Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

2009 ◽  
Author(s):  
M. Gabiccini ◽  
A. Bracci ◽  
M. Guiggiani
Keyword(s):  
Optimization Problems ◽  
Optimization Procedure ◽  
Target Area ◽  
Contact Pattern ◽  
Unified Framework ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Unconstrained Nonlinear Optimization ◽  
The One ◽  
Micro Topography

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth micro-topography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth, while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
M. Gabiccini ◽  
A. Bracci ◽  
M. Guiggiani
Keyword(s):  
Optimization Problems ◽  
Optimization Procedure ◽  
Target Area ◽  
Contact Pattern ◽  
Trial And Error ◽  
Unified Framework ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Unconstrained Nonlinear Optimization ◽  
The One

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth microtopography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here, the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Alessio Artoni ◽  
Andrea Bracci ◽  
Marco Gabiccini ◽  
Massimo Guiggiani
Keyword(s):  
Optimization Problems ◽  
Mathematical Framework ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Computational Speed ◽  
Tool Setting ◽  
Unconstrained Nonlinear Optimization ◽  
Time Required ◽  
Time Frames

Systematic optimization of the tooth contact pattern under load is an open problem in the design of spiral bevel and hypoid gears. In order to enhance its shape and position, gear engineers have been assisted by numerical tools based on trial-and-error approaches, and/or they have been relying on the expertise of skilled operators. The present paper proposes a fully automatic procedure to optimize the loaded tooth contact pattern, with the advantage of eventually reducing design time and cost. The main problem was split into two identification subproblems: first, to identify the ease-off topography capable of optimizing the contact pattern; second, to identify the machine-tool setting variations required to obtain such ease-off modifications. Both of them were formulated and solved as unconstrained nonlinear optimization problems. In addition, an original strategy to quickly approximate the tooth contact pattern under load was conceived. The results obtained were very satisfactory in terms of accuracy, robustness, and computational speed. They also suggest that the time required to optimize the contact pattern can be significantly reduced compared with typical time frames. A sound mathematical framework ensures results independent of the practitioner’s subjective decision-making process. By defining a proper objective function, the proposed method can also be applied to affect other contact properties, such as to improve the motion graph or to decrease the sensitivity of the transmission to assembly errors. Furthermore, it can be easily adapted to any gear drive by virtue of its systematic and versatile nature.

scholarly journals An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

2021 ◽  
Author(s):  
Mingxuan Zhao ◽  
Yulin Han ◽  
Jian Zhou
Keyword(s):  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Fuzzy Programming ◽  
Planning Problem ◽  
Monotone Functions ◽  
Solution Strategy ◽  
Deterministic Equivalent ◽  
The One ◽  
Short Time

Abstract The operational law put forward by Zhou et al. on strictly monotone functions with regard to regular LR fuzzy numbers makes a valuable push to the development of fuzzy set theory. However, its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which restricts its application in practice to a certain degree. In this paper, we propose an extensive operational law that generalizes the one proposed by Zhou et al. to apply to monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs), of which regular fuzzy numbers can be regarded as particular cases. By means of the extensive operational law, the inverse credibility distributions (ICDs) of monotone functions regarding regular LR-FIs can be calculated efficiently and effectively. Moreover, the extensive operational law has a wider range of applications, which can deal with the situations hard to be handled by the original operational law. Subsequently, based on the extensive operational law, the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs are presented. Furthermore, the proposed operational law is also applied to dispose fuzzy optimization problems with regular LR-FIs, for which a solution strategy is provided, where the fuzzy programming is converted to a deterministic equivalent first and then a newly-devised solution algorithm is utilized. Finally, the proposed solution strategy is applied to a purchasing planning problem, whose performances are evaluated by comparing with the traditional fuzzy simulation-based genetic algorithm. Experimental results indicate that our method is much more efficient, yielding high-quality solutions within a short time.

scholarly journals Entropy-Penalized Semidefinite Programming

2019 ◽  
Author(s):  
Mikhail Krechetov ◽  
Jakub Marecek ◽  
Yury Maximov ◽  
Martin Takac
Keyword(s):  
Machine Learning ◽  
Time Complexity ◽  
Optimization Problems ◽  
Linear Time ◽  
Broad Class ◽  
Low Rank ◽  
Learning Problems ◽  
Unified Framework ◽  
Gradient Computation ◽  
Machine Learning Applications

Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts. In this paper, we propose Entropy-Penalized Semi-Definite Programming (EP-SDP), which provides a unified framework for a broad class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit an efficient numerical algorithm, having (almost) linear time complexity of the gradient computation; this makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.

scholarly journals Virulence evolution of a parasite infecting male and female hosts

2017 ◽  
Author(s):  
Alison M. Wardlaw ◽  
Aneil F. Agrawal
Keyword(s):  
Death Rate ◽  
Host Population ◽  
Reproductive Value ◽  
Contact Pattern ◽  
Male And Female ◽  
Virulence Evolution ◽  
Host Type ◽  
Contact Patterns ◽  
Exploitation Rate ◽  
Evolutionarily Stable

AbstractParasites experience different tradeoffs between transmission and virulence in male and female hosts if the sexes vary in life history or disease-related traits. We determine the evolutionarily stable levels of exploitation by pathogens under two scenarios: an unconstrained pathogen that expresses different exploitation rates within each host type as well as a pathogen constrained to express the same exploitation rate in each sex. We show that an unconstrained horizontally-transmitted parasite evolves to express the same sex-specific exploitation rate within each sex as it would in a host population composed entirely of hosts with that sex’s resistance and intrinsic death rate. In contrast, the ESS exploitation rate of a constrained pathogen is affected by sex-differences in susceptibility and non-random contact patterns between host types that differ in resistance. As the amount of within-sex transmission increases, the ESS shifts closer to the optimum trait value in the more susceptible sex. Allowing for some degree of vertical transmission, the exploitation rate expressed in females (but not males) changes with contact pattern even in unconstrained pathogens. Differences in contact pattern and susceptibility play an important role in determining the ESS exploitation rate by shifting the reproductive value of each host type.

