In defense related programs, the use of capability-based analysis, design, and acquisition has been significant. In order to confront one of the most challenging features of a huge design space in capability based analysis (CBA), a literature review of
Recently, capability-based analysis, design, and acquisition have had a significant impact in defense related programs. The paradigm shift to capabilities-based acquisition is causing a fundamental shift in the way defense-related systems are both engineered and purchased. New mission needs and technological advancements have led to novel directives that are causing defense acquisition planning to utilize a capability-based approach. In particular, advancements in communication and transportation, combined with new and diverse enemies, have led to a call for increased joint operations, more integrated operations, and a better method of designing and acquiring systems and SoS (system of systems) to support these needs.
This capability-based mentality shares a natural link with architecting, in that capabilities are achieved through a series of activities. These activities can be represented as an operational architecture. Through the architecting process, they can be mapped to candidate solutions, which can then be evaluated and compared. These solutions provide the
The challenge presented by the sheer number of possible alternatives is compounded in SoS problems. In fact, not only is the number of alternatives extremely large, but the alternatives also vary in their specifications, including alternatives across all aspects of the DOTMLPF (doctrine, organization, training, materiel, leadership, people, and facilities) spectrum. It is difficult to gather enough information early on to make an informed decision, but it is also difficult to even determine the criteria by which two extremely different solutions can be compared. Even justifying the acquisition of a new system can be difficult, because it must be shown that the same mission level cannot be achieved with a new arrangement or new uses of existing systems. To further illustrate this challenge, consider a simple mission, which is comprised of completing 10 activities. Then consider that these activities can be performed in two different sequences, thus creating two operational alternatives. Furthermore, each activity can be performed by one of three candidate systems. Three possible organizations could be responsible for conducting this mission and, last, consider that there are two types of networks being considered for enabling communication in the architecture. There are then 2 organizational alternatives ×310 system alternatives ×3 organizational alternatives ×2 network alternatives, resulting in a total of 708,588 alternatives.
Thus, there are several criteria for a design space exploration method for CBA. First, it must be able to capture and define the large number of architectural alternatives available for consideration during the early phases of acquisition and systems engineering. Next, it must provide a way to filter through the design space and find only the promising alternatives for evaluation, while eliminating those that are either unrealistic or are not expected to meet mission goals. Finally, because even the filtering processes will still leave large numbers of alternatives to be evaluated, there must be a way to quickly and accurately evaluate the remaining alternatives.
Currently, the research of aerospace system of systems architecture alternatives for design space exploration focuses mainly on the
In order for large-scale computing to simplify the design space and to generate a full understanding of space exploration, especially for large-scale multidisciplinary design space exploration and optimization, the
In engineering design, optimization algorithms are often used to search among global optimal solutions in the design space; the method can be divided into two categories:
DOE is an essential basic experimental approach in engineering design optimization, which represents the performance of the design space through different distributions of sampling points. However, while the DOE method is capable of sampling within the developed design space and then analyzing on the sampled points, it cannot explore the design space through the sampling itself nor can it divide or reduce the scope of the design space.
As mentioned earlier, design space exploration is one of the application directions of the
Optimization algorithms of design space exploration, which belong to the latest developments in design optimization, can be used to explore and optimize the design space to find the global optimal solution or a feasible solution. The costs and computational load of the
Above all, we can see that there is a lack of effective methods to utilize various existing experimental and historical data, as well as data from aerospace SoS, leaving a need for knowledge-based design space exploration methods as a guide for system design optimization. For one thing, since a large amount of computer technology and simulation software in engineering applications is required for the process of aerospace SoS design, when there are large numbers of simulations and experiments, there will be massive amounts of data stored in the data warehouse. It is important to take advantage of this useful data for subsequent SoS design optimization and to then support aerospace SoS design space exploration. Secondly, the existing design space exploration methods are used to approximate and explore directly within the aerospace system design space. In the early phase, however, there is typically a lot of uncertainty and a definite lack of knowledge. The existing methods have a too large computational load and cannot hold up to the design practices and processes. It is imperative to guide the designer to focus on the design space area of concern.
Traditional aerospace SoS optimization is a process that flows from the design space to the performance space, called “
The general framework of the method.
The Bilayer exploration process.
