To enhance the efficiency of system modeling and optimization in the conceptual design stage of satellite parameters, a system modeling and optimization method based on System Modeling Language and Co-evolutionary Algorithm is proposed. At first, the objectives of satellite mission and optimization problems are clarified, and a design matrix of discipline structure is constructed to process the coupling relationship of design variables and constraints of the orbit, payload, power and quality disciplines. In order to solve the problem of increasing non-linearity and coupling between these disciplines while using a standard collaborative optimization algorithm, an improved genetic algorithm is proposed and applied to system-level and discipline-level models. Finally, the CO model of satellite parameters is solved through the collaborative simulation of Cameo Systems Modeler (CSM) and MATLAB. The result obtained shows that the method proposed in this paper for the conceptual design phase of satellite parameters is efficient and feasible. It can shorten the project cycle effectively and additionally provide a reference for the optimal design of other complex projects.

Remote sensing satellite is a well-known large-scale complex system whose design process involves multiple disciplines, such as mission analysis, orbit, remote sensing payload, structures, attitude determination and control system, power, thermal, communication and command data (C&DH), etc. It is a conventional system engineering. Satellite system design [

The conventional mode of satellite system design is document-centric, which is also known as Text-Based Systems Engineering (TBSE). With the appearance of serious problems caused by large amounts of information and constantly revised data. The inefficiency of TBSE that relies on ordinary files or other unrelated storage has become an obstacle for satellite system design. Proofreading, modification, and evaluation are time-consuming and need too many iterations in the design cycle [

Due to the high coupling between satellite subsystems, coordinating requirements and indicators are in trouble. In conceptual design, each subsystem can only obtain the best solution of a single discipline or a certain subsystem when the design optimization of each subsystem was carried out separately. If the optimization result changes, engineers who are responsible for the remaining subsystems would re-coordinate these indicators, which affect the research and development efficiency seriously. Moreover, there are too many conflicts between various disciplines in satellite system design, which may cause the optimization of the design scheme hardly converge to a unique solution and get a nonoptimal design. For example, thicker side panels in the satellite structure can increase safety, but thinner side panels are lighter, the balance between satellite quality and structural design is required. Hence, TBSE is no longer suitable for the analysis and design which become further complex. To deal with aforementioned challenges, Model-Based Systems Engineering [

Berrezzoug et al. [

The above research mainly focused on requirements analysis and function defining stage, and the connection between SysML and MDO is a “loose coupling”. While in this work, the main focus of SysML-based MDO is on the aspect of numerical processing, which runs through the entire design and optimization process. There are some tools developed to support MBSE in complex system design and modeling. However, none of them has got the functionality of supporting system optimization. There are some tools to support MDO, but none of them is integrated with design models in SysML. This work is motivated by this gap and aims to develop effective methods to support automatic system optimization for MBSE.

MBSE and MDO are both methods for designing complex products. They focus on modularity and coupling between multiple disciplines. In system analysis and design of aerospace, shipbuilding, and vehicles, the improvement of comprehensive performance of complex systems depends on coupling coordination between various disciplines. MBSE can describe and analyze the relationship between the product and its components from all aspects of the product life cycle formally and clearly, while the MDO method can achieve overall design optimization on the basis of model-based design. In this work, the MBSE model is used as an intermediate data model to facilitate the data exchange between different disciplines in analysis and improve the efficiency of resource optimization allocation and sharing. Meanwhile, it is more convenient than the process model in the previous MDO optimization strategy to process coupled information. However, there are relatively few researches on integrating the system model generated by the system design stage and the optimization model generated in the subsequent multidisciplinary optimization [

This paper proposes a modeling and optimization method for complex product and multidisciplinary system based on SysML and Co-evolutionary Algorithm (CEA) which aims to increase the efficiency of system modeling and optimization in the conceptual design phase of complex products. The method regard system objectives and optimization problems as a guide and establish an optimization model of efficiency evaluation indicators which involves quality analysis, track, payload, and power source disciplines. It uses Co-simulation by CSM and MATLAB for verification. The result shows that the improved genetic algorithm (GA) is more efficient at solving the multidisciplinary optimization problem on the basis of the SysML model after comparing and verifying the effectiveness and engineering value of the SysML-CEA method in the optimization of overall parameters of remote sensing satellites, and this method can also be applied in the design process of other complex products.

