CN111964670A - Array accelerometer-based ship six-degree-of-freedom motion measurement method - Google Patents

Array accelerometer-based ship six-degree-of-freedom motion measurement method Download PDF

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CN111964670A
CN111964670A CN202010629505.XA CN202010629505A CN111964670A CN 111964670 A CN111964670 A CN 111964670A CN 202010629505 A CN202010629505 A CN 202010629505A CN 111964670 A CN111964670 A CN 111964670A
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焦甲龙
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South China University of Technology SCUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B79/00—Monitoring properties or operating parameters of vessels in operation
    • B63B79/10—Monitoring properties or operating parameters of vessels in operation using sensors, e.g. pressure sensors, strain gauges or accelerometers
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B79/00—Monitoring properties or operating parameters of vessels in operation
    • B63B79/20—Monitoring properties or operating parameters of vessels in operation using models or simulation, e.g. statistical models or stochastic models
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/203—Specially adapted for sailing ships
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M10/00—Hydrodynamic testing; Arrangements in or on ship-testing tanks or water tunnels

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Abstract

The invention discloses a ship six-degree-of-freedom motion measurement method based on array accelerometers, wherein two accelerometers are respectively arranged at a ship bow and a ship stern and are respectively used for measuring the vertical acceleration and the transverse acceleration at the ship bow and the ship stern; two accelerometers are symmetrically arranged on the left and right sides of the middle part of the ship and used for measuring vertical acceleration; an accelerometer is arranged at the position of the centre of gravity of the hull for measuring the longitudinal acceleration. The invention can measure the six-degree-of-freedom movement of the ship by adopting seven accelerometers, and compared with the traditional contact type mechanical airworthiness instrument or non-contact type optical measuring instrument, all the accelerometers are fixedly arranged in the ship body and move along with the ship body, so that an additional fixed platform or an onshore base station is not required to be used as a reference datum. The method can be applied to ship model motion measurement in a water pool laboratory and ship motion attitude measurement in a real sea area environment.

Description

Array accelerometer-based ship six-degree-of-freedom motion measurement method
Technical Field
The invention relates to the technical field of ship tests, in particular to a ship six-degree-of-freedom motion measurement method based on an array type accelerometer.
Background
Different from the sailing state in the static water, when the ship sails in the waves, the six-degree-of-freedom swaying motion can be generated besides the linear motion along the sailing speed direction. The reciprocating oscillations of the vessel along the longitudinal (OX axis), transverse (OY axis) and vertical (OZ axis) axes through its centre of gravity G, respectively called surging, swaying and heaving motions, belong to the linear displacement motion; the angular oscillations of the vessel about the three axes OX, OY, OZ are called roll, pitch and yaw motions, respectively, which are angular displacement motions.
The effect of a ship's six-degree-of-freedom swaying motion in waves on the navigation performance of the ship is manifold and often harmful. For example, severe rolling can move cargo in the tanks, causing personnel on the vessel to sea and equipment to become less capable, and can even cause the vessel to overturn. Severe pitching and heaving motion induced slamming of the bow and bottom can cause structural damage and induced surging of the deck can cause water ingress into the cabin and damage to deck equipment. The swaying motion of the aircraft carrier is an important factor influencing the take-off and landing of the carrier-based aircraft. The marine accident caused by the violent swaying motion of the ship under the severe sea condition happens frequently, and the research and evaluation of the motion performance of the ship in the waves is one of the important tasks in the design stage of the ship.
The wave resistance of the ship is an important subject for researching the moving performance of the ship in waves, and the design and development of an excellent ship type, the research and development and application of anti-rolling equipment, the evaluation of ship navigation safety and the like can be guided by reasonably forecasting the moving characteristics of the ship under different wave conditions. The wave resistance test of the ship is an important task content in the design stage of the ship, and generally comprises a model test and a real ship test. The model test adopts a reduced scale model to measure the ship model motion response under the waves generated by the wave generator in the pool environment, and the real ship test adopts a real ship to carry out the test in the real sea wave environment.
