CN110887463A - Method and system for detecting fluctuation amplitude of sea waves based on inertial sensor - Google Patents
Method and system for detecting fluctuation amplitude of sea waves based on inertial sensor Download PDFInfo
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Abstract
The invention discloses a method and a system for detecting the fluctuation amplitude of sea waves based on an inertial sensor, wherein the method is realized based on the inertial sensor installed on equipment on the sea surface, and the method comprises the following steps: acquiring acceleration and angular velocity acquired by an inertial sensor; on the basis of the acceleration and the angular velocity, on the basis of eliminating the influence of the gravity acceleration of the inertial sensor, calculating the linear acceleration of the inertial sensor under a world coordinate system; filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range; and calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range. The method can detect the fluctuation amplitude of the sea waves in real time under the condition of any sea waves; and the influence of the accumulated error of the noise can be eliminated, and a more accurate result of the movement displacement of the sea waves is obtained.
Description
Technical Field
The invention relates to the field of ocean monitoring, in particular to a method and a system for detecting the fluctuation amplitude of sea waves based on an inertial sensor.
Background
Sea waves are the propagation of sea surface fluctuation shapes, water particles leave an equilibrium position, do periodic vibration and propagate in a certain direction to form a fluctuation, the vibration energy of the water particles forms kinetic energy, the fluctuation energy of the sea waves generates potential energy, and the accumulated amount of the two energies is surprising. In global oceans, the total energy of only the storms and swells is equivalent to half the solar energy reaching the outside of the earth. The energy of the ocean waves rolls forward in the direction of wave propagation. Thus, sea waves are in fact wave propagation of energy. The wave period of the sea waves ranges from a few tenths of a second to more than hours, the wave height ranges from a few millimeters to tens of meters, and the wavelength ranges from a few millimeters to thousands of kilometers.
The wave height of the wind waves, the surge waves and the near-shore waves is several centimeters to more than 20 meters, and the maximum wave height can reach more than 30 meters. The wave is the wave generated by the sea water under the action of wind force, a plurality of waves with different heights and lengths can be generated at the same time, the wave surface is steep, the wavelength is short, wave flowers or piece foams are often arranged near the wave crest, and the propagation direction is consistent with the wind direction. Generally speaking, the longer the wind in the same state acts on the sea surface, the larger the sea area range is, and the stronger the wind waves are; when the wind waves reach a fully grown state, the wind waves do not increase any more. The waves formed after the waves leave the area where the wind blows are called swell. The wind waves are generally classified into 10 levels and the swell into 5 levels according to the wave height. The level 0 is free of waves and surges, and the sea level is as same as the mirror; 5-grade large waves and 6-grade large waves correspond to 4-grade large surges, and the wave height is 2-6 meters; level 7, rough billows, level 8, rough billows, level 9, corresponding to level 5 billows, with wave height of 6.1 m to more than 10 m.
Ocean wave motion is one of the important forms of movement of seawater. There are fluctuations from the sea surface to the interior of the ocean. In big oceans, if the sea surface is wide, the wind speed is high, the wind direction is stable, and the blowing time is long, sea waves are necessarily strong, such as the frequent billows rolling on the ocean surface of the west wind belt of the northern and northern hemispheres; although the sea area of the equatorial calm zone and the calm zone of the auxiliary tropical zone of the south and north hemispheres is wide, the sea waves are generally very small because the wind power is weak and the wind direction is uncertain.
