A study on the estimation of sea-waves influence on the working depth of towed underwater vehicle

Chia sẻ: Thi Thi | Ngày: | Loại File: PDF | Số trang:10

Thêm vào BST

Báo xấu

19
lượt xem 1
download

Download Vui lòng tải xuống để xem tài liệu đầy đủ

The article presents the problem associated with the influence of seawaves on the working depth of a towed underwater vehicle (TUV) including: defining transfer function (TF) of the towing cable - underwater vehicle system; analyzing the sea-wave’s features, modeling and defining the TF of filter which forms the sea-waves; estimating the TFs of the system (TC - UV) and researching the influence of sea-waves to the TUV’s working depth in the time domain.

Chủ đề:

Bình luận(0) Đăng nhập để gửi bình luận!

Lưu

Nội dung Text: A study on the estimation of sea-waves influence on the working depth of towed underwater vehicle

Nghiên cứu khoa học công nghệ A STUDY ON THE ESTIMATION OF SEA-WAVES INFLUENCE ON THE WORKING DEPTH OF TOWED UNDERWATER VEHICLE Nguyen Phu Dang1*, Pham Tuan Thanh1, Tran Xuan Tinh1, Dao Sy Luat2 Abstract: The article presents the problem associated with the influence of sea- waves on the working depth of a towed underwater vehicle (TUV) including: defining transfer function (TF) of the towing cable - underwater vehicle system; analyzing the sea-wave’s features, modeling and defining the TF of filter which forms the sea-waves; estimating the TFs of the system (TC - UV) and researching the influence of sea-waves to the TUV’s working depth in the time domain. Simulating and evaluating the influence of sea-waves on the TUV’s vertical oscillation for a specific system will be considered at the end of the article. The received results can be used for designing and manufacturing TUVs, building a regulator to stabilize the TUV’s working depth against sea-waves and damper, as well as designing other specialized underwater devices. Keywords: Towed underwater vehicle, Transfer function, Sea-waves model, Objects with distributed parameters, Estimation of transfer function, Sea-wave’s spectral density. 1. INTRODUCTION Recently, Towed Underwater Vehicles (TUV) have been powerfully developed due to their good capabilities of exploring the ocean environment. In comparison to Autonomous Underwater Vehicles (AUV), TUVs are able to work much longer and much deeper under the water, to communicate much easier and more exacte to the ship, and to survey the ocean floor more quickly. Basically, to operate a TUV, it is necessary to have a 3-part system including ship, towed cable (TC), and underwater vehicle (UV) as the illustration in Fig. 1. The towed cable is an essential device for both mechanical and electrical connections. Moreover, it is “very important to many marine meassurement and salvage operations” [1]. Figure 1: The 3-part system of ship, towed Figure 2: The main tasks of this research. cable, and UV. However, working with a towed cable, also called umbilical cable, in the ocean environment with the presence of sea waves is not easy for an UV. The sea waves regularly make the cable elastic. The elastic causes the UV to operate unsteadily. There have been many researches dealing with the influence of sea waves on the components of the 3-part system such as [2] evaluated sea-waves noise effect on the ship, [3] analysed the influence of water waves on an AUV, [4] proposed an algorithm to analyse the viscoelastic effect of sea water on the cable. Tạp chí Nghiên cứu KH&CN quân sự, Số 42, 04 - 2016 77 Kỹ thuật điều khiển & Điện tử In earlier works, many researchers achieved positive results in estimating the effect of sea waves on the towed cable [1, 5]. E.g. [5] developed a numerical model of the towed cable system by using series of differential equations to analyse discrete elastic elements along the cable. In a similar way, [1] performed modeling towed cable systems dynamics by dividing the cable system into discrete elements and formulating the equations of motion for the elements. The drawback of [5] and [1] is the use of a large number of differential computations. In our research, the simple calculations for estimating sea-waves influence on the towed underwater vehicle are proposed. The simple calculations are taken from the approximations of the complex mathematical equations for modeling the sea waves and modeling the TC-UV system. The main works of the research are illustrated on Fig. 2. 