An architecture decomposition method of pneumatic catapult system based on OPM and DSM

Lu GAN, Gang YANG, Xianhui LI, Enze ZHU, Hu CHEN,Xiaohui WEI,*

a State Key Laboratory of Mechanics and Control of Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

b Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

c College of General Aviation and Flight, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

KEYWORDS Architecture decomposition;Cluster analysis;Design structure matrix;Object-process methodology;Pneumatic catapult system

Abstract The architecture strategy of the Unmanned Aerial Vehicle(UAV)pneumatic launch system should continue to evolve to adapt to complex and variable operating environments.Architecture representation, decomposition perspective, and cluster analysis play a vital role in the early phase of system architecture development.In order for the system to emerge anticipated and desirable intrinsic functional properties, an architecture decomposition method based on the Object-Process Methodology (OPM) and Design Structure Matrix (DSM) is put forward in this paper.The OPM is proposed to model the UAV launch process formally, and the matrix representation of the architecture of the pneumatic launch system is established.After the extension of the definition and operations of DSM,with the Idicula-Gutierrez-Thebeau Algorithm plus(IGTA+)clustering algorithm, the transformation of the pneumatic launch system architecture from process decomposition to function decomposition is demonstrated in this paper.The analysis shows that the architecture decomposition of the pneumatic launch system meets the functional requirements of stakeholders.

1.Introduction

With the accelerated evolution of war forms and military intelligence, Unmanned Aerial Vehicle (UAV) swarm operations will play a more important role in the future.As an advanced UAV launch technology, the pneumatic catapult launch has many advantages.More specifically, it can launch continuously, reset itself automatically, and make movement faster.Besides, it is easy to use.Therefore, the development of the UAV launch system based on the pneumatic catapult provides the fundamental guarantee to realize UAV swarm cooperative operations.

System development usually conforms to the life cycle stage of the systems engineering‘‘Vee”model developed by Refs.,1,2starting from business/task analysis, needs/requirements analysis,and architecture definition.More than 50%of the life cycle performance, cost, and environmental impact of the system are caused by decisions made in its early design phase.3Architecture development occurs in the early phase of systems engineering,and it also attempts to describe the attributes and characteristics of system elements that meet stakeholders’requirements.

It is generally believed that the core problem facing complex systems is how to integrate the components.In many cases,however,the reason why integration becomes so difficult lies in the fact that the categories of issues are not well defined at the architecture stage.Therefore, as an emerging research field,4system decomposition takes on considerable importance, significantly contributing to system architecture and its complexity.Decomposition is an explicit choice in system architecture,5and architecture development can benefit from more sophisticated system decomposition.6,7Unlike the traditional perspective based on the discipline, experience, or organization,this paper mainly focuses on the modeling method of system architecture and explores how different decomposition viewpoints affect the configuration of architecture.The purpose of architecture decomposition is to describe and analyze architecture from different perspectives and to support the decision making of architecture.

The remainder of this paper is structured as follows.Section 2 summarizes the literature related to system decomposition from three aspects: architecture representation,decomposition perspective, and cluster analysis, and points out the problems in traditional research.Section 3 presents a graphical Object-Process Methodology (OPM) model of the concept of UAV launch operation according to the requirements of stakeholders and then refines and expands the model to construct the Object-Process Diagram (OPD) and develop the Process-Object(PO)mapping matrix of the pneumatic catapult system architecture step by step.In Section 4,the Object-Process Design Structure Matrix(OPDSM)is constructed,and the Projected Design Structure Matrix (PRDSM) is obtained by the projection operation.The process-based architecture decomposition of the pneumatic catapult system is obtained.Then the PRDSM is reconfigured and grouped by the IGTA + for clustering, and function-based architecture decomposition of the pneumatic catapult system is obtained.Section 5 analyzes and discusses the differences between the two decomposition perspectives (i.e., process decomposition and function decomposition) and then provides the architecture decomposition principle to explain the relationship between the evolution of its internal process and the emergence of explicit functions.The conclusions are drawn in Section 6.

