An unmanned system (UAV)
Hedging with Futures and Options – Practice Problem
November 14, 2018Mathematics and Statistics
November 14, 2018Assignment
An unmanned system (UAV) has been designed for an autolanding capability. The UAV should be able to navigate and fly autonomously from any point within a defined three-dimensional (3D) space to a landstrip and land there without human intervention.
The UAV autolanding design capability must be tested by bringing the UAV to any location within a 3D space in front of the landing strip, and by initiating the automatic landing sequence. System testing considers three input factors (X, Y, and Z) representing the initial location of the UAV in space and one output which indicates a Test Success Score (TSS). TSS is a continuous variable representing either total success (TSS = 1), partial success (0 < TSS < 1), or complete failure (TSS = 0). TSS is computed based on the UAV touchdown rate of descent, UAV angles (pitch, roll, yaw) relative to landing strip centerline and speed as well as landing strip locations of touchdown as well as completion of UAV rolling. A failed test is declared if (a) the ground operator has to abort the UAV autolanding sequence and manually control it or (b) the UAV either touches down or completes its rolling run outside the emergency areas of the landing strip, or (c) the UAV has been damaged in the landing process.
The number of possible tests for this problem is, for all purposes, very large, and the cost of each test is considerable. The tests are limited by defining a specific set of values for each factor, or defining a set of rules for determining these values. Total number of alternatives for each factor are given in the table.
| UAV initial location (feet) | ||||
| Factor | Minimum | Maximum | Step size | Number of alternatives |
| UAV – X | 30 | 50 | 10 | 3 |
| UAV – Y | -20 | 20 | 10 | 5 |
| UAV – Z | 5 | 35 | 10 | 4 |
Deliverables:
- Draw charts to represent the position of the UAV in space (landing strip position in space needs to be shown).
- Determine the number of tests need to be performed according to the number of alternatives.
- Generate two TSS values for each test based on the potential UAV initial location.
- Consider only the minimum and maximum locations for the UAV and build a design of experiments analysis to identify the significant factors.
- Perform an analysis of variance (including the error estimation, sum of squares, and significance of factors).