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Articles 901 - 930 of 1158
Full-Text Articles in Aerospace Engineering
Experimental Implementation Of Adaptive-Critic Based Infinite Time Optimal Neurocontrol For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look
Experimental Implementation Of Adaptive-Critic Based Infinite Time Optimal Neurocontrol For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Recently the synthesis methodology for the infinite time optimal neuro-controllers for PDE systems in the framework of adaptive-critic design has been developed. In this paper, first we model an experimental setup representing one dimensional heat diffusion problems. Then we synthesize and implement an adaptive-critic based neuro-controller for online temperature profile control of the experimental setup.
Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis Of Distributed Parameter Systems Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis Of Distributed Parameter Systems Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.
Accuracy And Efficiency In Fem Modeling Of Turbofan Acoustic Radiation, Eivind Listerud, Walter Eversman
Accuracy And Efficiency In Fem Modeling Of Turbofan Acoustic Radiation, Eivind Listerud, Walter Eversman
Mechanical and Aerospace Engineering Faculty Research & Creative Works
It is shown that there is an increase in efficiency of acoustic radiation finite element modeling with the incorporation of cubic rather than quadratic serendipity elements. Cubic serendipity elements produce a given level of accuracy for acoustic pressure using a coarser mesh than required using quadratic elements, thus decreasing the CPU time needed for accurate modeling. These elements have been applied to the near field inlet and aft acoustic radiation models for a turbofan engine with the result of considerable reduction in the dimensionality of the problem without sacrificing accuracy. Visual observations of the gain in computational efficiency is supported …
Cfd Simulations Of Critical Components In Fuel Filling Systems, R. Banerjee, X. Bai, D. Pugh, Kakkattukuzhy M. Isaac, D. Klein, J. Edson, W. Breig, L. Oliver
Cfd Simulations Of Critical Components In Fuel Filling Systems, R. Banerjee, X. Bai, D. Pugh, Kakkattukuzhy M. Isaac, D. Klein, J. Edson, W. Breig, L. Oliver
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A comprehensive study is reported on the dynamics of critical components in the refueling process for passenger cars and light trucks. Nozzle, filler pipe, recirculation tube, tank, and canister are investigated. CFD simulations are conducted for flow rates of 4 liters/min (lpm) to 80 lpm for gasoline and up to 120 lpm for diesel fuel. Tank pressure, identified as a critical parameter controlling flow performance, is measured and utilized as a boundary condition. Flow simulation in a carbon canister, accomplished by treating the adsorbing carbon as a porous medium, indicates pressure drops which are in good agreement with published experimental …
Proper Orthogonal Decomposition Based Optimal Control Design Of Heat Equation With Discrete Actuators Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
Proper Orthogonal Decomposition Based Optimal Control Design Of Heat Equation With Discrete Actuators Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A new method is presented for the optimal control design of one-dimensional heat equation with the actuators being concentrated at discrete points in the spatial domain. This systematic methodology incorporates the advanced concept of proper orthogonal decomposition for the model reduction of distributed parameter systems. After deigning a set of problem-oriented basis functions an analogous optimal control problem in the lumped domain is formulated. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of adaptive critic neural networks. The control solution is then mapped back to the spatial domain using …
A Quantitative Similarity Metric For Design-By-Analogy, Daniel A. Mcadams, Kristin L. Wood
A Quantitative Similarity Metric For Design-By-Analogy, Daniel A. Mcadams, Kristin L. Wood
Mechanical and Aerospace Engineering Faculty Research & Creative Works
During the design and development of new products, design engineers use many techniques to generate and define new and "good" concepts. Inherent in this search for solutions is the conscious and unconscious reliance on prior experience and knowledge, or design-by-analogy. In this paper, a quantitative metric for design-by-analogy is developed. This metric is based on the functional similarity of products. By using this product-similarity metric, designers are able to formalize and quantify design-by-analogy techniques during concept and layout design. The methods, as developed in this paper, allow a designer with limited experience to develop sophisticated solutions that enhance the overall …