2.Literature review

2.1.System architecture representations

Before developing systems,representations of the system architecture must be created.System architecture refers to the structure of a system—embodied in its elements,their relationships to each other(and to the system’s environment),and the principles guiding its design and evolution—that gives rise to its functions and behaviors.8System architecture is designed to define the structure and behaviors of complex systems to satisfy their operational and functional requirements.9Hamza et al.10proposed a function-driven method to generate a universal system architecture.This approach relies on establishing links between functions and components to define the physical architecture based on the selected functions.Judt and Lawson 11proposed a method connecting requirements with functions and functions with components for architecture evaluation.Giles and Giammarco12formalized the design and architecture of the UAV swarm system on the basis of Model-Based Systems Engineering (MBSE) and a mission engineering approach.In the design of complex systems (e.g., industrial machinery, energy system, and electrical appliances), product architecture plays a key role in determining product behavior.13,14It is challenging to carry out a detailed quantitative evaluation of architecture design located upstream of the design process due to its complexity and ambiguity.Therefore,creating a representation of the basic system architecture is the foremost essential step of system development.

Although systems engineering has become a wellestablished discipline, system architecture, as an overall interdisciplinary engineering theory, is still in the early stage of development.15However, there is a methodology including a language and a modeling method.The methodology can use the system architecture theory to realize the representation of the system and undertake relevant research.Object-Process Methodology(OPM),developed by Dori,16is used for product design and systems engineering and has been used in conceptual modeling and system architecture in many domains.OPM can combine objects with processes and faithfully describe the architecture,function,and behavior of the system in a single and coherent model, which is applicable to almost any domain.16Crawley and Weigel17used OPM to represent the architecture of the system based on form, function, and concept.Osorio et al.15proposed a method based on system architecture theory, using OPM to study Complex Largescale interconnected Open Society-technical (CLOS) systems.Yaniv et al.18used OPM to establish model-based operational engineering and demonstrated the operation process of an airport from multiple views,which is helpful for system engineers in terms of architecture decision making.Since the architecture decomposition depends on the complexity of the system and the objects of analysis, OPM, which can realize multiperspective unified modeling, has many characteristics that can be used to study the system architecture.

2.2.Generation of grids

When defining the architecture of complex products, the general idea is to decompose products (systems) into smaller elements, such as subsystems and components.This is a critical step in that the rest of the platform development will depend on the choices made in the decomposition stage.Tilstra et al.6 showed that product flexibility can be improved by deeply exploring the lower level of product decomposition.Hirtz et al.19proposed a method of decomposing the system using a standardized set of function-basis-related terminology.Noemi et al.20analyzed the relationship between the level of system decomposition and the level of system modularization.From the system perspective, architecture decomposition usually follows a top-down approach.

It is generally believed that a system can be viewed from different perspectives at a system-wide level.However, unlike what is usually assumed,when focusing on a single perspective(such as a system perspective),the decomposition of the system can be carried out in a variety of alternative ways,so different infrastructure will be produced each time.Additionally,according to the perspectives of different stakeholders, the decomposition of the system will also be very different, which will have a far-reaching impact on the subsequent system architecture development.

However,literature on how to correctly decompose the system for architecture analysis and the relevant impact is scarce.Engel and Browning21built a design for adaptability to the exploded perspective of the system.Simon22acknowledged that the function decomposition results of complex systems are unlikely to be unique.AlGeddawy and ElMaraghy23presented how the decomposition level and the decomposition granularity affect the modularity of the system architecture.Suh et al.24decomposed the complex electromechanical system from three perspectives: assembly-based, function-based,and service-based, indicating that the choice of viewpoints and perspectives has a significant impact on architecture decision making.It can be found that there may be different viewpoints depending on the main concerns of individuals or teams.Besides,specific perspectives may also affect the system decomposition and subsequent system architecture.