Similar, relevant cases are first selected, according to the capability gap and required operational activities, in order to determine the initial aerospace system configuration, which provides foundational data for subsequent derivation of configuration rules. Secondly, it must be determined whether or not the parameter attributes are complete. Thirdly, if the attribute data of the configuration program is complete, then the configuration rules from the complete configuration decision table are derived, using RST. If incomplete data is included, then reasoning with corresponding use of RST in the incomplete configuration decision table is utilized.
In the process of complete rule reasoning, the selected attributes are first analyzed and the continuous data is discretized, using the FCM (fuzzy C-means) algorithm, which preprocesses data for the use of RST. Secondly, in accordance with the selected configuration, similar cases are collected from the corresponding performance estimates, along with a variety of configuration attribute data, constituting a configuration decision table. Again, the simplest related configuration rules from the configuration decision table are acquired with RST. Finally, when the performance space and the configuration space are positioned corresponding to configuration rules, the mapping from P-space to C-space can be completed.
In the incomplete configuration reasoning process, discretized continuous data must first be put into an incomplete configuration scheme. In accordance with the selected configuration, similar cases can be collected in the corresponding performance estimates, along with a variety of configuration attribute data, marking any uncertainties or missing data in the configuration alternatives with an “*.” The configuration decision table can then be compiled. Again, due to the incomplete data, there will be uncertain causality. The optimal configuration rules can thus be determined with the similarity function in Section
Aerospace system configuration can be defined as
The decision table for aerospace SoS C-space and P-space is defined as follows:
In the aerospace SoS configuration model, each attribute subset
For
As seen from the definitions, for the selected configuration
The division matrix of selected attributes
The division matrix and division function are used to infer the smallest reduction, which is a small subset of the attributes that can reflect implicit relationships in the selected configuration decision tables.
With the introduction of new technology or new systems, the relevant information is incompletely or vaguely stored, which leads to incomplete configuration space information. At this time, any attribute value field,
In the configuration alternatives decision table, SIM(
where SIM
Any configuration rules where
For any configuration in
For any configuration alternatives
Where
We use the
The definition of the membership function of each attribute vector to each attribute cluster is
In the process of discretization of continuous data, the minimal value of the following objective function is required:
The application procedures are summarized as follows.
Determine the target that needs to be analyzed and the related attributes that need to be discretized.
Determine a set of sampling points of the configuration attributes
After discretization of the configuration attributes, allocate the value of
Initialize the membership function matrix
Use
Calculate
If
After the C-space area of concern is determined, using the SOM method, the configuration space is mapped to part of the design space, and the subsequent optimization is then capable of meeting the design specifications and requirements only in the area of concern.
SOM is an unsupervised learning neural network, which is a type of data clustering and high-dimensional data visualization method. The purpose of visualization is to project data onto a graphical representation to provide a qualitative idea of its properties. Typically, the multidimensional data is mapped to the two-dimensional space with hexagonal grids. Therefore, SOM further maps the configuration space region to the smaller design space area, which is the area of concern in the design space. Unlike conventional geographical methods, SOM cannot provide any geographical features, coordinates, distances, and so on, but it can describe closeness or distribution of the input design variables. After the initial aerospace system configuration is determined, the input layer of the
In SOM, unsupervised learning clusters similar patterns together, while preserving the topology of the input space and maintaining a full connection of the input vectors to neurons in the output layer. There are two main goals to be achieved. The first is that the output layer searches for the winning unit with a closer weight vector to each input vector.
The second is that, in order to be closer to the input design variables and objective function vectors, weight vectors of the winning unit and its neighboring neurons will be updated. As a result, the
The detailed steps of SOM application are summarized as follows.
Assign the weight vector
Select
Get the neuron that has the least distance from input vectors.
Update the weight vectors of the winning unit and its neighboring neurons.
If the predefined iterative requirement is satisfied, stop. All the design variables and objective functions are projected onto the two-dimensional hexagonal grid. Otherwise, go to Step
In order to better demonstrate this method, a simple example problem will be used. This illustration is adapted from an example previously published by Griendling [
The following several alternatives were selected from numerous architecture alternatives as the basis for the aerospace SoS configuration. After processing the corresponding attribute values, the list was compiled, as shown in Table
The similar cases and corresponding data.
