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- Wind Tunnels_ Aerodynamics, Models and Experiments (Engineering Tools, Techniques and Tables)

The most common algorithm used was introduced by Shi and Eberhart as. In Eq. The trust parameters indicate how much confidence the current particle has in itself cognitive, c 1 and in the swarm social, c 2 , and will draw the particle to the positions corresponding to the respective best costs of these components. To some degree, the selection of the inertia and trust weights is problem dependent. A poor selection of parameters may lead to premature convergence to a locally optimal solution, or a solution that takes an excessive number of iterations to converge.

A good selection of parameters can be made through either trial and error or deduction and experience. Multi-objective optimization is necessary when two or more objectives are in conflict and a compromise between objectives is desired. This conflict is often the case when considering the requirements of multiple stakeholders in engineering design.

If there is no single solution that will simultaneously optimize each objective, there instead exists an infinite number of Pareto optimal solutions. A solution is Pareto optimal if any of the objective functions cannot be improved without degrading one or more of the other objective functions. A set of Pareto optimal solutions creates a Pareto front, which illustrates the tradeoffs in simultaneously meeting multiple objectives.

To select an optimal solution from the set of Pareto optimal solutions, subjective preference from the user is required; all Pareto optimal solutions are considered equally acceptable until the user preference is applied. In no-preference methods, the user does not indicate their preference often defaulting to equal weight, while a priori , a posteriori , and interactive methods utilize preference information before, after, and iteratively while searching for a solution, respectively Miettinen, An a priori method is implemented in this study, where equal weight is assigned to the two objectives before initiating the search.

These two objectives are normalized to rectify differences in magnitude and units. The model selected for this study was a low-rise building with a parapet wall of variable height as developed in Whiteman et al. The model was The parapet height was actively controlled by actuating the outer wall of the model using Nanotec linear stepper motors at each corner of the model, while the inner core of the model remained stationary.

This created a constant building size with a parapet wall of variable height, up to The model is shown in Figure 4 , including the outer wall vertically movable and inner model stationary. Urethane tubing and pressure taps were installed on both the outer and inner sides of the parapet wall. A total thickness of the model parapet wall and thus outer wall of 2. Based on the model dimensions and target design of a two-story office building, a model-scale was selected. Figure 4.

A Building model with a flush parapet wall and B a raised parapet wall. The pressure measured at each pressure tap was assumed to act over a unique, non-overlapping tributary area on the envelope of the model. Voronoi diagrams derived from Delaunay triangulation were used to calculate the tributary area of each tap Gierson et al. This is a reproducible, automated process, important when the envelope shape is changing during optimization. The flattened view of taps and corresponding tributary areas for the model with a parapet height of Figure 5. Tap locations, tributary areas, and surface numbers on a flattened representation of the model with a parapet of Surfaces 1 through 4 correspond to the four building walls.

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The edges that join the outer parapet surfaces Surfaces 1—4 and the inner parapet surfaces Surfaces 6—9 in Figure 5 are physically located at the top of the parapet and separated by the thickness of the parapet. Surfaces 5 and 10 are the top of the parapet wall and the roof, respectively.

As the parapet height increased, the tributary areas for both the outer building surface and inner parapet surface increased, while the tributary areas for both the top of the parapet wall and the roof remained constant. Horizontal base shear forces were calculated for the direction perpendicular to the long building dimension. Synchronous measurements from pressure taps located at the windward, leeward, and parapet walls Surfaces 1, 3, and 6 and 8 in Figure 5 , respectively were multiplied by the tap tributary areas to obtain local base shear force contributions.

The total base shear time history was then obtained from the summation of these forces as follows:.

The BLWT is 6. The surface pressures on the model building surfaces were measured using Scanivalve ZOC33 Scanivalve, For this study, the Terraformer was configured to simulate open terrain for the geometric scale of A more detailed description of the simulation of the upwind terrain used throughout this work can be found in Whiteman et al. Differential pressures were collected for s and calculated pressure coefficients were referenced to the velocity pressure at the model eave height.

In this study, three alternative objective functions were considered: 1 minimizing the magnitude of peak suction on the roof, inner parapet walls, and top of the parapet Surfaces 5—10 in Figure 5 , 2 minimizing the magnitude of peak suction and positive pressure on the roof, inner parapet walls, and top of the parapet Surfaces 5—10 in Figure 5 , and 3 minimizing both the magnitude of peak suction on the roof Surface 10 in Figure 5 and the magnitude of peak base shear see Base Shear Force Calculation.

As the parapet height increases, the peak suction nominally decreases for the roof surface and top of the parapet wall and increases for the inner parapet wall surfaces. Also, an increase in parapet height increases the peak positive pressure on the roof surface and windward side of the leeward parapet and increases the base shear of the structure. These observations are not comprehensive; however, they include all effects that influenced the optimal design.