2.3.Cluster analysis methods

In previous studies, product architecture design, especially modular design, has been discussed by transforming the components of complex systems and their interactions into any concise model(such as figures and matrices).25,26Design Structure Matrix (DSM) is a typical scheme in which components are mapped to the nodes of the matrix,respectively,and modular design can be considered through clustering operation.8Pimmler and Eppinger,27and Helmer et al.28proposed a product architecture design methodology through DSM analysis.Sosa et al.29,30discussed the jet engine system, describing the interactions between the exchanges of information, energy,and materials and physical adjacency and modularizing the system by clustering DSM.AlGeddawy and ElMaraghy31proposed a new method to determine the decomposition level of a variable manufacturing system by using DSM and a granularity index.Tilstra et al.7showed how to use the functional modeling method to create system decomposition, especially High-Definition Design Structure Matrix (HDDSM).32–34Gan et al.35used the HDDSM to model the product architecture of the UAV launch system, introduced a structural clustering algorithm for networks, and designed a better architecture modular configuration scheme for the UAV launch system.

Although there has been research on how to expand DSM,there is a paucity of research on how to generate DSM from OPM better.Sobol and Dori36followed a methodical fivestep approach for applying DSM to analyze and improve complex OPM system models.The method shows how the OPMto-DSM procedure works, and improves model modularization through DSM clustering or partitioning algorithms, thus integrating two complementary Model-Based Systems Engineering (MBSE) approaches—OPM and DSM.This research aims to expand the capability of the system engineer and benefit the development of the system architecture.

In addition, DSM has been widely used by scholars and various industries to improve the decomposition process of system architecture, organizational architecture, and process architecture.8In order to use DSM to perform architecture modeling and analysis,various clustering algorithms have been developed.Blondel et al.37proposed an algorithm that uses a two-stage method to detect ‘‘communities”to divide the system into optimal module configuration.Another widely used clustering algorithm is the Idicula-Gutierrez-Thebeau Algorithm (IGTA), and it is mainly based on the algorithm suggested by Idicula38and further developed by Gutierrez39and Thebeau.40Based on the idea of the stochastic hillclimbing optimization algorithm, it uses cluster coordination costs and the simulated annealing method to determine the optimal module configuration.On the basis of the penalty function method, Sinha et al.41considered design constraints(e.g.,maintenance,packaging,and heat),using IGTA to combine components into modules.Borjesson and Ho¨ltta¨-Otto42further developed IGTA and improved the speed of the algorithm by creating IGTA +.In the research conducted by Sanaei et al.,43the IGTA+clustering algorithm was modified to incorporate design constraints using the constraint matrix,and the feasibility of the algorithm was proved by using the function architecture of the syringe of the magnetic resonance imaging machine.As one of the main analyses in the design process of system architecture, the cluster analysis based on DSM can obtain the expected utility of the decomposition of the system into modules and facilitate insights into the effectiveness and rationality of system architecture from multiple perspectives, which has achieved immense popularity in the field of systems engineering.

2.4.Research gaps

The traditional decomposition method has two weaknesses in explaining and selecting the architecture.Firstly, the architecture model is too simple to consider the context of the system to guide the analysis and design of the system.Secondly,diverse perspectives of architecture have not been developed.The extant research has only divided the structure from the perspective of objects, failing to explain the evolution of system architecture fully.Taking the UAV launch system as the research object, this paper points out the operational requirements, considers the operational context, and focuses on system modeling based on OPM, attempting to decompose the architecture using DSM and explain the causes of the architecture presentation function from the perspective of process decomposition.

3.Creating pneumatic catapult system architecture

3.1.Requirements analysis and conceptual design

Requirements analysis and conceptual design are the first steps in the lifecycle of a new system,product,or project.44Requirements refer to standard indicators describing the function and performance of products based on the requests of stakeholders and real-world engineering constraints.Requirements are set to ensure that the designed product architecture satisfies the needs and objectives of stakeholders.

The present study takes into account the context of army aviation operations in which a small and medium-sized fixedwing UAV is supposed to be launched.Due to the article length limit,this paper simply lists the main functional requirements of the pneumatic catapult launch system:

(1) The system shall enable the UAV to take off by taxiing on the runway.

(2) The system shall be equipped with the pneumatic accelerator apparatus.

(3) The system shall be able to reset itself automatically after launch.

(4) The system shall be foldable and retractable.

(5) The system shall be easily transported on the battlefield.

