Enabling Decision-Based Design Using Solution Trajectory Correction and Backtracking Rules

2012 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos ◽  
Monica Majcher
Keyword(s):  
Optimal Design ◽  
Utility Function ◽  
Design Space ◽  
A Priori ◽  
Preference Order ◽  
Beam Design ◽  
Effective Decision ◽  
Suboptimal Design ◽  
Trajectory Correction ◽  
Decision Based Design

Optimization is needed for effective decision based design (DBD). However, a utility function assessed a priori in DBD does not usually capture the preferences of the decision maker over the entire design space. As a result, when the optimizer searches for the optimal design, it traverses (or ends up) in regions where the preference order among different solutions is different from the actual order. For a highly non-convex design space, this can lead to convergence to a grossly suboptimal design depending on the initial design. In this article, we propose two approaches to alleviate this issue. First, we map the trajectory of the solution as generated by the optimizer and generate ranking questions that are presented to the designer to verify the correctness of the utility function. We then propose backtracking rules if a local utility function is very different from the initially assessed function. We demonstrate our methodology using a mathematical example and a welded beam design problem.

Adaptive Geometry Representation of Turbine Vane Frames for Use in Optimization

2021 ◽  
Author(s):  
Sebastian F. Riebl ◽  
Christian Wakelam ◽  
Reinhard Niehuis
Keyword(s):  
Design Space ◽  
Cfd Simulation ◽  
A Priori ◽  
Three Dimensional ◽  
Optimization Method ◽  
Three Dimensions ◽  
Design Parameters ◽  
Adjustment Process ◽  
Turbine Vane ◽  
Integrated Concept

Abstract Turbine Vane Frames (TVF) are a way to realize more compact jet engine designs. Located between the high pressure turbine (HPT) and the low pressure turbine (LPT), they fulfill structural and aerodynamic tasks. When used as an integrated concept with splitters located between the structural load-bearing vanes, the TVF configuration contains more than one type of airfoil with sometimes pronouncedly different properties. This system of multidisciplinary demands and mixed blading poses an interesting opportunity for optimization. Within the scope of the present work, a full geometric parameterization of a TVF with splitters is presented. The parameterization is chosen as to minimize the number of parameters required to automatically and flexibly represent all blade types involved in a TVF row in all three dimensions. Typical blade design parameters are linked to the fourth order Bézier-curve controlled camber line-thickness parameterization. Based on conventional design rules, a procedure is presented, which sets the parameters within their permissible ranges according to the imposed constraints, using a proprietary developed code. The presented workflow relies on subsequent three dimensional geometry generation by transfer of the proposed parameter set to a commercially available CAD package. The interdependencies of parameters are discussed and their respective significance for the adjustment process is detailed. Furthermore, the capability of the chosen parameterization and adjustment process to rebuild an exemplary reference TVF geometry is demonstrated. The results are verified by comparing not only geometrical profile data, but also validated CFD simulation results between the rebuilt and original geometries. Measures taken to ensure the robustness of the method are highlighted and evaluated by exploring extremes in the permissible design space. Finally, the embedding of the proposed method within the framework of an automated, gradient free numerical optimization is discussed. Herein, implications of the proposed method on response surface modeling in combination with the optimization method are highlighted. The method promises to be an option for improvement of optimization efficiency in gradient free optimization of interdependent blade geometries, by a-priori excluding unsuitable blade combinations, yet keeping restrictions to the design space as limited as possible.

Optimal Design of a 2-UPR-RPU Parallel Manipulator

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Feibo Wang ◽  
Qiaohong Chen ◽  
Qinchuan Li
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Design Space ◽  
Parameter Design ◽  
Optimal Parameters ◽  
Force Transmission ◽  
Universal Joint ◽  
Practical Applications ◽  
Optimum Region ◽  
Dimensional Optimization

This paper investigates dimensional optimization of a 2-UPR-RPU parallel manipulator (where U is a universal joint, P a prismatic pair, and R a revolute pair). First, the kinematics and screws of the mechanism are analyzed. Then, three indices developed from motion/force transmission are proposed to evaluate the performance of the 2-UPR-RPU parallel manipulator. Based on the performance atlases obtained, a set of optimal parameters are selected from the optimum region within the parameter design space. Finally, the optimized parameters are determined for practical applications.