In this paper, the objective of the research and development mission for the remote sensing satellite is to monitor the forest fire situation and atmospheric environment in the Middle East, Africa and the regions between the north and south latitudes 40° in the world. The weight of the total satellite is required to be no more than 800 kg. Its orbit should achieve global coverage and meet energy security and it should have capabilities of camera imaging and image downloading with a resolution of less than 2.0 m. During orbit control, it is able to capture the initial attitude, and adjust inclination and orbit height. Before the orbit control, it can also perform a 90° roll/pitch attitude maneuver. In the process of orbit control, the attitude angle control accuracy is less than 3°. As for fuel configuration, it should meet the requirements for maintaining orbit and avoiding debris during the life, and de-orbit at the end of the life.

The acquisition of an index is one of the important parts in satellite design. Based on the concept of system engineering, indicators are defined and classified as measures of effectiveness (MOE), measures of performance (MOP) and technical performance measures (TPM). The MOE is used to measure the degree to which user needs are achieved in the system design, and establish a three-level index decomposition tree which consists of mission-level, system-level, and standalone-level. Index decomposition is necessary. On the one hand, index decomposition provides data support for the establishment of a multidisciplinary optimization mathematical model by using these indicators as parameters to measure the feasibility of the plan. On the other hand, these indicators can be decomposed into subsystems and standalone and used as value attributes to further perfect the logical architecture model. This paper focuses on analyzing the design of the key parameters that have a greater effect on the satellite design. It is the main content in the overall parameter design of the satellite which involves the disciplines like orbit, power, payload and quality. In this paper, the system’s optimization goals are determined by referring missions to remote sensing satellite and selecting important parameters as design variables. Hence, the method is universal.

According to the knowledge of the domain experts, an indicator decomposition tree in the system model is established by using these obtained indicators; it consists of task-level MOE, system-level MOP, and standalone-level TPM. MOE includes the observation area _{solar}

According to the index decomposition result in

In _{i}_{i} is the variable of each subsystem after quantification. _{i0} is a fixed value introduced for normalization.

According to the discipline analysis above, subsystems of the satellite are highly coupled and various parameters among different subsystems are related to each other. The coupling relationship among orbit, power, payload and mass are shown in the structural design matrix in

The orbit of the remote sensing satellite is sun-synchronous orbit. The output of the discipline parameter analysis includes Orbit period _{e}

In

The angle between the sun’s rays and the orbital surface can be seen in the equation below:

In

Under the condition that the eclipse zone factor _{e}

The orbital period T is calculated below:

In _{e}^{3} km^{3}/s^{2}. This discipline needs to meet the constraints of the sunshine duration _{s} and the earth shadow duration _{e}.

The ground coverage area can be represented by ψ, the half center angle of the satellite observation coverage width.

In

The output of power source parameter analysis includes solar array battery type, solar array output power, solar array area and battery pack rated capacity, etc. The type of solar array battery directly affects the design parameters, quality and area of the solar panel, and the system objective function would be affected indirectly. There are two kinds of batteries: silicon battery and gallium arsenide battery, they are represented as 0 and 1 respectively in the optimization. The power consumption of each subsystem can be divided into long-term power consumption _{0} and short-term power consumption _{s}. The minimum output power under a single-turn energy balance is _{c}_{N}

The long-term power consumption solar cell array needs to meet the charging power demand of the load and battery pack whose value is 649 W. The output power _{BOL}

In _{0} is the solar constant and _{0} = 1353 W/m^{2}. _{s} is the combined loss factor of the solar batteries array with a value of 0.98. _{t}

The mission requirement diagram demands that the satellite lifetime L should not less than 3 years. Due to the annual decline rate of the solar array’s output power being 2.2%, the output power at the end of the life can be calculated

The minimum rated capacity of the battery pack is calculated as follows:

In _{discharg} is the discharged power of the battery pack. _{OD} is the depth of discharge of a given battery pack with a value of 10.7%. _{L}_{s} is the short-term load power during the ground shadow period. _{cell} is the discharge voltage of the single battery. _{s} is the number of battery cells connected in series. _{Loss}

The calculation of the mass of the battery and the solar panel is as follows:

In _{DB}_{ac}

In _{solar}_{solar}^{2}. _{EOL}

The payload of the remote sensing satellite in this paper is a five-band CCD camera whose image quality can be determined by two major parts: image radiation quality and geometric quality. Its evaluation indicators include ground pixel resolution, imaging width, spectral band configuration and ground observation angle. The input of the payload discipline analysis model is the orbit height and the focal length of the CCD camera. The output is camera quality,

In ^{–5} m. Meanwhile,

The quality and power of the CCD camera are related to the incident aperture, the estimation equations of them are as follows:

In _{payload}_{payload}_{cam}

The spectral range is also a key indicator for satellite camera imaging. The spectrum range of the CCD camera generally selects a full chromatographic band and multiple multispectral bands in the range of 0.4 to 1.5 μm. The spectrum range of the CCD camera in this paper is 0.45∼0.52 μm, 0.52∼0.59 μm, 0.63∼0.69 μm, 0.77∼0.89 μm, 0.51∼0.73 μm.

On orbit signal-to-noise ratio (

In _{CCD}_{N1}_{N2}_{N3}_{N4}

In _{sat} is the quantized saturation voltage, and QN is the number of quantized bits. The constraints that the discipline should satisfy are as follows:

Model-based multidisciplinary design optimization (MBSE-MDO) is the inheritance and development of MDO on the basis of the MBSE system model. It obtains a set of engineering design variable that meet various constraints by exploring the coupling relationship between mathematical models, simulation analysis models and multi-disciplinary optimization models of these disciplines. The process of establishment of the SysML model in

According to the features of data interaction, the system can be divided into hierarchical and non-hierarchical systems shown in

Due to the different forms of organization in specific complex coupled design problems, MDO methods can be divided into two main groups: single-level optimization methods and multi-level optimization methods [

The disciplines such as orbit, payload, power and quality that mentioned in this paper have complex coupling relationships, which belong to a non-hierarchical system. The optimization problem in this paper requires analysis and optimization of each discipline-level module, so that the single-level optimization method is not used. The CSSO method requires the introduction of proxy model technology but all of the discipline model for the optimization problem in this paper are engineering estimation models. The ATC method is suitable for solving the distributed decision-making problem of the hierarchical structure [

CO algorithm is one of the methods applied to solve MDO problems which has been widely used in complex engineering problems. However, the CO algorithm has some defects. It usually falls into local solutions or cannot converge in nonlinear programming problems, causing multiple locally optimal solutions when meeting the nonconvex or even discontinuous design space of optimization problems in actual engineering problems. The multi-level optimization problem of CO research needs to establish two-level models: system level and subsystem level. The constraints at the system-level are the optimal target value after subsystem optimization and the optimal target value at the system-level can be obtained only when it meets the consistency constraints. The empty feasible region of the system level optimization model is inevitable, which makes the optimal design solution could not be obtained [

CO algorithm solves MDO problem by applying hierarchical strategy to decompose the complex system problem into multiple discipline-level problems and using a system-level optimization model to coordinate the discipline-level optimization results. The CO framework is shown in

(1) System-level mathematical model

In _{L}_{U}_{ij}^{*} is the optimal value of the _{j}_{i}^{*}(

(2) Discipline-level mathematical model

In _{i}_{i}_{i}^{*}. _{ij}_{j}^{*} is a system-level transmission variable. _{i}

The organizational structure of the CO model is consistent with actual problems, and the information exchange between different disciplines is required to simplify. However, the standard CO algorithm is prone to absent the Lagrange multipliers in the system-level optimization and difficult to satisfy Kuhn-Tucker [

A detailed analysis of the CO algorithm is shown in the section above. It can be seen that the nonlinear enhancement caused by the system decomposition and the complex coupling between disciplines led to the computational difficulties of the algorithm. The SysML-CEA algorithm can achieve collaboration among multiple disciplines by establishing a collaborative framework and integrating all the way of available discipline analysis (such as modules, tools, codes, etc.) which can solve MDO problems. SysML-CEA is a co-evolutionary algorithm based on SysML, which uses the improved GA [

System-level and discipline-level iterators use the improved GA to solve the problem represented by the model. Selection, crossover, and mutation operations in GA are improved to fix the numerical solution in multidisciplinary optimization in this section.