In the pool model test, a contact type mechanical airworthiness instrument or a non-contact type optical measuring instrument is generally adopted to record a motion signal of a ship model, the contact type mechanical airworthiness instrument is generally installed and fixed on a trailer, and a camera of the non-contact type optical measuring instrument is generally installed and fixed on the trailer or the ground. In short, the two types of seaworthiness instruments need to obtain the motion information of the ship model through measurement of the relative motion between the ship model and a reference platform by means of a stable fixed reference platform and further analysis. In addition, there are many other limitations to these two types of measurement methods. For example, the connecting rod of the mechanical airworthiness instrument contacted with the ship model has certain mass, so that the weight distribution of the model is different from the actual situation. The joint of the seaworthiness instrument and the ship model has a constraint acting force on the model, so that the stress condition of the ship model has a certain difference from the real condition. Mechanical airworthiness instruments can only measure motion in 3 to 5 degrees of freedom of the ship model, and it is difficult to measure motion in all 6 degrees of freedom. The non-contact optical measuring instrument is generally only suitable for the condition that a ship model does small-amplitude motion, when the motion amplitude or range of the ship is too large, the measurement precision is obviously reduced due to the problem of strong nonlinear numerical values, and the model cannot normally work when exceeding the visual field range captured by a lens.
On the other hand, in the real-vessel offshore test, since it is difficult to find a reference platform which translates along with the vessel, the offshore test generally adopts a complex and expensive inertial navigation system to measure the accelerations of three linear displacements and three angular displacements at the position of the center of gravity of the vessel. Although theoretically, the measured acceleration signal can be integrated for the first time to obtain corresponding speed information and integrated for the second time to obtain corresponding displacement information, the problems of measurement error, numerical calculation accuracy and the like exist. For example, long acceleration integration processes can result in divergence of velocity or displacement signals and drift of velocity or displacement zero, often with unsatisfactory results. In addition, the inertial gyroscope is heavy, difficult to use on small ship models, requires a large amount of electric energy for its operation, and is expensive to purchase.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art and provides a ship six-degree-of-freedom motion measurement method based on an array type accelerometer, which does not need an additional fixed platform or an onshore base station as a reference datum, and can be applied to ship model motion measurement in a pool laboratory and ship motion attitude measurement in a real sea area environment.
The purpose of the invention can be realized by the following technical scheme: a ship six-degree-of-freedom motion measurement method based on an array type accelerometer is characterized by comprising the following steps:
two accelerometers are respectively arranged at the bow and the stern and are respectively used for measuring the vertical acceleration and the transverse acceleration at the bow and the stern; two accelerometers are symmetrically arranged on the left and right sides of the middle part of the ship and used for measuring vertical acceleration; arranging an accelerometer at the position of the center of gravity of the ship body for measuring longitudinal acceleration;
establishing an inertial translational coordinate system O-XoYoZo, wherein the coordinate system keeps the same navigational speed and course angle with the ship and does uniform linear motion; establishing a fixed coordinate system G-XYZ fixedly connected with the ship body, wherein the coordinate system is fixed on the ship body and keeps relatively static with the ship body at any time;
the point G is the center of gravity of the ship, and the second derivative of the position variable at the center of gravity G to the time t can be expressed as the following formula:
Figure BDA0002567925140000031
wherein: a is a conversion matrix of an inertial coordinate system and a position vector fixedly connected in a ship body coordinate system; g is a gravity acceleration array; a isi(i-1, …,7) represents the output signal of the ith accelerometer, Ri(i-1, …,7) represents the distance of the ith accelerometer from the origin of coordinates in a coordinate system attached to the hull;
Figure BDA0002567925140000032
the nonlinear system of the angular velocity of the hull motion can be expressed as the following formula:
Figure BDA0002567925140000033
wherein ω isx、ωy、ωzThe angular speeds of rotation of the hull about three axes of a fixed coordinate system, F1(t)、F2(t)、F3(t) are respectively:
Figure BDA0002567925140000034
solving the equation (11) to obtain the angular velocity of the motion of the ship body, and obtaining three angular displacements of the motion of the ship body according to the angular velocity;
from the three angular displacements, a transformation matrix a can be obtained, so that the second integral of equation (6) can obtain three linear displacements at the hull center of gravity point G.