2. CONTENT OF THE STUDY 2.1. Modeling the TC-UV system Acording to [6], the TC – UV system contains distributed parameters. It can be described by the partial derivative differential equations or the integral equations, the integral-differential equations and many others,... which are more complex than the equations of objects with concentrated parameters. As a result, the TFs contain not only the high order rational fractions but also the inertial and transcendental expressions [6]. To model the structure of the TC - UV system in the form of TFs associated between displacement at the end of the cable attached to the UV x( L, s ) and traction at the cable's point attached to the winches T (0, s ) with displacement at the cable’s point attached to the winches x(0, s ) , we’ll consider a piece of cable as its axis coincides with the axis Oz when impacting the traction T, z is the cable’s length without load, y and x  y  z are cable’s length and its deformation with load (Fig. 3) respectively. Weight of the system (TC – UV) in the water; elastic force; inertial force occurs when speeding up the system (TC - UV) and water’s sticky mass as well as frictional force between the cable with water and cable’s frictional force are the main forces which act on the system (TC - UV). Figure 3: The surveyed model of cable´s piece and its deformation. In the specific conditions [7], the vertical oscillations of the cable’s cross section are described by differential equations: T  ET .F .x / z  .F . 2 x / z.t  , (1) 2 2 T / z  m. z / t   .x / t where, ET - cable’s elastic modulus, for the metal cables: ET  1,65.105 Mpa ; F - cable’s cross sectional area which equals the total area of the core’s cross sections [7];  - cable’s 78 N.P. Dang, P.T. Thanh, T.X. Tinh, D.S. Luat, “A study on… of towed underwater vehicle.” Nghiên cứu khoa học công nghệ friction coefficient; m - mass of a cable’s length per measurement unit (kg);  - the friction coefficient between the cable with water (s-1). After replacing   ET .F . mp to the first equation of (1) we have T  ET .F (x / z   mp . 2 x / z.t ) , (2) and after performing Laplace transform for the equations (1), (2) we have 2 T / z  m.s .x( z , s )   .s.x( z , s )  , (3) T  ET .F .(1   mp .s ).x( z , s ) / z with,  mp - time constant of cable’s internal friction (s). When performing Laplace transform for equations (3) according to the variable z, the linear algebraic equations are obtained, where T (0, s ), x(0, s ) - the images of traction (T) and the upper cable’s displacement, and u - argument of the Laplace image for the function of variable z: u.T (u , s )  T (0, s )  m.s 2 .x(u , s )   .s.x(u, s )  (4) T (u, s )  ET .F .(1   mp .s ).(u.x(u , s )  x(0, s )) Transforming the equations (4) into the Laplace image of the tractions of cable’s cross section from the distance z ( T (u , s ) ) and section’s displacement ( x(u , s ) ). After transforming them back to the original with variable z, we have:  z z T ( z , s )  T (0, s ).ch( w .r ( s ))  x(0, s ).Z w ( s ).sh( w .r ( s ))  , (5)  x( z , s )  x(0, s ).ch( z .r ( s ))  T (0, s ) .sh( z .r ( s ))  w Z w (s) w where, Z w ( s )  bw ( s 2   mp .s )(1   mp .s ), bw  m.w - the wave’s impedance; r ( s )  ( s 2   mp .s ) /(1   mp .s ) - propagation coefficient of oscillations in the operator; w  E T .F / m - wave’s propagation speed in the cable (m/s);  mp   / m - relative drag coefficient along the cable (1/s). Using Mason’s rules mentioned in [9] and the following relation T ( L, s )  (mno .s 2  kno .s ).x( L, s ) , (6) with, kno - water’s drag coefficient caused by vehicle’s movement; mno - vehicle’s mass in the water, the TFs which associate between displacement at the end of cable attached to the UV and traction at the cable's point attached to the winches with displacement at the point attached load will have form: 1 x ( L, s )  m .s 2  