Search Results

1 - 5 of 5 items :

  • "metoda najmniejszych kwadratów" x
Clear All

Statistical Calibration of Model Solution of Analytes

A new method based on spectrophotometric-partial least-squares procedure was proposed for simultaneously determination of thorium and zirconium using SPADNS (4,5-Dihydroxy-3-(p-sulfophenylazo)-2,7-naphthalene disulfonic acid, trisodium salt) as a color reagent. Absorbance measurements were made in the range of γ = 541÷620 nm with 1.0 nm steps in buffered solutions at pH 3.5. The linear ranges were obtained for 0.5÷11.5 and 1.5÷14.5 μg cm-3 for Th4+ and Zr4+ ions, respectively. The limits of detection were determined 0.4 and 1.2 μg cm-3 for thorium and zirconium, respectively. The standard deviation (n = 3) and recovery percent of 10 samples in the prediction set were obtained in the amplitude 0.22÷0.38 μg cm-3 and 91.3÷109.2, respectively. The proposed method was used for simultaneously determination of mentioned ions in spiked real water samples and wastewater. The results show that the method is applicable for the analysis of samples with similar matrix.


Blade Tip Timing (BTT) is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA) is recorded when a blade is passing a stationary sensor. The measurement data, in form of undersampled (aliased) tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.


In Blade Tip Timing several sensors installed circumferentially in the casing are used to record times of arrival (TOA) and observe deflections of blade tips. This paper aims to demonstrate methodology of model-based processing of aliased data. It focuses on the blade vibration excited by the forces synchronous with engine rotation, which are called integral responses. The driven harmonic oscillator with single degree of freedom (SDOF) is used to analyse blade vibration measured by tip-timing sensors during engine deceleration. When integral engine order EO is known, the linear sine fitting techniques can be used to process data from sensors to estimate amplitude, phase and frequency of blade vibration in each rotation. The oscillator model is implemented in MATLAB and used to generate resonance curves and simulate blade responses observed with tip sensors, installed in the axial compressor. Generated TOA data are fitted to the sine function to estimate vibration parameters. The validated procedure is then employed to analyze real test data.

. 80, 2016, pp. 71–78. [5] Tomczyk K., Layer E., Energy density for signals maximizing the integral-square error , Measurement, Vol. 90, 2016, pp. 224–232. [6] Foszcz D., Estymacja Parametrów Funkcji Regresji Metodą Klasyczną oraz Metodami Bootstrapowymi , Górnictwo i Geoinżynieria, Vol. 3(1), 2016, pp. 67–78. [7] Dorozhovets M., Ocena wpływu oddziaływan systematycznych na parametry niepewnosci podczas aproksymacji metoda najmniejszych kwadratow , PAK. Vol. 12, 2006, pp. 22–25. [8] Sun X.T., Jing X.J., Xu J., Cheng L., A Quasi-Zero-Stiffness-Based Sensor System

regressions for Populus grandientata on three sites in northern lower Michigan. Canadian Journal of Forest Research , 10: 92-101. Kraft G., 1884. Beiträge zur Lehre von den Durchforstungen, Schlagstellungen und Lichtungshieben. Hannover, Germany, Klindworth's. 26p. Kuchar L. 2004. Niebezpieczeństwa stosowania transformacji funkcji w aproksymacji metodą najmniejszych kwadratów przy modelowaniu zagadnień rolniczych. Acta Agrophysica , 3(1), 99-105. Lehtonen A. 2005. Estimating foliage biomass in Scots pine ( Pinus sylvestris ) and Norway spruce ( Picea abies ) plots