Product architecture is usually established in the concept development phase.14Concept is a product or system vision,idea,notion,or mental image.45It is a simplification of the system architecture.The concept describes the operation mode of the system and enables the exploration from demand to scheme.The concept is the starting point of researching and developing system architecture.

Conceptual design begins with a clear understanding of the context and environment in which the system is expected to operate.The program manager and system engineer should understand how their system fills the needs for which it is designed and the enterprise context within which it operates.This includes understanding the diverse or dissimilar mix of other systems (hardware, software, and human) with which the system needs to exchange information.46Context establishes place, informs function, and influences design.

Object-Process Methodology (OPM) provides a consistent method for studying system architecture.One can conceptually model any system in any domain by using stateful objects,processes, and relations among them.44OPM is a dual-mode model, which can be described in both graphic and textual ways, called Object Process Language (OPL) and Object Process Diagram (OPD), respectively.47If Object-Process Case Tool(OPCAT)47is used for OPM-based modeling,the corresponding OPL and OPD will be automatically generated.For the symbols of OPM entities (i.e., objects, states, and processes) and the corresponding OPL statements, one can refer to the article of Dori and Choder.48It should be mentioned that the modeling elements of objects and processes shall designate things in the model context.49

To sum up,according to the actual battle scenarios and the requirements of stakeholders, OPCAT is used for modeling to obtain the conceptual model of UAV launch operation, as shown in Fig.1.It can be seen from Fig.1 that the UAV was brought out of standby mode into the takeoff mode by stakeholders through the process of UAV launch operation with the help of the pneumatic catapult system.At the same time, for the purpose of ensuring the development of the system, it is necessary to effectively identify the system context of UAV launch operations(e.g.,environment,and transportation vehicles).

3.2.From concept to Level 1 architecture

System architecture is the embodiment of the concept,the allocation of physical/informational function to the elements of form, and the definition of relationships among the elements and with the surrounding context.45OPM can help identify the underlying processes connecting functions and forms.15The OPM language employs symbols to represent the elements(forms) and processes (functions) of a system’s architecture.16The word ‘‘object”in OPM contains a similar meaning of‘‘form”and ‘‘entity”.A function of an artificial system is its top-level value-providing process, as perceived by the beneficiary.44Therefore,the architecture can be expressed essentially as the mapping between processes and objects.

The object-process assertion is that one can conceptually model systems in any domain and at any level of complexity by using stateful objects,processes,and relations among them,along with refinement mechanisms of unfolding and inzooming.44Therefore, to develop the Level 1 architecture, we need to expand and develop the conceptual model in Fig.1.That is to say, we need to expand and refine the UAV launch operation process.After taking the battlefield environment into account, the UAV launch operation process can be divided into five subprocesses: deploying, preparing, launching, resetting, and evacuating according to the time sequence,as shown in Fig.2.The dashed line is the boundary that surrounds the system.Due to the principle of OPM graphic-text equivalence,44only OPD is used to represent the model in the following sections.

Applying refinement mechanisms of in-zooming and unfolding to stateful objects or processes,OPM can conceptually model systems at any level of complexity;44however, for complex products/systems, there are various OPL details,making the architecture model more trivial.In order to better manage the complexity of the system architecture, this paper creates a PO(process-object)matrix to represent the OPM system architecture equivalently.

Fig.3 maps the five subprocesses of Level 1 architecture to four subsystems, UAV, transport vehicle, and the environment, and uses ‘‘X”to mark interactions to obtain the mapping matrix between processes and objects.In terms of complexity, expressing the system architecture in the form of the matrix has the advantages of completeness and clarity.

3.3.From Level 1 architecture to Level 2 architecture

In Section 3.2, the UAV pneumatic catapult system is only roughly decomposed from the concept (‘‘black box”) into the abstract Level 1 architecture (‘‘gray box”).To obtain a more accurate Level 2 architecture (‘‘white box”), it is necessary to add more details to the Level 1 architecture of UAV launch operating, which means that it is necessary to decompose the five internal subprocesses in Fig.2 in turn.The composition of the pneumatic catapult system is shown in Fig.435, and the decomposition of the preparing subprocess of UAV launch operating is taken as an example for illustration, as shown in Fig.5.