As a preferred technical solution, xo (Q) is defined as a position vector of an arbitrary point Q in space in an inertial coordinate system O-XoYoZo, and x (Q) is defined as a position vector of a point Q in space in a coordinate system G-XYZ fixed to the hull, where the following relationship exists between the two:
Xo(Q)＝Xo(G)+AX(Q) (1)
taking the position variable in equation (1) as the second derivative of time t, considering that x (q) is a constant matrix, we can obtain:
Figure BDA0002567925140000041
by substituting the position coordinate information of the accelerometer into equation (3) and taking into account the influence of the gravitational acceleration g in the inertial coordinate system being [0,0, g ], it is possible to obtain:
Figure BDA0002567925140000042
according to the principles of vector superposition and coordinate transformation, the following can be rewritten:
Figure BDA0002567925140000043
as a preferred technical solution, it is proposed that,
Figure BDA0002567925140000044
wherein theta is a pitch angle,
Figure BDA0002567925140000045
The roll angle and psi is the yaw angle.
As a preferred technical scheme, A represents orthogonal transformation, then A-1The inverse matrix of A also represents the orthogonal transform and is equal to the transpose of ATI.e. A-1＝AT。
As a preferable technical scheme, the position information and the measurement information of other six accelerometers except the accelerometer at the gravity center point G are substituted into the equation (3), so that a nonlinear system equation (11) of the ship motion angular velocity can be obtained.
As a preferred technical scheme, the equation (11) is solved by adopting time domain stepping, and the angular speed omega at the k-th step time isx(k,t)、ωy(k,t)、ωz(k, t) is known, and the nonlinear system equation (11) can be solved by a stepwise iterative method as follows:
Figure BDA0002567925140000046
the angular velocity at the initial moment is: omegax(0)＝ωy(0)＝ωz(0)。
As a preferred solution, the angular velocity ω, i.e., (ω), can be directly solved by equations (11) and (12) based on the measured acceleration signalx,ωy,ωz) The following angular displacement formula is obtained:
Figure BDA0002567925140000051
solving equation (13) can obtain three angular displacements of ship motion, namely Euler angles
Figure BDA0002567925140000052
θ、ψ。
As a preferred solution, the integral at the left end in equation (13) can be solved by fourier transform and its inverse:
Figure BDA0002567925140000053
wherein F (x) and F-1(x) Respectively, a Fourier transform function and an inverse Fourier transform function, f (t) can represent an arbitrary function, and h (t) is a time derivative of f (t).
As a preferred solution, the output signals of the four accelerometers for measuring vertical acceleration are not independent.
As a preferred technical solution, the following relationship exists between the output signals of four accelerometers for measuring vertical acceleration:
Figure BDA0002567925140000054
wherein R is1、a1Respectively representing the distance between an accelerometer which is positioned at the bow of the ship and used for measuring the vertical acceleration and a gravity center G point and the measured acceleration value; r2、a2Respectively representing the distance between an accelerometer which is positioned at the stern and used for measuring the vertical acceleration and a gravity center G point and the measured acceleration value; r5、R6，a5、a6The distance between two accelerometers located in the middle of the ship and measuring the vertical acceleration and the gravity center G point and the measured acceleration value are respectively shown.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the accelerometers adopted by the invention are fixedly arranged in the hull and move along with the hull, so that an additional fixed platform or an onshore base station is not needed as a reference datum. The method can be applied to ship model motion measurement in a water pool laboratory and ship motion attitude measurement in a real sea area environment.
2. The invention only needs to adopt the single-axis accelerometer for measurement, thereby avoiding the problems of large mass, high acquisition cost, large consumption of electric energy for work and the like of adopting an inertial navigation system. The whole scheme has low cost and strong applicability.
