Means and Effects оf Constraining the Number of Used Cross-Sections in Truss Sizing Optimization

This paper looks at sizing optimization results, and attempts to show the practical implications of using a novel constraint. Most truss structural optimization problems, which consider sizing in order to minimize weight, do not consider the number of different cross-sections that the optimal solution can have. It was observed that all, or almost all, cross-sections were different when conducting the sizing optimization. In practice, truss structures have a small, manageable number of different cross-sections. The constraint of the number of different cross-sections, proposed here, drastically increases the complexity of solving the problem. In this paper, the number of different cross-sections is limited, and optimization is done for four different sizing optimization problems. This is done for every number of different cross-section profiles which is smaller than the number of cross-sections in the optimal solution, and for a few numbers greater than that number. All examples are optimized using dynamic constraints for Euler buckling and discrete sets of cross-section variables. Results are compared to the optimal solution without a constrained number of different cross-sections and to an optimal model with just a single cross-section for all elements. The results show a small difference between optimal solutions and the optimal solutions with a limited number of different profiles which are more readily applicable in practice

Development and application of heuristic optimization methods in mechanical constructions

U ovom radu izvršeno je definisanje pojma optimizacije, njen istorijski razvoj i matematička formulacija, sa akcentom na heurističku optimizaciju. Predstavljene su grupe metoda matematičke optimizacije, a heurističke metode su detaljnije opisane. Predstavljene su prednosti metoda GA, PSO, TLBO, koje su odabrane kao reprezentativne heurističke metode. Razvijene su modifikacije, hibridna metoda i nova heuristička optimizaciona metoda. Na osnovu metode GA, njegovim modifikovanjem, dobijena je metoda iGA. Modifikacija rTLBO razvijena je na osnovu originalnog TLBO algoritma. Razvijeni su novi pristupi hibridizacije heurističkih metoda, a „redna“ hibridizacija primenjena je za razvoj hGPT algoritma. Ovaj hibridni algoritam koristi iGA, PSO i TLBO algoritme. Na osnovu heurističke pojave, razvijena je originalna optimizaciona metoda nazvana DINDI. Metoda je izvedena na osnovu eksperimentalnih ispitivanja i praćenja deteta u toku igre (dečak Dindi). Razvijen je originalni optimizacioni softver, a u softver su implementirane razvijene heurističke metode. Softver je samostalan i omogućava opštost u pogledu optimizacije. Moguće je optimizovati bilo koji problem matematički formulisan ovim softverom. On omogućuje korisniku sve potrebne aktivnosti u fazama predprocesiranja, procesiranja i postprocesiranja. Razvijene metode testirane su prema preporukama iz literature i na načine kojima je moguće potvrditi njihove kvalitete. Za testiranja su korišćene test funkcije bez ograničenja, sa ograničenjima i inženjerske test funkcije. Prema preporukama iz literature, izvršeno je poređenje razvijenih metoda, sa atraktivnim metodama iz literature. Razvijena optimizaciona metoda (DINDI) primenjena je za rešavanje praktičnih problema mašinskog konstruisanja. Za problem optimizacije reduktora, razvijen je odgovarajući oblik univerzalnog matematičkog modela i sprovedena je optimizacija za konkretne primere reduktora. Za analizirane primere postižu se značajno bolje karakteristike reduktora primenom optimizacionog procesa. Za problem kontakta elemenata cikloreduktora razvijen je novi pristup i originalni matematički model. Ovaj pristup omogućava određivanje rastojanja između elemenata cikloreduktora, što je značajno, ne samo sa aspekta optimizacije, nego i sa aspekta razvoja alternativnih prenosnika snage. Konkretnim primerima je potvrđen kvalitet razvijenih matematičkih modela. Na osnovu obimnih ispitivanja i analiza, izvedeni su zaključci i predstavljene smernice i potencijalni pravci daljih istraživanja.This dissertation defines the term optimization, gives its historical development and mathematical formulation, with an accent on heuristic optimization. The mathematical optimization method group is presented, and heuristic methods are described in detail. As representative heuristic methods the advantages of GA, PSO, TLBO methods are shown. Modifications, a hybrid method and a new heuristic optimization method were developed. Based on GA, through its modification, the iGA method was created. The rTLBO modification was developed based on the original TLBO method. New approaches to hybridization of heuristic methods were developed, and “inline” hybridization was used to develop the hGPT algorithm. This hybrid uses iGA, PSO, and TLBO algorithms. Based on heuristic occurrences, an original optimization method was developed named DINDI. The method was developed based on experimental research and monitoring a child playing (a boy named Dindi). An original optimization software was developed which implements the developed heuristic methods. The software is a standalone program and allows for general use in terms of optimization. It is possible to optimize any mathematically formulated problem using this software. The software allows the user to access and use all necessary activities in the phases of preprocessing, processing and post processing. The developed methods of testing are compliant to guidelines from literature and to the methods of confirming their qualities. Unconstrained, constrained, and engineering test functions were used for testing. According to suggestions from literature, a comparison of developed methods with current methods from literature was conducted. The developed optimization method (DINDI) was used for solving practical problems in mechanical constructions. For the problem of gear train optimization a form of universal mathematical model was developed and the optimization for specific examples of gear trains was conducted. For the analyzed examples significant improvements of gear train characteristics are achieved through the optimization process. For the clearances problem of cyclodrive a new approach and original mathematical model were created. This approach allows for determining the distance between elements of a cycloid drive, which is notable, not only from an optimization aspect, but for development of alternative transmissions as well. Using specific examples the quality of the mathematical models was confirmed. Based on a vast amount of testing analyses, conclusions were made and presented with the addition of potential further directions of research

