Deterministic Walking Research Articles

Response Prediction to Walking-Induced Vibrations of a Long-Span Timber Floor

Long-span timber floors are susceptible to annoying floor vibrations caused by human activities, which, in many cases, govern the timber floor design. Consequently, a reliable prediction of floor vibration responses under human activities, which relies on appropriate walking load models, can be crucial in the design to keep timber floors remaining competitive in the commercial building market. Much of the current design guidance for timber floor vibrations have been established from short-span floors in a residential context, and as a result, many designers refer to established design methods formulated for use with concrete and steel-framed buildings. These guidelines predict the floor response based on a deterministic single-person walking load model that differs depending on the classification of the floor as either a high- or low-frequency floor, which are assumed as a transient or resonant floor response, respectively. Recent advances in modeling human walking have been made, including a single footfall trace load that avoids the need to classify the floor, as well as load models that incorporate a probabilistic approach. To date, an investigation on different walking load models to predict the vibration response of long-span timber floors has not been undertaken, partially due to the fact that there are limited examples in practice. This paper presents the results of a recently completed state-of-the-art research project involving full-scale testing of long-span timber floors and the development of novel numerical models to investigate the applicability of the deterministic walking load model used in current floor vibration design guides, as well as two innovative single-person walking load models for predicting the floor responses of a single long-span timber cassette floor. The numerical investigation was carried out with a finite-element model calibrated with experimentally obtained modal properties. The comparison between the predicted responses and the measured walking test results leads to the recommendation that a selection of an appropriate load model plays a crucial role in accurately and reliably predicting the floor response of a long-span timber cassette floor. Finally, the research undergirding this paper forms an essential basis for understanding the dynamic behavior of long-span timber floors for use in medium-rise timber buildings.

Dynamic behaviour of a timber footbridge with uncertain material properties under a single deterministic walking load

The dynamic study of a short span timber footbridge with uncertain mechanical properties under the action of a deterministic walking load model which represents one individual is presented. The aim of the work is to quantify the influence of the uncertain material properties in the natural and forced vibration problems of a short span timber footbridge. These structural systems made of timber are increasingly employed due to the high stiffness/weight ratio that this material exhibits. This feature can lead to lightweight structural systems in which the acceleration levels can exceed the human comfort limits. The assumed sources of uncertainties of this structural model are the Modulus of Elasticity (MOE) and the mass density. Also, the geometrical design of the boards that compose the laminated timber beams supporting the floor involves variability of the distances between finger joints. Probability Density Functions (PDFs) of the timber properties are formulated from the Principle of Maximum Entropy (PME). The finger joints distance generates the lengthwise variability of the MOE and the mass density in each board of the laminated beams. The PDFs of the natural frequencies of the structure, the mode shapes and the structural response are numerically obtained through the Finite Element Method (FEM) and statistic tools. In order to carry out this analysis, plate and laminated beam elements derived from the First Order Shear Deformation Theory (FSDT) are employed. The variation of the effective stiffness and mass along the elements due to the union of boards with different properties produces an important reduction of the standard deviation of the natural frequencies. The conditions in which the stochastic properties of the structure lead to unacceptable acceleration levels are studied. In some scenarios, the variation of the material properties can lead to unacceptable serviceability performances of the structure and a reduction in the pedestrian comfort, according to the codes in force. However, new design guidelines replace the line limits by comfort regions which are also discussed here.

An experiment on wear particle’s texture analysis and identification by using deterministic tourist walk algorithm

Purpose – This study aims to use a deterministic tourist walk to build a system that can identify wear particles. Wear particles provide detailed information about the wear processes taking place between mechanical components. Identification of the type of wear particles by image processing and pattern recognition is key to effective online monitoring algorithm. There are three kinds of particles that are particularly difficult to distinguish: severe sliding wear particles, fatigue spall particles and laminar particles. Design/methodology/approach – In this study, an identification method is tested using the deterministic tourist walking (DTW) method. This study examined whether this algorithm can be used in particle identification. If it does, can it outperform the traditional texture analysis methods such as Discrete wavelet transform or co-occurrence matrix. Different parameters such as walk’s memory size, size of image samples, different inputting vectors and different classifiers were compared. Findings – The DTW algorithm showed promising result compared to traditional texture extraction methods: discrete wavelet transform and co-occurrence matrix. The DTW method offers a higher identification accuracy and a simple feature vector. A conclusion can be drawn that the DTW method is suited for particle identification and can be put into practical use in condition monitoring systems. Originality/value – This paper combined DTW algorithm with wear particle identification problem.

Walking on Data Words

Data words are words with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of some basic decision problems. Specifically, we show that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that the class of non-deterministic Data Walking Automata has decidable emptiness, universality, and containment problems. We also prove that deterministic Data Walking Automata are strictly less expressive than non-deterministic Data Walking Automata, which in turn are captured by Class Memory Automata.

Parametric random generation of deterministic tree automata

Uniform random generators deliver a simple empirical means to estimate the average complexity of an algorithm. We present a general rejection algorithm that generates sequential letter-to-letter transducers up to isomorphism. We also propose an original parametric random generation algorithm to produce sequential letter-to-letter transducers with a fixed number of transitions. We tailor this general scheme to randomly generate deterministic tree walking automata and deterministic top–down tree automata. We apply our implementation of the generator to the estimation of the average complexity of a deterministic tree walking automata to nondeterministic top–down tree automata construction we also implemented.

Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure

String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure has the same power as deterministic automata walking on their input with k heads, additionally using a finite set of nested pebbles. This result is valid for strings, ordered trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes. For nondeterministic automata, the logic is restricted to positive occurrences of transitive closure. The special case of k=1 for trees, shows that single-head deterministic tree-walking automata with nested pebbles are characterized by first-order logic with unary deterministic transitive closure. This refines our earlier result that placed these automata between first-order and monadic second-order logic on trees.

Synchronization of internal and external degrees of freedom of atoms in a standing laser wave

We consider dissipative dynamics of atoms in a strong standing laser wave and find a nonlinear dynamical effect of synchronization between center-of-mass motion and internal Rabi oscillations. The synchronization manifests itself in the phase space as limit cycles, which may have different periods and riddled basins of attraction. The effect can be detected in fluorescence spectra of atoms as equidistant sideband frequencies with the space between adjacent peaks to be inversely proportional to the value of the period of the respective limit cycle. With increasing intensity of the laser field, we numerically observe cascades of bifurcations that eventually end up in settling a strange chaotic attractor. A broadband noise is shown to destroy a fine structure of the bifurcation scenario, but prominent features of period-1 and period-3 limit cycles survive under a weak noise. The character of the atomic motion is analyzed with the help of the friction force whose zeroes are attractor or repellor points in the velocity space. We find ranges of the laser parameters where the atomic motion resembles a random but deterministic walking of atoms erratically jumping between different wells of the optical potential. Such a random walking is shown to be fractal.

Domains of partial attributed tree transducers

The domains of partial attributed tree transducers (patt's) are the tree languages recognized by tree walking automata in universal acceptance mode. Moreover, the domains of patt's having monadic output are the tree languages recognized by deterministic tree walking automata.

Top-down tree transducers with two-way tree walking look-ahead

We consider top-down tree transducers with deterministic, nondeterministic and universal two-way tree walking look-ahead and compare the transformational powers of their deterministic and strongly deterministic versions by giving the inclusion diagram of the induced tree transformation classes. We also study the closure properties of these transformation classes with respect to composition.