Forensic Investigation Of Failed Mast Arms Of Traffic Signal Supported Structures, Genda Chen, Michael G. Barker, D. Scott Mackenzie, Christopher W. Ramsay, Joe Alderson, Lokeswarappa R. Dharani, Jiaqing Yu
Forensic Investigation Of Failed Mast Arms Of Traffic Signal Supported Structures, Genda Chen, Michael G. Barker, D. Scott Mackenzie, Christopher W. Ramsay, Joe Alderson, Lokeswarappa R. Dharani, Jiaqing Yu
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
In Missouri, 11 traffic signal mast arms fractured at the arm-post weld connection in 7 years. To reduce this fatigue failure, the Missouri Department of Transportation developed a fatigue-resistant weld profile that increases the weld leg and reduces the slope of the weld at the toe. This study investigated causes of the failed arms, compared performance of new and old weld profiles, and suggested retrofitting measures for further investigation. The scope included a metallurgical investigation of one failed field mast arm, laboratory fatigue testing of five prototype mast arms (two new and three old profiles), and laboratory failure analysis of …
Adaptive Critic-Based Neural Network Controller For Uncertain Nonlinear Systems With Unknown Deadzones, Pingan He, Jagannathan Sarangapani, S. N. Balakrishnan
Adaptive Critic-Based Neural Network Controller For Uncertain Nonlinear Systems With Unknown Deadzones, Pingan He, Jagannathan Sarangapani, S. N. Balakrishnan
Electrical and Computer Engineering Faculty Research & Creative Works
A multilayer neural network (NN) controller in discrete-time is designed to deliver a desired tracking performance for a class of nonlinear systems with input deadzones. This multilayer NN controller has an adaptive critic NN architecture with two NNs for compensating the deadzone nonlinearity and a third NN for approximating the dynamics of the nonlinear system. A reinforcement learning scheme in discrete-time is proposed for the adaptive critic NN deadzone compensator, where the learning is performed based on a certain performance measure, which is supplied from a critic. The adaptive generating NN rejects the errors induced by the deadzone whereas a …
A New Method For Suboptimal Control Of A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan
A New Method For Suboptimal Control Of A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this paper, a new nonlinear control synthesis technique (θ - D approximation) is presented. This approach achieves suboptimal solutions to nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB) equation approximately by adding perturbations to the cost function. By manipulating the perturbation terms both semi-globally asymptotic stability and suboptimality properties can be obtained. The convergence and stability proofs are given. This method overcomes the large control for large initial states problem that occurs in some other Taylor expansion based methods. It does not need time-consuming online computations like the state dependent Riccati equation (SDRE) technique. …
Effect Of Polymer-Surface Mobility On Adhesion In Poly(Methyl Methacrylate)-Tape System, Bhavesh C. Gandhi, Frank D. Blum, Lokeswarappa R. Dharani
Effect Of Polymer-Surface Mobility On Adhesion In Poly(Methyl Methacrylate)-Tape System, Bhavesh C. Gandhi, Frank D. Blum, Lokeswarappa R. Dharani
Chemistry Faculty Research & Creative Works
The interaction between two polymer layers, especially adhesion between them, plays an important role in polymer processing and other applications. Detailed knowledge of the molecular structure and dynamics of polymer interfaces, and how they relate to macroscopic mechanical properties, should help designers construct more functional systems. Unfortunately, there have been few studies where both molecular and macroscopic studies have been performed on similar systems. In previous studies from our group, we have probed the dynamics of poly(methyl acrylate) (PMA) and thermal behavior of poly(methyl methacrylate) (PMMA) on silica. These studies helped us paint a picture for strongly bound molecules on …
World Wide Web Resources For Materials Science, Serge Abrate
World Wide Web Resources For Materials Science, Serge Abrate
Mechanical and Aerospace Engineering Faculty Research & Creative Works
The internet makes technical information readily available in ways that were unthinkable a few years ago. This article shows how the World Wide Web (the web) can be used in a Materials Science class to enrich the educational process. Strategies for finding and evaluating information and are discussed. © 2002 Wiley Periodicals, Inc.
