Acoustic emission of fiberglass composite material during tensile loading is characterized experimentally by a set of records. Regularity of recorded data enables prediction of the sample rupture when approaching the critical loadings. For this purpose a new statistical method is formulated. The prediction is performed by comparing acoustic activity of tested and representative samples. Results of the prediction agree with the experimental data and confirm the hypothesis that acoustic emission detection provides a proper basis for a simple nondestructive testing of very complex fiberglass composite.

Random walk of particles during Chladni pattern formation is macroscopically treated as a diffusion process. The corresponding generalized diffusion equation is formulated based upon the generator of vibration driven random walk by following Einstein’s treatment of Brownian motion.

Visualization of interference phenomena by Chladni patterns is treated. The formation of the pattern in the Young's double-slit experiment is described by a new model of driven random walk exhibited by particles bouncing on a vibrating surface. In the model the mean length of horizontal displacement is described deterministically by the wave amplitude. The presented example indicates that such formation of interference patterns can take place without any pilot-waves associated to particles. In spite od this, the pheomenon remeinds to formation of interference patterns observed at scattering of particles in quantum mechanics.

Properties of lizard skin pattern (LSP) comprised of light and dark scales are characterized statistically and compared with the corresponding properties of a random binary field (RBF). The similarity function of these fields exhibits an outstanding peak that indicates their stochastic character. Stochastic properties are still more generally indicated by the probability distribution of scales in hexagonal cells comprised of a center and ring. It shows that similar scales are grouped together in LSP, but not in RBF. This difference is characterized by the conditional probability that reveals why LSP appears more striped than RBF. For generation of fields resembling LSP the cellular automaton (CA) is adapted to LSP by the non-parametric regression. Its deterministic performance is demonstrated by the operation on RBF. By adding a random number generator to this model the deterministic CA is generalized to a probabilistic one. Its actions cause more expressive changing of the input field as the actions of the deterministic CA.

The model of vibration driven random walk is adapted to description of foraging performed by simple organisms. Stochastic properties of foraging are described by the Gaussian random number generator, while the attraction of food is represented by a deterministic signal that directs walkers from surroundings to the food. This attraction causes transition from the Gaussian random walk to the Levy flight.

This research paper presents a new method for the automatic diagnosis of diseases using a personal computer. Forming a basis for the characterization of diseases, a wide set of symptoms is introduced, and a particular disease is characterized by a set of statistical weights assigned to those symptoms. Information about the patient’s state is provided by a graphic interface in which the user confirms symptom indicators. Agreement between these symptoms and classified symptoms of a particular disease is then estimated by the sum of corresponding weights, where the disease corresponding to the maximal agreement is proposed as the result of the diagnosis. A disease likelihood estimator is calculated and presented to assess the reliability of the diagnosis. With regard to the automatic assessment of the diagnosis the corresponding algorithm and the properties of the computer program are included. Finally, the effectiveness of this method of medical diagnosis is demonstrated through four typical examples involving differently expressed symptoms. The diagnostic system resembles semantically driven sensory-neural network.

Bouncing of sand particles on a vibrating membrane of a Chladni experiment is characterized statistically. Analysis of recorded particle trajectories reveals that bounces are circularly distributed and random. Their mean horizontal displacement is approximately proportional to the vibration amplitude above the critical level and about one fourth of the jump height. For the description of particle horizontal drifting a new model of vibration driven random walk is developed. Typical examples of Chladni patterns generated numerically by vibration driven random walk reveal a good agreement between simulated and experimentally observed properties.

Performance of a sensory-neural network developed for diagnosing of diseases is described. Information about patient's condition is provided by answers to the questionnaire. Questions correspond to sensors generating signals when patients acknowledge symptoms. These signals excite neurons in which characteristics of the diseases are represented by synaptic weights associated with indicators of symptoms. The disease corresponding to the most excited neuron is proposed as the result of diagnosing. Its reliability is estimated by the likelihood defined by the ratio of excitation of the most excited neuron and the complete neural network.

