Minimization of errors in discrete wavelet filtering of signals during ultrasonic measurements and testing

Error minimizing methods for discrete wavelet filtering of ultrasonic meter signals are considered. For this purpose, special model signals containing various measuring pulses are generated. The psi function of the Daubechies 28 wavelet is used to generate the pulses. Noise is added to the generated pulses. A comparative analysis of the two filtering algorithms is performed. The first algorithm is to limit the amount of detail of the wavelet decomposition coefficients in relation to signal interference. The minimum value of the root mean square error of wavelet decomposition signal deviation which is restored at each level from the initial signal without noise is determined. The second algorithm uses a separate threshold for each level of wavelet decomposition to limit the magnitude of the detail coefficients that are proportional to the standard deviation. Like in the first algorithm, the task is to determine the level of wavelet decomposition at which the minimum standard error is achieved. A feature of both algorithms is an expanded base of discrete wavelets ‒ families of Biorthogonal, Coiflet, Daubechies, Discrete Meyer, Haar, Reverse Biorthogonal, Symlets (106 in total) and threshold functions garotte, garrote, greater, hard, less, soft (6 in total). The model function uses random variables in both algorithms, so the averaging base is used to obtain stable results. Given features of algorithm construction allowed to reveal efficiency of ultrasonic signal filtering on the first algorithm presented in the form of oscilloscopic images. The use of a separate threshold for limiting the number of detail coefficients for each level of discrete wavelet decomposition using the given wavelet base and threshold functions has reduced the filtering error.

Systematically Measuring Ultra-diffuse Galaxies (SMUDGes). II. Expanded Survey Description and the Stripe 82 Catalog

We present 226 large ultra-diffuse galaxy (UDG) candidates (r e > 5.″3, μ 0,g > 24 mag arcsec−2) in the SDSS Stripe 82 region recovered using our improved procedure developed in anticipation of processing the entire Legacy Surveys footprint. The advancements include less constrained structural parameter fitting, expanded wavelet filtering criteria, consideration of Galactic dust, estimates of parameter uncertainties and completeness based on simulated sources, and refinements of our automated candidate classification. We have a sensitivity ∼1 mag fainter in μ 0,g than the largest published catalog of this region. Using our completeness-corrected sample, we find that (1) there is no significant decline in the number of UDG candidates as a function of μ 0,g to the limit of our survey (∼26.5 mag arcsec−2); (2) bluer candidates have smaller Sérsic n; (3) most blue (g–r < 0.45 mag) candidates have μ 0,g ≲ 25 mag arcsec−2 and will fade to populate the UDG red sequence we observe to ∼26.5 mag arcsec−2; (4) any red UDGs that exist significantly below our μ 0,g sensitivity limit are not descendent from blue UDGs in our sample; and (5) candidates with lower μ 0,g tend to smaller n. We anticipate that the final SMUDGes sample will contain ∼30 × as many candidates.

Wavelet filtering for solving the problem of selecting the outlines and analysis of the measurement results in the background of noise

Currently, the issue of developing new modern algorithms and methods is quite relevant, which will allow in an automated mode to analyze images (signals and the results of their measurements) against a background of noise. This task is relevant in the analysis and modeling of dynamic processes and objects, in the search for methods for automating their control. For the process of automating the processing of the results of computational experiments, it is important to implement the calculation of the derivatives of the first and second order against the background of noise.

Application of Wavelet Filtering to Vibrational Signals from the Mining Screen for Spring Condition Monitoring

The main task of mineral processing plants is to further process the raw material extracted in the mining faces into a concentrate with the highest possible concentration of the final product. In practice, it is a complex process in which several stages can be distinguished. After the ore has been transported to the surface by the skip shaft, one of the first steps is sieving the ore, which is typically performed using vibrating mining screens. In a typical Ore Enrichment Plant, the screening process is carried out by several such machines. This is a typical bottleneck in the technological chain. For this reason, the main challenge for users is to achieve the highest reliability and efficiency of these technical facilities. The solution is to focus on predictive maintenance strategies based on the development of monitoring and advanced diagnostic procedures capable of estimating the time of safe operation. This work was developed as part of an advanced diagnostic system ensuring comprehensive technical conditioning and early fault detection of components such as the engine, transmission, bearings, springs, and screen. This article focuses on vibration data. The problem of damage detection in the presence of periodically impulsive components resulting from falling feed material on the screen and its further screening process has been considered. These disturbances are of a non-Gaussian noise nature, the elimination of which is essential to extract the fault-related signal of interest. One solution may be to properly smooth and filter the raw signal. In this article, a wavelet filtering technique is applied. First, the wavelet filtering procedure is described. In the next step, the performance of a wavelet filter is investigated depending on its parameters. Then, the results of wavelet filtering are compared with such methods as low-pass filtering and smoothing using a moving average. Finally, the impact of wavelet filtering on the calculation of screen trajectories is investigated.

Effect of De-noising by Wavelet Filtering and Data Augmentation by Borderline SMOTE on the Classification of Imbalanced Datasets of Pig Behavior

Classification of imbalanced datasets of animal behavior has been one of the top challenges in the field of animal science. An imbalanced dataset will lead many classification algorithms to being less effective and result in a higher misclassification rate for the minority classes. The aim of this study was to assess a method for addressing the problem of imbalanced datasets of pigs' behavior by using an over-sampling method, namely Borderline-SMOTE. The pigs' activity was measured using a triaxial accelerometer, which was mounted on the back of the pigs. Wavelet filtering and Borderline-SMOTE were both applied as methods to pre-process the dataset. A multilayer feed-forward neural network was trained and validated with 21 input features to classify four pig activities: lying, standing, walking, and exploring. The results showed that wavelet filtering and Borderline-SMOTE both lead to improved performance. Furthermore, Borderline-SMOTE yielded greater improvements in classification performance than an alternative method for balancing the training data, namely random under-sampling, which is commonly used in animal science research. However, the overall performance was not adequate to satisfy the research needs in this field and to address the common but urgent problem of imbalanced behavior dataset.

The efficiency of using wavelet transforms for filtering noise in the signals of measuring transducers

Methods of wavelet filtering of noise in signals of measuring transducers using the threshold method of discrete wavelet transform are considered. To study the methods of wavelet filtering of noise, special model signals were used to estimate the filtering errors. A method has been developed for determining the parameters of wavelet filtering of noise with a threshold for all levels of decomposition, which makes it possible to determine the wavelet function, threshold function and filtering threshold of the detailing coefficients of the discrete wavelet decomposition. The influence of the parameters of the noise distribution, the noise level, the number of vanishing moments of the Daubechies wavelet function, the nature of the threshold function and the threshold value on the filtering error caused by the noises of non-stationary measuring signals has been investigated by the method of a computational experiment. The results of the study of six threshold functions are given with the addition of noise to the measuring signal with nonstationary amplitude, frequency and duty cycle of rectangular pulses. The signal of the Doppler sensors is investigated, the wavelet filtering parameters are calculated, which provide the minimum error. The obtained parameters are used to construct graphs of signals before and after filtering directly in the time domain using the inverse wavelet transform.