Optimization and Uncertainty Analysis of a Diesel Engine Operating Point Using CFD

2016 ◽  
Author(s):  
Daniel M. Probst ◽  
Peter K. Senecal ◽  
Peter Z. Qian ◽  
Max X. Xu ◽  
Brian P. Leyde
Keyword(s):  
Diesel Engine ◽  
Optimal Design ◽  
Analytical Model ◽  
Design Space ◽  
Uncertainty Propagation ◽  
Operating Point ◽  
Included Angle ◽  
Design Point ◽  
Injection Duration ◽  
Engine Operating Point

This study describes the use of an analytical model, constructed using sequential design of experiments (DOEs), to optimize and quantify the uncertainty of a Diesel engine operating point. A genetic algorithm (GA) was also used to optimize the design. Three engine parameters were varied around a baseline design to minimize indicated specific fuel consumption (ISFC) without exceeding emissions (NOx and soot) or peak cylinder pressure constraints. An objective merit function was constructed to quantify the strength of designs. The engine parameters were start of injection (SOI), injection duration, and injector included angle. The engine simulation was completed with a sector mesh in the commercial computational fluid dynamics (CFD) software CONVERGE, which predicted the combustion and emissions using a detailed chemistry solver with a reduced mechanism for n-heptane. The analytical model was constructed using the SmartUQ software using DOE responses to construct kernel emulators of the system. Each emulator was used to direct the placement of the next set of DOE points such that they improve the accuracy of the subsequently generated emulator. This refinement was either across the entire design space or a reduced design space that was likely to contain the optimal design point. After sufficient emulator accuracy was achieved, the optimal design point was predicted. A total of 5 sequential DOEs were completed, for a total of 232 simulations. A reduced design region was predicted after the second DOE that reduced the volume of the design space by 96.8%. The final predicted optimum was found to exist in this reduced design region. The sequential DOE optimization was compared to an optimization performed using a GA. The GA was completed using a population of 9 and was run for 71 generations. This study highlighted the strengths of both methods for optimization. The GA (known to be an efficient and effective method) found a better optimum, while the DOE method found a good optimum with fewer total simulations. The DOE method also ran more simulations concurrently, which is an advantage when sufficient computing resources are available. In the second part of the study, the analytical model developed in the first part was used to assess the sensitivity and robustness of the design. A sensitivity analysis of the design space around the predicted optimum showed that injection duration had the strongest effect on predicted results, while the included angle had the weakest. The uncertainty propagation was studied over the reduced design region found with the sequential DoE in the first part. The uncertainty propagation results demonstrated that for the relatively large variations in the input parameters, the expected variation in the ISFC and NOx results were significant. Finally, the predictions from the analytical model were validated against CFD results for sweeps of the input parameters. The predictions of the analytical model were found to agree well with the results from the CFD simulation.

Optimal Design of 6-UPU Parallel Mechanism

2011 ◽  
Vol 480-481 ◽  
pp. 1055-1060
Author(s):  
Guang Hua Wu ◽  
Lie Hang Gong ◽  
Xin Wei Ji ◽  
Zhong Jun Wu ◽  
Yong Jun Gai
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimal Design ◽  
Objective Function ◽  
Parallel Mechanism ◽  
Design Space ◽  
Jacobian Matrix ◽  
Optimal Model ◽  
The Real ◽  
Universal Joints

The methodology of the optimal design for the 6-UPU parallel mechanism (PM) is presented based on genetic algorithms. The optimal index which expressed by Jacobian matrix of the PM is first deduced. An optimal model is established, in which the kinematic dexterity of a parallel mechanism is considered as the objective function. The design space, the limiting length of the electric actuators and the limit angles of universal joints are taken as constraints. The real-encoding genetic algorithm is applied to the optimal design of a parallel mechanism, which is proved the validity and advantage for the optimal design of a similar mechanism.