In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal and quadratic lattice. With this aim a random initial field is transformed by a sequence of CA actions into a new pattern. On the hexagonal lattice this pattern resembles a lizard skin. The properties of CA are specified by the most simple majority rule that adapts selected cell state to the most frequent state of cells in its surrounding. The method could be of interest for manufacturing of textiles as well as for modeling of patterns on skin of various animals.

Instability of traffic flow on high-ways leads to non-linear development of jams with detrimental consequences. In order to avoid them we try to formulate an optimal control law by which the flow could be stabilized. For this purpose we describe the influence of speed limit on the stable regime by a new fundamental law that is formulated based upon experimental data of traffic flow. The corresponding non-linear relation indicates how the speed limit has to be adapted to the traffic density in order to provide conditions for a stable flow.

A sensory-neural network for automatic diagnosing of diseases is described. The network gathers information using the patient's answers to a questionnaire. Specific questions correspond to sensors that react when patients acknowledge symptoms. The signals from the sensors stimulate neurons in which the characteristics of the disease are stored in terms of synaptic weights assigned to indicators of symptoms. The response of a neuron is determined by the weighted sum of input stimuli. The disease corresponding to the most excited neuron represents the result of diagnosis. Its reliability is assessed by the likelihood defined as the relative excitation of the neuron with respect to all others. The performance of the network is demonstrated through characteristic examples of diagnosis.

Instability of the traffic flow on high-ways causes congestions and jams with detrimental consequences. To avoid them we propose a control law to stabilize the high-way traffic flow. The impact of speed limitation on a stable high-way traffic flow is described. The proposal to adopt a new law is based on experimental data and characteristics of driving on high-ways. The law foresees an optimal speed limit adaptation to the traffic density in order to provide conditions for a stable highway traffic flow.

Unconvenient driving conditions on high-ways often lead to evolution of traffic jams. Disturbances are most often the consequence of traffic accidents, adverse weather conditions or various works and can be described by the decreased road capacity. By estimating the road capacity drop, the traffic-information providers can forecast the evolution of jams at a disturbed section and inform the population about it in advance. The paper describes a new mathematical prediction method formulated using an intelligent unit developed for its execution. The unit first forecasts the traffic flow for a disturbed road section based upon records of the past traffic flow and then converts the forecast data into characteristics of the evolving jam by using the decreased value of the road capacity. The performance of the method is demonstrated by forecasting evolution of a jam at a disturbed section of a maximal traffic activity on a high-way in Slovenia.

Drifting of sand particles bouncing on a vibrating membrane of a Chladni experiment is characterized statistically. Records of trajectories reveal that bounces are circularly distributed and random. The mean length of their horizontal displacement is approximately proportional to the vibration amplitude above the critical level and amounts about one fourth of the corresponding bounce height. For the description of horizontal drifting of particles a model of vibration driven random walk is proposed that yields a good agreement between experimental and numerically simulated data.

This article deals with experimental description of physical laws by probability density function of measured data. The Gaussian mixture model specified by representative data and related probabilities is utilized for this purpose. The information cost function of the model is described in terms of information entropy by the sum of the estimation error and redundancy. A new method is proposed for searching the minimum of the cost function. The number of the resulting prototype data depends on the accuracy of measurement. Their adaptation resembles a self-organized, highly non-linear cooperation between neurons in an artificial NN. A prototype datum corresponds to the memorized content, while the related probability corresponds to the excitability of the neuron. The method does not include any free parameters except objectively determined accuracy of the measurement system and is therefore convenient for autonomous execution. Since representative data are generally less numerous than the measured ones, the method is applicable for a rather general and objective compression of overwhelming experimental data in automatic data-acquisition systems. Such compression is demonstrated on analytically determined random noise and measured traffic flow data. The flow over a day is described by a vector of 24 components. The set of 365 vectors measured over one year is compressed by autonomous learning to just 4 representative vectors and related probabilities. These vectors represent the flow in normal working days and weekends or holidays, while the related probabilities correspond to relative frequencies of these days. This example reveals that autonomous learning yields a new basis for interpretation of representative data and the optimal model structure.