Ingaasnsb/Gaas Quantum Wells For 1.55 Μm Lasers Grown By Molecular-Beam Epitaxy, Xiaodong Yang, J. B. Heroux, L. F. Mei, W. I. Wang
Ingaasnsb/Gaas Quantum Wells For 1.55 Μm Lasers Grown By Molecular-Beam Epitaxy, Xiaodong Yang, J. B. Heroux, L. F. Mei, W. I. Wang
Mechanical and Aerospace Engineering Faculty Research & Creative Works
InGaAsNSb/GaAs quantum wells (QWs) were grown by solid-source molecular-beam epitaxy using a N2 radio frequency plasma source. The effect of adding Sb during growth of InGaAsN/GaAs QWs was studied. X-ray diffraction, reflection high-energy electron diffraction and transmission electron microscopy studies indicate that Sb suppresses the three-dimensional growth and improves the interface of the QWs. X-ray diffraction and secondary ion mass spectroscopy analysis show that Sb gets incorporated into the quantum well, which becomes a quinternary compound that was previously unexplored. The introduction of Sb during growth of InGaAsN/GaAs QWs significantly enhances the optical properties of the QWs. 1.53 /spl …
Robust State Dependent Riccati Equation Based Guidance Laws, S. N. Balakrishnan, Ming Xin
Robust State Dependent Riccati Equation Based Guidance Laws, S. N. Balakrishnan, Ming Xin
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A robust state dependent Riccati equation based guidance/control is investigated in this study. In order to have a better design tool in terms of required interceptor accelerations, the target intercept geometry is formulated in a set of polar coordinates. With this formulation, we formulate a cost function with state dependent weights. In this study, we investigate the effects of such cost functions on the levels of interceptor accelerations. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the target acceleration. In this manner, we will not need target acceleration estimation explicitly in …
A Numerical Study Of Automotive Gas Tank Filler Pipe Two Phase Flow, R. Banerjee, Kakkattukuzhy M. Isaac, L. Oliver, W. Breig
A Numerical Study Of Automotive Gas Tank Filler Pipe Two Phase Flow, R. Banerjee, Kakkattukuzhy M. Isaac, L. Oliver, W. Breig
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Automotive refueling is gaining greater importance because fuel vapors released during refueling are believed to increase ozone levels in urban areas. As a step towards On-Board Refueling Vapor Recovery (ORVR) designs, vapor generation and transport during refueling needs to be understood to develop recovery techniques. The objective of the present study is to understand the fluid flow inside the automotive gas tank filler pipe using commercially available Computational Fluid Dynamics (CFD) software. This effort is expected to yield detailed flow field information, including air entrainment. The phenomena of well-back, the process of fuel flooding the filler pipe and flowing backwards …
Re-Examination Of The Crypto-Steady Pressure-Exchanger (Virtual Turbomachine), T. Scott, David W. Riggins
Re-Examination Of The Crypto-Steady Pressure-Exchanger (Virtual Turbomachine), T. Scott, David W. Riggins
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A crypto-steady pressure-exchanger (rotating center body ejecting fluid in a supersonic flow field) is investigated based on fundamental fluid dynamic principles. The results are then compared to computational fluid dynamic (CFD) simulations of a simplified device. On the basis of this comparison the device studied is correctly classified as an unsteady ejector instead of a type of turbomachinery. Entropy gains (total pressure losses) associated with the complex fluid-fluid and fluid-center body interactions are shown to be greater than total pressure gains due to work addition. Compared to a steady ejector, the virtual turbomachine shows increased entrainment (mixing) of the main …
Detection And Classification Of Impact-Induced Damage In Composite Plates Using Neural Networks, Rohit Dua, Steve Eugene Watkins, Donald C. Wunsch, K. Chandrashekhara, Farhad Akhavan
Detection And Classification Of Impact-Induced Damage In Composite Plates Using Neural Networks, Rohit Dua, Steve Eugene Watkins, Donald C. Wunsch, K. Chandrashekhara, Farhad Akhavan
Electrical and Computer Engineering Faculty Research & Creative Works
Artificial neutral networks (ANN) can be used as an online health monitoring systems (involving damage assessment, fatigue monitoring and delamination detection) for composite structures owing to their inherent fast computing speeds, parallel processing and ability to learn and adapt to the experimental data. The amount of impact-induced strain on a composite structure can be found using strain sensors attached to composite structures. Prior work has shown that strain-based ANN can characterize impact energy on composite plates and that strain signatures can be associated with damage types and severity. This paper reports the extension of this approach for damage classification using …
High Precision Solder Droplet Printing Technology: Principle And Applications, Qingbin Liu, M. Orme, Ming-Chuan Leu
High Precision Solder Droplet Printing Technology: Principle And Applications, Qingbin Liu, M. Orme, Ming-Chuan Leu
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Solder droplet printing technology, which is low-cost, noncontact, flexible, data-driven, and environmentally friendly, has emerged as an enabling technology for precisely placing fine solder deposits on a variety of small substrates. It is suitable for a variety of applications including direct chip attach site preparation, 3D substrates, fine line interconnect, substrate via fill, optoelectronics and many others. It enables manufacturing techniques that are impossible or unfeasible with current technology, such as localized replacement of solder on board, depositing solder in different thicknesses on the same board, or using more than one type of solder on the same board. This makes …
Robust State Dependent Riccati Equation Based Robot Manipulator Control, Ming Xin, S. N. Balakrishnan, Zhongwu Huang
Robust State Dependent Riccati Equation Based Robot Manipulator Control, Ming Xin, S. N. Balakrishnan, Zhongwu Huang
Mechanical and Aerospace Engineering Faculty Research & Creative Works
We present a new optimal control approach to robust control of robot manipulators in the framework of state dependent Riccati equation (SDRE) technique. To treat this highly nonlinear control system, we formulate it as a nonlinear optimal regulator problem. SDRE technique was used to synthesize an optimal controller to this class of robot control problem. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the parameter uncertainties. A typical two-link robot position control problem was studied to show the effectiveness of SDRE approach and robust extra control design to robotic application.
