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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft

The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best “truss” configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Lock’s fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples.

Kapania, Rakesh K.↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben Phillips↗
DOE OSTI2023

Multidisciplinary concurrent optimization framework for multi-phase building design process

Modern day building design projects require multidisciplinary expertise from architects and engineers across various phases of the design (conceptual, preliminary, and detailed) and construction processes. The Architecture Engineering and Construction (AEC) community has recently shifted gears toward leveraging design optimization techniques to make well-informed decisions in the design of buildings. However, most of the building design optimization efforts are either multidisciplinary optimization confined to just a specific design phase (conceptual/preliminary/detailed) or single disciplinary optimization (structural/thermal/daylighting/energy) spanning across multiple phases. Complexity in changing the optimization setup as the design progresses through subsequent phases, interoperability issues between modeling and physics-based analysis tools used at later stages, and the lack of an appropriate level of design detail to get meaningful results from these sophisticated analysis tools are few challenges that limit multi-phase multidisciplinary design optimization (MDO) in the AEC field. Here this paper proposes a computational building design platform leveraging concurrent engineering techniques such as interactive problem structuring, simulation-based optimization using meta models for energy and daylighting (machine learning based) and tradespace visualization. The proposed multi-phase concurrent MDO framework is demonstrated by using it to design and optimize a sample office building for energy and daylighting objectives across multiple phases. Furthermore, limitations of the proposed framework and future avenues of research are listed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1992

Multidisciplinary design optimization using response surface analysis

Aerospace conceptual vehicle design is a complex process which involves multidisciplinary studies of configuration and technology options considering many parameters at many values. NASA Langley's Vehicle Analysis Branch (VAB) has detailed computerized analysis capabilities in most of the key disciplines required by advanced vehicle design. Given a configuration, the capability exists to quickly determine its performance and lifecycle cost. The next step in vehicle design is to determine the best settings of design parameters that optimize the performance characteristics. Typical approach to design optimization is experience based, trial and error variation of many parameters one at a time where possible combinations usually number in the thousands. However, this approach can either lead to a very long and expensive design process or to a premature termination of the design process due to budget and/or schedule pressures. Furthermore, one variable at a time approach can not account for the interactions that occur among parts of systems and among disciplines. As a result, vehicle design may be far from optimal. Advanced multidisciplinary design optimization (MDO) methods are needed to direct the search in an efficient and intelligent manner in order to drastically reduce the number of candidate designs to be evaluated. The payoffs in terms of enhanced performance and reduced cost are significant. A literature review yields two such advanced MDO methods used in aerospace design optimization; Taguchi methods and response surface methods. Taguchi methods provide a systematic and efficient method for design optimization for performance and cost. However, response surface method (RSM) leads to a better, more accurate exploration of the parameter space and to estimated optimum conditions with a small expenditure on experimental data. These two methods are described.

Unal, Resit↗
NASA NTRS1993

Multidisciplinary design optimization - An emerging new engineering discipline

A definition of the multidisciplinary design optimization (MDO) is introduced, and functionality and relationship of the MDO conceptual components are examined. The latter include design-oriented analysis, approximation concepts, mathematical system modeling, design space search, an optimization procedure, and a humane interface.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1994

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.↗
NASA NTRS1994

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗
NASA NTRS1997

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

Balling, R. J.↗
NASA NTRS1998

A Framework for Preliminary Design of Aircraft Structures Based on Process Information

This report discusses the general framework and development of a computational tool for preliminary design of aircraft structures based on process information. The described methodology is suitable for multidisciplinary design optimization (MDO) activities associated with integrated product and process development (IPPD). The framework consists of three parts: (1) product and process definitions; (2) engineering synthesis, and (3) optimization. The product and process definitions are part of input information provided by the design team. The backbone of the system is its ability to analyze a given structural design for performance as well as manufacturability and cost assessment. The system uses a database on material systems and manufacturing processes. Based on the identified set of design variables and an objective function, the system is capable of performing optimization subject to manufacturability, cost, and performance constraints. The accuracy of the manufacturability measures and cost models discussed here depend largely on the available data on specific methods of manufacture and assembly and associated labor requirements. As such, our focus in this research has been on the methodology itself and not so much on its accurate implementation in an industrial setting. A three-tier approach is presented for an IPPD-MDO based design of aircraft structures. The variable-complexity cost estimation methodology and an approach for integrating manufacturing cost assessment into design process are also discussed. This report is presented in two parts. In the first part, the design methodology is presented, and the computational design tool is described. In the second part, a prototype model of the preliminary design Tool for Aircraft Structures based on Process Information (TASPI) is described. Part two also contains an example problem that applies the methodology described here for evaluation of six different design concepts for a wing spar.

