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at two different flight conditions), which are totaled for all components. The totals represent the goals that the model seeks to minimize (the blue cells). The goals can be individually analyzed or can be analyzed in an aggregate manner by calculating the variance from a given target (as shown in the figure), then summing the squares of the variances and minimizing the sum (shown in the red cell at the extreme lower right). Weighting factors have been applied to bias the optimization by priority of product cost (30% factor), then by weight (25% factor), then by heat load (22.5% for each condition). These can obviously be easily modified based on prevailing program conditions. The green cells just below the variables show the constraints that are applied to the calculated parameters. For each set of values of the variables, an entire model of the fuel system is evaluated at a large number of flight conditions that are defined by design tables. The fuel system model is not shown, but was included to validate the concept of optimization modeling. One issue associated with optimizing pumps and actuators concurrently stems from the basic relationship between them. ActuationLoad = (PumpAP - Losses) 9 PistonArea Since Pump AP and piston area are both variables that require optimization, the fact that a constraint (actuation load) that must be satisfied is the product of the variables leads to a non- linear situation. Although a bit more difficult, techniques for non-linear optimization exist which can still lead to successful application of this concept. One potential method would be to hold one of the variables such as pump impeller size fixed for a given run, store the results, generate another set of data with a different impeller size, and so on. Using the compiled results from the initial runs (actuator sizes are now optimized for each impeller size), this set of data can now be optimized for impeller size, in essence a two-step process. 111PDF Image | Improving Gas Turbine Engine Control System
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