kno .s  Wx ( L, s )    ch( L .r ( s ))  no .sh( L .r ( s ))  (7) x(0, s )  Z w ( s)   T (0, s )  m .s 2  kno .s  WT (0, s )    Z w ( s ).Wx ( L, s )  sh( L .r ( s ))  no .ch( L .r ( s ))  , (8) x(0, s )  Z w ( s)    where,  L  L / w - wave’s propagation time along the cable. In this case, the traction and the static deformation are neglected. Therefore, TFs (7) and (8) can be used not only for the vertical cable but also for the cable deviating from the vertical axis because of Tạp chí Nghiên cứu KH&CN quân sự, Số 42, 04 - 2016 79 Kỹ thuật điều khiển & Điện tử hydrodynamic forces, which are generated by the ship’s movement and TUV’s operation. For the cable “KGP-1-20” which has external diameter 23,4mm; m  1,63kg / m ; w  4020m / s ;  mp  0,01s;   0,05s 1 , and TUV with kno  1800kg / s; mno  5860kg , the TF (7) becomes: 1  L s2  0,0307s 5860.s2 1800.s L s2  0,0307s  Wx (L, s)  ch( . ) .sh( . ) (9)  4020 1 0,01s 6552,6. (s2  0,0307s)(1 0,01s) 4020 1 0,01s    2.2. Random sea-waves model Sea-waves are a nonstationary random process which has chaotic features. Each of sea- waves has a different amplitude and period. During the short time, sea-waves can be considered a stationary mechanical process. This simplifies the mathematical descriptions as well as the survey on the sea-wave’s influence on the various objects or the ship’s lurch. When the wave’s peaks  compliance with the rules of normal distribution [9], the spectral density of wave’s peaks can be defined based on the variance D and its expectations m by the following expression: 1  (  m )2  f ( )  exp   . (10) 2 D  2 D    The expectation and the variance do not allow us to realize the random process. To perform this, first its spectral density needs to be defined. For sea-waves, the expectation of wave’s peaks  equals zero, and correlation function K ( ) is defined by multiplying  (t ) by  (t   ) over time, where   t2  t1 , and T is the observation time to realize the private process T 1 K ( )   (t ) (t   )d ; T   (11) T 0 There is a relationship between the correlation function K ( ) and the spectral density S ( ) of the process  (t ) through the Fourier transform:  S ( )  2  K ( ) cos( )d (12) 0 There are many different ways to calculate the spectral density S ( ) of the sea- waves. In this case, we will just cite one of typical spectral calculated formulas. In accordance with results from [7, 9], the normalized spectral density of sea-waves is defined by expression S  12 ( x )  5 . x 5 exp(  1, 25. x  4 ) (13) with relative frequency: x   /  m ;  m  0, 7 1 ( m - spectrum’s maximum frequency,  - sea-wave’s average angular frequency). To receive some random process with given spectral density such as (13), the white noise which has constant spectral density at all angular frequencies   [0, ) need to be 80 N.P. Dang, P.T. Thanh, T.X. Tinh, D.S. Luat, “A study on… of towed underwater vehicle.” Nghiên cứu khoa học công nghệ transformed by using the filter, so that its TF is rational fraction and squared amplitude- frequency characteristic of this filter approximates the given spectral density. Therefore, a rational fraction that is closest to the exponential original of (13) needs to be defined. One of the typical algorithms used for estimating (13) is presented in [10]. The received approximate expression is: 4,34 x 6 s36 ( x)  (14) ( x 4  1,18 x 2  0,52)( x 4  1,38 x 2  1, 29)( x 4  2,95 x 2  11,73) The TF of the filter that forms sea-waves on the basis of expression (14) needs to be defined. The squared amplitude-frequency characteristic (the module of this filter) associated with spectral density through expression [10]: s ( x)  W f ( jx)W f ( jx) (15) In general , when the estimated spectrum ( x 2 )n s ( x)  As ( n  3) / 2 , (16) 4 2  ( x  n1i x  n0i ) i 1 satisfies the conditions of module: n - the odd numbers, and n1i - the real numbers with n1i  2 n0i , n0i  0 , then the filter’s TF becomes: sn W f ( s)  A f ( n 3) / 2 (17) 2  ( s  b1i s  b0i ) i 1 where: A f  As ; b0i  n0i ; b1i  2 n0i  n1i . Therefore, the TF of filter matching with estimated expression (13) will get the form: 3,694s 3 W f ( s)  (18) ( s 2  0,5111s  