Drawings
FIG. 1 is a schematic view of an accelerometer in an embodiment of the invention;
FIG. 2 is a schematic diagram illustrating the definition of two coordinate systems according to an embodiment of the present invention;
fig. 3 is a schematic diagram of the arrangement and the measuring direction of the accelerometer on the ship hull in the embodiment of the invention.
Wherein: 1: an accelerometer located on the bow for measuring vertical acceleration, 2: an accelerometer located at the stern for measuring vertical acceleration, 3: an accelerometer positioned on the bow for measuring the lateral acceleration; 4: an accelerometer for measuring lateral acceleration located at a stern, 5: an accelerometer for measuring vertical acceleration on the port side in the middle of the ship, 6: an accelerometer for measuring vertical acceleration on the starboard side in the middle of the ship, 7: an accelerometer located at the center of gravity of the hull for measuring longitudinal acceleration, R1: distance of accelerometer to center of gravity G point, labeled 1, R2: distance of accelerometer, reference number 2, to point of gravity G, R3: distance of accelerometer to center of gravity G point, labeled 3, R4: distance of accelerometer to center of gravity G point, labeled 4, R5: distance of accelerometer to center of gravity G point, labeled 5, R6: distance of the accelerometer, reference number 6, to the point of center of gravity G.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
As shown in fig. 1, seven single-axis acceleration sensors are employed in the present embodiment, and these acceleration sensors are arranged at the same level inside the hull. Two accelerometers are respectively arranged at the bow and the stern and are respectively used for measuring the vertical acceleration and the transverse acceleration at the bow and the stern, and the corresponding labels of the accelerometers are respectively 1, 3, 2 and 4. Two accelerometers are symmetrically arranged on the left and right sides of the middle part of the ship and used for measuring vertical acceleration, and the corresponding labels of the accelerometers are 5 and 6. An accelerometer, corresponding to the reference numeral 7, is arranged at the position of the centre of gravity of the hull for measuring the longitudinal acceleration.
As illustrated in fig. 2, to solve the vessel motion signal based on the measured acceleration time history signal, we introduce two right-handed rectangular coordinates:
1) the inertial translational coordinate system O-XoYoZo keeps the same navigational speed and course angle with the ship and does uniform linear motion, so that the influence of the navigational speed of the ship is counteracted, and the problem is simplified into that the ship does six-degree-of-freedom swinging motion at a static balance position.
2) A fixed coordinate system G-XYZ fixedly connected with the ship body, wherein a G point is the gravity center of the ship, GX points to the bow, and the direction pointed by the GX is called as the longitudinal direction; GY points to the port, and the direction in which GY points is called transverse; the GZ points upward, and the direction in which the GZ points is referred to as the vertical direction. The coordinate system is fixed on the ship body and keeps relative static with the ship body at any moment, namely, the coordinate system does the same motion in an inertial coordinate system along with the six-freedom-degree motion of the ship body.
When the ship is in a static state, a coordinate system G-XYZ fixedly connected with the ship body coincides with an inertial coordinate system O-XoYoZo. When the ship does swinging motion, the coordinate difference value of the position point on the ship between the coordinate system G-XYZ fixedly connected with the ship body and the inertial coordinate system O-XoYoZo is the ship motion displacement.
Defining Xo (Q) as a position vector of any point Q in space in an inertial coordinate system O-XoYoZo, and X (Q) as a position vector of the point Q in space in a coordinate system G-XYZ fixedly connected with the ship body, wherein the following relations exist between the two points:
Xo(Q)＝Xo(G)+AX(Q) (1)
wherein, A is a transformation matrix of the inertial coordinate system and a position vector fixedly connected in the hull coordinate system, and can be expressed as:
Figure BDA0002567925140000071
wherein the euler angles have the following meanings: theta is a longitudinal rocking angle,
Figure BDA0002567925140000072
The roll angle and psi is the yaw angle. Since A represents an orthogonal variationAlternatively, then A-1The inverse matrix of A also represents the orthogonal transform and is equal to the transpose of ATI.e. A-1＝AT。
Now, taking the second derivative of the position variable in equation (1) with respect to time t, considering that x (q) is a constant matrix, we can obtain:
Figure BDA0002567925140000073
the position coordinate information of the accelerometers, numbered 1,2, 3, 4, 7, is substituted into formula (3), and both ends of the vector equation are respectively multiplied by the unit vector of the measurement direction of each accelerometer, so as to obtain:
Figure BDA0002567925140000081
wherein, i ═ {1,0,0}TA unit vector in the X direction; j ═ {0,1,0}TIs a unit vector in the Y direction, k ═ 0,0,1}TAnd is a unit vector in the Z direction.
