The second part of the paper presents finite-dimensional models of linear elastic, elastic-strain hardening, elastic-perfectly plastic
and rigid-perfectly plastic structures. These models can be seen as a result of discretisation procedure applied to the models of solids derived in the Part I. The implications of sub-dividing degrees of freedom into those with prescribed external forces and those with given displacements are discussed. It is pointed out that the dual energy principles given in this part of the paper can serve as a direct basis for numerical computations.
This paper presents revised and extended version of theory proposed in the late 1970-ties by A. ˇCyras and his co-workers. This theory, based upon the notion of duality in mathematical programming, allows us to generate variational principles and to investigate existence and uniqueness of solutions for the broad class of problems of elasticity and plasticity. The paper covers analysis of solids made of linear elastic, elastic-strain hardening, elastic-perfectly plastic and rigid-perfectly plastic material. The novelty with respect to ˇCyras’s theory lies in taking into account loads dispersed over the volume and displacements enforced on the part of surface. A new interpretation of optimum load for a rigid-perfectly plastic body is also given.
The paper examines the usage of Convolutional Bidirectional Recurrent Neural Network (CBRNN) for a problem of quality measurement in a music content. The key contribution in this approach, compared to the existing research, is that the examined model is evaluated in terms of detecting acoustic anomalies without the requirement to provide a reference (clean) signal. Since real music content may include some modes of instrumental sounds, speech and singing voice or different audio effects, it is more complex to analyze than clean speech or artificial signals, especially without a comparison to the known reference content. The presented results might be treated as a proof of concept, since some specific types of artefacts are covered in this paper (examples of quantization defect, missing sound, distortion of gain characteristics, extra noise sound). However, the described model can be easily expanded to detect other impairments or used as a pre-trained model for other transfer learning processes. To examine the model efficiency several experiments have been performed and reported in the paper. The raw audio samples were transformed into Mel-scaled spectrograms and transferred as input to the model, first independently, then along with additional features (Zero Crossing Rate, Spectral Contrast). According to the obtained results, there is a significant increase in overall accuracy (by 10.1%), if Spectral Contrast information is provided together with Mel-scaled spectrograms. The paper examines also the influence of recursive layers on effectiveness of the artefact classification task.
The paper presents descriptions of bridge disintegration types and contact mass loss in the bridge stage. There is presented Matlab solvers to solve equation describing dynamic changes of temperature in the bridge region. The final result of program calculations is the mass loss and the volume of the metal of contacts which was lost during the bridge stage.
This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.
This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.
This paper derives analytical formulas for the systematic errors of the linear interpolated DFT (LIDFT) method when used to estimating multifrequency signal parameters and verifies this analysis using Monte-Carlo simulations. The analysis is performed on the version of the LIDFT method based on optimal approximation of the unit circle by a polygon using a pair of windows. The analytical formulas derived here take the systematic errors in the estimation of amplitude and frequency of component oscillations in the multifrequency signal as the sum of basic errors and the errors caused by each of the component oscillations. Additional formulas are also included to analyze particular quantities such as a signal consisting of two complex oscillations, and the analyses are verified using Monte-Carlo simulations.
The paper presents a novel method for the 3D shaping of different materials using a high-pressure abrasive water jet and a flat target image. For steering the process of movement of the jet, a principle similar to raster image way of record and readout was used. However, respective colors of pixels in such a bitmap are connected with adequate jet feed rate that causes erosion of material with adequate depth. Thanks to that innovation, one can observe spatial imaging of the object. Theoretical basis as well as spatial model of material shaping and experimental stand including steering program are presented in the paper. There are also presented methodic and some experimental erosion results, as well as practical example of object's bas-relief made of metal.
The paper presents a new method for simultaneous tracking of varying grid impedance and its uncertainty bounds. Impedance tracking consists of two stages. In the first stage, the actual noise estimate is obtained from least squares (LS) residua. In the second stage, the noise covariance matrix is approximated with the use of residual information. Then weighted least squares (WLS) method is applied in order to estimate impedance and background voltage. Finally uncertainty bounds for impedance estimation are computed. The robustness of the method has been verified using simulated signals. The proposed method has been compared to sliding LS. The results have shown, that the method performs much better than the LS for all considered cases, even in the presence of significant background voltage variations.
Quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. One of the most important factors affecting quality is the estimation accuracy of grid signal parameters. This paper presents a method of a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay side-lobes windows. The most important features of the method are elimination of the impact associated with the conjugate’s component on the results and its straightforward implementation. Moreover, the measurement time is very short ‒ even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass pre-filter. Even using a 40 dB FIR pre-filter for the grid signal with THD ≈ 38%, SNR ≈ 53 dB and a 20‒30% slow decay exponential drift the maximum estimation errors in a real-time DSP system for 512 samples are approximately 1% for the amplitude and approximately 8.5・10‒2 rad for the phase, respectively. The errors are smaller by several orders of magnitude with using more accurate pre-filters.