0,7208)( s 2  0,9465s  1,136)( s 2  1,974s  3, 425) Sea-waves impact on the TUV through the ship’s lurch. When the ship lurches, the point attached to the load (that is the end of cable which goes out of the winches put on the ship, then connected to the TUV) will oscillate. The TF associated between Laplace images of the vertical displacement at the point attached to the load x0 ( s) and the sea- waves  ( s ) becomes x0 ( s ) 2 W  s    (19)  (s) 2 3 s   s  2 2 0,8 where,   is the particular angular frequency [6,7]. T 2.3. The estimation of transfer functions There are the certain difficulties simulating the influence of sea-waves on the TUV’s working depth on the basis of (7). These difficulties stem from the TF Wx ( L, s) containing the inertial and transcendental expressions. The mathematical tools only allow us to perform with such expressions in the frequency domain, and cannot survey the object matching with this TF in the time domain. To solve this problem, it is necessary to Tạp chí Nghiên cứu KH&CN quân sự, Số 42, 04 - 2016 81 Kỹ thuật điều khiển & Điện tử perform an intermediate estimated step for transforming the complex TFs into rational expressions [11,12]. After replacing hyperbolic functions in (7) by the exponential correspondence, the TF becomes s 2  vmp s  L 1 mp s 2e Wx ( L, s )  (20) s 2  vmp s  s 2  vmp s  2 L 2 L 1 mp s mno s 2  kno s  1 mp s  1 e  .1  e  mw. ( s 2  vmp s )(1   mp s )     The function (20) by the rational fractions can be estimated in two ways: By estimating each of inertial and transcendental components by a rational fraction and then replacing these expressions to the original (20); By estimating a unique approximated expression using numerical method which will be considered in other studies. When following the first way, the wave TF s s Yw   , (21) Z w m.w. ( s 2   s )(1   s ) mp mp and the spread function of oscillation in the cable  s 2  vmp s   Wx  exp  L .  (22)  1   mp .s    will be estimated by the rational fractions. To estimate Yw , we express it by the product of two functions: Y (specific to friction of the cable with water) and Y (specific to friction in the cable):  mp Yw  Y .Y ; Y  s / ( s 2   mp s )  1/ (1  ); Y  1/ (1   mp s ) (23) s and then estimate each of the items [11]. The estimated algorithm for the function Y is as follows: 1- Replacing the variable s by the variable  mp .r and transform expression Y to r Y (r )  ; 2- Establishing the function: f  r 2  r  r ; 3- Performing Pade’s 2 r r estimation for the function f using Chebyshev’s polynomials in the previous segment by rational function f a so that the numerator’s order equals to the denominator’s order r ( m  n ); 4- Defining function f a1 by the formula: f a1  ; 5- The last estimated fa  r s expression Y a of the function Y is obtained by replacing r  to the function f a1 . v When performing according to this procedure with estimated segment [0.0002,0.2], the five order estimated function Y a is shown as: (s  0,4048vmp )(s  0,08523vmp )(s  0,01476vmp )(s  0,001161vmp )s Yva  (24) (s  0,7668vmp )(s  0,1883vmp )(s  0,03712vmp )(s  0,004918vmp )(s  0,0001296vmp ) 82 N.P. Dang, P.T. Thanh, T.X. Tinh, D.S. Luat, “A study on… of towed underwater vehicle.” Nghiên cứu khoa học công nghệ The component Y is estimated as follows: 1- Establishing the function: 1 q 1 f  ; q   mp .s ; 2- Performing Pade’s approximation for the function f using q Chebyshev’s polynomials in the previous segment by rational function f a so that the numerator’s order equals to the denominator’s order ( m  n ); 3- Finding out the function 1 f a1 by the formula: f a1  ; 4- The last estimated expression Y a is obtained by f a .q  1 replacing q   mp .s to the function f a1 . With the estimated piece [0.0002,0.2], the estimated function Y a is performed as follows: (1  0,4048 mp .s)(1  0,0852 mp .s)(1  0,0148 mp .s)(1  0,0012 mp .s) Y a  (25) (1  0,7668 mp .s)(1  0,1883 mp .s)(1  0,0371 mp .s)(1  0,0049 mp .s)(1  0,00013 mp .s) The function Wx is estimated by transforming it to the equivalence form  L W  W .W  exp(  s .( s  v )  s )  (1 /(1   . s )  m p )  x xv x mp mp , (26)  L   W xv  exp(  s .