As shown in Fig.5, the preparing subprocess of UAV launch operating is described as follows.First,the preparatory control unit controls the locking mechanism to lock the vehicle in the starting position.Then, the UAV is loaded onto the vehicle and fixed through the line brake cable.Next, the compressor is started through the preparatory control unit to pressurize and store energy for the accumulator.Finally,the UAV is in transition from non-activated state to activated state.

Fig.1 Conceptual model of UAV launch operating.

Fig.2 Level 1 architecture model of UAV launch operating.

According to this method,the remaining four subprocesses in the Level 1 architecture of UAV launch operating are further refined by unfolding and in-zooming.All 27 internal processes undergoing secondary decomposition are mapped and allocated to their corresponding 25 objects in turn to obtain the Level 2 architecture matrix representation of the pneumatic catapult system, as shown in Fig.6.

4.Decomposing pneumatic catapult system architecture

4.1.Process-based architecture decomposition

Fig.4 Components of UAV pneumatic launch system.

Fig.5 Refinement model of preparing subprocess of UAV launch operating.

In the process of system analysis and design, it is often necessary to collect and record the system and its relevant objects in its environment, as well as the process of changing these objects.For almost each process that is discovered or contemplated,the first questions asked refer to the objects involved in this process.Similarly,for each object identified in the system,a key question is what processes this object participates in.44It can be found that object and process are the two most basic elements of the system and the two most fundamental decomposition perspectives of the system.In addition to decomposing the system based on the traditional structural objects, it is more necessary to find a decomposition scheme in the behavioral process in order to understand the underlying architecture and its evolution better.

However,since the amount of information contained in the architecture of complex systems far exceeds people’s understanding,this paper uses OPM tools to make projections from a higher-dimension architecture model, incorporating all the information about objects and processes and their connections into the same matrix to create a coordinated and integrated view.

To represent the architecture of a system via projection, a Design Structure Matrix(DSM)is constructed.One advantage of matrix representation is that it can make calculations.This paper introduces a method to divide the DSM into several matrices and make projections accordingly.

Step 1.Creating the OPDSM.

Based on the ontology of OPM, DSM is extended in the following way to create an object-process-based DSM.

Eq.(1) is equivalent to decomposing the DSM matrix into four small matrix blocks.The upper left corner is the OO(object-object) matrix block, and the lower right corner is the PP (process-process) matrix block.OO (PP) matrix is a diagonal matrix.Each cell on its diagonal line is written with an identifier corresponding to the object (process), while the other cells are left blank.The PO (process-object) matrix is generated according to the method of creating the Level 2 architecture in Section 3.4, while the OP (object-process)matrix is obtained by transposing the PO matrix.

Step 2.Obtaining the PRDSM.

After creating the OPDSM, the matrix multiplication in symbolic form is carried out according to the following formula:

Eq.(2) will produce a symmetric matrix that can project objects onto the process, which is defined as the projected design structure matrix (PRDSM).It should be noted that to facilitate matrix operations, all ‘‘X”symbols in PO and OP matrices are expressed as ‘‘1”, and OO and PP matrices are set as identity matrices.In this way,only numbers are included in the obtained PRDSM.Executing the above two steps,according to the PO matrix in Fig.6,we obtained the PRDSM after processing and calculation, which is the process decomposition model of the pneumatic catapult system architecture,as shown in Fig.7.

4.2.Function-based architecture decomposition

According to OPM,16a system is defined as an object that exhibits a function,and the system’s externally delivered function is the system’s function at its highest hierarchical level.17Therefore, externally delivered function is the system’s (only)function, whereas internal functions are called processes.In this way, the function of the system is understood through the decomposition into processes.It can be seen that how external functions emerge from internal processes is the key to correctly explaining the adaptation and evolution of system architecture.

Based on the relationship between process and function, it can be inferred that by breaking down the process modules in the PRDSM architecture one by one, and then rearranging and aggregating them according to a reasonable algorithm,we can get a functional module featuring tight internal cohesion and loose external coupling.The IGTA + algorithm is used in this section to develop the architecture reconfiguration method from process to function, completing the functionbased architecture decomposition.

