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EN
Models for the automated analysis and simulation of the complex phenomena observable in built environment crowded by pedestrians have been studied for over thirty years. Nonetheless, one of the commonly agreed upon rules guiding regulation of distance among pedestrian, i.e. proxemics, was defined and discussed in static settings, whereas scenarios of interest generally deal with individual and collective movements in crowds. The present paper presents a systemic perspective on the research aimed at defining a dynamic form of proxemics. The paper firstly reports the results of an experiment focused on proxemics and pedestrians personal space, as the hidden dimension of human spatial behavior in crowded environments. We propose a representation of personal space through discrete potentials and an innovative crowding estimation method (i.e. Cumulative Mean Crowding), going beyond simple perceived density evaluation. The experimental setting is introduced and applied to appraise the potential impact of this novel pedestrian perception mechanism on innovative simulation models.
EN
Ultimate expansivity extends concepts of expansivity and positive expansivity. We consider one-sided variants of ultimate expansivity and pseudo-orbit tracing property (also known as the shadowing property) for surjective one-dimensional cellular automata. We show that ultimately right (or left) expansive surjective cellular automata are chain-transitive; this improves a result by Boyle that expansive reversible cellular automata are chain-transitive. We then use this to show that left-sided pseudo-orbit tracing property and right-sided ultimate expansivity together imply pseudo-orbit tracing property for surjective cellular automata. This reproves some known results, most notably some of Nasu’s. Our result improves Nasu’s result by dropping an assumption of chain-recurrence, however, we remark that this improvement can also be achieved using the Poincaré recurrence theorem. The pseudo-orbit tracing property implies that the trace subshifts of the cellular automaton are sofic shifts. We end by mentioning that among reversible cellular automata over full shifts we have examples of right expansive cellular automata with non-sofic traces, as well as examples of cellular automata with left pseudo-orbit tracing property but non-sofic traces, illustrating that neither assumption can be dropped from the theorem mentioned above. This paper is a generalized and improved version of a conference paper presented in AUTOMATA 2018.
EN
In this paper, the cellular automata model is applied to analyse cleavage and ductile fracture in front of a crack in three-point-bend specimens made of Hardox-400 steel. The research programme was composed of experiments followed by fractographic and numerical analyses. On the basis of microscopic observations, the sizes of cells used in the automata were determined. The algorithm enabled mapping of the two-dimensional crack surface as well as a simulation of temperature-dependent failure mechanisms by defining transition rules based on the modified Ritchie-Knott-Rice cleavage fracture criterion. The critical stress values were estimated and verified by the cellular automata model.
4
Content available Improving Image Sharpness by Surface Recognition
EN
The article proposes a rule for improving image sharpness and analyzes its implementation by means of the cellular automata formalism and neural networks. It has been proved, that the previously known contrasting algorithm, which uses a template and 3x3 pixels, can be improved considerably by repeatedly applying the iterative process over templates 2x2 with the rule "anti - blur" ( C 11 = C 11 x F - ( C 12 + C 21 + C 22) x S ) and gradient color correction at each step after the "anti - blur". Colors of images in the template are presented as real numbers (R, G, B). To correct the gradient (C11 < C12, C11 < C21, C11
EN
The study concerns modeling and simulation of the growth of biofilms with heterogeneous structureswith a discrete mathematical model based on theory of cellular automata. The article presents two-dimensional density distributions of biofilms for microbial processes: oxidation of ammonium byNitrosomonas europaeabacteria and glucose utilization byPseudomonas aeruginosabacteria. Theinfluence of limiting substrate concentration in the liquid phase on biofilm structure was determined.It has been shown that the value of death rate coefficient of microorganisms has the qualitative andquantitative influence on the density and porosity of the biofilm.
