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Single Loop Approach (SLA) |
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Single Loop Approach (SLA) |
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SLA is a reliability-based design optimization (RBDO) method. Reliability-based optimization methods take uncertainties in the design into account and search for designs that satisfy the design requirements with a required probability of success. A reliability-based design problem is formulated as follows:
Objective: |
min f(x, r, p) |
Constraints: |
P(g(x,r, p ≤ 0.0) > PS |
where,
x is the deterministic input variables.
r is the random input variables (affect the design, but are subject to uncertainties).
p is the pure random parameters (variables we have no control over, but affect the design, such as humidity and temperature).
The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. SLA collapses the nested optimization loops into an equivalent single-loop optimization process by using the Karush–Kuhn–Tucker optimality conditions of the inner reliability loops in the outer design optimization loop, therefore converting the probabilistic optimization problem into a deterministic optimization problem. Single loop means the reliability estimate may not be accurate during the intermediate stages of the optimization. The reliability estimate is only valid in the final converged iteration.
| • | SLA is far more efficient than the traditional double-loop RBDO algorithm. |
| • | SLA’s efficiency and accuracy is ranked in between the two other RBDO methods in HyperStudy. |
| • | An extension of SLA is implemented in HyperStudy to allow for robust design optimization. Robust design optimization attempts to minimize the objective variance in order to reduce its sensitivity to design variations and consequently increase the design's robustness. The implementation in HyperStudy is based on the use of percentiles for the objective function and is turned on via the Robust Optimization setting in the Specification step. |
| • | SLA terminates if one of the conditions below are met: |
| - | One of the convergence criteria are satisfied (SQPEPS or DVCONV). |
| - | The maximum number of allowable iterations (MAXDES) is reached. |
| - | An analysis fails and the “Terminate Optimization” option is the default (IGFAIL). |
| • | The reliability analysis is carried out by searching for the most probable point (MPP). Issues such as non-uniqueness of the MPP and highly non-linear output response functions can reduce the accuracy of the reliability calculation. |
The flowchart below illustrates the different phases of the SLA process.
In the Specifications step, you can change the settings of SLA from the following tabs:
In the Settings tab, you can access the settings listed below. Please note that for most applications the default settings work optimally, and you may only need to change the Maximum Iterations and Robust Optimization.
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In the More tab, you can access the setting listed below. Please note that for most applications, the default settings work optimally.
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