Rais-Rohani, Masoud↗
NASA NTRS1999

Configuration Management of an Optimization Application in a Research Environment

Multidisciplinary design optimization (MDO) research aims to increase interdisciplinary communication and reduce design cycle time by combining system analyses (simulations) with design space search and decision making. The High Performance Computing and Communication Program's current High Speed Civil Transport application, HSCT4.0, at NASA Langley Research Center involves a highly complex analysis process with high-fidelity analyses that are more realistic than previous efforts at the Center. The multidisciplinary processes have been integrated to form a distributed application by using the Java language and Common Object Request Broker Architecture (CORBA) software techniques. HSCT4.0 is a research project in which both the application problem and the implementation strategy have evolved as the MDO and integration issues became better understood. Whereas earlier versions of the application and integrated system were developed with a simple, manual software configuration management (SCM) process, it was evident that this larger project required a more formal SCM procedure. This report briefly describes the HSCT4.0 analysis and its CORBA implementation and then discusses some SCM concepts and their application to this project. In anticipation that SCM will prove beneficial for other large research projects, the report concludes with some lessons learned in overcoming SCM implementation problems for HSCT4.0.

Townsend, James C.↗
NASA NTRS1999

NASA Aeronautics Multidisciplinary Analysis and Design Fellowship Program

This program began as a grant from NASA Headquarters, NGT-10025, which was in effect from 10/l/93 until 10/31/96. The remaining funding for this effort was transferred from NASA Headquarters to NASA Langley and a new grant NGT-1-52155 was issued covering the period II/l/96 to 5/15/99. This report serves as the final report of NGT-1-52155. For a number of years, Virginia Tech had been on the forefront of research in the area of multidisciplinary analysis and design. In June of 1994, faculty members from aerospace and ocean engineering, engineering science and mechanics, mechanical engineering, industrial engineering, mathematics and computer sciences, at Virginia Tech joined together to form the Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles. The center was established with the single goal: to perform research that is relevant to the needs of the US industry and to foster collaboration between the university, government and industry. In October of 1994, the center was chosen by NASA headquarters as one of the five university centers to establish a fellowship program to develop a graduate program in multidisciplinary analysis and design. The fellowship program provides full stipend and tuition support for seven U. S. students per year during their graduate studies. The grant is currently being administered by the NMO Branch of NASA Langley. To advise us regarding the problems faced by the industry, an industrial advisory board has been formed consisting of representatives from industry as well as government laboratories. The present membership includes major aerospace companies: Aurora Flight Sciences, Boeing: Philadelphia, Boeing: Long Beach, Boeing: Seattle, Boeing: St. Louis, Cessna, Ford, General Electric, Hughes, Lockheed-Martin: Palo Alto, Northrop-Grumman, Sikorsky, smaller, aerospace software companies: Aerosoft, Phoenix Integration and Proteus Engineering, along with representatives from government agencies, including: NASA Ames, Langley and Lewis. The function of the advisory board is to channel information from its member companies to faculty members concerning problems that need research attention in the general area of multidisciplinary design optimization (MDO). The faculty and their graduate students make presentations to the board on their research. The board makes recommendations on the research and suggests new areas and problems which need attention. Many students participating in the program spend 3-6 months in industry working on their research projects. We are completing the fifth year of the fellowship program and have had four advisory board meetings in Blacksburg. Ten students have spent the three month periods in industry. In addition to the research element of the MAD Center efforts we also have an academic component. We have developed a menu of design-related graduate courses and two new courses: one in Aerospace Manufacturing and another in MDO. Some of the MAD Center activities are described on the world-wide web at http://www.aoe.vt.edu/mads.html The MAD Center represents an innovative approach for joint Industry-Government-University cooperation in the development of a comprehensive program in engineering education which addresses the design needs of industry. The following charts list detail of the grant: mission of the MAD center, faculty members, purpose of the advisory board, board members, summary of the graduate and undergraduate program, history of the fellowship program, mission of the fellowship program, requirements of MAD fellows, course requirements, students supported, advisory board participants, and MAD center research papers

Grossman, B.↗
NASA NTRS1995

On Developing a Taxonomy for Multidisciplinary Design Optimization: A Decision-Based Perspective

In this paper, we approach MDO from a Decision-Based Design (DBD) perspective and explore classification schemes for designing complex systems and processes. Specifically, we focus on decisions, which are only a small portion of the Decision Support Problem (DSP) Technique, our implementation of DBD. We map coupled nonhierarchical and hierarchical representations from the DSP Technique into the Balling-Sobieski (B-S) framework (Balling and Sobieszczanski-Sobieski, 1994), and integrate domain-independent linguistic terms to complete our taxonomy. Application of DSPs to the design of complex, multidisciplinary systems include passenger aircraft, ships, damage tolerant structural and mechanical systems, and thermal energy systems. In this paper we show that Balling-Sobieski framework is consistent with that of the Decision Support Problem Technique through the use of linguistic entities to describe the same type of formulations. We show that the underlying linguistics of the solution approaches are the same and can be coalesced into a homogeneous framework with which to base the research, application, and technology MDO upon. We introduce, in the Balling-Sobieski framework, examples of multidisciplinary design, namely, aircraft, damage tolerant structural and mechanical systems, and thermal energy systems.