6
Content available remote Detection of Modic changes in MR images of spine using local binary patterns
EN
Background and objective: With increase in prevalence of lower back pain, fast and reliable computer aided methods for clinical diagnosis associated with the same is needed for improving the healthcare reach. The magnetic resonance images exhibit a change in signal intensity on the vertebral body close to end plates, which are termed as Modic changes (MC), and are known to be clear indicators of lower back pain. The current work deals with computer aided methods for automating the classification of signal changes between normal and degenerate cases so as to aid physicians in precise and suitable diagnosis for the ailment. Methods: In order to detect Modic changes in vertebrae, initially the vertebrae are segmented from sagittal MR T1 and T2 imaged using a semi automatic cellular automata based segmentation. This is followed by textural feature extraction using Local Binary Patterns (LBP) and its variants. Various classifiers based on machine learning approaches using Random Forest, kNN, Bayes and SVM were evaluated for its classification performance. Since medical image dataset in general have bias towards healthy and diseased state, data augmentation techniques were also employed. Results: The implemented method is tested and validated over a dataset containing 100 patients. The proposed framework achieves an accuracy of 81% and 91.7% with and without augmentation of data respectively. A comparative study with the state of art methods reported in literature shows that the method proposed in better in terms of computational cost without any compromise on classification accuracy. Conclusion: A novel approach to identify MC in vertebrae by exploiting textural features is proposed. This shall assist radiologists in detecting abnormalities and in treatment planning.
EN
Permutation flow shop scheduling problem deals with the production planning of a number of jobs processed by a set of machines in the same order. Several metaheuristics have been proposed for minimizing the makespan of this problem. Taking as basis the previous Alternate Two-Phase PSO (ATPPSO) method and the neighborhood concepts of the Cellular PSO algorithm proposed for continuous problems, this paper proposes the improvement of ATPPSO with a simple adaptive local search strategy (called CAPSO-SALS) to enhance its performance. CAPSO-SALS keeps the simplicity of ATPPSO and boosts the local search based on a neighborhood for every solution. Neighbors are produced by interchanges or insertions of jobs which are selected by a linear roulette scheme depending of the makespan of the best personal positions. The performance of CAPSO-SALS is evaluated using the 12 different sets of Taillard’s benchmark problems and then is contrasted with the original and another previous enhancement of the ATPPSO algorithm. Finally, CAPSO-SALS is compared as well with other ten classic and state-of-art metaheuristics, obtaining satisfactory results.
EN
Purpose: During weld metal structure formation the possibility of impact on its mechanical properties are much more limited in comparison with metallurgy and technology of steel production. Adding of the inoculants to the welding pool is one of the promising methods of influencing the structure and mechanical properties of the weld metal. Design/methodology/approach: Cellular automata (CA) with additions of finite difference method (FDM) is one of the best ways to simulate dendritic growth process with the surfaceactive inoculants. It`s easy to add new rules of interaction between the inoculants and dendrite surface to the cellular automata model. Findings: It was found that average distance between primary dendrites axis decrease with increase of the inoculants wetting angle by melt iron. Obtained results were confirmed experimentally on weld metal samples that were obtained by the welding of HSLA steels with the surface-active inoculants. Research limitations/implications: The inoculants with size that comparable with cells size of the model (≈0.4 microns) were distributed evenly in computational area. Practical implications: Adding of surface-active inoculants to the melt metal improve structure and mechanical properties of weld metal. Different refractory particles (TiC, TiN, SiC, TiO2, Al2O3 and ZrO2) can be used. Originality/value: Refractory inoculants adding to the melt metal are wide used in metallurgy as crystallization centers and heat absorbers. Inoculants that were added to the welding pool of high-strength low-alloyed (HSLA) steel welds could also influence on crystallization processes of weld metal as surface active particles. In the contact point between the dendrite surface and the surface-active inoculant, a surface energy is change depending of the inoculant surface properties. Different refractory particles (TiC, TiN, SiC, TiO2, Al2O3 and ZrO2) were used.
EN
Software solution for cryptographic hash functions based on sponge construction with inner state implemented as two-dimensional cellular automata (CA) has been developed. To perform pseudorandom permutation in round transformation function several combinations of CA rules 30, 54, 86, 150 and 158 have been proposed. The developed hashing mechanism provides effective parallel processing, ensures good statistical and scattering properties, enables one to obtain hash of a varying length and reveals strong avalanche effect.
PL
Za pomocą oprogramowania zostały opracowane kryptograficzne funkcje skrótu (hash) na podstawie gąbki kryptograficznej, której stan wewnętrzny został zrealizowany w postaci dwuwymiarowych automatów komórkowych (KA). W celu implementacji permutacji pseudolosowych zaproponowano kombinację zasad obróbki CA 30, 54, 86, 150 i 158 w celu realizacji funkcji transformacji rundy. Opracowany mechanizm haszowania pozwala na skuteczne przetwarzanie równoległe, zapewnia jakościowe charakterystyki statystyczne i rozproszenia, pozwala na otrzymanie skrótu o zmiennej długości i ujawnia stabilny efekt lawinowy.
