CN115857011B - A Method for Obtaining Seismometer Transfer Function Based on Regional Optimal Fitting - Google Patents

Abstract

The invention provides a method for solving a seismometer transfer function based on region optimization fitting, which comprises the following steps: acquiring a transfer function to be solved of a target seismometer; preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function; performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer; loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer; constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform; and solving the regional optimization objective function to obtain a transfer function with completed calibration. The invention constructs the region optimization objective function by utilizing the theoretical impulse response function and the actual impulse response waveform and solves the region optimization objective function, thereby not only greatly reducing the operation amount of the transfer function calibration work, but also improving the calibration precision of the transfer function on the basis.

Description

A Method for Obtaining Seismometer Transfer Function Based on Regional Optimal Fitting

technical field

The invention relates to the technical field of seismic detection, in particular to a method for obtaining a transfer function of a seismometer based on area optimal fitting.

Background technique

Seismometer is the core component of seismic detection, and the calculation of its transfer function directly affects the accuracy of seismic detection data. The transfer function calibration methods widely used at present are the step response calibration method and the sine wave calibration method.

The step response method is mainly based on response curve fitting. On the one hand, the convergence algorithm used in this method has a large amount of calculation; on the other hand, the calculation accuracy is low because the influence of environmental noise cannot be eliminated. The sine wave calibration method has high calibration accuracy, but in order to ensure its accuracy, the density of frequency points must be increased, and the lower the frequency, the longer the period. Long-term testing may lead to two problems. One is the change of environmental noise, which causes the reduction of test accuracy; the other is that for the testing of very wideband and ultra-wideband seismometers, the calibration workload is extremely huge.

Contents of the invention

In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a method for obtaining the transfer function of the seismometer based on the optimal fitting of the area to solve the problem of low calibration accuracy of the transfer function of the seismometer.

To achieve the above object, the present invention provides the following scheme:

A method for obtaining a transfer function of a seismometer based on area optimal fitting, comprising:

Obtain the transfer function of the target seismometer to be solved;

Based on the step response, the transfer function to be solved is initially calibrated to obtain the transfer function for the preliminary solution;

Carry out Fourier inverse transform to the transfer function of described preliminary solution, obtain the theoretical impulse response function of target seismometer;

Loading a pulse signal at the input end of the target seismometer to obtain the actual impulse response waveform of the target seismometer;

constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform;

The calibrated transfer function is obtained by solving the area optimization objective function.

Preferably, the transfer function to be solved is:

Among them, H(s) is the transfer function to be solved, ξ is the damping coefficient, ω _n is the natural frequency, A is a constant coefficient, A=KI ₀ /m, K is the sensitivity of the seismometer, I ₀ is the applied to the seismometer DC current, m is the mass of the seismometer moving coil.

Preferably, the transfer function to be solved is obtained by preliminary calibration of the transfer function to be solved based on the step response, including:

Carry out inverse Laplace transform to the transfer function to be solved to obtain the seismometer step response curve;

Utilize the extremum point and inflection point on the step response curve of the seismometer to construct the preliminary solution formula of the transfer function;

A transfer function for preliminary solution is obtained according to the preliminary solution formula of the transfer function.

Preferably, the step response curve of the seismometer is:

Among them, e(t) is the step response curve of the seismometer.

Preferably, the preliminary solution formula of the transfer function is:

Among them, T ₁ is the inflection point of the seismometer's step response curve, and T ₀ is the extreme point of the seismometer's step response curve.

Preferably, said constructing an area optimization objective function according to said theoretical impulse response function and said actual impulse response waveform includes:

Using the formula:

Construct the objective function of regional optimization; where, Δ is the objective function of regional optimization, Bi ₍ t) is the actual impulse response waveform, _bi (t) is the theoretical impulse response function, and N is the length of _Bi (t).

