AI-Based Multiﬁdelity Surrogate Models to Develop Next Generation Modular UCAVs

The next generation low-cost modular unmanned combat aerial vehicles (UCAVs) provide the opportunity to implement innovative solutions to complex tasks, while also bringing new challenges in design, production, and certiﬁcation subjects. Solving these problems with tools that provide fast modeling in line with the digital twin concept is possible. In this work, we develop an artiﬁcial intelligence (AI) based multiﬁdelity surrogate model to determine performance parameters of innovative modular UCAVs. First, we develop a data generation algorithm that includes a high-ﬁdelity model based on computational ﬂuid dynamics methods and a low-ﬁdelity model based on computational aerodynamic approaches. In the next step, a new transfer learning-based surrogate model is generated using multiﬁdelity data. Thanks to this approach, the developed AI model more accurately predicted the ﬂow conditions that were missing in the high-ﬁdelity data with the data obtained from the low-order model. The performance of the proposed AI-based surrogate model is to be investigated in terms of accuracy, robustness, and computational cost using a generic modular UCAV conﬁguration.


I. Introduction
F uture battlespace is expected to be dominated by unmanned combat systems with major advances in autonomy.
In the first stage, these systems are planned to fulfill the tasks given both in formation and separately under the tactical command of a manned leadership in the Manned-Unmanned Teaming (MUM-T) concept [1].According to this theme, the Unmanned Combat Aerial Vehicles (UCAVs) will potentially have intelligence gathering, electronic warfare, air-to-air and air-to-ground combat capabilities via their artificial intelligence-enabled autonomy [2].In addition, it is considered that these systems can be used not only with fighter jets but also with other types of aircrafts such as tankers, bombers, and transports in different scenarios [3].
Low prices are the most prominent feature of these "Attritable/Reusable" or "Loyal/Robotic wingman" concept UCAVs.In the U.S. Air Force terminology attritable/reusable term is used to define a new class of UAVs that low cost, which means cheaply enough to be lost in combat and then affordably replaced, highly reliable, and have a few years of the life cycle [4].To be more specific, according to the mission equipment they carry, while the unit cost of these vehicles is expected to be between $2-15 million, the unit cost of an operational latest F-16 variant is between $64-80 million and the F-35 is around $100 million [5,6].When life cycle cost (LCC) is taken into account, this difference will increase in favor of low-cost UCAVs [7,8].In addition, it is possible to field several low-cost attritable UCAVs for $10.9 million, which is the pilot combat ready training cost of the F-22, a manned 5th-generation air superiority aircraft [9].Because the cost directly affects the mass, a future air force can consist of much greater number of UCAVs than jet fighters [10].Considering their ability to perform independent missions, they can be deployed and stored in many different locations.All this will enable such systems to deploy, produce and sustain mission sorties at a sufficient pace to generate and preserve combat mass in a contentious battlefield [11].As can be seen from Fig. 1, many companies are interested in such concepts.
The UCAVs in the flexible mission concept carry various equipment according to the different operational tasks.This equipment can be expressed as changing sensors, radar systems, and payloads.Besides, performance requirements such as endurance, range, maneuverability, and radar cross-section area also vary according to the task.As a consequence of the multi-role concept, adaptable modular configurations become inevitable.The adaptable configuration mentioned here includes a "plug and play (PNP)" design philosophy for both the hardware/software and the main aircraft components such as wings, fuselage sections, and engines.As a case in point, MQ-28A , developed by the Boeing Airpower Teaming System, is expected to carry various unnamed sensors on its reconfigurable nose to conduct particular Intelligence Surveillance, Reconnaissance (ISR) scenarios [12].Similarly, in Royal Air Force's The Lightweight Affordable Novel Combat Aircraft (LANCA) project, a rapidly reconfigurable UAV is pointed out to perform different roles, including intelligence, surveillance, and reconnaissance (ISR), electronic warfare, and strike missions [13].On the Kratos XQ-58, in addition to the modular nose and payload section, the wing and wing leading edges are planning to exchange to meet changing mission requirements [4].The open architecture of a proposed modular UCAV, which is suitable for continuous updating, necessitates an innovative approach in both design, production, and certification processes.The modular system, which contains a large number of combinations, will generate many configurations and at the end of the design process, each of them must go through a different certification procedure.Here, serious and effort-demanding problems arise such as the connection of different structural parts, their strength in different operational conditions, and the ability of connected sets to meet flight performance requirements.A possible solution to the problem at hand is digital engineering (DE).This approach could provide significant long-term development, production, operations, and sustainment efficiencies in these type game-changing programs [20].For example, General Atomics' Autonomous Collaborative Platform (ACP), known as Gambit, is designed using digital engineering to accelerate its market time and reduce acquisition cost [19].Especially digital twins provide great benefits in design optimization and upgrade analysis, performance validation and optimization, product improvement and calibration [21].As seen in the development process of Boeing T-7, an advanced jet trainer program, the precise digital twins of each aircraft are generated for upgrades, enhancements, and data-driven maintenance, both for the real product and its digital copy throughout their life cycle.Thus, the company provides a 25% reduction in development time, a 50% reduction in software costs, and an 80% reduction in assembly hours or 200 fewer people to design and build [22].
Taken from a broad perspective, it is possible to optimize the design of UCAV for each specific scenario.In a modular design, changeable lifting surfaces (wing, tail, or canard), nose, and payload section, propulsion systems can be generated, and these components can be brought together in a lego-like structure.As illustrated in Fig. 2 , the proposed concept includes several modular components.For instance, a wing with a smaller span and reduced radar cross-section area can be used in the combat mission , while large wings that allow for carrying higher weights for longer times could be used for the ISR mission.Determining the most suitable components for each mission scenario ends up with searching for different optimum points in an extensive design space.The optimization procedure needs huge calculations and iterations to reach the optimum point, such as using traditional methods to obtain relevant aerodynamic, structural-like features is difficult due to time and computational costs.To overcome this issue, numerical evaluation can be applied through a surrogate model that calculates the performance characteristics of given configurations.In this study, AI-based multifidelity surrogate analysis tools will be developed to both design optimization and digital twin models of complete modular UCAVs.