Lewis, Kemper↗
NASA NTRS1999

Multidisciplinary Optimization Branch Experience Using iSIGHT Software

The Multidisciplinary Optimization (MDO) Branch at NASA Langley Research Center is investigating frameworks for supporting multidisciplinary analysis and optimization research. An optimization framework call improve the design process while reducing time and costs. A framework provides software and system services to integrate computational tasks and allows the researcher to concentrate more on the application and less on the programming details. A framework also provides a common working environment and a full range of optimization tools, and so increases the productivity of multidisciplinary research teams. Finally, a framework enables staff members to develop applications for use by disciplinary experts in other organizations. Since the release of version 4.0, the MDO Branch has gained experience with the iSIGHT framework developed by Engineous Software, Inc. This paper describes experiences with four aerospace applications: (1) reusable launch vehicle sizing, (2) aerospike nozzle design, (3) low-noise rotorcraft trajectories, and (4) acoustic liner design. All applications have been successfully tested using the iSIGHT framework, except for the aerospike nozzle problem, which is in progress. Brief overviews of each problem are provided. The problem descriptions include the number and type of disciplinary codes, as well as all estimate of the multidisciplinary analysis execution time. In addition, the optimization methods, objective functions, design variables, and design constraints are described for each problem. Discussions on the experience gained and lessons learned are provided for each problem. These discussions include the advantages and disadvantages of using the iSIGHT framework for each case as well as the ease of use of various advanced features. Potential areas of improvement are identified.

Padula, S. L.↗
NASA NTRS1999

Multidisciplinary Optimization Branch Experience Using iSIGHT Software

The Multidisciplinary Optimization (MDO) Branch at NASA Langley is investigating frameworks for supporting multidisciplinary analysis and optimization research. A framework provides software and system services to integrate computational tasks and allows the researcher to concentrate more on the application and less on the programming details. A framework also provides a common working environment and a full range of optimization tools, and so increases the productivity of multidisciplinary research teams. Finally, a framework enables staff members to develop applications for use by disciplinary experts in other organizations. This year, the MDO Branch has gained experience with the iSIGHT framework. This paper describes experiences with four aerospace applications, including: (1) reusable launch vehicle sizing, (2) aerospike nozzle design, (3) low-noise rotorcraft trajectories, and (4) acoustic liner design. Brief overviews of each problem are provided, including the number and type of disciplinary codes and computation time estimates. In addition, the optimization methods, objective functions, design variables, and constraints are described for each problem. For each case, discussions on the advantages and disadvantages of using the iSIGHT framework are provided as well as notes on the ease of use of various advanced features and suggestions for areas of improvement.

Padula, S. L.↗
NASA NTRS2000

Development of a Composite Tailoring Procedure for Airplane Wings

The quest for finding optimum solutions to engineering problems has existed for a long time. In modern times, the development of optimization as a branch of applied mathematics is regarded to have originated in the works of Newton, Bernoulli and Euler. Venkayya has presented a historical perspective on optimization in [1]. The term 'optimization' is defined by Ashley [2] as a procedure "...which attempts to choose the variables in a design process so as formally to achieve the best value of some performance index while not violating any of the associated conditions or constraints". Ashley presented an extensive review of practical applications of optimization in the aeronautical field till about 1980 [2]. It was noted that there existed an enormous amount of published literature in the field of optimization, but its practical applications in industry were very limited. Over the past 15 years, though, optimization has been widely applied to address practical problems in aerospace design [3-5]. The design of high performance aerospace systems is a complex task. It involves the integration of several disciplines such as aerodynamics, structural analysis, dynamics, and aeroelasticity. The problem involves multiple objectives and constraints pertaining to the design criteria associated with each of these disciplines. Many important trade-offs exist between the parameters involved which are used to define the different disciplines. Therefore, the development of multidisciplinary design optimization (MDO) techniques, in which different disciplines and design parameters are coupled into a closed loop numerical procedure, seems appropriate to address such a complex problem. The importance of MDO in successful design of aerospace systems has been long recognized. Recent developments in this field have been surveyed by Sobieszczanski-Sobieski and Haftka [6].

Chattopadhyay, Aditi↗
NASA NTRS1998

Distributed Parallel Processing and Dynamic Load Balancing Techniques for Multidisciplinary High Speed Aircraft Design

Multidisciplinary design optimization (MDO) for large-scale engineering problems poses many challenges (e.g., the design of an efficient concurrent paradigm for global optimization based on disciplinary analyses, expensive computations over vast data sets, etc.) This work focuses on the application of distributed schemes for massively parallel architectures to MDO problems, as a tool for reducing computation time and solving larger problems. The specific problem considered here is configuration optimization of a high speed civil transport (HSCT), and the efficient parallelization of the embedded paradigm for reasonable design space identification. Two distributed dynamic load balancing techniques (random polling and global round robin with message combining) and two necessary termination detection schemes (global task count and token passing) were implemented and evaluated in terms of effectiveness and scalability to large problem sizes and a thousand processors. The effect of certain parameters on execution time was also inspected. Empirical results demonstrated stable performance and effectiveness for all schemes, and the parametric study showed that the selected algorithmic parameters have a negligible effect on performance.

Krasteva, Denitza T.↗