PL
W pracy przedstawiono podstawowe wiadomości o metodzie do modelowania matematycznego procesów i zjawisk zawierających przepływ gazu i cieczy nazywanej Lattice Boltzmann Method (LBM - Metoda kratowego równania Boltzmanna). Trzema głównymi kierunkami stosowania LBM w opracowaniach autorów są: przepływ cieczy o swobodnej powierzchni z uwzględnieniem wymiany ciepła i przemiany stanu skupienia; ciągły przepływ cieczy i gazu; przemiany fazowe. W pracy przedstawiono wyniki modelowania oraz zastosowania metody do modelowania procesów przemysłowych i jej wykorzystanie w procesie dydaktycznym. Zwrócono uwagę na przewagi opisywanej metody oraz duże możliwości przyspieszenia obliczeń poprzez ich zrównoleglenie na współczesnych procesorach graficznych (GPU - graphics processing unit) .
EN
The basic information about the Lattice Boltzmann Method (LBM), used for numerical modeling of the processes and phenomena contained fluid flow, is presented in the paper. Three main direction of application of the LBM developed and described by the authors are: fluid flow with free surface, taking into account conductive heat transfer and changes of state of matter; continuous fluid flow; and phase transformations. Results of simulations by LBM as well as its application to industrial processes and for teaching are presented in the paper. Attention is paid to advantages of the method and possibility to accelerate its calculations through their parallelization on modern graphics processing units (GPUs).
EN
Cellular Automata (CA) model of carbonitride precipitation in microalloyed steels is presented in the paper. The model accounts for an increase of dislocation density due to plastic deformation and predicts kinetics of precipitation as well as stereological parameters of precipitates. Precipitation of compounds plays crucial role in controlling of properties of alloys. In low alloyed steels the microalloying elements: Ti, Nb, V are added in order to control their microstructure and mechanical properties. The most important tool in development of new processing technologies is numerical modelling. Modelling is a mathematical description of the relation between the main process variables and the resulting material properties. Many thermodynamics models were developed in the second half of the 20th century. For example the model of carbonitrides precipitation in microalloyed steels is considered works of Dutta & Sellars (1987), Dutta et al. (1991), Dutta et al. (2001). The models allow calculate kinetics of precipitation and stereological parameters of precipitates as a function of processing parameters. CA model proves to be very efficient in modelling various phenomena in materials science. The transition rules transfer the mathematical model and the knowledge regarding precipitation into the cellular automata space.
12
PL
Cel: Celem artykułu jest zaprezentowanie autorskiego oprogramowania CrowdSim służącego do modelowania dynamiki pieszych. W oprogramowaniu zaimplementowano algorytmy bazujące na dwuwymiarowym modelu automatu komórkowego Cellular Automata(CA). Uwzględniono w nich strategiczne możliwości pieszych dotyczące wyboru wyjścia (model CA-A) oraz możliwości powstawania zakłóceń płynności ruchu i blokad (model CA-B). Zaimplementowanie różnych pod względem złożoności modeli dało możliwości porównania ich efektywności, funkcjonowania oraz stopnia realizmu otrzymywanych wyników. Projekty i metody: W celu lepszego i bardziej wiarygodnego wyznaczania ścieżek poruszania się pieszych zaproponowano dwie modyfikacje usprawniające działanie algorytmów symulacyjnych. Pierwszą z nich było wprowadzenie zaawansowanych algorytmów rankingujących komórki: SRA (Simple Ranking Algorithm), BFS-RA (Breadth First Search Ranking Algorithm) i ARA (Advanced Ranking Algorithm). Wartość rankingu danej komórki w procesie symulacji jest dla każdego z aktorów wyznacznikiem drogi, po której się porusza. Kolejnym autorskim usprawnieniem było wprowadzenie do definicji automatu komórkowego pojęcia pamięci aktora, dzięki czemu piesi podczas symulacji, pamiętając swoje ostatnie ruchy, poruszają się bardziej płynnie i realistycznie. Wyniki: Na potrzeby porównania modeli przygotowana została specjalna mapa budynku o wymiarach kontygnacji 40 na 22,5 metra (900 m2 ) zdolnego pomieścić maksymalnie 3000 osób. Przeprowadzone symulacje wykazały, że w przypadku