Fig. 2 Proposed modular UCAV configuration
As is known, different performance, life cycle cost, and stealth requirements result in different designs and flight regimes.However, when the up-to-date UCAVs are examined, a concentration in the high-subsonic/transonic regime is observed as seen in Fig. 3. Transonic flow regime means that there are both subsonic and supersonic airflow around the vehicle.There will be dramatic increases in drag and separations in flow due to shock waves that occur while in this regime.At this point, considering the complexity of the flow, computationally expensive computational fluid dynamics (CFD) based analysis tools are generally preferred.However, in the early phases of design studies, thousands of aerodynamic analyses are required for the combination of different geometries and flow conditions as a part of design optimization.For this reason, it is preferable to use low-order methods, which are much cheaper computationally than CFD methods, but also provide lower accuracy [23].To overcome this problem surrogate models are used in several applications.
*Some data are obtained from official/unofficial sources as an estimated or targeted performance parameter

Fig. 3 Maximum speed vs maximum take-off weight of combat UAVs
When the literature is examined, it is observed that surrogate model algorithms are frequently used in two-dimensional turbine blade or airfoil optimization [24] [25-37].In addition, there are surrogate models used in transonic and supersonic wing optimization.Several statistical or machine learning-based surrogate model studies can be found in the literature [38][39][40][41][42][43][44].When artificial intelligence-based surrogate models are compared with classical methods, it has been observed that as the data set grows, classical methods with statistical approaches become unnecessary and there is the order of magnitude differences in favour of AI methods in terms of computation time [45].However, there are question marks about the robustness of AI-based models.For this reason, there is a gap in the literature regarding a comprehensive AI-based surrogate model with mixed fidelity.Also in our previous studies, we have developed a deep learning based surrogate model [46] using data generated by our low-fidelity NLLT aerodynamic tool [47] which can characterize the nonlinear aerodynamic performance of conventional small UAVs.In these studies, we have experienced that AI-based surrogate models are fast and accurate tools with very strong interpolation capability, and we further developed the reduced order model and used it as an aero solver in an optimization application [48].With the surrogate aerodynamic model developed in this study, we show that both the flight performance parameters and the aerodynamic loads on the configuration can be calculated quickly and accurately.Specifically, in this paper, we aim to illustrate that the trustworthy surrogate model from the mix-fidelity data set can be used as a solver in the design optimization cycle.
In the context of this study, we focused on the transfer learning approach, unlike previous studies, to predict the aerodynamic performance of configurations.The difference between transfer learning from traditional machine learning algorithms is that learning a new task is based on previously learned tasks.The main idea behind transfer learning is to extract knowledge from some related domains to help a neural network algorithm to achieve better performance in the domain of interest [49,50].In general, current progress in transfer learning is on the use of image-based convolutional neural networks for classification or clustering problems.However, in this study, we will apply Network-Based Deep Transfer Learning capabilities for multifidelity regression problems.Network-based deep transfer learning can be explained as the reusing of the partial network that is pre-trained in the source domain, including its network structure and connection parameters, and transfer it to be a part of a deep neural network used in the target domain [51].The need for transfer learning occurs when there is a limited supply of target training data.This may be because the data is rare, the data being expensive to collect and label, or the data being inaccessible [52].Therefore, transfer learning is an approach that can solve the problem of aerodynamic analysis methods in the design cycle described previously.
