ACCURACY ANALYSIS OF THE MODEL EXPERIMENTS ON DIPPING PURSE SEINE MODELS AT SIDE STREAM
Abstract and keywords
Abstract (English):
The research aim is to analyze accuracy of the experimental data obtained during the experiments in the hydraulic channel of "MariNPO", LLC (Kaliningrad) in 2014. During the experiments, three purse seine models were immersed under different loading of a leadline (0 kg, 0.248 kg, 0.338 kg) and different speed of the current (0.2 m/s, 0.3 m/s, 0.4 m/s). Seven experiments were carried out for each model (0 kg and 0.2 m/s; 0.248 kg and 0.2, 0.3, 0.4 m/s; 0.338 kg and 0.2, 0.3, 0.4 m/s). To confirm reliability of the data there was carried out the analysis of the total error which included: instrumental error, cargo error, measurement error of the net the models were made of, inaccuracy of immersion, displacement of the seine along OY axis, approximation error. To approximate the pilot data there was chosen the method of ordinary least squares. Approximation was conducted with a straight line (linear regression), polynomial n (polynomial regression), and a combination of arbitrary functions. The least error (6.82%) was obtained in the experiment 0 kg and 0.3 m/s, maximum (14.76%) - in the experiment 0.338 kg and 0.2 m/s. When the error doesn’t exceed 15%, subject to the adequate precision of measurement, the results of the experiments should be considered satisfactory.

Keywords:
purse seine, approximation, mathematical model
Text
The experiments of submerging purse seine models in the hydraulic channel of "MariNPO", LLC were conducted in 2014; the experimental results have been earlier introduced [1]. Three models of a purse seine were built with different leadline loading: 0 kg, 0.248 kg, 0.338 kg. The characteristics of the experimental purse seines are given in Table 1. Table 1 Characteristics of the purse seine models* Model Lж, m Hж, m Lвп, m Hп, m a, mm d, mm ux uy F0 1 10 2.1 7 1.5 10.0 1.16 0.7 0.714 0.210 2 6.0 0.4 0.133 3 10.0 0.95 0.190 * Lж - length of top selection in harness; Hж - height of seine in harness; Lвп - length of top selection; Hп - height of seine in landing; ux - horizontal landing coefficient; uy - vertical landing coefficient. Experimental measurements were done in still water, as well as in a flow having velocity 0.2 m/s, 0.3 m/s, 0.4 m/s. Iimmersion time, immersion depth, displacement of the leadline along OY axis, approximation error were being measured during the experiments. The purpose of the research was to justify the reliability of the data obtained. Error calculation In order to confirm the reliability of the data, it is necessary to calculate the error. The error consists of instrumental error (stopwatch, ruler, hydrometric flowmeter C-31), cargo error, error of the net the models were made of (mesh size, thread diameter), immersion error, displacement of the seine along OY axis, and approximation error. The following formula is used to estimate the overall error: where δtot - overall error of the experiment; δinstr - relative instrumental error; δc - relative cargo error; δn - relative net webbing error; δimm - relative error of purse seine immersion; δdisp - relative error of purse seine displacement; δappr - relative approximation error. The relative error was calculated using the formula: where δx - relative deviation of the value; - arithmetic mean value; ε1 - absolute error of the value. Absolute error ε1 is calculated using the formula: where - mean square deviation of the values; tβα - Student’s coefficient, which depends on the number of degrees of freedom (n - 1) and confidence probability β. Mean square deviation where n - number of measurements; xi - i-st element of measurement. Table 2 shows the results of calculating the relative error of the measurement values. Table 2 Error results Error Relative error, δ Model 1 Model 2 Model 3 V = 0.2 m/s V = 0.3 m/s V = 0.4 m/s V = 0.2 m/s V = 0.3 m/s V = 0.4 m/s V = 0.2 m/s V = 0.3 m/s V = 0.4 m/s Thread diameter, d 0.58% 1.19% 0.71% Mesh size, а 0.47% 0.64% 0.39% Cargo weight, P 0,01% Flowmeter C-31 0.4% - for 0.2 m/s; 0.6% - for 0.3 m/s; 0.8% - for 0.4 m/s Ruler 5% Stopwatch 0.01% Table 3 shows the results of calculating the relative error of the immersion of the seine. Table 3 Error of immersion and error of displacement of purse seine in immersion, % Load; flow velocity Model 1 Model 2 Model 3 Immersion of purse seine Displacement of purse seine Immersion of purse seine Displacement of purse seine Immersion of purse seine Displacement of purse seine 0 kg; 0.2 m/s 4.96 3.37 