The dot product in formula (4) is a scalar, and can be regarded as 5 scalar equations. The first equation and the second equation both represent acceleration information in the Z direction, the third equation and the fifth equation represent acceleration information in the Y direction, and the fifth equation represents acceleration information in the X direction. According to the interpolation principle, the first two-equation and the third four-equation are combined to obtain equation information at the coordinate origin G, and three scalar equations in the equation set are rewritten into a matrix form. Taking into account the influence of the gravity acceleration g ═ 0,0, g ] in the inertial coordinate system, it is possible to obtain:
Figure BDA0002567925140000082
according to the principles of vector superposition and coordinate transformation, the following can be rewritten:
Figure BDA0002567925140000083
wherein:
Figure BDA0002567925140000084
wherein: a isi(i-1, …,7) represents the output signal of the ith accelerometer, Ri(i-1, …,7) represents the distance of the ith accelerometer from the origin of coordinates (the G point of the vessel's center of gravity) in a coordinate system attached to the hull.
The left end of equation of motion (6) is the translational acceleration of center of gravity G, and the right end contains variables including matrix P and transformation matrix a, where P can be derived from the measured acceleration signal and equation (7). Therefore, once the values of the matrix a at different time points are obtained through calculation, the integral of the equation (5) can be used for obtaining the speed and displacement information of three translations (surging, swaying and heaving) of any point Q on the ship body.
The following describes the method of solving matrix a, where the solution of angular acceleration is a prerequisite for solving matrix a.
The angular acceleration can be obtained by subtracting the output of each pair of accelerometers, numbered 1 and 2, 3 and 4, 5 and 6. For example, substituting the measurement results of the accelerometers, labeled 5 and 6, into equation (3), and multiplying both ends of the vector equation by the unit vector of the measurement direction of each accelerometer, respectively, can obtain:
Figure BDA0002567925140000091
Figure BDA0002567925140000092
order to
Figure BDA0002567925140000093
Then, according to the formulas (8) and (9), it can be seen that
Figure BDA0002567925140000094
Furthermore, from the knowledge of the theoretical mechanics of rigid bodies, it can be known
Figure BDA0002567925140000095
Wherein
Figure BDA0002567925140000096
Wherein ω isx、ωy、ωzThe angular velocities of rotation of the hull about three axes of a fixed coordinate system, respectively, and their respective Euler angles: (
Figure BDA0002567925140000097
θ, ψ) is:
Figure BDA0002567925140000098
can also be known
Figure BDA0002567925140000099
Wherein
Figure BDA00025679251400000910
Thus, it is obtained that,
Figure BDA00025679251400000911
(obtaining of this formula: according to the calculation formula of matrix B, its element B can be directly obtained32Is equal to the rightmost end of the formula; f1(t) can be according to
Figure BDA00025679251400000912
And equation (10).
