Nonlinear Analysis of Mineral Wool Fiberization Process

In this paper, the mineral wool fiberization process on a spinner wheel was studied by means of the nonlinear time series analysis. Melt film velocity time series was calculated using computer-aided visualization of the process images recorded with a high speed camera. The time series was used to reconstruct the state space of the process and was tested for stationarity, determinism, chaos, and recurrent properties. Mineral wool fiberization was determined to be a low-dimensional and nonstationary process. The 0-1 chaos test results suggest that the process is chaotic, while the determinism test indicates weak determinism

The dynamics of laser droplet generation

We propose an experimental setup allowing for the characterization of laser droplet generation in terms of the underlying dynamics, primarily showing that the latter is deterministically chaotic by means of nonlinear time series analysis methods. In particular, we use a laser pulse to melt the end of a properly fed vertically placed metal wire. Due to the interplay of surface tension, gravity force and light-metal interaction, undulating pendant droplets are formed at the molten end, which eventually completely detach from the wire as a consequence of their increasing mass. We capture the dynamics of this process by employing a high-speed infrared camera, thereby indirectly measuring the temperature of the wire end and the pendant droplets. The time series is subsequently generated as the mean value over the pixel intensity of every infrared snapshot. Finally, we employ methods of nonlinear time series analysis to reconstruct the phase space from the observed variable and test it against determinism and stationarity. After establishing that the observed laser droplet generation is a deterministic and dynamically stationary process, we calculate the spectra of Lyapunov exponents. We obtain a positive largest Lyapunov exponent and a negative divergence, i.e., sum of all the exponents, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In addition to characterizing the dynamics of laser droplet generation, we outline industrial applications of the process and point out the significance of our findings for future attempts at mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos [supplementary material available at http://www.matjazperc.com/chaos/laser.html

Time series analysis based study of a mass-spring-like oscillation and detachment of a metal pendant droplet

The subject of this study is the vertical mass-spring-like oscillation of a pendant droplet and its resonant detachment, which was experimentally observed in the process of laser droplet generation from a metal wire. The process was characterized by various time series, which were generated from a sequence of infrared intensity images of the process. Following a visual inspection of pendant droplet images and an analysis of a wavelet based time-frequency map of the dropletʼs vertical displacement time series, the pendant dropletʼs oscillation is described by a time-variable mass-spring system. Based on the characteristics of the time-frequency map, the resonant nature of the pendant droplet detachment was demonstrated. Additionally, an algebraic expression was formulated, which can be used to predict the detached dropletʼs diameter as a function of the laser pulse frequency

Adaptive optimization of heating curves in buildings heated by a weather-compensated heat pump

his article is concerned with the weather compensated heating of buildings by means of air-to-water heat pumps. A novel adaptive method is proposed for on-line optimization of the heating curve that defines the relation between the heating temperature and the outdoor temperature. Parametrization of the linear heating curve with two reference points is presented, with the aim of providing good tracking of the desired indoor temperature by adaptively adjusting the reference points of the heating curve. Two adaptation strategies are investigated, and a wide range of adaptation constants is explored. The use of these methods is demonstrated on two different buildings, simulated in Transient System Simulation Tool (TRNSYS). The simulation model was validated on a reference building. The results of adaptive optimization show good performance, which is comparable to and even better than the performance based on referential optimal static heating curves

Semi-supervised vibration-based classification and condition monitoring of compressors

Semi-supervised vibration-based classification and condition monitoring of the reciprocating compressors installed in refrigeration appliances is proposed in this paper. The method addresses the problem of industrial condition monitoring where prior class definitions are often not available or difficult to obtain from local experts. The proposed method combines feature extraction, principal component analysis, and statistical analysis for the extraction of initial class representatives, and compares the capability of various classification methods, including discriminant analysis (DA), neural networks (NN), support vector machines (SVM), and extreme learning machines (ELM). The use of the method is demonstrated on a case study which was based on industrially acquired vibration measurements of reciprocating compressors during the production of refrigeration appliances. The paper presents a comparative qualitative analysis of the applied classifiers, confirming the good performance of several nonlinear classifiers. If the model parameters are properly selected, then very good classification performance can be obtained from NN trained by Bayesian regularization, SVM and ELM classifiers. The method can be effectively applied for the industrial condition monitoring of compressors

Stability diagrams and chatter avoidance in horizontal band sawing

The paper presents recurrence plot based stability analysis of the horizontal band sawing process of structural steel profiles. The analysis is performed in the parameter space defined by the cutting speed, the distance between the blade supports, and the feed rate. The corresponding stability diagrams have been constructed using the recurrence plot characteristic, the determinism of the sound pressure emitted by the process, which quantifies the process predictability. The topology of the experimentally obtained stability diagrams revealed non-linear non-monotonic dynamic behaviour, which made two different chatter avoidance strategies possible by cutting speed variation