3.32 4.49 2.75 2.41 0.248 kg; 0.2 m/s 3.79 2.20 2.41 4.17 6.30 4.49 0.248 kg; 0.3 m/s 2.75 1.27 2.45 5.31 4.82 4.49 0.248 kg; 0.4 m/s 3.21 4.71 3.84 2.92 3.31 4.50 0.338 kg; 0.2 m/s 3.28 2.52 4.95 2.34 5.03 4.50 0.338 kg; 0.3 m/s 3.58 1.92 6.08 2.54 4.39 4.49 0.338 kg; 0.4 m/s 3.59 6.53 4.21 3.86 4.81 2.92 For representation of the obtained experimental data as a function y = f(x) we use approximation [2]. For our approximation, let us choose the least squares method - this is the most common way of approximating the data [3]. The method provides the minimum sum of deviation squares from the approximating function to the experimental points, and it also does not require passage of the approximating function through all the experimental points. Using the least squares method, the most common is straight line approximation (linear regression), n-degree polynomial approximation (polynomial regression), and the approximation by a combination of arbitrary functions ("linfit" function). As a calculation example let us take model 2 under 0 kg loading and flow velocity equal to 0.2 m/s. The input data for calculation of approximation were estimated on the basis of the work theory [4]. The input data: where τ - relative immersion time of the purse seine; ν - relative immersion rate of the purse seine; ω - relative displacement of the purse seine along the OY axis in immersion. To calculate the linear regression, integrated in MathCAD functions such as slope (evaluate slope coefficient of a straight line) and intercept (finds the point of intersection with the y-axis) are used. The linear regression is given by: where To calculate the polynomial regression, regress and interp functions are used. The polynomial regression of the 2nd degree is given by: To calculate approximation by a combination of functions, built-in "linfit" function is used. Approximating function is given by: Let us plot on a graph and compare approximation results (Fig. 1, 2). Fig. 1. Approximation results of the experimental data of the relative immersion rate Fig. 2. Approximation results of the experimental data of the relative displacement of purse seine Approximation error can be calculated using the following formula: where δА - approximation error; νА - relative immersion rate of the purse seine in approximation. Table 4 shows approximation error results of the relative immersion rate of the purse seine. Table 4 Approximation error results of the relative immersion rate of the purse seine Load; flow velocity Model 1 Model 2 Model 3 Linear regression Polynomial regression "linfit" function Linear regression Polynomial regression linfit” function Linear regression Polynomial regression "linfit" function 0 kg; 0.2 m/s 9.45 9.05 8.09 15.25 7.89 12.77 15.25 5.79 12.77 0.248 kg; 0.2 m/s 4.86 1.76 4.34 10.73 7.7 10.16 10.74 4.85 8.76 0.248 kg; 0.3 m/s 3.41 3.35 4.34 4.59 0.64 4.66 12.1 5.48 11.73 0.248 kg; 0.4 m/s 2.60 0.91 2.30 2.59 0 4.03 7.92 0.64 7.73 0.338 kg; 0.2 m/s 4.86 1.76 4.34 17.9 8.59 16.11 9.61 8.46 8.08 0.338 kg; 0.3 m/s 3.41 3.35 4.34 8.77 3.48 7.3 12.1 5.48 11.73 0.338 kg; 0.4 m/s 3.25 3.07 3.48 5.97 1.14 5.33 6.47 0 7.62 Table 5 shows approximation error results of the relative displacement of the purse seine in immersion. Table 5 Approximation error results of the relative displacement of the purse seine in immersion Load; flow velocity Model 1 Model 2 Model 3 Linear regression Polynomial regression "linfit" function Linear regression Polynomial regression "linfit" function Linear regression Polynomial regression "linfit" function 0 kg; 0.2 m/s 5.94 6.65 5.99 7.21 3.12 7.58 7.21 3.12 7.58 0.248 kg; 0.2 m/s 13.67 6.41 9.23 3.18 2.99 2.29 10.46 6.6 9.84 0.248 kg; 0.3 m/s 5.79 0.39 5.41 5.69 1.09 6.14 2 1.73 2.28 0.248 kg; 0.4 m/s 0.53 0.32 1.52 1.08 0 1.30 0.42 0.21 1.16 0.338 kg; 0.2 m/s 5.33 3.55 4.25 15.47 9.34 14.14 6.77 5.99 5.81 0.338 kg; 0.3 m/s 2.86 1.18 3.38 6.06 4.06 5.52 1.84 1.44 1.97 0.338 kg; 0.4 m/s 1.08 0.43 1.62 1.11 0.11 2.01 1.37 0 2.01 Table 6 shows overall error of the experiments with the purse seine models. Table 6 Overall error of the experiments with the purse seine models, % Load; flow velocity Model 1 Model 2 Model 3 0 kg; 0.2 m/s 13.70 11.41 9.08 0.248 kg; 0.2 m/s 9.13 10.88 12.36 0.248 kg; 0.3 m/s 6.82 7.94 10.12 0.248 kg; 0.4 m/s 7.72 7.66 7.61 0.338 kg; 0.2 m/s 7.65 14.76 13.37 0.338 kg; 0.3 m/s 7.42 9.96 9.88 0.338 kg; 0.4 m/s 9.53 7.84 10.08 Measurement accuracy is considered adequate when the error does not go beyond 15%.
References

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