modelu CA aktorzy gromadzą się przy jednym z wyjść, podczas gdy pozostałe zostają w większości nieużywane. Wynika to z faktu, że w modelu CA brakuje funkcji kosztu, zatem aktor zawsze wybiera wyj-ście najbliższe. Inaczej sprawa ma się w przypadku modelu CA-A. Tu aktorzy w miarę równo obciążają każde z wyjść; są oni w stanie podjąć decyzje odnośnie do wyboru wyjścia nie tylko na podstawie odległości, ale również zagęszczenia osób przy danym wyjściu. W przypadku porównania modeli CA-A i CA-B praktycznie niezauważalne są różnice w otrzymanych statystykach obciążenia wyjść. Dopiero po bliższym przyjrzeniu się ruchowi aktorów podczas symulacji widać, że jeśli w przypadku czystego modelu CA-A ludzie poruszają według idealnego porządku, o tyle w modelu CA-B zauważalne są chwilowe blokady i zakleszczenia aktorów.Wnioski: Stworzone i zaprezentowane w niniejszej pracy oprogramowanie CrowdSim może posłużyć zarówno projektantom, architektom lub konstruktorom, jak i służbom porządkowym, ochronie danego obiektu lub organizatorom imprez masowych. Symulacje wykonane wielokrotnie dla jednego scenariusza przy różnych parametrach wejściowych uwidoczniają problemy i wąskie gardła mogące pojawić się w trakcie ewakuacji z zagrożonego obiektu. Przeprowadzanie takich symulacji na etapie projektowym może bardzo pozytywnie wpłynąć na bezpieczeństwo osób użytkujących dany obiekt, jak również poprawić jego funkcjonalność.
EN
Aim: Phe aim of the article is to present CrowdSim, proprietary software for modeling the dynamics of pedestrians. The software offers algorithms based on a 2-dimensional model of aCellular Automaton (CA). They include strategic pedestrian choices of the exit (CA-A model) and the formation of blockages (Model CA-B). Implementation of various models in terms of their complexity provided the opportunity to compare their efficiency, functioning and realism of the results obtained.Project and methods: In order to better and more credibly determine pedestrian paths, two modifications were proposed to improve the operation of simulation algorithms. The first of these was the introduction of advanced algorithms ranking cells: SRA (Simple Ranking Algorithm), BFS-RA (Breadth First Search Ranking Algorithm) and ARA (Advanced Ranking Algorithm). The value of the ranking of a given cell in the simulation process is for each BITP VOL. 52 ISSUE 4, 2018, pp. 46–66, https://dx.doi.org/10.12845/bitp.52.4.2018.3SAFETY & FIRE TECHNIQUERESEARCH AND DEVELOPMENT47of the actors the determinant of the path on which it moves. Another proprietary improvement was the introduction of the concept of actor's memory to the definition of a cellular automata, thanks to which pedestrians, while remembering their last movements, move more smoothly and realistically.Results: For the purposes of model comparison, a special map of the building with the dimensions of 40 to 22.5 meters (900 m2) has been prepared, able to accommodate a maximum of 3000 people. The simulations showed that in the case of the CA model, the actors gather at one of the outputs while the others are mostly unused. This is due to the fact that the CA model lacks the cost function, so the actor always chooses the nearest output. Things are different in the case of the CA-A model. Here, the actors equally burden each exit, they are able to make decisions regarding the choice of the exit not only on the basis of the distance but also the concentration of actors at the given exit. When comparing the CA-A and CA-B models, there are practically no differences in the received output load statistics. Only after a closer look at the movement of the actors during the simulation can be seen that if in the case of a clean CA-A model people move according to the ideal order, in the CA-B model there are momentary blockages and deadlocks of actors.Conclusions: CrowdSim software created and presented in this work can be used by designers, architects or constructors as well as law enforcement, protection of a given facility or organizers of mass events. Simulations made repeatedly for one scenario with different input parameters reveal problems and bottlenecks that may appear during evacuation from an object at risk. Conducting such simulations at the design stage can have a very positive impact on the safety of people using a given facility, as well as improve its functionality.