scholarly journals Optimal Tooth Numbers for Compact Standard Spur Gear Sets

1982 ◽  
Vol 104 (4) ◽  
pp. 749-757 ◽  
Author(s):  
M. Savage ◽  
J. J. Coy ◽  
D. P. Townsend
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Design Space ◽  
Spur Gear ◽  
Gear Ratio ◽  
Contact Ratio ◽  
Bending Fatigue ◽  
Gear Mesh ◽  
Compact Design ◽  
Center Distance

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

scholarly journals Mechanistic Modeling of Biochemical Systems Without A Priori Parameter Values Using the Design Space Toolbox v.3.0

2020 ◽  
Author(s):  
Miguel Á. Valderrama-Gómez ◽  
Jason G. Lomnitz ◽  
Rick A. Fasani ◽  
Michael A. Savageau
Keyword(s):  
Design Space ◽  
A Priori ◽  
Design Principles ◽  
Mechanistic Modeling ◽  
Design And Optimization ◽  
Biological Design ◽  
Biological Phenomena ◽  
Biochemical Systems ◽  
Space Formalism ◽  
Parameter Values

SummaryMechanistic models of biochemical systems provide a rigorous kinetics-based description of various biological phenomena. They are indispensable to elucidate biological design principles and to devise and engineer systems with novel functionalities. To date, mathematical analysis and characterization of these models remain a challenging endeavor, the main difficulty being the lack of information for most system parameters. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism that enables mechanistic modeling of complex biological processes without requiring previous knowledge of the parameter values involved. This is achieved by making use of a phenotype-centric modeling approach, in which the system is first decomposed into a series of biochemical phenotypes. Parameter values realizing phenotypes of interest are predicted in a second step. DST3 represents the most generally applicable implementation of the Design Space formalism to date and offers unique advantages over earlier versions. By expanding the capabilities of the Design Space formalism and streamlining its distribution, DST3 represents a valuable tool for elucidating biological design principles and guiding the design and optimization of novel synthetic circuits.

Quantifying Design Freedom in Decision-Based Conceptual Design

2000 ◽  
Author(s):  
William H. Wood
Keyword(s):  
Conceptual Design ◽  
Design Space ◽  
Design Evaluation ◽  
Design Problems ◽  
The Cost ◽  
Analysis Models ◽  
Decision Based Design ◽  
The Impact ◽  
Design Freedom ◽  
Probabilistic Entropy

Abstract Formal methods for conceptual design must embrace the uncertainty that pervades the earliest parts of the design process. Operating over this uncertainty, decision-based design measures the value of restricting the design space as well as the impact of refining design evaluation or analysis models. Missing from this framework is the cost in terms of design freedom of restricting the design space. We propose a measure of design freedom based on probabilistic entropy and demonstrate its application to two example conceptual design problems.

Representations of Well-Founded Preference Orders

1983 ◽  
Vol 35 (3) ◽  
pp. 496-508 ◽  
Author(s):  
Douglas Cenzer ◽  
R. Daniel Mauldin
Keyword(s):  
Utility Function ◽  
Binary Relation ◽  
Linear Order ◽  
Equivalence Classes ◽  
Preference Order ◽  
Real Numbers ◽  
Order Preserving Map ◽  
Preference Orders ◽  
Reasonable Sense ◽  
Natural Relation

A preference order, or linear preorder, on a set X is a binary relation which is transitive, reflexive and total. This preorder partitions the set X into equivalence classes of the form . The natural relation induced by on the set of equivalence classes is a linear order. A well-founded preference order, or prewellordering, will similarly induce a well-ordering. A representation or Paretian utility function of a preference order is an order-preserving map f from X into the R of real numbers (provided with the standard ordering). Mathematicians and economists have studied the problem of obtaining continuous or measurable representations of suitably defined preference orders [4, 7]. Parametrized versions of this problem have also been studied [1, 7, 8]. Given a continuum of preference orders which vary in some reasonable sense with a parameter t, one would like to obtain a continuum of representations which similarly vary with t.

Sign in / Sign up

Export Citation Format

Share Document