Engineering applications of heuristic multilevel optimization methods

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Coordination of the subproblem optimizations is shown to be typically achieved through the use of exact or approximate sensitivity analysis. Areas for further development are identified

Functional Methods and Effective Potentials for Nonlinear Composites

A formulation of variational principles in terms of functional integrals is proposed for any type of local plastic potentials. The minimization problem is reduced to the computation of a path integral. This integral can be used as a starting point for different approximations. As a first application, it is shown how to compute to second-order the weak-disorder perturbative expansion of the effective potentials in random composite. The three-dimensional results of Suquet and Ponte-Casta\~neda (1993) for the plastic dissipation potential with uniform applied tractions are retrieved and extended to any space dimension, taking correlations into account. In addition, the viscoplastic potential is also computed for uniform strain rates.Comment: 20 pages, accepted for publication in JMP

Shape sensitivity analysis of wing static aeroelastic characteristics

A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted with Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wind induced drag, as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle, and tip twist angle. Results of sensitivity studies indicate that: (1) approximations based on analytical sensitivity derivatives can be used over wide ranges of variations of the shape parameters considered, and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite-difference alternative

Recent advances in approximation concepts for optimum structural design

The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture

An expert system for choosing the best combination of options in a general-purpose program for automated design synthesis

An expert system was developed to aid a user of the Automated Design Synthesis (ADS) general-purpose optimization computer program in selecting the best combination of strategy, optimizer, and one-dimensional search options for solving a problem. There are approximately 100 such combinations available in ADS. The knowledge base contains over 200 rules, and is divided into three categories: constrained problems, unconstrained problems, and constrained problems treated as unconstrained problems. The inference engine is written in LISP and is available on DEC-VAX and IBM PC/XT computers

Development and application of optimum sensitivity analysis of structures

The research focused on developing an algorithm applying optimum sensitivity analysis for multilevel optimization. The research efforts have been devoted to assisting NASA Langley's Interdisciplinary Research Office (IRO) in the development of a mature methodology for a multilevel approach to the design of complex (large and multidisciplinary) engineering systems. An effort was undertaken to identify promising multilevel optimization algorithms. In the current reporting period, the computer program generating baseline single level solutions was completed and tested out

Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/\nu$ to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E (Rapid Comm

Etude du cycle nycthéméral de la teneur en oxygène dissous en bassins de pisciculture par la méthode des moyennes mobiles. Relation avec la température et l'insolation

