134 J. Hartig et al. Fig. 14.2 Modular Active Spring-Damper System (MASDS) The MASDS developed at the Collaborative Research Center (CRC) 805 “Control of Uncertainties in Load-Carrying Structures in Mechanical Engineering” serves as an application example for the proposed approach. The MASDS is a structural dynamic system based on an aircraft landing gear, see Fig. 14.2. The MASDS consists of two load-bearing structures of beams, connected via a joint module and a semi-active spring-damper. To quantify and evaluate the system response to drop impact tests in different test scenarios the MASDS is equipped with a variety of sensors to measure force, displacement, strain and acceleration. A 3-axial strain gauge force sensor is used to measure the forces that are introduced via the elastic foot. Above and below the spring-damper module 1-axial strain gauge force sensors (SG) are installed. The forces in the support housing of the upper structure are measured by 3-axial piezoelectric force sensors (PFS). Accelerometers are used to determine the acceleration of the upper structure, the demonstrator elastic foot and the spring-damper module. Displacement sensors, attached at the upper and lower gears of the supporting structure provide the measurement of the spring-damper module compression. Furthermore, tensile, pressure and bending loads of a multitude of bars are detected by strain gauges. By utilization of symmetries and different physical models redundant data is generated deliberately. The upper truss structure of the MASDS consists of symmetrical tetrahedral elements, which represent a rod system. The assumption of a perfectly perpendicular drop impact to the ground results in three symmetrical force paths passing the three support points (1–3) and the outermost rods. The force in each support points (1–3) is measured by 3-ax. piezoelectric force sensors. Strain gauges located in the surrounded rods are used to measure normal and bending strains, see Fig. 14.4. Under the assumption of a perpendicular drop impact, the resulting quantities can be investigated with 9 sensors used in redundant data sources of four models for this subassembly of the test rig. (i) Due to symmetry, the sum of the forces in x- and y-direction of all three piezoelectric force sensors must be zero. (ii) The force equilibrium at each support point has to be fulfilled in each direction. As shown in in the proposed approach (c.f. Fig. 14.3), the plausibility of each data sources needs to be verified by checking whether the signals are within certain limits derived from the characteristics of the examined system like mass, dimensions, sensor and mechanical properties. In the next step the conflict detection for the data sources takes place. Data induced conflicts emerge when confidence intervals of the sources do not overlap. The uncertainty of measured data is specified by confidence intervals. The assumption is made that the values show a gaussian distribution. The level of confidence is 95%. The uncertainty is propagated through the different models with gaussian error propagation. The propagation was implemented by using automatic differentiation (AD). Applied to an algorithm AD automatically gives the value of the algorithm as well as its derivative. AD is implemented by overloading the operators (e.g. addition, multiplication, trigonometric functions) of the used programming language. This makes the treatment of uncertain values straightforward and flexible. The following example deals with an application error of the 3-ax piezoelectric force sensor at the housing support 1, see Fig. 14.4. The wiring was done in such a way that the components in y- and z- direction are interchanged. In addition to that, the eventuality of an unexpected impact angel during a drop test is regarded by setting an inclination angle of 6◦ so that
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