scholarly journals On implicit variables in optimization theory

2021 ◽  
Vol Volume 2 (Original research articles) ◽  
Author(s):  
Matúš Benko ◽  
Patrick Mehlitz
Keyword(s):  
Optimization Problems ◽  
Constraint Qualifications ◽  
Optimization Theory ◽  
Mathematical Optimization ◽  
General Setting ◽  
Necessary Optimality Conditions ◽  
Detailed Comparison ◽  
Mordukhovich Stationarity ◽  
Stationarity Conditions ◽  
The One

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory. Comment: 34 pages

An enhanced surrogate-assisted differential evolution for constrained optimization problems

2021 ◽  
Author(s):  
Rafael de Paula Garcia ◽  
Beatriz Souza Leite Pires de Lima ◽  
Afonso Celso de Castro Lemonge ◽  
Breno Pinheiro Jacob
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Optimization Procedure ◽  
Nearest Neighbors ◽  
Engineering Optimization ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Constrained Optimization Problems ◽  
Engineering Problems ◽  
Complex Engineering

Abstract The application of Evolutionary Algorithms (EAs) to complex engineering optimization problems may present difficulties as they require many evaluations of the objective functions by computationally expensive simulation procedures. To deal with this issue, surrogate models have been employed to replace those expensive simulations. In this work, a surrogate-assisted evolutionary optimization procedure is proposed. The procedure combines the Differential Evolution method with a Anchor -nearest neighbors ( –NN) similarity-based surrogate model. In this approach, the database that stores the solutions evaluated by the exact model, which are used to approximate new solutions, is managed according to a merit scheme. Constraints are handled by a rank-based technique that builds multiple separate queues based on the values of the objective function and the violation of each constraint. Also, to avoid premature convergence of the method, a strategy that triggers a random reinitialization of the population is considered. The performance of the proposed method is assessed by numerical experiments using 24 constrained benchmark functions and 5 mechanical engineering problems. The results show that the method achieves optimal solutions with a remarkably reduction in the number of function evaluations compared to the literature.

scholarly journals An Adaptive Multi-Swarm Competition Particle Swarm Optimizer for Large-Scale Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 521 ◽  
Author(s):  
Fanrong Kong ◽  
Jianhui Jiang ◽  
Yan Huang
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Particle Swarm ◽  
The Other ◽  
Large Scale Optimization ◽  
Particle Swarm Optimizer ◽  
Competition Mechanism ◽  
Benchmark Suite ◽  
Scale Optimization ◽  
The One

As a powerful tool in optimization, particle swarm optimizers have been widely applied to many different optimization areas and drawn much attention. However, for large-scale optimization problems, the algorithms exhibit poor ability to pursue satisfactory results due to the lack of ability in diversity maintenance. In this paper, an adaptive multi-swarm particle swarm optimizer is proposed, which adaptively divides a swarm into several sub-swarms and a competition mechanism is employed to select exemplars. In this way, on the one hand, the diversity of exemplars increases, which helps the swarm preserve the exploitation ability. On the other hand, the number of sub-swarms adaptively changes from a large value to a small value, which helps the algorithm make a suitable balance between exploitation and exploration. By employing several peer algorithms, we conducted comparisons to validate the proposed algorithm on a large-scale optimization benchmark suite of CEC 2013. The experiments results demonstrate the proposed algorithm is effective and competitive to address large-scale optimization problems.

Instrumental expertise and musical timbre modulate the spatial representation of pitch

2020 ◽  
Vol 73 (8) ◽  
pp. 1162-1172 ◽  
Author(s):  
Carlotta Lega ◽  
Zaira Cattaneo ◽  
Noemi Ancona ◽  
Tomaso Vecchi ◽  
Luca Rinaldi
Keyword(s):  
Mental Representation ◽  
Horizontal Plane ◽  
Spatial Representation ◽  
Vertical Plane ◽  
Unified Framework ◽  
Instrumental Training ◽  
Younger Age ◽  
Bottom Side ◽  
The One ◽  
Pitch Space

Humans show a tendency to represent pitch in a spatial format. A classical finding supporting this spatial representation is the Spatial–Musical Association of Response Codes (SMARC) effect, reflecting faster responses to low tones when pressing a left/bottom-side key and to high tones when pressing a right/top-side key. Despite available evidence suggesting that the horizontal and vertical SMARC effect may be differently modulated by instrumental expertise and musical timbre, no study has so far directly explored this hypothesis in a unified framework. Here, we investigated this possibility by comparing the performance of professional pianists, professional clarinettists and non-musicians in an implicit timbre judgement task, in both horizontal and vertical response settings. Results showed that instrumental expertise significantly modulates the SMARC effect: whereas in the vertical plane a comparable SMARC effect was observed in all groups, in the horizontal plane the SMARC effect was significantly modulated by the specific instrumental expertise, with pianists showing a stronger pitch–space association compared to clarinettists and non-musicians. Moreover, the influence of pitch along the horizontal dimension was stronger in those pianists who started the instrumental training at a younger age. Results also showed an influence of musical timbre in driving the horizontal, but not the vertical, SMARC effect, with only piano notes inducing a pitch–space association. Taken together, these findings suggest that sensorimotor experience due to instrumental training and musical timbre affect the mental representation of pitch on the horizontal space, whereas the one on the vertical space would be mainly independent from musical practice.

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