Similarly, the derivation process is similar to equations (8) and (9), and the position information and measurement signals of the accelerometers numbered 1 and 2, 3 and 4, 5 and 6 are all substituted into equation (3), and the output results of each pair of accelerometers are subtracted, so that a nonlinear system about the angular velocity of the hull motion can be obtained:
Figure BDA00025679251400000913
wherein ω isx、ωy、ωzThe angular speeds of rotation of the hull about three axes of a fixed coordinate system, F1(t)、F2(t)、F3(t) are respectively:
Figure BDA0002567925140000101
the angular velocity ω, i.e., (ω), can be solved directly on the basis of the measured acceleration signal by equations (11) and (12)x,ωy,ωz). Once the angular velocity ω is found, the euler angles of the vessel motion in the matrix a can be found by solving the following equation, which corresponds to equation (10):
Figure BDA0002567925140000102
it should be noted that the output signals of the 4 accelerometers (i ═ 1,2,5,6) are not independent, because the accelerometers 1,2,5,6 measure vertical acceleration. The vertical acceleration at the G point of the center of gravity can be obtained from the pair of accelerometer measurements, reference numerals 1 and 2, and similarly, the vertical acceleration at the G point of the center of gravity can also be obtained from the pair of accelerometer measurements, reference numerals 5 and 6, which are equal. Therefore, the following relationship exists between them (the measurement and analysis results of the cross-test data can be achieved accordingly):
Figure BDA0002567925140000103
according to the derivation process of the formula, the measurement of the six-degree-of-freedom motion of the ship can be summarized as follows:
1) firstly, solving equation (11) can obtain three angular velocities omega of ship motionx、ωy、ωzThe solving method is as follows;
2) solving equation (13) can thenObtaining three angular displacements of the vessel's motion, i.e. Euler angles
Figure BDA0002567925140000104
Theta, psi, the solution method is as follows;
3) then, substituting the Euler angle into the equation (2) to obtain a conversion matrix A;
4) and finally, solving the second integral of the equation (6) to obtain three linear displacements at the gravity center point G of the ship body.
The solving process of the nonlinear differential equation (11) is as follows:
angular velocity ω at the k-th step time when equation (11) is solved for time domain steppingx(k,t)、ωy(k,t)、ωz(k, t) is known, and the system (11) can be solved by stepwise iterative methods as follows:
Figure BDA0002567925140000111
the angular velocity at the initial moment is: omegax(0)＝ωy(0)＝ωz(0)。
The solving process of the nonlinear differential equation (13) is as follows:
the left-hand integral in equation (13) can be solved by fourier transform and its inverse, for example:
Figure BDA0002567925140000112
wherein F (x) and F-1(x) Respectively, a Fourier transform function and an inverse Fourier transform function, f (t) can represent an arbitrary function, and h (t) is a time derivative of f (t). .
It should be noted that, in consideration of the relationship between the number of the equation sets and the number of the unknown quantities, the six-degree-of-freedom motion of the ship can be solved completely theoretically by adopting 6 accelerometers. As a preferred solution of the present invention, the purpose of using 7 accelerometers in this embodiment is: the method has the advantages that firstly, the solution equation is simplified, so that the six-degree-of-freedom motion of the ship can be calculated more efficiently, and secondly, the measurement and analysis results of cross inspection data can be realized.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A ship six-degree-of-freedom motion measurement method based on an array type accelerometer is characterized by comprising the following steps:
two accelerometers are respectively arranged at the bow and the stern and are respectively used for measuring the vertical acceleration and the transverse acceleration at the bow and the stern; two accelerometers are symmetrically arranged on the left and right sides of the middle part of the ship and used for measuring vertical acceleration; arranging an accelerometer at the position of the center of gravity of the ship body for measuring longitudinal acceleration;
establishing an inertial translation coordinate system O-XoYoZo; the coordinate system keeps the same navigational speed and course angle with the ship to do uniform linear motion; establishing a fixed coordinate system G-XYZ fixedly connected with the ship body, wherein the coordinate system is fixed on the ship body and keeps relatively static with the ship body at any time;
the point G is the center of gravity of the ship, and the second derivative of the position variable at the center of gravity G to the time t can be expressed as the following formula:
Figure FDA0002567925130000011
wherein: a is a conversion matrix of an inertial coordinate system and a position vector fixedly connected in a ship body coordinate system; g is a gravity acceleration array; a isi(i-1, …,7) represents the output signal of the ith accelerometer, Ri(i-1, …,7) represents the distance of the ith accelerometer from the origin of coordinates in a coordinate system attached to the hull;
Figure FDA0002567925130000012
the nonlinear system of the angular velocity of the hull motion can be expressed as the following formula:
Figure FDA0002567925130000013
wherein ω isx、ωy、ωzThe angular speeds of rotation of the hull about three axes of a fixed coordinate system, F1(t)、F2(t)、F3(t) are respectively:
Figure FDA0002567925130000021
solving the equation (11) to obtain the motion angular velocity of the hull, and obtaining three angular displacements of the ship motion according to the angular velocity;
from the three angular displacements, a transformation matrix a can be obtained, so that the second integral of equation (6) can obtain three linear displacements at the hull center of gravity point G.