Robust Adaptive Critic Based Neurocontrollers For Missiles With Model Uncertainties, Zhongwu Huang, S. N. Balakrishnan
Robust Adaptive Critic Based Neurocontrollers For Missiles With Model Uncertainties, Zhongwu Huang, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A Lyapunov theory-based controller is proposed in this paper for robustness against model uncertainties in the control of a missile. The controller design consists of two parts; in the first phase, an optimal nonlinear controller is designed with neural networks for tracking. This is based on the adaptive critic method that consists of one neural network called the supervisor or critic and a second network called an action network or a controller. Each network is trained through the output of the other network and equations related to optimal control. When their outputs are mutually consistent, the controller network output is …
Fatigue Assessment Of Traffic Signal Mast Arms Based On Field Test Data Under Natural Wind Gusts, Genda Chen, Jingning Wu, Jiaqing Yu, Lokeswarappa R. Dharani, Michael G. Barker
Fatigue Assessment Of Traffic Signal Mast Arms Based On Field Test Data Under Natural Wind Gusts, Genda Chen, Jingning Wu, Jiaqing Yu, Lokeswarappa R. Dharani, Michael G. Barker
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
In recent years, several states including Missouri, Wyoming, California, and Texas experienced fracture failures of traffic signal mast arms. Almost all the failures are associated with the propagation of defects or cracks. It is therefore imperative to evaluate existing mast arms using a simple yet accurate procedure. A statistical methodology is proposed to predict the fatigue life of signal mast arm structures on the basis of field-measured strain data. The annual occurrence of various stress levels is determined using the historical wind speed data in the vicinity of a mast arm structure and the strain readings of the structure under …
Amplitude Modulated Droplet Formation In High Precision Solder Droplet Printing, Qingbin Liu, M. Orme, Ming-Chuan Leu
Amplitude Modulated Droplet Formation In High Precision Solder Droplet Printing, Qingbin Liu, M. Orme, Ming-Chuan Leu
Mechanical and Aerospace Engineering Faculty Research & Creative Works
There are many methods used at present to apply solder to wafers, ceramics, laminate and flex circuit boards, and other substrates. Among these, high-precision solder droplet printing technology, which is noncontact, data driven, flexible and environmentally friendly, is a key enabling technology. This technology selectively deposits solder droplets only where required, and therefore needs no mask or secondary resist removal, uses materials more efficiently and creates less waste than other methods. Currently, continuous droplet formation from capillary streams is mainly achieved by application of the well-known Rayleigh instability in which a sinusoidal disturbance is applied to the stream, resulting in …
Adaptive Critic Based Neuro-Observer, Xin Liu, S. N. Balakrishnan
Adaptive Critic Based Neuro-Observer, Xin Liu, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A new Neural Network (NN) based observer design method for nonlinear systems represented by nonlinear dynamics and linear/nonlinear measurement is proposed in this paper. In this new approach, as the first step, the observer design problem is changed into a "controller" design problem by establishing the error dynamics, and then the Adaptive Critic (AC) based approach is applied on this error dynamics to design a 'controller', such that the errors are driven to zero. The resulting observer has inherent robustness from the AC based design approach. Some simulations are presented to illustrate the effectiveness of this approach.
An Optimal Control Based Treatment Strategy For Parturient Paresis Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
An Optimal Control Based Treatment Strategy For Parturient Paresis Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
An optimal online feedback treatment strategy is developed for the parturient paresis of cows, based on nonlinear optimal control theory. A limitation in the development of an existing mathematical model for calcium homeostasis is addressed and the model is extended to incorporate control inputs. An optimal feedback controller is synthesized for the nonlinear system using neural networks. Though the main aim of this paper is to solve the biomedical control problem, the methodology presented in this paper is a general computational tool, which can be applied to solve a fairly general class nonlinear optimal control problems.