COMPARISON OF APPROACHES TO 10 BAR TRUSS STRUCTURAL OPTIMIZATION WITH INCLUDED BUCKLING CONSTRAINTS

The complex problem of truss structural optimization, based on the discrete design variables assumption, can be approached through optimizing aspects of sizing, shape, and topology or their combinations. This paper aims to show the differences in results depending on which aspect, or combination of aspects of a standard 10 bar truss problem is optimized. In addition to standard constraints for stress, cross section area, and displacement, this paper includes the dynamic constraint for buckling of compressed truss elements. The addition of buckling testing ensures that the optimal solutions are practically applicable. An original optimization approach using genetic algorithm is verified through comparison with literature, and used for all the optimization combinations in this research. The resulting optimized model masses for sizing, shape, and topology or their combinations are compared. A discussion is given to explain the results and to suggest which combination would be best in a generalized example

Modeliranje sezonskih promena temperature vode akumulacije Ćelije

This paper presents the results of measurements and numerical modeling of water temperature changes in reservoir Celije in the period from April to October 2012. Reservoir Celije on the river Rasina, for many years attracts the attention of the general public and researchers, due to the importance of water management and impact of wastewater from the upper part of the basin. Reservoir Celije is a major source of PUC Krusevac Waterworks, but is also the recipient of municipal and industrial wastewater from the municipalities of Brus and Blace. Paper uses a two-dimensional model (CE QUAL W2), with transverse averaged hydrodynamic equations for the velocity and temperature field modeling in the vertical longitudinal plane. Data on the water temperature were collected in the field sampling campaigns, using multi - parameter probes. Model calibration enabled good comparison of measured and calculated temperatures, with average absolute deviation of about 0.7oC. For enhanced model performance, it would be necessary to reduce the uncertainty of the input data, which can be achieved by re- commissioning of the measuring station Ravni (upstream of the reservoir) and setting automatic weather station in the vicinity of the barrier.U radu je dat prikaz rezultata merenja i modeliranja sezonskih promena temperature vode u akumulaciji Ćelije u periodu od aprila do oktobra 2012. godine. Akumulacija Ćelije na Rasini, već duži niz godina privlači pažnju šire javnosti i istraživača, obzirom na vodoprivredni značaj i stepen ugroženosti otpadnim vodama iz gornjeg dela sliva. Akumulacija Ćelije je glavno izvorište kruševačkog vodovoda, ali je ujedno i recipijent komunalnih i industrijskih otpadnih voda iz opština Brus i Blace. U radu je korišćen dvodimenzionalni model (CE QUAL W2), sa poprečno osrednjenim hidrodinamičkim jednačinama za modeliranje polja brzina i polja temperatura u vertikalnoj podužnoj ravni. Podaci o temperaturi vode su prikupljeni u kampanjama terenskih merenja, primenom multiparametarskih sondi. Kalibracijom modela, postiglo se dosta dobro poklapanje izmerenih i izračunatih temperatura, sa prosečnim apslutnim odstupanjem od oko 0,7oC. Za unapređen učinak modela, potrebno bi bilo smanjiti neodređenost ulaznih podataka, što bi se postiglo ponovnim puštanjem u pogon merne stanice Ravni (uzvodno od akumulacije) i postavljanjem kompletne automatske meteorološke stanice u blizini pregradnog profila