EN
The paper presents the cellular automaton (CA) model for tracking the development of dendritic structure in non-equilibrium solidification conditions of binary alloy. Thermal, diffusion and surface phenomena have been included in the mathematical description of solidification. The methodology for calculating growth velocity of the liquid-solid interface based on solute balance, considering the distribution of the alloy component in the neighborhood of moving interface has been proposed. The influence of solidification front curvature on the equilibrium temperature was determined by applying the Gibbs Thomson approach. Solute and heat transfer equations were solved using the finite difference method assuming periodic boundary conditions and Newton cooling boundary condition at the edges of the system. The solutal field in the calculation domain was obtained separately for solid and liquid phase. Numerical simulations were carried out for the Al-4 wt.% Cu alloy at two cooling rates 15 K/s and 50 K/s. Microstructure images generated on the basis of calculations were compared with actual structures of castings. It was found that the results of the calculations are agreement in qualitative terms with the results of experimental research. The developed model can reproduce many morphological features of the dendritic structure and in particular: generating dendritic front and primary arms, creating, extension and coarsening of secondary branches, interface inhibition, branch fusion, considering the coupled motion and growth interaction of crystals.
EN
In narrow water channels, ship traffic may be affected by water flows and ship interactions. Studying their effects can help maritime authorities to establish appropriate management strategies. In this study, a two-lane cellular automation model is proposed. Further, the behavior of ship traffic is analyzed by setting different water flow velocities and considering ship interactions. Numerical experiment results show that the ship traffic density-flux relation is significantly different from the results obtained by classical models. Furthermore, due to ship interactions, the ship lane-change rate is influenced by the water flow to a certain degree.
PL
Wydzielenia węglikoazotków mikrododatków V, Nb i Ti silnie wpływają na mikrostrukturę i własności mechaniczne stali mikrostopowych. Do przewidywania własności mechanicznych stali wymagane są takie parametry wydzieleń jak zawartość (ułamek objętości) i rozmiar (średni promień cząstek). Modele matematyczne opisujące proces wydzielania pozwalają określić te parametry. Modele te opierają się na równaniach algebraicznych opisujących zarodkowanie i kinetykę wzrostu wydzieleń. Rozwój nauk informatycznych umożliwia przeprowadzanie symulacji procesów wydzieleniowych. Jednym z dostępnych narzędzi informatycznych do przeprowadzenia symulacji jest metoda automatów komórkowych. W artykule przedstawiono model automatu komórkowego do obliczania rozmieszczenia i zawartości wydzieleń węglikoazotków w stalach mikrostopowych zawierających dodatki Ti, Nb lub V.
EN
Carbonitrides precipitations of microalloying elements, V, Nb and Ti, strongly influence the microstructure and mechanical properties of high strength low alloy steels. To predict the mechanical properties of these steels parameters of precipitates such as size (mean radius) and content (volume fraction) are required. Mathematical models describing the carbonitrides precipitation process enable to calculate these parameters. The development of computer science enables simulations of precipitation process. The models are based on the algebraic equations describing the nucleation and growth kinetics of precipitates. One of the available tools to simulate the precipitation processes is the method of Cellular Automata. Cellular Automata model proves to be very efficient in modelling various phenomena in materials science. Cellular Automata model of carbonitride precipitation in microalloyed steels containing such elements as Ti, Nb or V is presented in the paper. The model predicts kinetics of precipitation as well as stereological parameters of precipitates.
EN
In this paper, we extend existing results about simulation and intrinsic universality in a model of tile-based self-assembly. Namely, we work within the 2-Handed Assembly Model (2HAM), which is a model of self-assembly in which assemblies are formed by square tiles that are allowed to combine, using glues along their edges, individually or as pairs of arbitrarily large assemblies in a hierarchical manner, and we explore the abilities of these systems to simulate each other when the simulating systems have a higher "temperature" parameter, which is a system wide threshold dictating how many glue bonds must be formed between two assemblies to allow them to combine. It has previously been shown that systems with lower temperatures cannot simulate arbitrary systems with higher temperatures, and also that systems at some higher temperatures can simulate those at particular lower temperatures, creating an infinite set of infinite hierarchies of 2HAM systems with strictly increasing simulation power within each hierarchy. These previous results relied on two different definitions of simulation, one (strong simulation) seemingly more restrictive than the other (standard simulation), but which have previously not been proven to be distinct. Here we prove distinctions between them by first fully characterizing the set of pairs of temperatures such that the high temperature systems are intrinsically universal for the lower temperature systems (i.e. one tile set at the higher temperature can simulate any at the lower) using strong simulation. This includes the first impossibility result for simulation downward in temperature. We then show that lower temperature systems which cannot be simulated by higher temperature systems using the strong definition, can in fact be simulated using the standard definition, proving the distinction between the types of simulation.