The rest of the paper is organized as follows: In the "Methodology" section, the main algorithm of the paper is briefly given.In the "Multifidelity Aerodynamic Performance Modelling" section, aerodynamic models are explained, providing insight into their mathematical basis.In the "Surrogate Performance Modelling via Machine Learning" section, in-depth information is given about data sets, sampling algorithm, and the structure of the machine learning algorithm.In the "Application of the Model" section, an example application of the developed model is performed.Finally, the conclusions are presented, and the objectives planned to be achieved in future studies are explained.

II. Methodology
The performance of an aircraft is mainly related to geometry, flow direction, Reynolds number and Mach number.For the main performance parameters, lift (  ) and drag coefficients (  ), this relationship can be expressed as follows: in here Reynolds number is about boundary layer development while the Mach number is about compressibility.In order to determine these parameters, solution methods are used in which the flow is modeled and complex equation sets are tried to be solved.However, with a capable regression model and sufficient data, it is possible to eliminate this whole process.A performance mapping between given function inputs and aerodynamic performance coefficient outputs is possible with machine learning algorithms.

Fig. 4 Surrogate model-based design optimization algorithm
Our proposed approach is illustrated in Fig. 4. In this proposed approach, firstly, configurations are generated in the design space by using sampling algorithms.In the next step, a high-fidelity dataset based on SU2 [53] CFD tool and a low-fidelity dataset based on VSPAERO [54] are generated.After that artificial neural network-based multifidelity surrogate model is developed as the main focus of the study.Transfer learning has been integrated into this model, making it more generalizable, reliable, and robust.
Additionally, we tested the algorithm using the generic modular UCAV configurations.The generic combat UAV configuration given in Fig. 5 is used in both data generation and test applications.This configuration simply consists of a wing, fuselage, and a V-tail.More detailed information about this model can be found in the data generation section below.

Fig. 5 Baseline UCAV configuration III. Multifidelity Aerodynamic Performance Modelling
As the basis of the geometry model, the open-source Vehicle Sketch Pad (OpenVSP) software of NASA is used, which allows the user to create three-dimensional parametric models of generic aircraft configurations defined by common engineering parameters [55].OpenVSP's ability to quickly generate configurations and export this geometry in different formats provides usability in the conceptual and preliminary design processes [56,57].In this study, OpenVSP -Python API integration was preferred, which provides coding flexibility to design a large number of configurations.

Fig. 6 Multifidelity aerodynamic performance modelling algorithm
The generic UCAV configurations were analyzed with the VSPAERO panel method as a low-fidelity analysis tool and with SU2 CFD solver as high fidelity tool.The mesh required for CFD analysis was generated using OpenVSP and GMSH [58].All these integrations are provided through the Python script prepared for the project.A representative flow diagram of the algorithm is given in Fig. 6.
The aerodynamic models and their mathematical backgrounds are briefly explained in the following subsections.In addition, in subsection C, the performance of these models was validated by comparing them with an experimental study.