Select operation

In selection operation, several chromosomes are selected from the primary population to form a new population and then obtain a convergent population finally after enough iterations in which the fitness value of chromosomes in this population will tend to the optimal solution. The most commonly used method for the chromosome probability calculation is the roulette selection method while the improved selection operation uses the best retention strategy after roulette selection to completely retain the chromosomes with the highest fitness in the population to the next generation.

Cross operation

In crossover operation, the improved crossover pairs individuals with low fitness and low fitness, and pairs with high fitness and high fitness. Chaotic sequences [_{1} (λ_{1}^{2}, λ_{2}^{2}, λ_{3}^{2}, …λ_{10}^{2}) and U_{2} (λ_{1}^{2}, λ_{2}^{2}, λ_{3}^{2}, …λ_{10}^{2}), the chaotic sequence would be used in form of the equation below:

In _{n}_{n+1} is the initial value of the chaos iteration of the next generation. The chaos value generated in each generation is kept and multiplied by 10 to get the locus in the chromosome.

Mutation operation

The mutation operation is the operation that mutate the target value of a certain segment of genetic gene on the chromosome, which would generate a new chromosome. By pre-setting the mutation rate of the gene, the position of the mutation gene would selected randomly. An improved mutation operator is applied to ensure that the optimal chromosome mutation rate changes adaptively during the process of solution. The improved adaptive mutation rate is shown as follows:

In _{m}_{max}_{min}_{max}

The improved GA is adopted to optimize the two-level model of CO respectively as the step below. First, the discipline-level optimizer obtains the input variable of the discipline from the system-level optimizer and uses it as a fixed value in the optimization of the discipline. Secondly, variables of discipline-level design are combined for analyzing to obtain the discipline output variables, constraint values, and the D-value between discipline design variables and system-level design variables. The optimization goal is to minimize the D-value under the premise of satisfying the constraints. Finally, the system-level optimizer coordinates the D-value between these disciplines. The process of solution is shown in

Step 1: Design variables are initialized and expected values are assigned to the discipline-level optimizer. The initial value of the design variables, the constraint value, and the maximum number of iterations of the model are defined based on the demand of the problem.

Step 2: The discipline-level optimizer receives the input optimizer optimization indicators and combines these design variables of the system. GA is used in optimization to obtain the optimization results of design variables in the subsystem.

Step 3: GA parameters in Step 2 which include population, number of individuals, chromosome length, and genetic generation number are assigned. The operation of the genetic operator is performed to obtain the individual with the greatest fitness.

Step 4: After the completion of the optimization of each discipline, the optimal target value _{i}_{i}^{*} (

Step 5: Whether the consistency constraints meet the condition would be judged. If they meet the condition, the algorithm would finish the iterative process and get the result. Otherwise, it would return to Step 2 to continue execution.

(1) System-level mathematical model

In _{i}_{i}_{i0}_{i}^{*} (

(2) Orbit discipline-level model

In _{e}

(3) Payload discipline-level model

In _{payload}_{payload}

(4) Power discipline-level model

In _{solar}_{ac}, m_{solar}

The normalization method [^{2}∼10^{3} such as orbit height, required power, and satellite quality are all reduced by 10^{2} times. While variables with a range of 10∼10^{2} are reduced by 10 times. Variables in range of 0∼10 are taken the original value. Due to the condition for the constraints of the original equation are stringent and hard to satisfy, the algorithm is adjusted in this paper for which the new condition is that _{i}^{*} (_{i}

CSM enables to perform calculation based on the parameter diagram of the system model. It contains a built-in script compiler that can implement languages such as JavaScript and Python and execute simple mathematical models. However, standard library files in CSM are insufficient and cannot use mature discipline analysis codes. By integrating the Matlab into the CSM, the usage of the M file is realized and the calculation of the CO model is completed, as

In standard CO algorithm the two-level model is solved by the sequential quadratic programming (SQP) algorithm and GA while in SysML-CEA algorithm it is solved by the improved GA. In order to ensure the accuracy of the D-value between two optimization results, several consecutive optimizations are performed as follows:

The optimization model of satellite multidisciplinary design is determined on the basis of actual needs to ensure that the system optimization target is the maximum of index of user requirements and it includes system-level design variables, discipline-level design variables, constraints, and several coupling state variables in these disciplines. Expected values of the subject-level optimization model are assigned in initialization and the population size of the GA is set to 50, the maximum genetic algebra is set to 60, and the maximum number of models call for CO is set to 100.