Sea waves can be seen as being composed of an infinite number of component waves of different amplitudes, different frequencies, different directions, and disordered phases. These component waves constitute the wave spectrum. This spectrum describes the distribution of ocean wave energy relative to the individual component waves, hence the name "energy spectrum". It is used to describe the distribution of energy within ocean waves with respect to frequency and direction. To study the important concept of sea waves. It is generally assumed that ocean waves are formed by the superposition of a number of random positive arcs. The constituent waves of different frequencies have different amplitudes and thus different energies. A function S (ω) of the circular frequency ω is provided, and the energy of each component wave of the sea wave is proportional to S (ω) ω, in the interval from ω to (ω + ω), and S (ω) represents the energy of these component waves, which represents the distribution of energy over frequency, and is therefore called the frequency spectrum or energy spectrum of the sea wave. Similarly, a function S (ω, θ) is provided which includes the circular frequency ω and wave direction θ of the component waves, and the energy of each component wave is proportional to S (ω, θ) ω θ in the interval from ω to (ω + ω) and from θ to (θ + ω), so that S (ω, θ) represents the distribution of energy to ω and θ, referred to as the directional spectrum of the ocean wave. Converting the circular frequency of the component wave into a wave number to obtain a wave number spectrum; the frequency ω is converted to 2 π (the frequency is the reciprocal of the period), resulting in the number of S () spectra expressed. The above various spectra are collectively referred to as the wave spectrum.
The method for calculating the wave spectrum comprises two methods: the first is to derive a semi-theoretical and semi-empirical wave spectrum by utilizing the wave height and period obtained by observation; the second method is to calculate the correlation function by using the record of the time variation of the wave surface measured by a fixed point, and then calculate the spectrum. Spectra were also developed by establishing energy balance equations. The spectrum obtained at present is mainly determined on the basis of observation data. However, due to the lack of accurate wind and wave observation, some of the proposed spectra are very different from each other. The analysis and research of the wave spectrum are very important, the reflection parts of the breakwater and the sea surface to the radar can be reasonably designed according to the wave spectrum, and wave factors such as wave height, period and the like can be calculated by utilizing the wave spectrum.
For ships and buoys at sea, it is very important to detect the motion amplitude of sea waves, but currently, there is no relevant effective means and method.
Disclosure of Invention
The invention aims to overcome the technical defects and provides a method for detecting the fluctuation amplitude of sea waves based on an inertial sensor.
In order to achieve the above object, the present invention provides a method for detecting a wave fluctuation amplitude based on an inertial sensor, the method being implemented based on the inertial sensor installed on a sea surface, the method comprising:
on the basis of the acceleration and the angular velocity acquired by the inertial sensor, calculating the linear acceleration of the inertial sensor in a world coordinate system on the basis of eliminating the influence of the gravity acceleration of the inertial sensor;
filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range;
and calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range.
As an improvement of the above method, the linear acceleration of the inertial sensor in the world coordinate system is calculated based on the acceleration and the angular velocity acquired by the inertial sensor and on the basis of eliminating the influence of the gravitational acceleration of the inertial sensor; the method specifically comprises the following steps:
at the time t and in a sensor body coordinate system, detection data of the inertial sensorComprises the following steps:
whereinThe unit of the acceleration of the inertial sensor in the three directions of x, y and z is m/s2 under a sensor body coordinate system;the angular velocity of the inertial sensor in three angles of overturning, pitching and yawing is in unit of rad/s under a sensor body coordinate system;
according to the rotation matrix R (t) of the inertial sensor, calculating the linear acceleration of the inertial sensor in the world coordinate system
Subtracting the gravity acceleration from the linear acceleration to obtain an acceleration f (t) after eliminating the influence of gravity:
wherein the content of the first and second substances,is composed ofThree components of (a); f. ofx(t),fy(t),fz(t) is the linear acceleration of the inertial sensor in the x, y, z directions, respectively.
