Sensors, signals, surveys, and maps

Once a simulation has been performed, it is important extract the relevant data from the computation and present this information in the most appropriate format. This post processing task has two aspects: the visualization of the results using three dimensional graphics, and the plotting of certain computed quantities on two- or three-dimensional plots. The visualization of simulation results can be performed using the post processing code DymShow. The plotting of specific computed quantities is discussed in this section. Plots are generated using various standards and sizes.

For the purpose of the discussion, assume that the dynamic response of a beam extending from coordinate xr to coordinate xt has been simulated from time ti to time tf. The data generated from the simulation will include the structural response of the beam at all points xr < x < xt, along the span of the beam, for all times ti < t < tf. This situation is depicted in a conceptual manner in fig. 1: the results of the simulation are defined over a rectangular area in the time-space representation.

Figure 1. Schematics of the different post-processing tool: sensors, surveys, and maps.

In view of the large size of the data set computed by the simulation, subsets must be selected to generate meaningful plots. Three basic options are available.

Sensors

A sensor extracts from the simulation data set time histories of a number of scalar quantities and plot these quantities on a two dimensional graph. In fig. 1, a sensor is represented by a horizontal line. The plot generated by a typical sensor is shown in fig. 2. The concept of such “numerical sensor” is similar to the concept of “physical sensor.” For instance, in the physical world, a strain gauge can be used to measure the strains and curvatures as a function of time at a specific location along the span of a beam. Similarly, in the numerical world, a sensor can be defined that extracts the strains and curvatures of a beam for all time ti < t < tf. Typically, the quantities to be evaluated and plotted by the sensor are defined by four input parameters.

  • The object of the model that is to be sensed. Sensor can be defined for most of the object of the model, beams, lifting lines, or joints, see.
  • The nature of the quantity to be sensed; for instance, in a beam, it is possible to sense displacements and rotations, linear and angular velocities, linear and angular accelerations, forces and moments, or strains and curvatures. In a lifting line, the relevant quantities are airstation displacement and rotations, linear and angular velocities, angle of attack and Mach number, aerodynamic loads and moments. For a revolute joint, it is possible to sense displacements and rotations at the two sides of the joint, of the relative rotation of the two components.
  • If the quantities to be sensed are of a vector or tensor nature, the various components can be measured in different reference frames specified by the user. For instance, because a strain gauge is bonded to the external surface of a beam, it measures strains and curvatures in a local coordinate system attached to the beam. Hence, to correlate computed strains with their measured counterparts, the predicted strain components should be sensed in the same, beam attached local frame. Note that if the beam undergoes large displacements and rotations, the orientation of this frame varies along the beam span. On the other hand, is is often more convenient to represent displacement components in an inertial frame, or a a moving frame attached at the root of the beam.
  • Finally, the quantities to be sensed are extracted at a specific location of the element. For instance, if the sensed element is a beam, the location of the sensor along the beam span must be specified.
Figure 2. Typical sensor plotting the time history of the three components
of the sectional force vector at one point of a beam as a function of time.

Signals

A signal is directly associated with a sensor, which typically extract several quantities at a specific location of the system, as a function of time. For instance, a sensor for the forces at a specific span-wise location along a beam will provide the time histories of six quantities: three forces and three moments. These six quantities are the “six channels” of the sensor. A signal further specifies a channel of the sensor. For the beam example, the first channel is the axial force in the beam, the next two channels are the two shear forces, the fourth channel the torque in the beam and the last two channels are the two bending moments. In summary, a signal is the data generated by a specific channel of a sensor, i.e. it is a single function of time.

Postprocessing operations can be defined for signals. The data can be scaled, the time axis can be shifted or stretched, and portions of the time history can be eliminated. Finally, the signal can be filtered or Fourier analyzed. Signals provide a convenient way of looking post-processed data, but also serve another purpose. Signals can be used as inputs to controllers, or for further post-processing operations, such as stability analysis.

Surveys

A survey extracts from the simulation data set the spatial distributions of a number of scalar quantities and plot these quantities on a two dimensional graph. In fig. 1, a survey is represented by a vertical line. The plot generated by a typical survey is shown in fig. 3. In the physical world, it is possible to measure strains at a number of locations along the span of the beam to obtain a “discrete strain survey.” Clearly, in the numerical world, it is also possible to obtain a strain survey along a beam span by defining a number of sensors along its span. This option, however, is not convenient because a large number of sensors would be required to obtain a detailed distribution of strain along the beam span. A single survey will extract the strains and curvatures at a given instant, along the beam span, i.e. for all locations xr < x < xt. Typically, the quantities to be evaluated and plotted by the survey are defined by four input parameters.

  • The object of the model that is to be surveyed. Surveys can be defined for many objects of the model such as, beams, and lifting lines.
  • The nature of the quantity to be surveyed; for instance, in a beam, it is possible to survey displacements and rotations, linear and angular velocities, forces and moments, or strains and curvatures. In a lifting line, the relevant quantities are airstation displacement and rotations, linear and angular velocities, angle of attack and Mach number, aerodynamic loads and moments. Surveys also allow the evaluation of mode shapes for static simulations. In this case, it becomes possible to survey the eigen displacements and rotations, eigen forces and moments, or eigen strains and curvatures along the span of the beam.
  • If the quantities to be surveyed are of a vector or tensor nature, the various components can be measured in different reference frames specified by the user.
  • Finally, the quantities to be surveyed are extracted at a specific instant in time. The survey gives a “snap-shot” of the distribution of certain quantities in the structure at a given instant.
Figure 3. Typical survey plotting the third eigenmode along the span of a beam.

Maps

A map extracts from the simulation data set the distribution in space and time of a single scalar quantity and plots this quantity on a three dimensional graph. In fig. 1, a map is represented by the rectangular area. The plot generated by a typical map is shown in fig. 4. A map can be seen as a combination of sensors and surveys, but is only able to deal with a single scalar quantity at a time. The plot associated with a map is a three-dimensional graph. For spatial maps, the x and y coordinates of points along an object, measured in the map frame, are plotted along the x-axis and y-axis of the graph, respectively, and the quantity evaluated by the map is plotted along the z-axis. For temporal maps, time is plotted along the x-axis, location along an object is plotted along the y-axis and the quantity evaluated by the map is plotted along the z-axis. The quantities to be evaluated by the map are defined by four input parameters:

  • The object of the model that is to be mapped. Maps can be defined for many objects of the model such as, beams, and lifting lines.
  • The nature of the quantity to be mapped; for instance, in a beam, it is possible to map single components of displacements and rotations, linear and angular velocities, forces and moments, or strains and curvatures. In a lifting line, the relevant quantities are airstation single components of displacement and rotations, linear and angular velocities, angle of attack and Mach number, aerodynamic loads and moments.
  • If the quantities to be mapped are of a vector or tensor nature, the various components can be measured in different reference frames specified by the user.
Figure 4. Typical map plotting the distribution of torsion moment in a beam as a function of space and time.