The laser droplet-formation process (LDFP) is a part of the novel joining technology for forming high-temperature joints. The advantages of this technology are: good heat-input control, good control of the added material and limited local heating. A molten metal droplet is used as the basic unit for the filling material, and a determination of the process parameters for the formation of droplets with desired properties is crucial. A physical and numerical model of the process was built to allow a theoretical determination of the process parameters. The numerical model enables a simulation of the process at different sets of parameters and a genetic algorithm optimization was implemented to find the best set. To verify this general procedure for determination and optimization of the parameters, we applied it in a specific case of a nickel wire. On the basis of the numerical model of the process, laser pulses for pendant-droplet formation and droplet detachment were determined and applied in experiments. With numerically determined laser pulses pendant-droplet formation and detachment were accomplished. In most cases, the process showed a very high repeatability. The encouraging experimental verification shows that a numerical approach is a very helpful tool for a determination of the process parameters and a better understanding of the process. It significantly reduces the number of necessary experiments when the laser droplet-formation setup or the target droplet properties are changed.

A two-dimensional pattern represents a fingerprint of the process that generated it. It is therefore expected that the information about the production process can be extracted from the pattern. In this paper, a non-parametric statistical method for modelling chaotic two-dimensional patterns and the estimation of the characteristic parameters is proposed. It is based on the joint probability density function of samples taken from known two-dimensional patterns representing a database. A new pattern with an unknown production process is reproduced by comparing parts of the new pattern with samples taken from the database. Because the samples in the database also include information about the production process, relevant parameters and the type of production process can be estimated simultaneously with the reproduction of patterns.

This article presents a theoretical basis for the development of a cascade neural network. A definition of the cascade stems from the hierarchical expansion of a general dynamical law used for the time series description and corresponds to a creation of a multilayer neural network. A particular layer predicts changes in the time series from a certain number of past data. The network complexity, determined by the dimension span and the population size of the neurons, is increasing until a proper prediction performance is achieved on a given time series. The adapted network is then applicable for a forecasting. The operation of the proposed architecture is demonstrated by the examples including a regular and a chaotic time series.

In laser droplet generation from a metal wire a droplet is generated by laser heating of the wire-end. In the paper a problem of laser droplet sequence generation, which results in unsuccessful droplet detachment is considered. To solve this problem, a control system and strategy for laser droplet sequence generation are proposed. The control bases on in-process monitoring of the initial position and temperature of the wire-end are presented. The results show that by ensuring proper initial wire-end position and stationary wire-end temperature which can be influenced by laser pulse parameters, a reliable generation of a droplet sequence can be achieved.

Experimental characterization of complex physical laws by probability density function of measured data is treated. For this purpose we introduce a statistical Gaussian mixture model comprised of representative data and probabilities related to them. To develop an algorithm for adaptation of representative data to measured ones we introduce the model cost function by the sum of discrepancy and redundancy. All statistics are expressed by the information entropy. An iterative method is proposed for searching the minimum of the cost function that yields an optimal model. Since representative data are generally less numerous than measured ones, the proposed method is applicable for compression of overwhelming experimental data measured by automatic data-acquisition systems. Such a compression is demonstrated on the characterization of traffic flow rate on the Slovenian roads network. The flow rate during a particular day at an observation point is described by a vector comprised of 24 components. The set of 365 vectors measured in one year is optimally compressed to just 4 representative vectors and related probabilities. These vectors represent the flow rate in normal working days and weekends or holidays, while the related probabilities correspond to the relative frequencies of these days. However, the number of representative data depends on the accuracy of PDF estimation.