As an improvement of the above method, the step of calculating the rotation matrix r (t) of the inertial sensor specifically includes:
wherein s is a weighting parameter;then k isPDetermines the cut-off frequency, k, of the complementary filterIDetermines the time, k, for eliminating the static deviationIHas a size of kP0.01-0.1 times of;
Rw(t) is a gyroscope-based rotation matrix of the inertial sensor at time t, and the period of sensor data acquisition is deltatThen the inertial sensor is at t + deltatThe moment gyroscope-based rotation matrix is Rw(t+δt):
When t is 0, Rw(t) is an identity matrix;
Ra(t) is the rotation matrix of the inertial sensor at time t based on the acceleration sensor:
wherein θ (t), Φ (t), and ψ (t) are the pitch angle, roll angle, and yaw angle detected by the acceleration sensor, respectively:
as an improvement of the above method, the z-axis acceleration of the inertial sensor in the world coordinate system is filtered by using a band-pass filter, so as to obtain the z-axis acceleration in the sea wave frequency spectrum range; the method specifically comprises the following steps:
designing a band-pass filter with cut-off frequencies of 0.04Hz and 0.25Hz, sampling frequency of 100Hz and transfer function of H(s):
using the band-pass filter to pair z-axis accelerations f superimposed with low and high frequency noisez(t) filtering.
As an improvement of the above method, based on the z-axis acceleration in the wave spectrum range, the fluctuation amplitude of the wave in the z-axis direction is calculated by quadratic integration, specifically:
acceleration f based on z axisz(t), calculating the fluctuation amplitude of the sea waves in the z-axis direction by a quadratic integration method:
wherein p isz(t) and vz(t) displacement and movement speed of the sea waves in the z direction at the moment t respectively; p is a radical ofz(0)=0,vz(0)=0。
As an improvement of the above method, the method further comprises: filtering the displacement and the movement speed of the sea waves in the z direction:
with a transfer function of H1High pass Filter pair of(s)'z(t) and v'z(t) filtering:
the cut-off frequency of the high-pass filter is 0.01 Hz.
The invention also provides a wave fluctuation amplitude detection system based on the inertial sensor, which comprises:
the detection module is used for acquiring the acceleration and the angular velocity acquired by the inertial sensor;
the calculation module is used for calculating the linear acceleration of the inertial sensor under a world coordinate system on the basis of eliminating the influence of the gravity acceleration of the inertial sensor on the basis of the acceleration and the angular velocity; filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range; and calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range.
The invention has the advantages that:
1. the method can detect the fluctuation amplitude of the sea waves in real time under the condition of any sea waves;
2. the method can eliminate the influence of the accumulated error of the noise and obtain a more accurate result of the movement displacement of the sea waves.
Drawings
FIG. 1 illustrates the acceleration component of an IMU when the IMU is not subject to other external forces, but only gravity, at a given attitudeA schematic diagram of the relationship with the gravitational acceleration g;
FIG. 2 is a schematic diagram of IMU detection signals mixed with high frequency noise and low frequency noise;
FIG. 3 is an amplitude response curve for a band pass filter;
FIG. 4 is a schematic diagram of an IMU detection signal with low frequency noise and high frequency noise filtered;
FIG. 5 is a schematic diagram of a calculated z-direction movement velocity of a sea wave;
FIG. 6 is a schematic diagram of a calculated z-direction motion position of a sea wave;
FIG. 7 is a graph comparing a filtered wave velocity estimate to a true value;
FIG. 8 is a graph comparing a wave displacement estimate to a true value after filtering;
fig. 9 is a schematic diagram of an inertial sensor-based wave amplitude detection system.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Example 1
The embodiment 1 of the invention provides a sea wave fluctuation amplitude detection method based on an inertial sensor, which is suitable for installing the inertial sensor for integrally measuring acceleration and angular velocity on a buoy and a ship and detecting the fluctuation amplitude of the sea wave by an inertial measurement, calculation and filtering method. The Inertial sensor can be an Inertial Measurement Unit (IMU), and is installed on a ship, a buoy and a marine rescue device.
The method comprises the following steps:
step 1) processing information of an inertial sensor, eliminating the influence of gravity acceleration of the inertial sensor, and calculating linear acceleration;
step 1-1) detection information of inertial sensor
The inertial sensor detects acceleration and gyroscope data at a frequency f, and the detection data of the sensor at time t is represented as acceleration and gyroscope information in the coordinate system of the sensor itself (represented by symbol b):
whereinAcceleration in three directions of x, y and z under the self coordinate system is represented by m/s 2;the angular velocity is in rad/s under the self coordinate system and at three angles of overturning, pitching and yawing.