The discipline optimizer of orbit, payload and power disciplines is executed respectively, and the improved GA is used to search and optimize the discipline objective function. After the optimization, the objective function value of the discipline is returned to the system-level optimizer as a constraint, and the optimal value of design variables of each discipline is returned at the same time.

After the objective function and design variables from the discipline-level are received by the system-level optimizer, it searches and optimizes the objective function and updated system-level design variables are obtained as the input of the discipline analysis model to continue on the optimization.

Whether the maximum number of calls to the discipline model is reached is judged in this step. If it is reached, the iteration and output the current optimal solution would be stopped. Otherwise, the workflow would return to Step (2) and continue with the next iteration until the optimization process is completed.

The satellite CO model is optimized and solved separately and the optimization results are shown as follows. The system objective function value result in ^{−4} in the fifth iteration and satisfies system consistency constraints so that the first set of optimized design variables is obtained. Due to the solving process applying the hierarchical solution strategy of the CO method, the objective function approximates the result only when the three disciplines satisfy the consistency constraint at the same time. The objective function value tends to converge after ten iterations. In contrast, the SysML-CEA algorithm satisfies the consistency constraint in the fourth iteration and the objective function value is converged after the eighth iteration, which means the efficiency is significantly better than the standard CO algorithm. In the iteration of SysML-CEA algorithm, the improved GA adopted by the optimizer performs a large-scale search on the solution set. In order to prevent falling into the local optimum when searching out the solution near the optimal value, an adaptive mutation rate is set in this paper.

Discipline | Variables/constraints | Symbol | Unit | Range | Initial | SQP | GA | SysML-CEA |
---|---|---|---|---|---|---|---|---|

Orbit | Orbit height | [500, 800] | 700 | 684.53 | 703.6 | 738.4 | ||

Local time of descending node | [8, 15] | 10 | 8.5 | 8.5 | 8.5 | |||

Sunshine time | ≥3600 | 4200 | 4356.3 | 4875.3 | 5298.7 | |||

Earth shadow time | ≤2400 | 1800 | 1356.5 | 1241.8 | 1008.8 | |||

payload | CCD camera focal length | [0.2, 1] | 0.6 | 0.35 | 0.38 | 0.43 | ||

Signal-noise ratio | ≥45 | 46.5 | 47.1 | 47.3 | 48.3 | |||

power | Rated battery capacity | A⋅h | [50, 100] | 80 | 92.5 | 87.3 | 83.4 | |

Solar array material type | -- | [0, 1] | 0 | 1 | 1 | 1 | ||

Solar windsurfing area | [5, 20] | 5 | 10.25 | 12.18 | 11.03 | |||

End-of-life output power | ≥800 | 1200 | 1356.3 | 1159.4 | 1078.6 | |||

Mass | Sat quality | [600, 800] | 700 | 716.4 | 693.7 | 674.3 |

This paper proposes an MDO based on MBSE for remote sensing satellite models’ research and development tasks. Analysis modeling and multidisciplinary coupling analysis for the orbit, payload, power supply and quality disciplines are completed. The SysML-CEA algorithm solution of the multidisciplinary optimization model is researched and the importance of the integration of MBSE and MDO in satellite conceptual demonstration and program design is confirmed.

The coupling relationship of the design variable related to subsystems in the MDO optimization problem is sorted out and the overall optimization objective function is established, which is based on the research mission and discipline knowledge of remote sensing satellite. The index variables are assigned to the corresponding discipline by the establishment of a three-level index decomposition tree. Based on the MBSE system model and discipline analysis model for multi-discipline design optimization, a co-evolutionary algorithm based on SysML is proposed. An improved GA that can solve two levels of the CO model is proposed to deal with problems of nonlinearity and coupling enhancement in discipline decomposition. The efficiency of the SysML-CEA algorithm in satellite multidisciplinary optimization design is verified by comparing the solution process.

The MDO method based on SysML has good expansibility. In addition to being applied to the remote sensing satellite in this paper, it can also be used to solve the design problems of other complex products. SysML MDO method can effectively save the time of information processing and integrate the computing strategy into one platform for processing, and facilitate information transmission.