Fig.6 A PO mapping matrix showing Level 2 architecture of pneumatic catapult.

The IGTA algorithm has been considered to be one of the most common algorithms used for product modularization so far.42In order to increase the computing efficiency of the IGTA algorithm, the IGTA + modified the original IGTA algorithm twice, namely, ‘‘Suppressed Multi-cluster Allocation”(SMA) and ‘‘improved termination criterion”.These two improvements were independent of each other.For a detailed description of the IGTA+, one can refer to Ref.42This paper adopts the assumption of non-overlapping clustering and uses the matrix form for calculating, so only the first improvement is needed.

Fig.8 shows the flowchart of the improved IGTA + with SMA.The algorithm uses a stochastic hill-climbing approach,which uses two random numbers to control stochastic behavior to avoid local optima.Instead of always selecting the cluster with the highest bid,it randomly selects the cluster with the second highest bid with a specified probability.Only when the new clustering solution has a lower ‘‘TotalCost”compared with the best total cost obtained so far will these elements be relocated to the new cluster.

Fig.7 Representation of architecture decomposition of process-based pneumatic catapult system using PRDSM.

There are two steps required to implement SMA: dealing with multi-cluster condition and calculating TotalCost more efficiently.

Step 1.Dealing with multi-cluster condition.

If there are two or more multi-clustering situations with the best bid, the IGTA will assign the selected elements to all the clustering containing the best bid,namely,multi-cluster allocation.As shown in the red dotted box in Fig.8,when the SMA feature is enabled,the IGTA+adds the criteria for determining the best bid quantity and randomly assigns the selected elements to the one cluster with the highest bid to handle multicluster condition.The IGTA + sacrifices multi-cluster allocation so that each element has and belongs to only one cluster,which provides a necessary condition for improving the computing efficiency of TotalCost.

Step 2.Calculating TotalCost more efficiently.

The simplified calculation for SMA comes from No.1 in Table 1 collapsing the original DSM into a Cluster-DSM.No.2 defines the intra-cluster cost as the sum of the interactions within each cluster weighted by the corresponding cluster size.No.3 defines the extra-cluster cost as the sum of the interactionsamong different clusters weighted by the size of DSM.No.4 indicates that TotalCost is the sum of the intra-cluster cost and the extra-cluster cost.These equations represent costs in the form of the matrix,enabling the IGTA+process to iterate in multiples of the size of the DSM,thus speeding up the calculation.

Fig.8 Flowchart of improved IGTA + with SMA.

Table 1 IGTA + equations for calculating TotalCost.

The improved IGTA + with SMA is concerned with the grouping of elements into homogeneous modules based on their interdependencies, which will maximize interactions within the modules while minimizing the interactions between modules.50More specifically, it rearranges the subprocess elements corresponding to the rows (columns) in the process modules in Fig.7 by grouping the subprocesses that are more closely connected to each other into one group.In this way,the subprocesses within the same group have higher coupling,and their coupling with other groups is reduced.Moreover, the function-based architecture decomposition of the pneumatic catapult system can be obtained, as shown in Fig.9.Evolving system architecture through reconfiguration enables designers to focus only on the corresponding modules and changes within modules, significantly simplifying the design architecture and improving the efficiency of computational procedures.

5.Analysis and discussion of architecture decomposition

5.1.Decomposition principle of ‘‘2 Down, 1 Up”

Although these two kinds of architecture decomposition are generated by the mathematical operation, and the modulebased algorithm can produce analytical optimization, this theoretical optimization only looks at the system partition from a single perspective due to the discrete behavior and the scale of the problem.Therefore,in order to judge whether the system is decomposed correctly, this paper improves the principle of ‘‘2 Down,1 Up”45to effectively explore and explain the design of the system architecture.

The idea of this principle is that for a hierarchical system,the real information about how to cluster or group the system one level down from the reference is present in the structure and interaction two levels down.As shown in Fig.10, from Level 0 concept unfolding and in-zooming to Level 1 architecture, it should go all the way to Level 2 architecture (‘‘2 Down”).A projection is performed to obtain the process modules (‘‘1 Up”), and then the clustering is carried out to obtain the function modules (‘‘1 Up”).