High-Temperature Characteristics Of 1.3 Μm Ingaasn:Sb/Gaas Multiple-Quantum-Well Lasers Grown By Molecular-Beam Epitaxy, Xiaodong Yang, J. B. Heroux, M. J. Jurkovic, W. I. Wang
High-Temperature Characteristics Of 1.3 Μm Ingaasn:Sb/Gaas Multiple-Quantum-Well Lasers Grown By Molecular-Beam Epitaxy, Xiaodong Yang, J. B. Heroux, M. J. Jurkovic, W. I. Wang
Mechanical and Aerospace Engineering Faculty Research & Creative Works
1.3 μm InGaAsN:Sb/GaAs multiple-quantum-well laser diodes have been grown by solid-source molecular-beam epitaxy using Sb as a surfactant. A low threshold of 1.1 kA/cm² was achieved for broad-area laser diodes under pulsed operation at room temperature. High-temperature device characterization revealed characteristic temperatures (T₀) of 92 and 54 K for operating temperatures below and above 75°C, respectively, as well as a lasing-wavelength temperature dependence of 0.36 nm/°C.
Development Of A Functional Basis For Design, Robert B. Stone, Kristin L. Wood
Development Of A Functional Basis For Design, Robert B. Stone, Kristin L. Wood
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Functional models represent a form independent blueprint of a product. As with any blueprint or schematic, a consistent language or coding system is required to ensure others can read it. This paper introduces such a design language, called a functional basis, where product function is characterized in a verb-object (function-flow) format. The set of functions and flows is intended to comprehensively describe the mechanical design space. Clear definitions are provided for each function and flow. The functional basis is compared to previous functional representations and is shown to subsume these attempts as well as offer a more consistent classification scheme. …
Midcourse Guidance Law With Neural Networks, Dongchen Han, S. N. Balakrishnan
Midcourse Guidance Law With Neural Networks, Dongchen Han, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A neural network-based synthesis of an optimal midcourse guidance law is presented in this study. We use a set of two-neural networks; the first network called 'a critic' outputs the Lagrange's multipliers arising in an optimal control formulation and second network called 'an action network' outputs the optimal guidance/control. In this so-called 'adaptive critic' approach, the inputs to the networks are the current values of the states. This approach needs no external training. System equations, optimality conditions and the costate equations are used in conjunction with the network outputs to provide the targets for the neural networks. When the critic …
Editorial, Ahmed Noor, Victor Birman
Editorial, Ahmed Noor, Victor Birman
Mechanical and Aerospace Engineering Faculty Research & Creative Works
No abstract provided.
Carryover For Hypersonic '+' And 'X' Configuration Delta Fin Missiles, Harlan F. Nelson
Carryover For Hypersonic '+' And 'X' Configuration Delta Fin Missiles, Harlan F. Nelson
Mechanical and Aerospace Engineering Faculty Research & Creative Works
The Zonal Euler Solver code (ZEUS) is used to predict hypersonic missile flow fields and to determine the carryover factors for the effect of the body on wing lift, Kw(B), and for the effect of the wing on body lift, KB(w). Results are presented for Mach 4, 6, 8, and 10 at an angle of attack of 2 deg. The missile has a conical nose and a cylindrical fuselage with a 1-degree flair angle. Both 'x' and '+' fin configurations are considered. Results are given for 20 and 30 deg semi vertex angles as a function of fur span to …
Tuning Parameter Tolerance Design: Foundations, Methods, And Measures, Daniel A. Mcadams, Kristin L. Wood
Tuning Parameter Tolerance Design: Foundations, Methods, And Measures, Daniel A. Mcadams, Kristin L. Wood
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this paper, a novel technique is presented to solve tolerance design problems. To achieve the desired performance tolerance, the technique uses a subtle, but significant, change in the design: the addition of a tuning parameter in place of an increase in component precision. Statistical models are used to develop a framework for the tuning parameter design method. Also developed is a new, dimensionless design metric which ranks candidate tuning parameters. A step-by-step method is developed for the application of tuning parameters using this metric. The step-by-step tuning parameter design method is applied to a heavy-duty manual stapler as a …
Using Quantitative Functional Models To Develop Product Architectures, Robert B. Stone, Kristin L. Wood, Richard H. Crawford
Using Quantitative Functional Models To Develop Product Architectures, Robert B. Stone, Kristin L. Wood, Richard H. Crawford
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Developing product architectures is a key phase in design and development processes. It encompasses the transformation from functional model to alternative product layouts. In this paper, we introduce a methodology for representing a functional model of a product in a quantitative manner. In addition to describing product functionality, the quantitative functional model also incorporates customer need ratings. Product design knowledge can be archived and transmitted in databases using this novel representation. Numerical manipulations of such a database assist in developing product architectures. In particular, product families and customer need ratings for modules are easily computed. Prior to the methodology, a …