Dynamic Behaviour of a Two-Stage Cycloidal Speed Reducer of a New Design Concept

Traditional cycloidal speed reducers (with two cycloid discs per one stage, mutually turned by an angle of 180°) are well known for their remarkable dynamic stability. This paper analyses dynamic behaviour of a two-stage cycloidal speed reducer of a new concept, in which only one cycloid disc is used for each stage in order to further enhance its compactness. Lagrange’s displacement equations have been used to develop independent dynamic models for both the first and the second stage (six degrees of displacement freedom for the first stage, and eight degrees of displacement freedom for the second stage). A normal force acting at the contact of the cycloid disc teeth and the corresponding ring gear roller has been taken as an excitation force. For the newly designed two-stage cycloidal speed reducer, systems of differential displacement equations of the first and second stage have been solved using the Matlab – Simulink software package. A comprehensive analysis of the obtained diagrams of elastic dynamic contact forces of the first and second stage has revealed a certain analogy. In terms of dynamics, the cycloid disc of the second stage behaves similarly to the cycloid disc of the first stage. Since these cycloid discs are mutually turned by an angle of 180°, it can be concluded that from the aspect of the cycloid disc load, the two-stage cycloidal speed reducer of a new design concept exhibits good dynamic balance and stability

INFLUENCE OF USING DISCRETE CROSS-SECTION VARIABLES FOR ALL TYPES OF TRUSS STRUCTURAL OPTIMIZATION WITH DYNAMIC CONSTRAINTS FOR BUCKLING

The use of continuous variables for cross-sectional dimensions in truss structural optimization gives solutions with a large number of different cross sections with specific dimensions which in practice would be expensive, or impossible to create. Even slight variations from optimal sizes can result in unstable structures which do not meet constraint criteria. This paper shows the influence of the use of discrete cross section sizes in optimization and compares results to continuous variable counterparts. In order to achieve the most practically applicable design solutions, Euler buckling dynamic constraints are added to all models. A typical space truss model from literature, which use continuous variables, is compared to the discrete variable models under the same conditions. The example model is optimized for minimal weight using sizing and all possible combinations of shape and topology optimizations with sizing

Determination of Real Clearances Between Cycloidal Speed Reducer Elements by the Application of Heuristic Optimization

The actual cycloidal speed reducer elements differ from their theoretical ideal due to existing tolerances; therefore, the cycloid disc behaves like a corrected one. This study is oriented towards determining contacts in corrected cycloid speed reducer profiles from the aspect of geometry. Based on this geometry, an objective function was developed for the optimization with some limitations. Heuristic optimization was used to determine the position of the cycloidal drive elements when a contact was established and, consequently, to determine clearances in other places. Some limitations were set so that the model could reflect a real contact. In this study, a TLBO algorithm was used for the optimization of a cycloidal speed reducer. Clearances were analysed for different correction values of the cycloid disc profile of an actual cycloidal drive and the optimization procedure was presented. The results provide a real picture of the contact in the presence of inevitable machining tolerances