Although Fig.10 shows that the function modules is reconfigured from the process modules, this does not mean that the function-based architecture decomposition is necessarily better than the process-based scheme.These two decomposition methods only represent two ideas for the architecture division of the pneumatic catapult system.If the emphasis is on the UAV launch sequence, it will be better to adopt the grouping method according to the process.However, if we pay more attention to the reliability of the pneumatic catapult system throughout the mission, the grouping method according to the function will be more appropriate.

5.2.Distinction and connection

Decomposition by process is to assign one or more subprocess elements to each module in chronological order, so that the process can be clearly divided.As shown in Fig.7, the UAV launch process is divided into five process modules:deploying,preparing,launching,resetting,and evacuating.The advantage of decomposition by process is that it is more direct and specific, which can be obtained by linearly arranging the order of each subprocess.

Fig.9 Function-based architecture decomposition of pneumatic catapult system.

Decomposing by function means reorganizing the subprocesses arranged in chronological order to realize each functional module of the system.As shown in Fig.9, the launch process of UAV can be reconfigured into seven functional modules, including pneumatic functioning, taxiing, transporting & directing, UAV functioning, folding & lifting, resetting,and power supplying.This also verifies that the architecture design scheme of the pneumatic catapult system is consistent with the functional requirements analysis from the perspective of stakeholders.

However, whether based on the process or function, the interaction between modules is inevitable.Therefore, neither of these two decomposition views is perfect.

What needs to be emphasized here is the correlation between process and function—the process performs the emergent function, and the realization of function needs the process.It is because process is how the system changes along the time dimension, which is objective and specific, whereas function is what value the system delivers to its stakeholders through its operation, which is subjective and abstract.The value of the function to the stakeholders is often implicit,mostly expressed in the system process.The architecture decision should help the system fully adapt to the changes of external processes to fully realize the functions required by the system.It should be said that the function can be perfect only when the process is complete.

Fig.10 Decomposition of ‘‘2 Down, 1 Up”.

6.Conclusions

Based on the requirements of stakeholders, considering the context of UAV launch operations, from concept to the Level 1 architecture and then to Level 2 architecture, this paper creates OPD views between objects and processes through the links between the structure and the process and the abstraction refinement mechanism.Besides, the architecture model of the pneumatic catapult system is represented by the mapping matrix in this paper.This OPM representation method aligns with the top-down forward engineering thinking mode.

Although the system is decomposed in a well-defined hierarchical way at different refinement levels, both object and process factors are included in the system architecture,whether it is the analytical representation of the OPM diagram or the mapping representation of thePOmatrix.Therefore, combined with DSM technology, this paper proposes a method of projecting objects onto the process,provides the underlying logic of operators for hierarchical decomposition, and completes the pneumatic catapult system architecture based on process decomposition.

Function decomposition broadly refers to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts.51Only when the constituent processes possess a certain level of modularity can a compressed representation of the global function be obtained.Based on this analysis idea,this paper reconfigures the Level 2 process module groups through the IGTA + clustering algorithm to complete the pneumatic catapult system architecture based on function decomposition.

The decomposition principle of‘‘2 Down,1 Up”shows that when it comes to process-based architecture decomposition and function-based architecture decomposition, it is not necessary to decide which is right and which is wrong or which is good and which is bad.They just give different views and a sense of the alignment of clustering on these two different planes.

Although the final competitive advantage of the system is largely affected by the decomposition perspective and its modularization, the most critical decision in the decomposition of the architecture should be the selected decomposition view,not just the number of modules.Through the alignment of the planes of decomposition,we can gain insights into the relationship between process and function and complete the modular processing to reduce the complexity of the system.These are helpful to explore and verify the system composition that is more consistent with the requirements of stakeholders and establish a reasonable and elegant system architecture.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Defense Outstanding Youth Science Foundation, China (No.2018-JCJQZQ-053) and the Natural Science Foundation of Jiangsu Province, China (No.BK20220911).