EN
A k-limited automaton is a linear bounded automaton that may rewrite each tape square only in the first k visits, where k≥ 0 is a fixed constant. It is known that these automata accept context-free languages only. We investigate deterministic k-limited automata towards their ability to perform reversible computations, that is, computations in which every configuration has at most one predecessor. A first result is that, for all k≥ 0, sweeping k-limited automata accept regular languages only. In contrast to reversible finite automata, all regular languages are accepted by sweeping 0-limited automata. Then we study the computational power gained in the number k of possible rewrite operations. It is shown that the reversible 2-limited automata accept regular languages only and, thus, are strictly weaker than general 2-limited automata. Furthermore, a proper inclusion between reversible 3-limited and 4-limited automata languages is obtained. The next levels of the hierarchy are separated between every k and k + 3 rewrite operations. We investigate closure properties of the family of languages accepted by reversible k-limited automata. It turns out that these families are not closed under intersection, but are closed under complementation. They are closed under intersection with regular languages, which leads to the non-closure under concatenation, iteration, and homomorphisms. Finally, it turns out that all k-limited automata accept Church-Rosser languages only, that is, the intersection between context-free and Church-Rosser languages contains an infinite hierarchy of language families beyond the deterministic context-free languages.
EN
This paper is an introduction to the computational complexity theory. I believe that the standard courses in complexity theory make some things much more important than they really are, while things which I find extremely interesting are marginalized. Thus, it can be seen as my subjective view on what is important and interesting in computational complexity, and what is not. We state the basic facts from computational complexity theory using the blackboard computations (one-dimensional cellular automata) as the standard computation model; we argue the benefits of such approach. This article is somewhat based on my series of talks from Warsztaty Logiczne 2014 in Białka Tatrzańska, although these talks covered more topics, such as NL=coNL, and links between BPP and the polynomial hierarchy.
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Content available Model ewakuacji wykorzystujący automaty komórkowe
PL
Cel: Zapewnienie ludziom bezpieczeństwa podczas zgromadzeń i imprez masowych wymaga m.in. analizy warunków ewakuacji oraz właściwej organizacji ewakuacji w czasie zagrożenia. Modelowanie procesu ewakuacji to jeden z możliwych wariantów analizowania i planowania bezpiecznej ewakuacji zarówno z budynków, obiektów, jak i z terenu przeznaczonego na zorganizowanie imprezy. Celem artykułu jest zaprezentowanie praktycznego wykorzystania automatów komórkowych w modelowaniu ewakuacji oraz porównanie otrzymanych wyników z wynikami modelowania wykonanego dzięki wykorzystaniu oprogramowania komercyjnego. Dodatkowym celem pracy jest porównanie kosztu obliczeniowego modelowania ewakuacji przy zastosowaniu automatu komórkowego z kosztem obliczeniowym modelowania ewakuacji przy wykorzystaniu modelu Social Force. Projekty i metody: Posłużono się automatem komórkowym z siatką o stałych wymiarach 0,5 x 0,5 m. Podstawowym założeniem dla modelu ruchu były wartości pól warstwy statycznej Floor Field, obliczane zgodnie z metryką euklidesową, oraz algorytmem zachłannym. Wyznaczono wartość parametru μ = 0,55 określającą prawdopodobieństwo przejścia osoby do sąsiedniej komórki automatu. Implementację modelu wykonano w języku Python, korzystając z biblioteki do obliczeń naukowych Numpy i biblioteki matematycznej Math. Wyniki modelowania ewakuacji przy wykorzystaniu proponowanego modelu porównano z wynikami modelowania przy wykorzystaniu programu FDS+Evac dla pomieszczenia o wymiary 11,5 x 9 m z jednym wyjściem ewakuacyjnym i z dwoma wyjściami ewakuacyjnymi. Ponadto wykonano modelowanie i zestawiono uzyskane wyniki z wynikami programów FDS+Evac, Pathfinder oraz TraffGo zgodnie z testem Międzynarodowej Organizacji Morskiej (International Maritime Organization – IMO) IMO 9 dla 1000 osób. Wyniki: Stwierdzono, że zarówno przy modelowaniu ewakuacji z pomieszczenia zaproponowanego przez autorów, jak i przy modelowaniu ewakuacji z pomieszczeń zaproponowanych w teście IMO 9 oszacowane czasy ewakuacji są zbieżne z czasami oszacowanymi przy wykorzystaniu programów mających zastosowanie w inżynierii bezpieczeństwa