A. Low Fidelity Aerodynamic Model
Low-order aerodynamic models are used to predict aircraft performance cheaply and quickly by making some assumptions in flow conditions and geometry.Although the potential flow-based panel methods, which is one of the well-known computational aerodynamics methods, provide more complex geometry modeling and solution than semi-empirical, lifting line and vortex lattice methods (VLM), it remains at a lower level compared to CFD solutions.Because this approach uses the simplest form obtained from the Navier-Stokes equations describing the flow, neglecting all viscous and heat transfer terms.When the impact of these assumptions is considered physically, it becomes clear that skin friction drag, separation, and transonic shocks cannot be calculated [59].However, panel methods also have advantages over other computational aerodynamic methods such as the vortex lattice method.While VLM models ignore thickness and apply boundary conditions (BCs) on an average mean surface, panel methods can model blunt geometries and apply BCs on the actual surface.
Panel methods can be briefly described as numerical schemes used to solve the linear, inviscid, irrotational flow equation at subsonic or supersonic freestream Mach numbers.The name of the equation that panel codes solve is the Prandtl-Giauert equation.For steady subsonic flow this equation is usually can be defined as: For subsonic flows, Eq. ( 2) is elliptical.This type of equation allows any disturbance to be felt everywhere in the flow field, although the effect usually disappears with distance.To model the effect of the geometry on the flow, the singularities are distributed over the entire geometry and their strengths are calculated over the surface velocity boundary conditions.The velocities induced by each ring vortex at a specified control point are calculated using the law of Biot-Savart.The contribution of each vortex loops and trailing wakes at a given  control point is calculated as follows: Then freestream velocity component is added to the induced velocity and tangency boundary condition applied as: In the panel method model, shade wakes are represented as vortex filaments that leave the sharp trailing edges of wings and possibly bodies.The strength of these filaments is determined by the Kutta condition, which allows the flow to leave the trailing edge properly.Also in VSPAERO, the location of these vortex filaments is solved iteratively in the overall flow field solution.Further details of the panel method algorithm can be found in the literature [60].At the end of the process, the whole problem is reduced to the solution of a set of linear equations: where ì  represents the unknown circulation strengths.To reduce the computational cost, VSPAERO use an iterative method, the generalized minimal residual method (GMRES), for the numerical solution of this system of linear equations.
where ì   → − → 0 as  → ∞.Using preconditioned GMRES algorithm, matrix-free evaluation of the residual is obtained.In this application, Precondition matrix was selected as an approximate LU decomposition of .After calculating the strength of the singularities, the aerodynamic forces and moments affecting the geometry are obtained.
Various correction factors are used to take into account the local compressible effects that occur especially in the high-speed subsonic regime.The most popular of these is the Prandtl-Glauert rule, but a better model, the Karma-Tsien rule, is used in this study.In this model, the freestream Mach number is used to correct the pressure coefficient (  ).It is defined as: where  ∞ is the freestream Mach number and   0 is the potential flow coefficient of pressure.Since the panel method gives an inviscid solution, the parasite drag values are calculated with a semi-empirical approach.VSPAero general analysis parameters are summarized in Table 1.The wake iteration is limited to 5 as it can be seen in the analysis settings.Because, usually sufficient convergence rate is achieved in the third iteration.

B. High Fidelity Aerodynamic Model
High-order aerodynamic models are used to predict aircraft performance with high accuracy.In this study, a compressible Euler solver is selected as a high fidelity model.In this model, the viscous and thermal conductivity terms are neglected from the Navier-Stokes equation and the compressible Euler equations are obtained.These equations can be defined in differential form as [61]: where  is a generic source term, the conservative variables are the working variables and are given by where  is the fluid density,  is the total energy per unit mass,  is the static pressure, and the convective flux is In the Euler solver, the equations are discretized in space using a finite volume method on a vertex-based schemes.As a solution inviscid performance coefficients are obtained.In the algorithm, the skin friction drag calculated by the OpenVSP module is added to the SU2 solution and the total drag value is calculated.