( s  v )  s ), W x  1 /(1   m p .s ) m p and then estimate each of them. The element Wxv is estimated through the following steps: 1- Establishing function f r1 according to expression: f r1   mp ( r (r  1)  r ); r  s / mp ; 2- Defining the function f r 2 by the formula: f r 2  f r1 / vmp .r ; 3- Performing Pade’s estimation for the function f r 2 using Chebyshev’s polynomials in the previous segment by rational function f r 2 a with the numerator’s order ( m  3 ) and the denominator’s order ( n  4 ); 4- Defining the function f f s 2 a by formula: f s 2 a  r 2 a ; r  s / vmp ; 5- The estimated expression Wxva for the vmp .r 0,5.v mp (1  e ) original Wxv is defined by using formula: Wxva  1  f s 2 a .k ; k  . The 0,5.vmp estimated TF Wxva with estimated piece [0.0001, 1] becomes: 0,9986(1  exp(0,5vmp )) L (s  0,3925vmp )(s  0,0598vmp )(s  0,0033vmp )s Wxva  1  (27) (s  0,5518vmp )(s  0,1327vmp )(s  0,0152vmp )(s  0,00032vmp ) The ingredient Wx is estimated by the Bessel’s polynomials Bn ( s) . The estimated function Wx a becomes: m   a  Wx a  exp((1  a).s ). Wbn  s   ; a  1 (28)   m  Bn (0) where Wbn ( s )  with Bn ( s) – n-th order Bessel polynomial, and Bn (0) is its value Bn ( s ) when s  0 . when m  2; n  4 , the estimated function Wx a becomes: Tạp chí Nghiên cứu KH&CN quân sự, Số 42, 04 - 2016 83 Kỹ thuật điều khiển & Điện tử   0,5 mp    11025exp110.  .L.s      L    mp  0,5 Wxa  2 2 ;a 3,6.  (29)    0,5    0,5   L  25a2mpLs2 28,962. mp  Ls 9,14 25a2mpLs2 21,09. mp  Ls 11,48    L     L    with  L  50 mp , L  0,5s . In the domain  L  0,5  0,1 , the estimated functions with smaller order of denominator are used to reduce the estimated errors 0,5 105exp((1  a) L s)   mp  Wx a  ; a  2,5.  (30)   (a L s)2  5,792a L s  9,1401) (a L s)2  4,2076a L s  11,484)   L  2.4. Evaluating the sea-waves influence on the change of TUV´s depth With the filter forming the sea-waves which has the TF (18), the TF which defines the change of TUV’s working depth by acting of sea-waves becomes: W fL ( s )  W f ( s )W ( s )Wx ( L, s ) , (31) where W ( s ) - the TF which represents the relationship between the vertical displacement of the point attached to the load x0 and wave peaks  (19); Wx ( L, s ) - the TF which represents the relationship between the UV’s vertical displacement and cable’s point attached to the winches x0 (9). Based on the above results, Fig. 4 shows the structure diagram which simulates the influence of sea-waves on the change TUV’s depth using (31) and the estimated expressions (18), (19), (24), (25), (27), (29), in which, blocks “Transfer fnc”, “Transfer Fnc1”, “Transfer Fnc2” describe the filter forming sea-waves (18), it represents the change of wave peaks over time. The block "Transfer Fnc3" represents vertical displacement of the point attached to the load, which described by the transfer function (19) with   1 . The block "Transfer Fnc4" matches the transfer function: 1/(mno .s  kno ) . Subsystem, Subsystems 1,2,3,4 are created by the blocks "Transfer Fnc" and "Transport Delay", they match with the estimated expressions (24,25,27,29). The calculation was performed for the cable “KGP-1-20” and the simulating results are showed on the Fig. 5. Figure 4: The structure diagram evaluates the change of TUV’s depth under the sea-waves. Fig. 5a shows that the ship plays the role of a low-pass filter. Displacement of point attached to the load will be slower than the wave peaks, and the fast oscillating 84 N.P. Dang, P.T. Thanh, T.X. Tinh, D.S. Luat, “A study on… of towed underwater vehicle.” Nghiên cứu khoa học công nghệ components were eliminated. Fig. 3b reflects the complex process in the system (TC - UV). In this case, when simulating the change of TUV’s working depth, the delay due to wave’s spread along the cable was neglected, in which, the displacement of the cable’s end attached to the UV will be slower than the displacement of point attached to the load, with L  8km , a period  L  L / w  2s . a) b) Figure 5: The acting of sea-waves to the system (Ship – TC – UV). a) The change of wave peaks (line (1)) and displacement of point attached load (line (2)); b) The change of TUV’s working depth (line (1)) and displacement of point attached load (line (2)). 