pożarowego. Ponadto wykazano, że zastosowanie automatu komórkowego przy modelowaniu ewakuacji 1000 osób pozwala na wykonanie modelowania 20-krotnie szybciej niż w przypadku modelu Social Force zaimplementowanego w programie FDS+Evac. Średni koszt modelowania 1 s ewakuacji przy wykorzystaniu automatu komórkowego zależy liniowo od liczby osób podlegających ewakuacji, inaczej niż to jest w przypadku modelu Social Force, w którym czas modelowania zwiększa się wykładniczo w stosunku do liczby osób. Wnioski: Modele ewakuacji wykorzystujące automaty komórkowe, w przeciwieństwie do modelu Social Force, umożliwiają modelowanie ruchu dużych grup ludzi przy niższym koszcie obliczeniowym. Zastosowanie automatów komórkowych pozwala na wprowadzanie dodatkowych warstw wpływających na ruch ludzi przy niewielkim zwiększeniu się złożoności obliczeniowej. Wprowadzenie dodatkowych założeń i warstw do modeli opartych na automatach komórkowych umożliwi bardziej rzeczywiste odwzorowanie ewakuacji przy niewielkim wzroście kosztu zużycia zasobów sprzętowych. Ponadto narzędzia pozwalające na szybkie szacowanie czasu ewakuacji w przystępny dla inżynierów sposób byłyby pomocne w prawidłowym projektowaniu budynków. Obecnie komercyjne programy wymagają specjalistycznej wiedzy z zakresu modelowania. Zastosowanie prostego interfejsu z szybkim algorytmem szacowania czasu ewakuacji może przynieść wymierne korzyści w postaci poprawy bezpieczeństwa w projektowanych budynkach i obiektach budowlanych.
EN
Aim: The safety of people during meetings and public events requires an analysis of the conditions of evacuation and the proper organisation of escape in times of danger. Modelling the evacuation process is one of the options for analysing and planning the safe evacuation of the buildings, facilities and spaces during events. The aim of the article was to present the practical use of cellular automata for evacuation modelling and comparing the results with the results achieved using commercial software. Additionally, the objective of this work was to compare the cost of computational evacuation modelling of cellular automata with the “Social Force” model. Project and methods: The authors used cellular automata on the grid with a fixed size of 0.5 m x 0.5m. The basic premise for the traffic model was the “Floor Field” static layer with Euclidean metric and the greedy algorithm. The determined value μ = 0.55 indicated the probability of the transition of a person to the neighbouring automat cell. The implementation of the model was made in “Python”, using the library for scientific computing “Numpy”, and the maths library “Math”. We compared the results of modelling the evacuation using the proposed model with the program “FDS + Evac” for room size 11.5 x 9 m with one and two emergency exits. Furthermore, the modelling was done and the results were juxtaposed with the results of the programs “FDS + Evac”, “Pathfinder” and “TraffGo”, using the example of a test of the International Maritime Organisation (IMO 9) covering the evacuation of 1,000 people. Results: For both the evacuation modelling proposed by the authors and the IMO 9 test estimated evacuation times are consistent with the times estimated using programs applicable in fire-safety engineering. It was further found that the use of cellular automata for modelling the evacuation of 1,000 people allows modelling 20 times faster than in the “Social Force” model implemented in the “FDS + Evac” program. The average cost of modelling of 1 s of evacuation using cellular automata depends linearly on the number of persons subjected to evacuation, in contrast to the “Social Force” model, where the modelling time will increase exponentially with the number of people. Conclusions: Evacuation models based on cellular automata, in contrast to the “Social Force” model, provide the ability to model the movement of large groups of people at a lower computing cost. The use of cellular automata allows the introduction of additional layers affecting the movement of people with a small increase in computational complexity. Introducing additional assumptions and layers to cellular automata models allow a more realistic representation of the evacuation with the small increase in the cost of the equipment used. Furthermore, a tool allowing fast estimates of the evacuation time in a manner accessible to engineers would help in the correct designing of buildings. Current commercial programs require expertise in the field of modelling. Using a simple interface with a fast algorithm estimating evacuation times can bring measurable benefits in terms of improving the safety of designed buildings and construction works.