According to the specific embodiments provided by the invention, the invention discloses the following technical effects:

The present invention provides a method for calculating the transfer function of a seismometer based on regional optimal fitting. Compared with the prior art, the present invention constructs the regional optimal objective function by using the theoretical impulse response function and the actual impulse response waveform, and Solving it can not only greatly reduce the computational load of the transfer function calibration work, but also improve the calibration accuracy of the transfer function on this basis.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some of the present invention. Embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without paying creative labor.

Fig. 1 is a flow chart of a method for obtaining a seismometer transfer function based on regional optimal fitting in an embodiment provided by the present invention;

FIG. 2 is a schematic diagram of a method for obtaining a transfer function of a seismometer based on area optimization fitting in an embodiment of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Reference herein to an "embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The occurrences of this phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is understood explicitly and implicitly by those skilled in the art that the embodiments described herein can be combined with other embodiments.

The terms "first", "second", "third" and "fourth" in the specification and claims of the present application and the drawings are used to distinguish different objects, rather than to describe a specific order . Furthermore, the terms "include" and "have", as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, including a series of steps, processes, methods, etc. are not limited to the listed steps, but optionally also include steps that are not listed, or optionally also include inherent aspects of these processes, methods, products or equipment. other steps.

The purpose of the present invention is to provide a method for obtaining the transfer function of the seismometer based on the optimal fitting of the area to solve the problem of low calibration accuracy of the transfer function of the seismometer.

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Please also refer to Figure 1-2, a method for calculating the transfer function of a seismometer based on regional optimal fitting, including:

Step 1: Obtain the transfer function of the target seismometer to be solved;

In practical applications, the transfer function of a seismometer at low frequencies can be described by a second-order system:

Among them, ξ is the damping coefficient, ω _n is the natural frequency, A is a constant coefficient,

A＝KI ₀ /m

K is the sensitivity of the seismometer, I ₀ is the DC current applied to the seismometer, and m is the quality of the moving coil of the seismometer.

Step 2: Preliminary calibration of the transfer function to be solved based on the step response to obtain the preliminary solution of the transfer function;

Further, step 2 includes:

Carry out inverse Laplace transform to the transfer function to be solved to obtain the seismometer step response curve;

Utilize the extremum point and inflection point on the step response curve of the seismometer to construct the preliminary solution formula of the transfer function;

A transfer function for preliminary solution is obtained according to the preliminary solution formula of the transfer function.

Below in conjunction with specific embodiment, the above-mentioned preliminary solution of the present invention is further described:

Taking inverse Laplace transform for formula (1), according to the motion equation of the seismometer, we can get:

Equation (2) is the curve of the step response of the seismometer.

Take the derivative of e(t), let e'(t)=0, the extreme point of the response curve can be obtained, let e'(T ₀ )=0, we have

output voltage maximum

Equivalent to

In formula (5), T ₀ is the extreme point of the response curve, which is measurable, only ξ is an unknown quantity, and ω _n can be obtained by calculating ξ.

Deriving e'(t) and setting e"(t)=0, we can get

It can be seen from formula (6) that T ₁ =2T ₀ . _{T 1} is the inflection point of the response curve.

Substituting T ₀ and T ₁ into formula (2), and dividing, we have:

Substituting formula (4) into formula (7):

By solving formula (8), ξ and ω _n can be obtained.

Substituting the values of ξ, ω _n and T ₀ into formula (2), the sensitivity can be obtained

Thus, the transfer function of the seismometer is preliminarily obtained.

Step 3: Carry out Fourier inverse transform to the transfer function of described preliminary solution, obtain the theoretical impulse response function of target seismometer;

Step 4: Loading a pulse signal at the input end of the target seismometer to obtain the actual impulse response waveform of the target seismometer;

Step 5: constructing an area optimization objective function according to the theoretical impulse response function and the actual impulse response waveform; wherein, the area optimization objective function of the present invention is:

Construct the objective function of regional optimization; where, Δ is the objective function of regional optimization, Bi ₍ t) is the actual impulse response waveform, _bi (t) is the theoretical impulse response function, and N is the length of _Bi (t).

Step 6: Solving the objective function of the area optimization to obtain the calibrated transfer function.