2. The method as claimed in claim 1, wherein xo (Q) is the position vector of any point Q in space in the inertial coordinate system O-XoYoZo, and x (Q) is the position vector of point Q in space in the coordinate system G-XYZ attached to the hull, and the following relationship exists between the two:
Xo(Q)＝Xo(G)+AX(Q) (1)
taking the position variable in equation (1) as the second derivative of time t, considering that x (q) is a constant matrix, we can obtain:
Figure FDA0002567925130000022
by substituting the position coordinate information of the accelerometer into equation (3) and taking into account the influence of the gravitational acceleration g in the inertial coordinate system being [0,0, g ], it is possible to obtain:
Figure FDA0002567925130000023
according to the principles of vector superposition and coordinate transformation, the following can be rewritten:
Figure FDA0002567925130000024
3. the array accelerometer-based ship six-degree-of-freedom motion measurement method according to claim 1 or 2,
Figure FDA0002567925130000025
wherein theta is a pitch angle,
Figure FDA0002567925130000026
The roll angle and psi is the yaw angle.
4. The method as claimed in claim 3, wherein A represents orthogonal transformation, and A represents a six-degree-of-freedom motion measurement method of the ship-1The inverse matrix of A also represents the orthogonal transform and is equal to the transpose of ATI.e. A-1＝AT。
5. The method for measuring six-degree-of-freedom motion of the ship based on the array type accelerometers, according to claim 2, is characterized in that position information and measurement information of six accelerometers except the accelerometer at the gravity center point G are substituted into equation (3), and a nonlinear system equation (11) of the angular velocity of the motion of the ship body can be obtained.
6. The method for measuring six-degree-of-freedom motion of a ship based on the array type accelerometer of claim 5, wherein equation (11) is solved by time domain stepping, and the angular velocity ω at the k-th step isx(k,t)、ωy(k,t)、ωz(k, t) is known, and the nonlinear system equation (11) can be solved by a stepwise iterative method as follows:
Figure FDA0002567925130000031
the angular velocity at the initial moment is: omegax(0)＝ωy(0)＝ωz(0)。
7. The method as claimed in claim 5, wherein the angular velocity ω (ω) is obtained by directly solving equations (11) and (12) based on the measured acceleration signalx,ωy,ωz) The following angular displacement formula is obtained:
Figure FDA0002567925130000032
solving equation (13) can obtain three angular displacements of ship motion, namely Euler angles
Figure FDA0002567925130000033
θ、ψ。
8. The array accelerometer-based ship six-degree-of-freedom motion measurement method according to claim 7, wherein the integral of the left end in equation (13) can be solved by Fourier transform and its inverse:
Figure FDA0002567925130000034
wherein F (x) and F-1(x) Respectively, a Fourier transform function and an inverse Fourier transform function, f (t) can represent an arbitrary function, and h (t) is a time derivative of f (t).
9. The method as claimed in claim 1, wherein the output signals of the four accelerometers used for measuring the vertical acceleration are not independent.
10. The array-type accelerometer based ship six-degree-of-freedom motion measurement method of claim 9, wherein the output signals of four accelerometers for measuring vertical acceleration have the following relationship:
Figure FDA0002567925130000041
wherein R is1、a1Respectively representing the distance between an accelerometer which is positioned at the bow of the ship and used for measuring the vertical acceleration and a gravity center G point and the measured acceleration value; r2、a2Respectively representing the distance between an accelerometer which is positioned at the stern and used for measuring the vertical acceleration and a gravity center G point and the measured acceleration value; r5、R6，a5、a6The distance between two accelerometers located in the middle of the ship and measuring the vertical acceleration and the gravity center G point and the measured acceleration value are respectively shown.
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