length) has to be chosen, represented by the outer design parameter optimization loop. This proce-... 

The first design of a satellite for a specific mission is based on the main criteria payload and orbit, and includes the draft design of relevant sub-systems. Three optimizing loops follow for estimation of system budget, definition of packaging and relocation of routing (Fig. 10.11). Due to the multidisciplinary nature of satellite... 

On the other hand, when more than one fault can influence the system at the same time, advanced diagnostic methods are used. These methods are based on parameter estimation. Sensitivity bond graph formulation [12] allows real-time parameter estimation and thus it is possible not only to isolate multiple faults but also to quantify the fault severities. Parameter estimation in single fault [2] or multiple fault scenarios [12] are essential steps to be performed before fault accommodation. The parameter estimation scheme also gives the temporal evolution of system parameters. Thus, it is possible to identify and quantify different kinds of fault occurrences. A progressive fault shows gradual drift in estimated parameter values and intermittent fault shows spikes in the estimated parameter values. The advances made in the field of control theory have made it possible to develop state and parameter estimators for various classes of nonlinear systems. Analytical redundancy relations may also be used in optimization loop for parameter estimation because it avoids the need for state estimation. Interested readers may see Ref. [3] for further details and some solved examples. 

Example 7.2.2 This can be seen, when solving the truck example for different values of the adiabatic coefficient k. When k exceeds a value between 1,542 and 1.545, the relative translation p o changes its sign. This leads to the physically unrealistic situation shown in Fig. 7.2. Although technically irrelevant, these values of K can occur within the optimization loop as intermediate results. 

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