Below the present invention is described in conjunction with specific embodiment to the construction process of objective function and its solution process:

Inverse Fourier transform is performed on the transfer function H(s) obtained in the above steps to obtain the theoretical impulse response function b(t) of the seismometer.

Load the pulse signal at the input end of the seismometer to be tested, record the impulse response waveform B(t) of the seismometer, the length of B(t) is N, and substitute the abscissa of each point of B(t) into b(t).

The area optimization objective function to be solved is:

Set the coefficients of the theoretical transfer function obtained in the above steps as the independent variable vector (x), and find the parameter that minimizes the objective function Δ near x.

The present invention adopts an area optimization algorithm, that is, a Nelder-Mead simplex algorithm, to solve an area optimization objective function. This algorithm uses a simplex of n+1 points for an n-dimensional vector x. First add 5% of each component x ₀ (i) to x 0 to generate a simplex around the _initial estimate x ₀ . Then using the two above n vectors as elements of the simplex except _x0 , iteratively modify the simplex as follows:

Let x(i) represent the point list i=1,...,n+1 in the current simplex.

Sorts the points in the simplex in order of smallest function value Δ(x(1)) to largest function value Δ(x(n+1)). At each step of the iteration, this algorithm discards the current worst point x(n+1) and accepts another point in the simplex.

generate reflection points

r=2m-x(n+1),

in

and calculate Δ(r).

If Δ(x(1)) ≤ Δ(r) < Δ(x(n)), then accept r and terminate the iteration.

If Δ(r) < Δ(x(1)), then calculate the extension point s

s=m+2(m-x(n+1))

and calculate Δ(s).

If Δ(s) < Δ(r), accept s and terminate the iteration.

Otherwise, accept r and terminate the iteration.

If Δ(r)≥Δ(x(n)), execute between m and x(n+1) or r.

If Δ(r)<Δ(x(n+1)), calculate

c=m+(r-m)/2

And compute Δ(c). If Δ(c) < Δ(r), accept c and terminate the iteration.

Otherwise, proceed to step 7.

If Δ(r)≥Δ(x(n+1)), calculate

cc=m+(x(n+1)-m)/2

And calculate Δ(cc). If Δ(cc) < Δ(x(n+1)), accept cc and terminate the iteration.

Otherwise, proceed to step 7.

Calculate n points

v(i)=x(1)+(x(i)-x(1))/2

And calculate Δ(v(i)), i=2,...,n+1. The simplex in the next iteration is x(1), v(2), ..., v(n+1).

The present invention further explains the calibration process of the transfer function in combination with specific application scenarios below:

In the first step, the step response initially calibrates the transfer function of the seismometer:

EDAS-24GN is selected as the seismic data acquisition device of this embodiment, and its error is less than 1/10000. A +1V step voltage is applied to the input terminal of the seismometer to be tested, and the sampling rate is set to 800sps, and the voltage signal at the input terminal of the seismometer and the step response waveform of the seismometer are recorded.

According to the step response waveform, read the peak time T ₀ , T ₁ can be obtained from formula (4) and formula (6), and read the E(T ₀ ) and E(T ₁ ) values of the response curve E(t), Substitute E(T ₀ ) and E(T ₁ ) into formula (8) to solve the nonlinear one-variable function about ξ. In this embodiment, the bisection method is used to solve ξ, and the upper and lower limits of the bisection method are [1.001, 10]. Substitute ξ and T ₀ into formula (5) to obtain the natural frequency ω _n .

Substitute the values of ξ, ω _n and T ₀ into formula (2) to obtain the sensitivity K.

Thus, the theoretical values of the coefficients a ₁ , b ₁ , b ₂ , b ₃ of the seismometer transfer function H(s) are preliminarily obtained.

In the second step, the exact transfer function of the seismometer is obtained using the area optimization algorithm

The unit pulse signal is loaded at the input end of the seismometer to be tested, the sampling rate is set to 800sps, and the impulse response waveform B(t) of the seismometer is recorded.

Use the area optimization algorithm to obtain an accurate transfer function based on the theoretical transfer function obtained in the above steps and the measured impulse response function.