Step 1-2) attitude resolution
Since the sensor mounted on the buoy may be in various postures, the detected acceleration information includes components of the gravitational acceleration in three directions, and cannot represent the actual motion acceleration of the sensor, it is first necessary to convert the detected acceleration vector into the acceleration in the world coordinate system, and eliminate the influence of the gravitational acceleration. Fig. 1 shows the relationship between the detected values of three accelerations and the acceleration due to gravity when the IMU is in a certain attitude.
Therefore, the influence of the gravitational acceleration is to be eliminated from the acceleration information detected by the IMU. The influence of the gravitational acceleration is eliminated, the pitch angle and the roll-over angle of the IMU need to be calculated, and the attitude of the IMU can be calculated according to the information of the gyroscope.
Step 1-2-1) gyroscope-based attitude calculation:
Rw(t) is a gyroscope-based rotation matrix of the inertial sensor at time t, and the period of sensor data acquisition is deltatThen the inertial sensor is at t + deltatThe moment gyroscope-based rotation matrix is Rw(t+δt):
When t is 0, Rw(t) is an identity matrix;
step 1-2-2) attitude calculation based on acceleration at rest:
due to the problems of zero drift, temperature drift and the like of the gyroscope, the accuracy of the rotation matrix calculated by the iteration method can be lost along with the advance of time. In order to solve the problem, the static moment of the IMU can be detected, when the IMU is static, the gravity acceleration is utilized to calculate the flip angle and the pitch angle of the IMU, the flip angle and the pitch angle are used as attitude observation when the IMU is static, and the attitude calculation error of the IMU is corrected.
Theta (t), phi (t) and psi (t) are respectively a pitch angle, a roll angle and a yaw angle detected by the acceleration sensor;
based on the calculation formula from the euler angle to the rotation matrix, the rotation matrix detected by the acceleration sensor can be calculated as:
step 1-2-3) complementary filtering
The complementary filtering is taking
Wherein s is a weighting parameter;then k isPDetermines the cut-off frequency, k, of the complementary filterIDetermines the time, k, for eliminating the static deviationIHas a size of kP0.01-0.1 times of;
step 1-3) eliminating the influence of gravity and calculating the linear acceleration
After the rotation matrix is obtained based on the complementary filtering, the linear acceleration of the IMU in the world coordinate system can be calculated according to the rotation matrix:
subtracting the gravity acceleration from the linear acceleration to obtain an acceleration detection result after eliminating the gravity influence:
wherein the content of the first and second substances,is composed ofThree components of (a); f. ofx(t),fy(t),fz(t) is the linear acceleration of the inertial sensor in the x, y, z directions, respectively.
Step 2), extracting signals in a sea wave frequency range from the online acceleration detection signals;
step 2-1) multifrequency decomposition of linear acceleration signals
The frequency of the sea wave is generally in the range of 0.05Hz to 0.2Hz, so the calculated f (t) sequence signal can be filtered by designing a band-pass filter, other high-frequency or low-frequency signals are filtered, and the linear acceleration signal belonging to the frequency range of the sea wave is extracted. To facilitate the calculationBased only on fz(t) calculating the fluctuation amplitude of the sea waves. Superimposing low and high frequency noisez(t) the signal may be represented as an accumulation of a plurality of frequency signals:
wherein N represents fzAnd (t) is mainly formed by mixing signals with N frequencies, wherein part of the signals with N frequencies are sea wave signals and also comprise high-frequency noise and low-frequency noise signals. FIG. 2 shows a set of simulated generated f mixed with low frequency noise and high frequency noisez(t) sequence of signals, f can be seenz(t) superimposed by a high frequency noise and a low frequency slowly varying signal. To accurately calculate the motion amplitude of the sea wave, it is necessary to filter out these high and low frequency noises.
