Accuracy analysis of the Model experiments on dipping purse seine models at side stream Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

DOI: 10.24143/2073-5529-2017-4-43-48 UDC 639.2.081.117.4

V. V. Makarov, A. A. Nedostup

ACCURACY ANALYSIS OF THE MODEL EXPERIMENTS ON DIPPING PURSE SEINE MODELS AT SIDE STREAM1

Abstract. 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.

Key words: purse seine, approximation, mathematical model.

Introduction

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 L^, m Нж, m LB„, m Нп, m a, mm d, mm Ux uy Fo

1 10.0 1.16 0.210

2 10 2.1 7 1.5 6.0 0.4 0.7 0.714 0.133

3 10.0 0.95 0.190

LM - length of top selection in harness; H - height of seine in harness; LBn - length of top selection; Hn -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:

^ =

^instr I2 + f + f ^Y + f AJ + f idJ + f JfflL. 1

100% J {100% J {100% J {100% J

100%

100%

where 5tot - overall error of the experiment; Sinstr - relative instrumental error; Sc - relative cargo error;

1 The paper has been prepared in the framework of the RFBR grant "Mathematical, physical and simula-

tion modeling of net fishing gear and aquaculture" No. 15-08-00464-a.

2

5n - relative net webbing error; 5imm - relative error of purse seine immersion; 5dlsp - relative error of purse seine displacement; 5appr - relative approximation error. The relative error was calculated using the formula:

s

5 x = pi 100% , x

where 5x - relative deviation of the value; x - arithmetic mean value; s1 - absolute error of the value. Absolute error si is calculated using the formula:

S1 = ОХ X W

S1 = Оx X ^р,

where оx - mean square deviation of the values; tpa - Student's coefficient, which depends on the number of degrees of freedom (n - 1) and confidence probability p. Mean square deviation о x

а- =

Еы (^ - * )2

n ( n -1)

where n - number of measurements; x, - i-st element of measurement.

Table 2 shows the results of calculating the relative error of the measurement values.

Table 2

Error results

Relative error, ö

Model 1 Model 2 Model 3

Error СЛ "Й СЛ "Й СЛ "Й s /m s /m s /m s /m s /m s /m

<N m 4. <N m <N m

О .0 .0 .0 .0 .0 .0 .0 .0

Thread diameter, d 0.58% 1.19% 0.71%

Mesh size, a 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 = fx) 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 approxi-

f 0.2 ^ f 0.858> f0.448^

0.4 0.707 0.426

0.6 v = 0.783 ro = 0.448

0.8 0.8 0.435

, 1 J v 0.858J v 0.458J

mating function through all the experimental points. Using the least squares method, the most common is straight line approximation (linear regression), «-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:

t =

where t - relative immersion time of the purse seine; v - relative immersion rate of the purse seine; © -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 j-axis) are used. The linear regression is given by:

An (T )= A + B X T,

where

A = intercept ( t, v ), B = slope ( t, v ).

To calculate the polynomial regression, regress and interp functions are used. The polynomial regression of the 2nd degree is given by:

f2 (t) = a1 x t2 + a2 x t + a3.

To calculate approximation by a combination of functions, built-in "linfit" function is used. Approximating function is given by:

An (t)= a~+- + b sin(t). t +1

Let us plot on a graph and compare approximation results (Fig. 1, 2).

t i 0.9

: s

0.7 0.6

o,:

0.J 0.3 0.; 0.1 o1

Poly nomial regression

"Linfit" function

\

Linear regressi on

0.2j

0,5

0J5

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:

v - v„

5„ =

r А

VA

where SA - approximation error; vA - 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

Model 1 Model 2 Model 3

Load; flow velocity Linear ;gression ■a a •a .o a a 33 j? & "linflt" unction Linear ;gression ■a a •a .o a a « j? & linflt" unction Linear ;gression ■a a •a .2 a § « j? & "linflt" unction

Рч '- г- Рч '- Рч '-

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

Model 1 Model 2 Model 3

c "S c c "S c c "S c

Load; flow velocity s- .2 & % ij % s •§ © Cfl c © ÏS s- .2 & % ij % s •§ © Cfl c © ÏS s- .2 & % ij % s •§ © 5C c © ÏS

.5 Si £ Si S c .5 Si £ Si S c .5 Si £ Si S c

J & W) — S3 r <2 J & W) — S3 r <2 J eg & we — S3 r <2

£ £ £ Si £ Si

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

1. Makarov V. V., Nedostup A. A. Opyty s modeliami koshel'kovykh nevodov po pogruzheniiu nizhnei podbory [Experiments with models of purse seines on immersing the lower gear]. Sbornik materialov III Mezhdunarodnoi nauchno-tekhnicheskoi konferentsii «Aktual'nye problemy osvoeniia biolo-gicheskikh resur-sov Mirovogo okeana». Part I. Vladivostok, Dal'rybvtuz, 2014. P. 195-198.