C. Validation of Aerodynamic Models
In this subsection, the accuracy of existing aerodynamic models will be tested using NASA's wind tunnel experimental study.The experiment was carried out in the Langley high-speed 7-by 10-foot tunnel using a closed test section.The test geometry, consisting of a swept wing and fuselage suitable for the UCAV configuration, was tested at high subsonic flow and various aerodynamic force-moment parameters were collected.In addition, jet boundary and blockage corrections were applied to the static aerodynamic results.Table 2 summarizes parameters related to testing geometry and flow conditions.The results obtained from the analysis are illustrated together with the experimental data in Fig. 7.It is clearly observed that the panel method results are close to the experimental data, especially in low angles of attack.In this study, the panel method provided an acceptable level of accuracy, since the analysis was performed under cruise conditions.

Fig. 7 Test Case: Comparison of lift and total drag coefficients
Further, the results of the high fidelity aerodynamic model are also evaluated in this graph.As expected, the CFD method is able to calculate the lift and drag coefficients more accurately.Results can be improved with changes in analysis settings, but this is beyond the focus of the paper.

IV. Surrogate Performance Modelling via Machine Learning
One of the key challenges in the design of UCAVs is the lack of fast and precise aerodynamic performance digital twins that can be utilized as a part of the optimization cycles.Toward this objective, in this study, we generate a black-box function that can predict the aerodynamic characteristics of UCAV configurations including compressibility effects by using deep learning algorithms.To be specific, an artificial neural network architecture is designed and trained using the data set created by the aerodynamic analysis models presented in the previous section.Thus, an instant solution can be provided using only geometry and flow parameters, without the need for analysis loops to calculate the performance of a new configuration.

A. Data Generation
In Table 3, geometry parameters and ranges for wing configurations are given.Each configuration was analyzed using high fidelity tool for two different Mach numbers: 0.5 and 0.6.The Latin hypercube sampling (LHS) was used for generating a quasi-random sampling distribution [62].Thanks to this algorithm, it is possible to cover all design space with a limited data point.

Airfoil Root Chord Span Taper Ratio Sweep Mach
Wing NACA 64-008A 3m 7m -14m 0 -1 0°-40°0.5 and 0.6 In this study, the initial data set with 1250 configurations (2500 total data points for two different Mach numbers) were used, but this number can be increased with various geometric combinations.Example wing configurations of the dataset generation algorithm are given in Fig. 8.As can be seen in the figure, configurations with different characteristic features have been produced in terms of various wingspans, taper ratios, and sweep angles.

Fig. 8 Example wing configurations of the dataset generation algorithm
In addition, a total of 4500 data points were produced using the low fidelity tool to be used in the transfer learning algorithm.Some configurations in this dataset also have results at flow conditions between 0.5 and 0.6 Mach.

B. Feature Extraction
To determine feature parameters, the initial data set is examined.In order to evaluate the relationship between parameters, the correlation matrix was calculated with Pearson's method.In Fig. 9, positive correlations between parameters are shown in dark blue and negative correlations in light blue.The color densities are proportional to the correlation values.

C. Artificial Neural Networks Model
In this subsection, the artificial neural network structure and its mathematical basis are explained in detail.As an initial model structure, the classical backpropagation algorithm performs learning on multilayer feed-forward neural network was used.Then, the Network-Based Deep Transfer Learning approach was used to train these models.
Before establishing the network structure, the training and the test sets are individually scaled to prevent the convergence problem caused by the difference in the magnitude of the inputs.As shown in Eq. 11, min-max scaling was applied to the dataset.
A multi-layer perceptron architecture was built to predict the aerodynamic performance coefficients,  , using .For a fully-connected network with  hidden layers, this amounts to the following modeling equations relating the input features , to its target prediction .
A generic structure of a deep neural network consisting of a multilayer perceptron with  input features and  layers.It is composed of sequentially connected layers, which comprise sets of neurons that are combinations of mathematical operations followed by nonlinear activation functions.The model parameters  are defined as  = {, }, where  = {  }  =1 , and  = {  }  =1 .The output of the l  ℎ layer is: =        +   ( = 1, . . ., ) where   is the neuron number and   is a nonlinear activation function of a specific l  ℎ layer, and   is the input of the l  ℎ layer and also the output of the l-1  ℎ layer.In addition to this,   and   are learnable parameters and called weight and bias terms of that layer respectively.Finally, the output of the last layer is a result of the composite and complex mapping defined as: In transfer learning these learnable parameters,   and   , are shared between the models to extract knowledge from some related domains to help a neural network algorithm to achieve better performance.Finally, a neural network model is built to predict the lift coefficient by using the parameters summarized in Table 4. Initially, a discrete model was trained with only high fidelity data for comparison purposes.In the next step, a new model was trained using the low-fidelity data.Then, some of the weight and bias parameters of this model was carried to the high-fidelity model training.The learning curves of the high-fidelity and transfler learning models are shown in Fig. 11, respectively.

