There is an old maxim, sometimes attributed to Albert Einstein, that all things should be made as simple as possible, but no simpler. Regardless of the origin, there is some truth to this saying, especially when applied to engineering disciplines. Engineers strive to create solutions to real-world needs given the realities of the time to deploy and the cost of deployment. The design engineers are not necessarily searching for the perfect solution, simply the optimal solution given these constraints. Sometimes that optimal solution is a highly elegant solution, leveraging simplicity in the service of short development and manufacturing times and reduced cost. Simpler solutions are often easier to understand and characterize as well, making them more robust and reliable. Their relative lack of complexity demands fewer components, relaxed margins and tolerances, and higher confidence levels. To be sure, exquisite systems demand exquisite solutions, at which point the engineer’s consideration of second- and third-order effects is important. But these systems are often built from the ground up, starting with the fundamental architecture and structure, the basics of interfaces and functionality, upon which the details are then further developed.
In my book, and on this website, I use simplified examples by necessity to discuss and explain basic, fundamental concepts relating to resilient space systems. These examples represent a beginning, not an end. Or, perhaps, a means to an end, as most of the concepts can be extrapolated to whatever level of detail is necessary. I don’t always delve into those details, and at most will imply the extension of a concept, but rest assured that they are there. For my purposes that exercise is left to the reader, or to a later book.
One example of this is the use of piecewise linear functions in describing system time-domain responses to a threat. In practice, the function may be any shape that represents a true expected system response., and the mathematics can accommodate it. But in many cases such complex responses do not contribute to the illustration of the concept and can actually detract from it. Likewise, when discussing the basics of path diversity and the methods of calculating resilience, simple architectures are presented. The example encompasses nodes, links, and paths as representations of satellite communications systems. Threats can disable one or more nodes and links. My examples consider a binary, effects-based model in which the node and/or link either is fully functional or fully disabled. In truth, links could be partially degraded, with some capacity between 100% and zero, and this can be incorporated into resilience calculations as robustness. However, it is simply an extension of the basic modeling methodology.
As soon as complex threats are fully considered in a physics-based approach, the resilience calculations will rise in complexity as well. This is to be expected. Unless simply bounding performance in a worst-case analysis is sufficient, the mathematical models will include all of the details that describe the interaction of the threat with the system and the associated forecast outcomes expressed as system responses. Again, the methodology itself is unchanged, but the complexity of the underlying model can potentially become much more complicated.
As an introduction to the topic, simple examples fulfill the need and help provide a path to future extensions. Simplicity is valued, but not always achievable depending upon the required fidelity of the product, in this case understanding and calculation of the resilience of space systems. As system designers, simple elegant solutions should always be a goal, and that includes devising ways to make future space systems more resilient. But practically speaking, these systems are quite complex by their very nature and so this goal may not be fully achievable, but elegance can still be approached with imaginative design.
