1 Design Challenge and Performance Criteria

In Project Assignment 1, the system of a transmission pipeline was examined and a model regarding the purpose of routing has been proposed. The pipeline itself, its interaction with the environment and the facilities along the route were identified as key characteristics and therefore analyzed in further research and finally implemented into an ontology. Regarding the goal of supporting the early stages of pipeline planning and especially the routing, a parametric model to support the process will be the result of this assignment. To achieve an effective script and in the latter to meet the goals of this assignment, the first step is to reduce the complexity of the model. The specific design challenge will be narrowed down to implement a parametric model for a pipeline from a variable start point to a variable end point, with several waypoints in-between which allow the creation of an individual path. Considering the interaction with the environment, the terrain will be the only component, since the implementation of soil types, land use, crossings etc. would drastically increase the size of the model. To demonstrate the possibilities of parametric routing and optimization, one element of the environment will be enough in this case. Thus, the terrain will be implemented as a height map to simulate the topology of the region and affect the route in its z-axis displacement. Facilities along the route will be ignored to simplify the task. Although their locations are highly relevant in early phases, the spacing is dependent on fluid dynamics and the techniques of pumping/compressing, which would be too complex given the tasks of this assignment. As described in part 1 of the project, the geometry and dimensioning of the components of the pipeline can be neglected for the duration of route optimizations, so that the representation of the pipeline is symbolic, and the focus lies on the parameterization of the routing.

Because feasibility studies are driven by the overall costs of the project, the main cost drivers of the pipeline route will be the performance criteria of the parametric model. The definition and operationalization of those criteria is rather intuitive and will include the following measures:

1. Length of the pipeline from start to end point.
2. Cumulated absolute elevation of the route.
3. Cumulated curvature of all waypoints.
4. Maximum curvature out of all waypoints.

The construction costs are positive related to the length (in meters) of the pipeline, and therefore chosen as the first objective which must be minimized during planning. The second objective is chosen to consider the increased costs of construction works in sloped terrain and its effects on fluid pressure imbalances, so that the height difference (in meters) between two following waypoints must be minimized. The third and fourth objectives take the complexity of bending pipes into account and are mapping the cumulated and maximum curvature at the locations of all waypoints, where in general minimal curvatures are preferred. It is calculated with the angle (in radians) of the incoming versus the outgoing segment at each waypoint.

2 Parametric Model

This chapter provides an overview of the conceptual preparation of the script and the steps to implement the design challenge via software in explicit geometry representations and output measures. The altering of input values will then enable the creation of different design options, which are part of the chapter hereafter.

Chapter 2 Parametric Model

2.1 Concept

The parametric model is divided in two parts, whereby the first one is the simulation of a terrain and the second one the creation of the pipeline. Both parts have their own input parameters, but the output of the terrain-script will be used as input data for the pipeline route as well. The pipeline-script will on the one hand compute the performance criteria as output and on the other hand provide the geometric representation of the pipe.

To create a terrain which serves the purpose of optimizing a route through prevailing mountains, the goal is to represent existing topography or to simulate some with generative mountains. The second option will be sufficient to meet the goals of this assignment. Out of plenty of methods to generate parametric mountains, the chosen workflow includes the randomized population of points onto a rectangle, which also serves as the size of the considered region for the route. The points will then be moved vertically with random amplitudes to create peaks and valleys. A 3D-surface with the size of the base rectangle will then be smoothly fitted through the elevated points.

The pipeline will be located inside the base rectangular of the terrain and is defined with its start and end point in the first step. The second step allows the user to set an arbitrary number of waypoints, which are located also inside the base rectangular and are connected to create a planar polyline from start to end. The polyline will then be projected onto the terrain, with a three-dimensional route as a result. This 3D-polyline is used for both the calculation of the performance criteria and the geometric representation. The following diagram illustrates the concept.

Fig. 1: Conceptual design of the parametric model

2.2 Implementation

For the implementation of the parametric model, Rhino Grasshopper was chosen. It provides a multitude of components to compute geometry by wiring blocks in sequences and therefore create parametric scripts. The output-geometry is rendered inside the Rhino viewport.
The conceptual process for creating a random height map was stated above. The configuration of Grasshopper components to achieve the needed terrain was inspired by online resources for scripting generative mountains (Grasshopper 4 Rhino – Tutorial Central, 2022; Parametric House, 2022). Several input values are in control of the base size, minimum and maximum height displacements, the random seed for the positions and density of the mountains. Being

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Chapter 3 Selected Design Options

a parametric framework, the terrain serves as an addition to the actual parametric model of the pipeline. Consequently, the terrain is once set and remains static throughout the route analysis of the pipeline. With the help of visualizing contour lines and a gradual coloring, the characteristic of the landscape is easily understandable.

Regarding the pipeline itself, the input parameters for the creation of the planar polyline are composed of two groups: Firstly, the start and end points are fixed throughout the analysis of one route and must be set beforehand by x-/y-values within the boundaries of the map. A line will then be drawn between those points and divided in sections depending on the number of waypoints. The inputs for the locations of the waypoints belong to the second group of parameters, which allows the manipulation of the route to navigate through the terrain. Every input has a numerical domain of 0 to 100 and describes the orthogonal deviation from the initial line, whereby the value of 50 represents the center of the individual axis. The amplitude of the deviation is individual for every point and consists of the available space inside the map. The maximum deviation is evaluated by an orthogonal projection to the rectangular boundaries with the corresponding distance as individual limits (see Fig. 2). This procedure allows the users to intuitively change the layout of the route without the need to set x/y-coordinates for every waypoint location and therefore double the amount of input parameters. The polyline is then projected onto the surface object of the terrain in z direction to evaluate the length and height differences. The resulting projected polyline serves not only for the extraction of the performance criteria, but also for the visual representation of the system. To reach a visual pleasing and understandable representation of the system, the projected polyline’s edges are smoothed and used as path for the extrusion of a circle-shape to represent the pipe with a 3D body. The start and end points are each represented with a 3D box to mark the location of the supply and demand facility. The configuration of the Grasshopper components can be seen in the Appendix, the rendered model in Chapter 3.

2.3 Design Space

Since the complexity of interaction with the environment was reduced to the terrain heights, the design options are limited to the geometrical routing based on the waypoints. Within the boundaries of the map, the user has the possibility to set the route to any desired layout. The effects of the terrain are visible through the performance measures of the pipeline. Limitations of this model and opportunities for further development are stated in chapter 4. The exploration of the design space is not only manually possible, but also with the help of optimization algorithms. An example on behalf of this parametric model is shown in the Appendix.

3 Selected Design Options of waypoints from the dashed line

The following Tab. 1 contains three selected options for routing the pipeline between the preset facilities. Option 1 performs best in terms of the cumulated elevation, in contrary to option 3 which has the shortest path and minimal curvature. The selected route of option 2 serves as a trade-off. In regard of the decision process, the weighing or monetizing of the criteria would lead to the optimal design given the engineering challenge.