V. Applications of the Model
In this section, the outcomes of several test examples of the current surrogate model are presented to show its prediction and generalization capability.For this purpose, the performance of different configurations in the test set tried to be estimated with the AI model.
The results reveal high-accuracy estimations with mean absolute errors of 0.0028 for the high fidelity model and 0.0027 for the transfer learning model.To monitor the success of the entire test set of the models, the value of the coefficient of determination,  2 , is calculated and the results are visualized in Fig. 12.In these figures, the x-axis and y-axis represent the real and predicted lift coefficient values, respectively.Each dot in the figure illustrates a different UCAV configuration.The value of  2 was obtained in the order of 0.93 in both models.When the  2 values are examined, it can be thought that there is no improvement in the prediction capacity of the model.However, the new model obtained by transfer learning increased the estimation capacity of the high fidelity model by using the information extracted from the low-fidelity model about the Mach number-lift coefficient relationship.It is possible to examine this situation specifically over the mach-lift coefficient curve of a generic configuration.As previously explained, the HF-model had only 0.5 and 0.6 Mach numbers data and was trained with this sparse data.In the LF-model, there were data from 0.5, 0.525, 0.55, 0.575 and 0.6 Mach numbers (see Fig. 10.However, the new model obtained by transfer learning increased the estimation capacity of the high fidelity model by using the information extracted from the low-fidelity model about the Mach number-lift coefficient relationship.It is possible to examine this situation specifically over the mach-lift coefficient curve of a generic configuration.As previously explained, the HF-model had only 0.5 and 0.6 Mach number data and was trained with this sparse data.In the LF-model, there were data from 0.5, 0.525, 0.55, 0.575 and 0.6 Mach numbers (see Fig. 10.

Fig. 13 Mach number -Lift coefficient curve for a generic configuration
As can be seen from Fig. 13, the prediction accuracy of the high fidelity (HF) model is not as successful as the transfer learning (TL) model.While the Mach number and the lift coefficient are expected to increase together, the high fidelity model could not catch this physical relationship due to the sparse dataset.However, thanks to Transfer learning, this effect has been properly modeled with the multifidelity approach.
In addition, an artificial neural networks model was developed for the drag coefficient prediction.In the Fig. 14, the x-axis and y-axis represent the real and predicted drag coefficient values, respectively.This time the value of  2 was obtained in the order of 0.91 in high fidelity model.This level of accuracy is acceptable, especially of the conceptual and preliminary design phases.There was no need to develop a transfer learning algorithm for drag coefficient.However further implementations are possible to predict drag components.

VI. Conclusions
Major improvements in autonomy indicate that war environments will change rapidly in the future.In this concept, modular air vehicles, which stand out as a low-cost solution for different mission scenarios, also require cost-oriented practical approaches in design, production and certification.It is possible to solve these problems with fast and computationally inexpensive modeling tools.This paper presents a new machine learning based surrogate model to predict the aerodynamic performance of combat UAVs.Thanks to the developed model, it will possible to quickly analyze the main wing sets for different mission requirements.In addition, using the transfer learning approach, the performance of the model has been increased with the multifidelity approach in flow conditions where the database is sparse.The algorithm will capable of calculating the performance of a given geometry in milliseconds.This will be particularly interesting for digital twin and virtual certification processes.

Fig. 9
Fig. 9 Correlation matrix of the data set

Fig. 10
Fig. 10 Lift coefficient respect to feature parameters

Fig. 11
Fig. 11 Learning curves of high fidelity model and transfer learning model