Step 2-2) band-pass filter design for extracting sea wave frequency band signals
A band-pass filter is designed for this purpose. As the frequency range of the sea waves is mainly concentrated between 0.05Hz and 0.2Hz, the band-pass filter with the cut-off frequency of 0.04Hz and 0.25Hz is adopted. The sampling frequency of the band-pass filter is 100Hz, and a Butterworth filter model is adopted.
The amplitude and phase response curves of the filter are shown in fig. 3, and signals in the range of signal frequencies below 0.04Hz and above 0.25Hz will be attenuated quickly, eliminating the effects of these noise signals.
Converting the band-pass filter into a quartic transfer function to obtain:
using this filter on the superimposed low and high frequency noise f shown in FIG. 2z(t) filtering to obtain the signal of FIG. 4. Applying the filter described above for the transfer function to the signal fz(t) the filtering process is essentially a recursive formula of discrete difference equations transformed by the continuous transfer function. Obtaining:
in the form of a difference equation of (a). Wherein k1, k2, λk,ηkAre parameters of the difference equation obtained from h(s).
Difference equation based on filtering, pair fz(t) filtering can result in the signal of fig. 4. It can be seen that both high and low frequency noise is successfully filtered compared to the signal of figure 2. This provides a reliable signal for calculating the amplitude of motion of the ocean waves.
Step 3) calculating the fluctuation amplitude of the sea waves through quadratic integration
In order to calculate the fluctuation amplitude of the sea waves, the displacement of the sea waves in the x and y directions does not need to be calculated, and only the displacement distance of the sea waves in the z-axis direction needs to be calculated. So that after noise filtering is obtained, the acceleration f is based on the z-axisz(t), calculating the fluctuation amplitude of the sea waves in the z-axis direction by a quadratic integration method:
wherein p isz(t) and vz(t) displacement and movement speed of sea wave in z direction at time t, and initial value pz(0)=0,vz(0)=0。
Fig. 5 and 6 show the velocity and the moving position based on the z-direction line after the noise filtering, and it can be seen that there is a relatively large deviation in the calculation result, mainly because the low frequency noise cannot be eliminated.
Considering that the z-axis direction movement speed and movement position of the sea wave are periodic signals with 0 mean value, in order to eliminate the accumulated errors of the movement speed and movement position of the sea wave, p is required to be addedz(t),vz(t) is converted to a 0-mean periodic signal. See pz(t),vz(t) is not currently a zero-mean periodic signal because of interference from low frequency signals. For eliminating low-frequency signals, pz(t),vz(t) filtering with a high pass filter as follows to filter out low frequency interference signals.
The cut-off frequency of the filter is 0.01Hz, and the filter is used for cutting off low-frequency noise interference. After filtering by a filter, the estimated wave heave speed is compared with the real speed of the actual wave heave, such as shown in fig. 7, and the displacement of the wave heave is compared with the heave displacement of the real wave, such as shown in fig. 8. It can be seen that the estimated wave speed and wave displacement are very close to the true values.
Example 2
As shown in fig. 9, embodiment 2 of the present invention provides a system for detecting the heave amplitude of sea waves based on an inertial sensor, the system comprising:
the detection module is used for acquiring the acceleration and the angular velocity acquired by the inertial sensor;
the calculation module is used for calculating the linear acceleration of the inertial sensor under a world coordinate system on the basis of eliminating the influence of the gravity acceleration of the inertial sensor on the basis of the acceleration and the angular velocity; filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range; calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range;
and the communication module is used for sending the fluctuation amplitude of the sea waves in the z-axis direction in a wireless communication mode.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (7)
1. An inertial sensor-based wave fluctuation amplitude detection method is realized based on an inertial sensor installed on a sea surface device, and comprises the following steps:
acquiring acceleration and angular velocity acquired by an inertial sensor;
on the basis of the acceleration and the angular velocity, on the basis of eliminating the influence of the gravity acceleration of the inertial sensor, calculating the linear acceleration of the inertial sensor under a world coordinate system;
filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range;
and calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range.