PL
W artykule przedstawiono metodę obliczania przepustowości wlotów nadrzędnych w modelu ruchu wykorzystującym automat komórkowy. Sposoby obliczania przepustowości i warunków ruchu dla skrzyżowań bez sygnalizacji świetlnej określa instrukcja wydana przez Generalną Dyrekcję Dróg Krajowych i Autostrad. Nie może zostać ona użyta w pewnych przypadkach, związanych szczególnie z blokowaniem strumienia pojazdów na wylotach skrzyżowania. Nie może być ona także wykorzystana dla zmiennych obciążeń ruchem. Zaproponowano użycie automatu komórkowego do modelowania skrzyżowań tego typu. Podstawowy model Nagela-Schreckenberga uzupełniono o zasady ruchu na skrzyżowaniach z pierwszeństwem przejazdu, możliwość uwzględnienia pojazdów ciężkich oraz procedury zachowania bezpiecznej odległości pomiędzy pojazdami. Przewidziano możliwość stosowania w modelu obiektów blokujących strumień pojazdów – na przykład przejść dla pieszych. Zaproponowano i szczegółowo omówiono sposób obliczenia przepustowości wlotów nadrzędnych skrzyżowań z pierwszeństwem przejazdu. Przygotowano i przetestowano uproszczony model małego, jednopasowego, czterowlotowego skrzyżowania bez sygnalizacji świetlnej. Przeprowadzono szereg symulacji, które pokazały podobieństwa i różnice pomiędzy wynikami uzyskiwanymi z wykorzystaniem obowiązującej procedury obliczeniowej oraz automatu komórkowego. Uzyskano dobrą zgodność z obowiązującą procedurą obliczeniową, szczególnie w zakresie średnich i małych obciążeń. Wyniki uzyskiwane z symulacji dla dużych obciążeń były mniejsze niż uzyskiwane zgodnie z obowiązującą instrukcją. Przetestowane elementy składowe po walidacji pozwolą na budowanie modeli skrzyżowań dowolnego rodzaju, nawet nietypowych oraz symulację sytuacji nieuwzględnionych w obowiązującej instrukcji obliczeniowej.
EN
This paper shows a method of calculation of capacity of the priority entries in a cellular automata model. The method of calculating the capacity and lost time for some types of priority intersections was shown in Generalna Dyrekcja Dróg Krajowych i Autostrad instruction. However, this instruction should not be used for some cases, especially those including phenomenon that cause blocking the traffic stream on intersection exits. This instruction also should not be used in case of changing load too. Usage of a cellular automata for modeling of traffic for this kind of intersections was proposed. Basic Nagel-Schreckenberg model was extended by inter alia traffic rules on the priority intersections, possibility of using heavy vehicles and procedures of keeping safe distance between vehicles. Possibility of using objects which block the stream of vehicles, such as pedestrian crossings, was included. The method of calculating capacities for priority entries was proposed and examined. Simplified model of small, one-lane, four-entry priority intersection was prepared and tested. A multiple simulations were conducted. Similarities and differences between the results from two calculating methods: obligatory instruction and the model of priority intersection using a cellular automata were shown and analyzed. Such model was consistent with obligatory method of calculation, especially for small and medium loads. For large loads, the capacities from cellular automata model were smaller then calculated with obligatory method. After the validation of the model, its elements will be used to build models of any kind of priority intersections, even untypical. It will be possible to simulate situations not taken into account in obligatory method of the priority intersections calculations.
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