The optimization problem was physically constrained by the model-scale minimum and maximum parapet height of 0 and The lower and upper physical bounds of the parapet height were chosen so that the optimal solution was confidently located within the entire search space. The summary of objective functions, surfaces, and approach wind angles considered for this study for both non-stochastic and stochastic algorithms are given in Tables 1 and 2.

The model-scale parapet heights were rounded to the nearest 0.

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## Wind tunnels : aerodynamics, models, and experiments / Justin D. Pereira, editor - Details - Trove

A tolerance of 0. Based on the desired tolerance and Eq. Increasing the parapet height will reduce the suction on the roof surface, which is the major benefit of installing parapet walls. At the same time, however, increasing the parapet height will increase the suction on the inner parapet surfaces.

This balance creates the design tradeoff explored in Case 1. The objective is selected as a minimization of the maximum magnitude of the peak suction considering the roof, inner parapet surfaces, and the top of the parapet. Cyber-physical systems optimization was conducted with results summarized in Table 3 and Figure 7. Peak suction values for both GSS intermediate points at each iteration are shown in Table 3.

The convergence of the search space toward the optimum height of 7.

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The initial domain bounds iteration 1 were [0, At iteration 1, the intermediate points produced parapet heights h p of 4. As a result, the domain [0, 4. This procedure was repeated for the maximum number of iterations. Table 3. Figure 7. Parapet height iteration history using golden section search Case 1. The variability of peak suction due to experimental testing is seen for iterations 12 through 18, as both intermediate points have the same parapet heights for these iterations.

This balance is expected because the suction on the roof, top of the parapet, and inner parapet surface were given equal weight in the objective function. The optimal result corresponds to a full-scale parapet height of 1.

This parapet height simultaneously minimizes suction on the roof and inner parapet walls. The optimal height found satisfies this limit of 1.

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Figure 8. Figure 9. As the parapet height increases, the positive pressure increases for regions of the roof and the windward side of the leeward parapet. Positive pressures on the roof are additive to gravity loads, which can increase the forces on structural members. Positive pressures on the windward side of the leeward parapet wall are additive to the base moment and base shear of the parapet wall and the structure.

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Formally, the objective of Case 2 is to minimize the maximum magnitude of peak suction and peak positive pressures on the roof, inner parapet surfaces, and top of the parapet. The relative importance of reducing suction versus positive pressure is not considered; they are treated equally. CPS optimization was conducted with results summarized in Table 4 and Figure The convergence of the search space toward the optimum height of 6. Similar to Case 1, there is variability of the maximum suction due to the experimental testing best seen for iterations 12 through The results for the envelope of peak suction pressures at the optimal parapet height are similar to those of Figures 8 and 9.

The optimal height corresponds to a full-scale parapet height of 1. Table 4. Figure Parapet height iteration history using golden section search Case 2. The results of the two non-stochastic GSS optimization runs are compared herein to the two stochastic PSO runs reported in Whiteman et al. Across all four runs, the same phenomenon peak suction governed the optimal design, enabling this comparison. The GSS algorithm exhibited faster convergence; 18 iterations with 2 tested parapet heights per iteration were required for the GSS algorithm total 36 tests.

With a relaxation on the final search space size tolerance, the total number of tests could be realistically cut from 36 to 22 based on Figures 7 and For the PSO algorithm, 13 iterations with 5 tested parapet heights per iteration were required total 65 tests. Although the GSS algorithm exhibited faster convergence, there was a higher observed variability with the final optimal values compared to those of the PSO algorithms; optimal heights of 7. The difference in optimal solution from run to run is due to the experimental variability in BLWT testing. In the GSS algorithm, although the previous intermediate point which was reused was retested, each test held higher significance in the optimization procedure as it directly affected the search space of the next iteration.

The PSO algorithm requires more tested parapet heights per iteration to create the swarm effects and has the same search space for every iteration i. There is an observed tradeoff between convergence speed and perceived accuracy based on repeatability. The type of algorithm which would best be applied to the CPS approach is problem dependent and should be chosen based upon multiple factors, including but not limited to the expectation of local minima, number of design variables, variance in results for repeated tests, and allowable testing time.

In particular, the GSS algorithm is not suitable for multiple design variables or a design space with local minima.

## Wind Tunnels_ Aerodynamics, Models and Experiments (Engineering Tools, Techniques and Tables)

The PSO algorithm can readily handle optimization problems that are multi-variate, multi-objective, constrained, and with local minima in the solution space. Additionally, PSO is less sensitive to the variability of experimental testing. For its versatility, PSO is selected for the proceeding multi-objective optimization. The objective was to determine the optimal parapet height that achieves the best compromise in reducing peak suction on the roof and peak building base shear.