Dans ce travail, le cycle journalier de l'oxygène dissous en bassins de pisciculture semi-intensive a été étudié en relation avec des données météorologiques. Nous disposions pour cela de 22 semaines d'enregistrements (mesures horaires) de janvier 1988 à décembre 1989, dont une semaine de mesures sous glace. Chaque période de mesures a été traitée comme une série chronologique en pratiquant une décomposition saisonnière par la méthode des moyennes mobiles qui permet d'extraire à partir d'une série de mesures la tendance sur la période étudiée et la composante journalière.Cette méthode, montre que le cycle nycthéméral de l'oxygène dissous garde son aspect et classique toute l'année, excepté sous la glace. Toutefois, l'amplitude journalière de la teneur en oxygène varie beaucoup selon la saison, et nous avons pu distinguer une période estivale où le métabolisme de l'étang semblait accéléré. L'analyse du cycle nycthéméral de l'oxygène dissous, dans lequel on distingue production et consommation, comparé à ceux de la température de l'eau et de l'insolation journalière moyenne, a permis d'étudier ce phénomène et de montrer l'importance des facteurs météorologiques dans la détermination du bilan de l'oxygène dissous en étang.Dissolved oxygen is a very important factor in fish ponds, particularly under intensive conditions. Thus, the daily fluctuations of dissolved oxygen have been studied in different countries and under different conditions (lakes, ponds, rivers), but with data series generally limited to a few measurements per day. The automatic data recorder of the IRRA'S experimental station provides very long series of data concerning of dissolved oxygen, temperature and meteorological factors through hourly measurements which allow the use of mathematical analysis like the moving average method. This automatic data recorder bas been in use since September 1987 and the data obtained have been analysed in research on summer oxygen deficit prevention. After 3 years' measurements it was interesting to investigate the annual change in the daily fluctuations of the dissolved oxygen. For this, daily hourly measurements of dissolved oxygen, temperature and solar radiations were taken and examined during 22 weeks from January 1988 to December 1989 (one week under ice cover). Oxygen data were analysed using seasonal decomposition by the moving average method, and the results were compared with the temperature and solar radiation measurements.The measurements were taken from 6 of the 16 IRRA'S experimental ponds (in the Dombes region, to the North-East of Lyon, France) and in a fish pond. All these ponds were semi-intensive fish-ponds stocked with Carp (Cyprinus carpio) Tench, (Tinca tinca), Grass Carp (Ctenopharingodon idella) and Silver Carp (Hypophthalmichthys molitrix).The seasonal decomposition through the moving average method devides the time series data into a trend (long term fluctuations), seasonal indices (or daily component) and residuals, but only seasonal indices, representing the daily variations, are studied here. The daily component was next spin into oxygen production and consumption if respiration is taken to be constant over one day and can be evaluated through the night oxygen decrease (EDELINE et al., 1968; ROMAIRE and BOYD, 1978; BARTHELEMY and COUTURE, 1990).Through this method, it appeared that the daily fluctuations of dissolved oxygen had the same classical aspect all the year round, except under ice cover, where it was impossible to observe a significant oxygen production. Such fluctuations, which are the result of the effect of oxygen production and consumption, have also been observed under different conditions (BOUD and LICHTKOPPLER, 1979; SIN and CHIU,1982; KEPENYES and VARADI, 1984; MARZOLF and SAUNDERS, 1984; GINOT, 1988; COUTURE, 1988). The aspect of the daily cycles was relatively constant but it was possible to distinguish 3 periods according to the amplitude of these cycles :- a winter period with less than 2 mg/l daily variations,- a summer period when these variations were greater titan 4 or 7 mg/l,- an intermediate period in spring and autumn.As these 3 periods did not occur at the same time of the year for 1988 & 1989, it appeared that the meteorological conditions (temperature and solar radiations) were important factors for determining these periods in the year.The study of oxygen production and consumption gave the same conclusions.These results have been compared with meteorological data : mean water temperature over 7-day periods (168 measurements), plus mean cumulative daily solar radiations over 7 days.There appeared significant correlations between the oxygen production and the consumption, with these meteorological factors, but these relations were different for the « summer » period (June to October) and the rest of the year. There was a delay between the period when temperature and solar radiations are best for primary production (June and July) and the period when the pond’s metabolism is maximum.There have been no measurements on primary production or algal population dynamics to explain these results clearly, but considering the observations of GRYGIEREK and WASILEWSKA (1979) and ELORANTA (1985) it is possible to give an explanation. In May-June the ponds are characterized by clear water (a higher than 60 cm transparency was observed) with low density algal populations, thus the pond ecosystem is not ready to use thermic and light energy. This delay between meteorological conditions and oxygen dynamics have been observed by ELORANTA (1985) and BOYD (1985).These results are useful in pond management, particularly when it is necessary to prevent oxygen depletion. The risk of oxygen deficits is greater in August-September, when the ecological conditions are very unstable owing to the important daily oxygen fluctuations. In this case, meteorological changes like temperature decreases or rain-fall can perturb the ecosystem and cause algal die-off with a great risk of oxygen depletion.The aim of this study was to show the possibilities of seasonal decomposition by the moving average method in the analysis of oxygen measurements. When it is possible to get long serie data, with constant skip, this method is very valuable for studying long term and daily fluctuations. The decomposition of the daily component through the method of EDELINE et al. (1968) also gives indications on primary production and oxygen consumption