2. Makarov E. G. Inzhenernye raschety v Mathcad 15 [Engineering calculations in Mathcad 15]. Saint-Petersburg, Piter Publ., 2011. 400 p.

3. Tarasevich Iu. Iu. Chislennye metody na Mathcad'e. Astrakhan, Izd-vo AGPU, 2000. 70 p. URL: http://www.ict.edu.ru/lib/index.php?a=elib&c=getForm&r=resDesc&d=light&id_res=4514 (accessed at: 20.07.2016).

4. Nedostup A. A., Makarov V. V. Postanovka zadachi vyvoda bezrazmernykh zavisimostei protsessa pogruzheniia setnoi stenki koshel'kovogo nevoda [Setting the task of derivation of dimensionless dependencies of submerging the wall net of the purse seine]. Izvestiia Kaliningradskogo gosudarstvennogo tekhnicheskogo universiteta, 2015, no. 39, pp. 55-62.

The article submitted to the editors 5.07.2017

INFORMATION ABOUT THE AUTHORS

Makarov Vyacheslav Valerievich — Russia, 236022, Kaliningrad; Kaliningrad State Technical University; Postgraduate Student of Commercial Fishery Department; vyacheslav .makarov @klgtu.ru.

Nedostup Alexander Alekseevich - Russia. 236022. Kaliningrad; Kaliningrad State Technical University; Candidate of Technical Sciences, Assistant Professor; Head of Commercial Fishery Department; [email protected].

В. В. Макаров. А. А. Недоступ

АНАЛИЗ ТОЧНОСТИ МОДЕЛЬНЫХ ЭКСПЕРИМЕНТОВ ПО ПОГРУЖЕНИЮ МОДЕЛЕЙ КОШЕЛЬКОВОГО НЕВОДА ПРИ УСЛОВИИ БОКОВОГО ТЕЧЕНИЯ

Цель исследования - анализ точности данных, полученных экспериментальным путем в 2014 г. в гидроканале ОАО «МариНПО» (Калининград). В ходе экспериментов осуществлялось погружение трех специально построенных моделей кошелькового невода с различной загрузкой нижней подборы (0; 0,248 и 0,338 кг) и при различной скорости течения (0,2; 0,3 и 0,4 м/с) - по 7 экспериментов для каждой модели (0 кг и 0,2 м/с; 0,248 кг и 0,2; 0,3 и 0,4 м/с; 0,338 кг и 0,2; 0,3 и 0,4 м/с). Для подтверждения достоверности полученных данных был проведен расчет общей погрешности, включающей в себя инструментальную погрешность; погрешность веса грузов; погрешность измерений дели, из которой были сделаны модели; погрешность погружения невода; погрешность смещения невода оси OY; погрешность аппроксимации. Для аппроксимации экспериментальных данных был выбран метод наименьших квадратов. Аппроксимация была проведена прямой линией (линейная регрессия), полиномом n-й степени (полиномиальная регрессия) и комбинацией произвольных функций. Наименьшая погрешность (6,82 %) была получена в эксперименте 0 кг и 0,3 м/с, наибольшая (14,76%) - в эксперименте 0,338 кг и 0,2 м/c. Учитывая, что точность измерений считается достаточной, когда погрешность не выходит за рамки 15 %, результаты экспериментов следует признать удовлетворительными.

Ключевые слова: кошельковый невод, аппроксимация, математическая модель.

СПИСОК ЛИТЕРА ТУРЫ

1. Макаров В. В., Недоступ А. А. Опыты с моделями кошельковых неводов по погружению нижней подборы // Сб. материалов III Междунар. науч.-техн. конф «Актуальные проблемы освоения биологических ресурсов Мирового океана». Ч. I. Владивосток: Дальрыбвтуз, 2014. С. 195-198.

2. Макаров Е. Г. Инженерные расчеты в Mathcad 15: учеб. курс. СПб.: Питер, 2011. 400 с.

3. Тарасевич Ю. Ю. Численные методы на Mathcad^. Астрахань: Изд-во АГПУ, 2000. 70 с. URL: http://www.ict.edu.ru/lib/index.php?a=elib&c=getForm&r=resDesc&d=light&id_res=4514 (дата обращения: 20.07.2016).

4. Недоступ А. А., Макаров В. В. Постановка задачи вывода безразмерных зависимостей процесса погружения сетной стенки кошелькового невода // Изв. Калининград. гос. техн. ун-та. 2015. № 39. С. 55-62.

Статья поступила в редакцию 5.07.2017

ИНФОРМАЦИЯ ОБ АВТОРАХ

Макаров Вячеслав Валерьевич - Россия, 236022, Калининград; Калининградский государственный технический университет; аспирант кафедры промышленного рыболовства; vyacheslav.m akarov @к1дШ.ги.

Недоступ Александр Алексеевич — Россия, 236022, Калининград; Калининградский государственный технический университет; канд. техн. наук, доцент; зав. кафедрой промышленного рыболовства; [email protected].