Analiza uticaja izgradnje sistema HE na Ibru na kvalitet vode

Water quality impact assessment of the River Ibar hydropower cascade project is analyzed in this paper, as one of possible aspects of environmental impact assessment. Based on available data provided by authorized institutions, the current state of River Ibar ecological and chemical status is determined in accordance with the methodology prescribed by legislation. The ecological status of the water course between Raska and Kraljevo is rated as moderate, with evaluation considered as reliable. At the same time, the chemical status is rated as good. Quantitative assessment of possible impacts on water quality is conducted by dual approach: 1) application of hydrodynamic model, utilized for analysis of possible thermal regimes in cascade reservoirs, and 2) application of the 'method of analogy' to the existing, well studied reservoir 'Celije', the reservoir with similar morphological characteristics and water quality conditions at the entrance of the system. Results indicate that future cascade reservoir system will represent a number of aquatic ecosystems that will perform as a transitional form between river and lake systems. From the environmental perspective, it is important that thermal stratification of reservoirs during the warm seasons is not expected to be established. Consequently, the eutrophic potential of the River Ibar, based on significant content of macroelements in water, is not expected to be fully realized.U radu su analizirani mogući uticaji izgradnje kaskade protočnih hidroelektrana na deonici reke Ibar između Raške i Kraljeva na kvalitet vode, kao jedan od mogućih aspekata uticaja ovih objekata na životnu sredinu. Analizom raspoloživih podataka o kvalitetu vode reke Ibar, najpre je urađena ocena ekološkog i hemijskog statusa. Utvrđeno je da se na posmatranom delu vodotoka ekološki status može ocenitiumerenim, pri čemu se ocena može smatrati pouzdanom, dok je hemijski status ocenjen dobrim. Kvantitativna procena uticaja na kvalitet vode je urađena primenom dvojnog pristupa: 1) primenom hidrodinamičkog modela sistema HE, kojim je simuliran očekivani termički režim u planiranim akumulacijama, i 2) primena 'metode analogije' u odnosu na procese koji su evidentiranina postojećoj akumulaciji 'Ćelije'. Rezultati ukazuju da će planirane akumulacije na Ibru predstavljati niz akvatičnih ekosistema koji će se ponašati i funkcionisati kao prelazni oblik između rečnih i jezerskih sistema. Pri tome, neće biti uslova za formiranje stabilne termičke stratifikacije vode u toplijem delu godine, što će usloviti nemogućnost potpune realizacije eutrofikacionog potencijala, koji nesumnjivo postoji, imajući u vidu sadržaj makroelemenata u vodi reke Ibar u postojećim uslovima