Alternative | Cost | Time | Risk | Support level |
|
Evaluation results |
---|---|---|---|---|---|---|
1 | 99 | 112 | High | I | 0.67 | 1 |
2 | 110 | 110 | High | I | 0.55 | 1 |
3 | 95 | 150 | General | I | 0.71 | 1 |
4 | 108 | 108 | General | II | 0.52 | 2 |
5 | 125 | 125 | General | II | 0.49 | 2 |
6 | 86 | 190 | High | II | 0.67 | 3 |
7 | 146 | 192 | High | II | 0.68 | 2 |
8 | 108 | 90 | General | II | 0.71 | 3 |
9 | 60 | 65 | General | II | 0.72 | 4 |
10 | 74 | 79 | General | II | 0.80 | 5 |
11 | 102 | 80 | General | II | 0.66 | 4 |
12 | 94 | 94 | High | II | 0.54 | 5 |
13 | 80 | 45 | High | I | 0.61 | 6 |
14 | 66 | 78 | General | II | 0.59 | 5 |
Using the standard rough set theory for data mining, the continuous data should be discretized. In order to facilitate attribute processing, the attribute set
Therefore, the attribute
A sample attribute classification is shown in Table
The classification of sample attributes.
|
|
|
|
|
|
|
---|---|---|---|---|---|---|
|
2 | 3 | 2 | 1 | 1 | 1 |
|
3 | 3 | 2 | 1 | 2 | 1 |
|
2 | 5 | 1 | 1 | 1 | 1 |
|
3 | 3 | 1 | 2 | 2 | 2 |
|
4 | 4 | 1 | 2 | 2 | 2 |
|
2 | 6 | 2 | 2 | 1 | 3 |
|
5 | 6 | 2 | 2 | 1 | 2 |
|
3 | 2 | 1 | 2 | 1 | 3 |
|
1 | 1 | 1 | 2 | 1 | 4 |
|
1 | 2 | 1 | 2 | 1 | 5 |
|
3 | 2 | 1 | 2 | 1 | 4 |
|
2 | 2 | 2 | 2 | 2 | 5 |
|
2 | 1 | 2 | 1 | 1 | 6 |
|
1 | 2 | 1 | 2 | 2 | 5 |
Calculated by the software
The decision rules deduced from Table
Among which Rule
Rule
Uncertainty rules are as follows.
In the first mapping layer, the rules list which attributes have the greatest impact on the performance of the aerospace SoS.
Configuration rules show that cost and time are the core attributes of the decision table that influence the evaluation results.
In the process of aerospace SoS design or selection, the designer can select the satisfactory alternatives based on the extracted configuration rules, narrowing the range of options for candidate configuration alternatives.
In practical applications, decisions can be made according to the above rules of certainty and uncertainty.
After the first mapping, suppose that the designer needs to get the alternatives with evaluation results of 6. He can then choose configuration alternatives according to the rules
Before analysis with the SOM, a surrogate model must be established to approximately express the relationship between the variables and objective functions. Sampling 100 sets of data from the existing simulation database using the
Figures
The SOM result I.
The SOM result II.
Objective function
For the sake of a bigger value of
In this way, the value range of P-success should be (0.645, 0.679), rather than (0.612, 0.679), the cost of area is reduced to (81, 93), and the value range of time is reduced to (45, 60).
In Figure
Therefore, compared with the initial design space, the interval of design variables has largely narrowed.
In this paper, we studied capability-focused aerospace system of systems architecture alternative design space exploration problems with bilayer mapping. Our results suggest that the RST method can effectively map aerospace system performance space to the configuration space, while a different configuration space is mapped to different regions, efficiently narrowing the design range and providing new ideas for the quick selection of alternatives. At the same time, the SOM method can effectively map the configuration space of aerospace system of systems to the design space and reduce the design dimension or range. This allows the focus to remain on the areas of concern. The optimized efficiency of aerospace system of systems design is fundamentally improved and, as mentioned above, the proposed method effectively explores the design space, reducing the design space range. Starting with the initial stage of the aerospace system of systems design, the method is optimized in the conceptual design phase, sufficiently solving the problem of computing complexity and search difficulty.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported in part by the National Natural Science Foundation of China under Grant nos. 61273198 and 71031007. The authors are grateful to the anonymous reviewers for their valuable comments and suggestions to improve their work.