3. CONCLUSION The paper presents the solution for estimating influence of sea-waves on the TUV’s working depth. This solution are performed with the following activities: modeling the structure of the TC - UV system, modeling the random form of sea-waves, estimating the expressions of sea-wave’s spectrum and ship’s lurch. The proposed solution is successfully tested on the Matlab – Simulink simulation experiments. Based on this solution, it is possible to carry out other research on synthesizing and evaluating the automatic control system to stabilize the TUV’s working depth by a cable by adjusting according to the noise (random sea-waves). REFERENCES [1]. Kamman J. W., T. C. Nguyen, and J. W. Crane. “Modeling Towed Cable Systems Dynamics”. Proceeding of OCEANS, vol. 5, pp. 1484-1489, 1989. [2]. Patterson A. M., J. H. Spence, and R. W. Fischer. “Evaluation of underwater noise from vessels and marine activities”. In the IEEE/OES RIO Acoustics Symposium, pp. 1-9, 2013. [3]. Sgarioto D. E. “The influence of shallow water waves on the REMUS autonomous underwater vehicle”. DTA Report, ISSN 1175-6594, 2011. [4]. Bezverkhii A. I., V. F. Kornienko, and N. A. Shul´ga. “The viscoelastic effect of the cable on the dynamics of an underwater towed system suspended from a buoy”. In the International Applied Mechanics, Vol. 37, No. 8, 2001. [5]. Buckham B., M. Nahon. “Dynamics and control of a towed underwater vehicle system, part I: model development”. Ocean Engineering 30 (2003) 453–470. [6]. Рапопорт Э.Я. “Анализ и синтез систем автоматического управления с распределенными параметрами”. Э.Я. Рапопорт. - М.: Высш. шк., 2005. [7]. Судовые устройства: Спровочник/ Под ред. М.П. Александрова. – Л.: Судостроение, 1987. – 656с. [8]. Герасимова Г.Н. и другие. “Топологические методы анализа в электротехнике и Tạp chí Nghiên cứu KH&CN quân sự, Số 42, 04 - 2016 85 Kỹ thuật điều khiển & Điện tử автоматике”: - Владивосток: Дальнаука, 2001.-232с. [9]. “Справочник по теории корабля”: В 3-х т. Т. 2. Статика судов. Качка судов. Судовые движители/ Под ред. Я.И. Войткунского. – Л.: Судостроение, 1985. – 440с. [10]. Мошиц Г., Хорн П. “Проектирование активных фильтров”. – М.: Мир, 1984.– 320с. [11]. Демидович, Б.П., “Основы вычислительной математики”, Б. П. Демидович, И. А. Марон. — 5-е изд., стер. — СПб.: Лань, 2006. — 672 с. [12]. Gubarev V. F., “Rational Approximation of distributed parameter systems”, J. Cybernetics and Systems Analysis. – 2008. – Vol. 44. – №2. – Pp. 234-246. TÓM TẮT NGHIÊN CỨU ĐÁNH GIÁ SỰ ẢNH HƯỞNG CỦA SÓNG BIỂN ĐẾN ĐỘ SÂU HOẠT ĐỘNG CỦA THIẾT BỊ THÁM HIỂM DƯỚI NƯỚC ĐƯỢC LAI DẮT BẰNG DÂY Bài báo trình bày các vấn đề có liên quan tới sự ảnh hưởng của sóng biển đến độ sâu hoạt động của các thiết bị thám hiểm dưới nước không người lái được lai dắt bằng dây bao gồm: Xác định hàm truyền của hệ dây- thiết bị thám hiểm. Phân tích các đặc trưng sóng, mô hình hóa sóng biển và xác định hàm truyền của bộ lọc hình thành sóng biển. Xem xét vấn đề xấp xỉ hóa hàm truyền của hệ dây – thiết bị và khảo sát tác động của sóng biển đến độ sâu hoạt động của thiết bị trong miền thời gian. Phần cuối bài báo tiến hành mô phỏng sóng biển và đánh giá tác động của sóng biển đến sự dao động của thiết bị theo phương thẳng đứng đối với một hệ dây – thiết bị cụ thể. Các kết quả của bài báo có thể được sử dụng khi thiết kế chế tạo các thiết bị thám hiểm dưới nước được lai dắt bằng dây đặc biệt là khi xây dựng các bộ điều chỉnh ổn định độ sâu hay bộ giảm chấn gắn trên thiết bị thám hiểm, cũng như việc thiết kế các thiết bị chuyên dụng khác. Từ khóa: Thiết bị thám hiểm dưới nước, Hàm truyền, Mô hình hóa sóng biển, Đối tượng có tham số phân bố, Xấp xỉ hóa hàm truyền, Mật độ phổ sóng biển. Nhận bài ngày 31 tháng 3 năm 2016 Hoàn thiện ngày 14 tháng 4 năm 2016 Chấp nhận đăng ngày 20 tháng 4 năm 2016 Địa chỉ: 1Học viện Kỹ thuật quân sự- 236 Hoàng Quốc Việt Bắc Từ Liêm Hà Nội. 2 Đại học Đồng Nai – Số 4 Khu phố 3 Lê Quý Đôn, Biên Hòa, Đồng Nai. * Email: npdangdtys@yahoo.com.vn 86 N.P. Dang, P.T. Thanh, T.X. Tinh, D.S. Luat, “A study on… of towed underwater vehicle.”