First, call the impulse function in matlab, and the theoretical impulse response curve b(t) can be obtained directly from the various coefficients in formula (11).

Then, set the independent variable x=[a ₁ , b ₁ , b ₂ , b ₃ ] of the optimization algorithm, and import the measured value B(t) into matlab. The initial value x ₀ of the independent variable is set to the theoretical value obtained in the first step, and the objective function of the optimization algorithm is the error sum of squares Δ between the theoretical response curve and the measured response curve, see formula (10).

Finally, area optimization fitting is carried out on the objective function Δ. In this embodiment, the fminsearch function is called to perform optimization calculation. The calculation results are used as the coefficients of formula (10), which is the precise transfer function of the seismometer.

According to the specific embodiments provided by the invention, the invention discloses the following technical effects:

The present invention uses the theoretical impulse response function and the actual impulse response waveform to construct the area optimization objective function and solves it, which can not only greatly reduce the calculation amount of the transfer function calibration work, but also improve the transfer function on this basis. calibration accuracy.

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the method disclosed in the embodiment, since it corresponds to the device disclosed in the embodiment, the description is relatively simple, and for the related information, please refer to the description of the device part.

In this paper, specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; meanwhile, for those of ordinary skill in the art, according to the present invention Thoughts, there will be changes in specific implementation methods and application ranges. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims (2)

1. A method for determining a seismometer transfer function based on a region optimization fit, comprising:

acquiring a transfer function to be solved of a target seismometer;

preliminarily calibrating the transfer function to be solved based on the step response to obtain a preliminarily solved transfer function;

the transfer function to be solved is as follows:

wherein H(s) is a transfer function to be solved, ζ is a damping coefficient, ω _n For natural frequency, a is a constant coefficient, a=ki ₀ M, K is seismometer sensitivity, I ₀ For the direct current applied to the seismometer, m is the mass of the seismometer moving coil;

the step response-based preliminary calibration of the transfer function to be solved to obtain a preliminary solved transfer function comprises the following steps:

carrying out inverse Laplace transformation on the transfer function to be solved to obtain a seismometer step response curve;

constructing a transfer function preliminary solving formula by utilizing extreme points and inflection points on the step response curve of the seismometer;

obtaining a preliminarily solved transfer function according to the transfer function preliminarily solving formula;

specifically, for the inverse Lawster transform (1), according to the seismometer motion equation, it is possible to obtain:

equation (2) is the curve of the step response of the seismometer;

deriving e (T), let e '(T) =0, and obtaining extreme point of response curve, and setting e' (T) ₀ ) =0, have

Maximum output voltage

Equivalent to

In the formula (5), T ₀ The extreme point of the response curve is measurable, only xi is unknown quantity, and the ω can be obtained by solving xi _n ；

Derivative e '(t) and let e' (t) =0, to obtain

From formula (6), T ₁ ＝2T ₀ .T ₁ Is the inflection point of the response curve;

will T ₀ 、T ₁ Substitution formula (2), division, has:

substituting formula (4) into formula (7) has:

solving (8) to obtain ζ and ω _n ；

Will be xi, omega _n And T ₀ The value is substituted into (2) to obtain the sensitivity

Thus, the transfer function of the seismometer is preliminarily obtained;

performing Fourier inverse transformation on the preliminarily solved transfer function to obtain a theoretical impulse response function of the target seismometer;

loading pulse signals at the input end of the target seismometer to obtain an actual pulse response waveform of the target seismometer;

constructing a region optimization objective function according to the theoretical impulse response function and the actual impulse response waveform;

and solving the regional optimization objective function to obtain a transfer function with completed calibration.

2. A method of deriving a seismometer transfer function based on a region-optimized fit according to claim 1, characterized in that said constructing a region-optimized objective function from said theoretical impulse response function and said actual impulse response waveform comprises:

the formula is adopted:

constructing a region optimization objective function; where Δ is the region optimization objective function, B _i (t) is the actual impulse response waveform, b _i (t) is a theoretical impulse response function, N is B _i Length of (t).

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