2. An inertial sensor-based wave fluctuation amplitude detection method according to claim 1, wherein the linear acceleration of the inertial sensor in the world coordinate system is calculated based on the acceleration and angular velocity acquired by the inertial sensor, on the basis of eliminating the influence of the gravitational acceleration of the inertial sensor; the method specifically comprises the following steps:
at the time t and in a sensor body coordinate system, detection data of the inertial sensorComprises the following steps:
whereinThe unit of the acceleration of the inertial sensor in the three directions of x, y and z is m/s2 under a sensor body coordinate system;the angular velocity of the inertial sensor in three angles of overturning, pitching and yawing is in unit of rad/s under a sensor body coordinate system;
according to the rotation matrix R (t) of the inertial sensor, the world coordinates of the inertial sensor are calculatedLinear acceleration under tether
Subtracting the gravity acceleration from the linear acceleration to obtain an acceleration f (t) after eliminating the influence of gravity:
3. An inertial sensor-based wave fluctuation amplitude detection method according to claim 2, wherein the calculation step of the rotation matrix r (t) of the inertial sensor specifically includes:
wherein s is a weighting parameter;then k isPDetermines the cut-off frequency, k, of the complementary filterIDetermines the time, k, for eliminating the static deviationIHas a size of kP0.01-0.1 times of;
Rw(t) is a gyroscope-based rotation matrix of the inertial sensor at time t, and is set to transmitThe period of sensor data acquisition is deltatThen the inertial sensor is at t + deltatThe moment gyroscope-based rotation matrix is Rw(t+δt):
When t is 0, Rw(t) is an identity matrix;
Ra(t) is the rotation matrix of the inertial sensor at time t based on the acceleration sensor:
wherein θ (t), Φ (t), and ψ (t) are the pitch angle, roll angle, and yaw angle detected by the acceleration sensor, respectively:
4. an inertial sensor-based wave fluctuation amplitude detection method according to claim 1, wherein a band-pass filter is used to filter z-axis acceleration of the inertial sensor in a world coordinate system, so as to obtain z-axis acceleration in a wave spectrum range; the method specifically comprises the following steps:
designing a band-pass filter with cut-off frequencies of 0.04Hz and 0.25Hz, sampling frequency of 100Hz and transfer function of H(s):
using the band-pass filter to pair z-axis accelerations f superimposed with low and high frequency noisez(t) filtering.
5. An inertial sensor-based wave fluctuation amplitude detection method according to claim 4, wherein the fluctuation amplitude of the waves in the z-axis direction is calculated by quadratic integration based on z-axis acceleration in a wave spectrum range, specifically:
acceleration f based on z axisz(t), calculating the fluctuation amplitude of the sea waves in the z-axis direction by a quadratic integration method:
wherein p isz(t) and vz(t) displacement and speed of motion, p, of the sea wave in the z direction at time tz(0)=0,vz(0)=0。
6. A method of detecting the heave amplitude of a sea wave based on an inertial sensor according to claim 5, further comprising: filtering the displacement and the movement speed of the sea waves in the z direction:
with a transfer function of H1High pass filter pair of(s)z(t) and vz(t) filtering:
the cut-off frequency of the high-pass filter is 0.01 Hz.
7. An inertial sensor-based wave amplitude detection system, the system comprising:
the detection module is used for acquiring the acceleration and the angular velocity acquired by the inertial sensor;
the calculation module is used for calculating the linear acceleration of the inertial sensor under a world coordinate system on the basis of eliminating the influence of the gravity acceleration of the inertial sensor on the basis of the acceleration and the angular velocity; filtering the z-axis acceleration of the inertial sensor under a world coordinate system by using a band-pass filter to obtain the z-axis acceleration in a sea wave frequency spectrum range; and calculating the fluctuation amplitude of the sea waves in the z-axis direction through quadratic integration based on the z-axis acceleration in the sea wave frequency spectrum range.
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