Analiza uticaja izgradnje sistema HE na Ibru na kvalitet vode

Water quality impact assessment of the River Ibar hydropower cascade project is analyzed in this paper, as one of possible aspects of environmental impact assessment. Based on available data provided by authorized institutions, the current state of River Ibar ecological and chemical status is determined in accordance with the methodology prescribed by legislation. The ecological status of the water course between Raska and Kraljevo is rated as moderate, with evaluation considered as reliable. At the same time, the chemical status is rated as good. Quantitative assessment of possible impacts on water quality is conducted by dual approach: 1) application of hydrodynamic model, utilized for analysis of possible thermal regimes in cascade reservoirs, and 2) application of the 'method of analogy' to the existing, well studied reservoir 'Celije', the reservoir with similar morphological characteristics and water quality conditions at the entrance of the system. Results indicate that future cascade reservoir system will represent a number of aquatic ecosystems that will perform as a transitional form between river and lake systems. From the environmental perspective, it is important that thermal stratification of reservoirs during the warm seasons is not expected to be established. Consequently, the eutrophic potential of the River Ibar, based on significant content of macroelements in water, is not expected to be fully realized.U radu su analizirani mogući uticaji izgradnje kaskade protočnih hidroelektrana na deonici reke Ibar između Raške i Kraljeva na kvalitet vode, kao jedan od mogućih aspekata uticaja ovih objekata na životnu sredinu. Analizom raspoloživih podataka o kvalitetu vode reke Ibar, najpre je urađena ocena ekološkog i hemijskog statusa. Utvrđeno je da se na posmatranom delu vodotoka ekološki status može ocenitiumerenim, pri čemu se ocena može smatrati pouzdanom, dok je hemijski status ocenjen dobrim. Kvantitativna procena uticaja na kvalitet vode je urađena primenom dvojnog pristupa: 1) primenom hidrodinamičkog modela sistema HE, kojim je simuliran očekivani termički režim u planiranim akumulacijama, i 2) primena 'metode analogije' u odnosu na procese koji su evidentiranina postojećoj akumulaciji 'Ćelije'. Rezultati ukazuju da će planirane akumulacije na Ibru predstavljati niz akvatičnih ekosistema koji će se ponašati i funkcionisati kao prelazni oblik između rečnih i jezerskih sistema. Pri tome, neće biti uslova za formiranje stabilne termičke stratifikacije vode u toplijem delu godine, što će usloviti nemogućnost potpune realizacije eutrofikacionog potencijala, koji nesumnjivo postoji, imajući u vidu sadržaj makroelemenata u vodi reke Ibar u postojećim uslovima

Modeliranje sezonskih promena temperature vode akumulacije Ćelije

This paper presents the results of measurements and numerical modeling of water temperature changes in reservoir Celije in the period from April to October 2012. Reservoir Celije on the river Rasina, for many years attracts the attention of the general public and researchers, due to the importance of water management and impact of wastewater from the upper part of the basin. Reservoir Celije is a major source of PUC Krusevac Waterworks, but is also the recipient of municipal and industrial wastewater from the municipalities of Brus and Blace. Paper uses a two-dimensional model (CE QUAL W2), with transverse averaged hydrodynamic equations for the velocity and temperature field modeling in the vertical longitudinal plane. Data on the water temperature were collected in the field sampling campaigns, using multi - parameter probes. Model calibration enabled good comparison of measured and calculated temperatures, with average absolute deviation of about 0.7oC. For enhanced model performance, it would be necessary to reduce the uncertainty of the input data, which can be achieved by re- commissioning of the measuring station Ravni (upstream of the reservoir) and setting automatic weather station in the vicinity of the barrier.U radu je dat prikaz rezultata merenja i modeliranja sezonskih promena temperature vode u akumulaciji Ćelije u periodu od aprila do oktobra 2012. godine. Akumulacija Ćelije na Rasini, već duži niz godina privlači pažnju šire javnosti i istraživača, obzirom na vodoprivredni značaj i stepen ugroženosti otpadnim vodama iz gornjeg dela sliva. Akumulacija Ćelije je glavno izvorište kruševačkog vodovoda, ali je ujedno i recipijent komunalnih i industrijskih otpadnih voda iz opština Brus i Blace. U radu je korišćen dvodimenzionalni model (CE QUAL W2), sa poprečno osrednjenim hidrodinamičkim jednačinama za modeliranje polja brzina i polja temperatura u vertikalnoj podužnoj ravni. Podaci o temperaturi vode su prikupljeni u kampanjama terenskih merenja, primenom multiparametarskih sondi. Kalibracijom modela, postiglo se dosta dobro poklapanje izmerenih i izračunatih temperatura, sa prosečnim apslutnim odstupanjem od oko 0,7oC. Za unapređen učinak modela, potrebno bi bilo smanjiti neodređenost ulaznih podataka, što bi se postiglo ponovnim puštanjem u pogon merne stanice Ravni (uzvodno od akumulacije) i postavljanjem kompletne automatske meteorološke stanice u blizini pregradnog profila