CN114239253B - Initiating explosive device detonation process parameter identification method - Google Patents

Initiating explosive device detonation process parameter identification method Download PDF

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CN114239253B
CN114239253B CN202111491893.0A CN202111491893A CN114239253B CN 114239253 B CN114239253 B CN 114239253B CN 202111491893 A CN202111491893 A CN 202111491893A CN 114239253 B CN114239253 B CN 114239253B
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李俊红
储杰
杨奕
宗天成
宋伟成
蒋一哲
蒋泽宇
张泓睿
严俊
肖康
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Abstract

The invention provides a method for identifying parameters of an initiating explosive device detonation process, belongs to the technical field of initiating explosive device parameter identification, and solves the problem of low convergence speed of a gradient descent algorithm. The technical scheme is as follows: the identification method specifically comprises the following steps: step 1) establishing a Volterra model of the initiating explosive device detonation process; and 2) constructing an identification process of a Levenberg-Marquardt recursion algorithm. The beneficial effects of the invention are as follows: the method establishes a parameter identification model of the initiating explosive device detonation process, utilizes a Levenberg-Marquardt recursion algorithm to identify the parameters of the detonation process, has the characteristics of high convergence rate and high estimation precision, and has good applicability to parameter identification of the initiating explosive device detonation process.

Description

Method for identifying priming process parameters of initiating explosive device
Technical Field
The invention relates to the technical field of initiating explosive device parameter identification, in particular to a method for identifying initiating explosive device detonation process parameters.
Background
The initiating explosive is a general name of components and devices which are filled with gunpowder or explosive, generate combustion or explosion after being stimulated by the outside, and are used for igniting the gunpowder, detonating the explosive or doing mechanical work for one-time use. The initiating explosive device is very sensitive to factors such as the temperature and the humidity of the environment, and nonlinearity exists in the detonation process, so that a serious error exists between a theoretical result and an actual result. The Volterra series model is the expansion of an impulse response function in a linear system in a nonlinear system, and the impulse response function of the linear system can express the inherent characteristic of a circuit system, so the Volterra series model can also express the inherent nonlinear characteristic of the system in the initiating explosive device detonation process. The Volterra series can accurately describe the detonation process of the initiating explosive device without being influenced by factors such as environment and the like. So far, many scholars have proposed different identification methods: such as least squares, random gradients, newton-gaussian, gradient descent, etc.
The least square method has not ideal identification precision and often has poor identification effect in practical application; the random gradient method has low identification precision and slow convergence; the gradient descent method has stable convergence but low convergence speed, while the Newton-Gaussian method has high convergence speed, and can solve the problem of low convergence speed of the gradient descent algorithm, but the Newton-Gaussian method may cause the situation that the algorithm is not converged.
How to solve the above technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a method for identifying the parameters of the initiating explosive device in the detonation process; the internal nonlinear characteristic of the system in the initiating explosive device detonation process can be accurately expressed by the Volterra model adopted by the invention; the Levenberg-Marquardt recursion algorithm provided by the invention is an algorithm combining a gradient descent method and a Newton-Gaussian method, and compared with the traditional algorithm, the algorithm has better identification precision and convergence rate, and can be well suitable for parameter identification in the initiating process of initiating explosive devices.
The invention is realized by the following measures: a method for identifying parameters in the initiating explosive device detonation process specifically comprises the following steps:
step 1) establishing a Volterra model of the initiating explosive device detonation process;
and 2) constructing an identification process of a Levenberg-Marquardt recursion algorithm.
As the method for identifying the parameters of the initiating explosive device detonation process, the step 1) specifically comprises the following steps:
step 1-1), constructing a Volterra model of the initiating explosive device initiation process:
the initiating explosive device detonation process model can be expressed by Volterra series
Figure BDA0003399689380000021
Figure BDA0003399689380000022
Wherein h is n (τ 1 ,τ 2 ,…,τ n ) Is an n-order Volterra kernel function of a nonlinear system, u (t) is input, and y (t) is output;
identifying a Volterra model, providing a discrete nonlinear Volterra model, and adding noise, wherein the expression is shown as a formula (3), and h is n (τ 1 ,τ 2 ,…,τ n ) A Volterra kernel function for a non-linear system, with u (t) as input, y (t) as output, and v (t) as system noise, where n represents the nth order, M n Representing the corresponding memory length;
Figure BDA0003399689380000023
wherein D (z) is a back shift operator z -1 Polynomial of (2)
Figure BDA0003399689380000024
Step 1-2) according to the formula (3), the relation between output y (t) and input u (t) and system noise v (t) can be deduced as shown in the formula (11);
defining a Volterra kernel vector h of the nonlinear system, a parameter vector d of a noise part and a parameter vector theta of the nonlinear system as follows:
Figure BDA0003399689380000025
Figure BDA0003399689380000026
Figure BDA0003399689380000027
information vector
Figure BDA0003399689380000028
And
Figure BDA0003399689380000029
are respectively defined as
Figure BDA00033996893800000210
Figure BDA0003399689380000031
Figure BDA0003399689380000032
Figure BDA0003399689380000033
As the method for identifying the parameters of the initiating explosive device detonation process, the step 2) specifically comprises the following steps:
step 2-1), the initiating explosive device detonation circuit is divided into a charging circuit and a discharging circuit for initiating explosive devices, the initiating explosive devices are detonated through circuit discharging, the power supply voltage of the charging circuit is set as the input of a system, and the discharging current in the discharging circuit is set as the output of the system;
step 2-2) deducing a Levenberg-Marquardt recursion algorithm:
order to
Figure BDA0003399689380000034
And
Figure BDA0003399689380000035
respectively representing the estimation of Volterra kernel vector h, the estimation of parameter vector d of noise model and the estimation of parameter vector theta of nonlinear system, which are respectively defined as
Figure BDA0003399689380000036
Figure BDA0003399689380000037
Figure BDA0003399689380000038
Figure BDA0003399689380000039
And
Figure BDA00033996893800000310
are respectively information vectors
Figure BDA00033996893800000311
And
Figure BDA00033996893800000312
by estimating of
Figure BDA00033996893800000313
Replacement information vector
Figure BDA00033996893800000314
And
Figure BDA00033996893800000315
can be obtained from the unknown variable v (t-i)
Figure BDA00033996893800000316
And
Figure BDA00033996893800000317
the following were used:
Figure BDA00033996893800000318
Figure BDA00033996893800000319
defining a criterion function as
Figure BDA00033996893800000320
The gradient and the hessian matrix can be obtained by calculation as
Figure BDA00033996893800000321
Figure BDA00033996893800000322
According to the LM recursive algorithm,
Figure BDA00033996893800000323
and
Figure BDA00033996893800000324
satisfies the following recursive expression
Figure BDA0003399689380000041
According to formula (11), obtaining
Figure BDA0003399689380000042
Using estimated values
Figure BDA0003399689380000043
Substitution
Figure BDA0003399689380000044
Available estimates of v (t)
Figure BDA0003399689380000045
Is composed of
Figure BDA0003399689380000046
The combination of equations (8), (12) - (16) and (18) - (21) constitutes the Levenberg-Marquardt recursion algorithm that recognizes the Volterra system;
step 2-3) let t =1, set p 0 Is a very large number, e.g. p 0 ＝10 6 Is provided with
Figure BDA0003399689380000047
u(t)＝0，y(t)＝0，
Figure BDA0003399689380000048
for t is less than or equal to 0, wherein I l Refers to a column vector of dimension l, whose elements are all 1;
step 2-4) collecting input data u (t) and output data y (t);
step 2-5) construction of respective
Figure BDA0003399689380000049
And
Figure BDA00033996893800000410
Figure BDA00033996893800000411
Figure BDA00033996893800000412
Figure BDA00033996893800000413
step 2-6) construction of gradient
Figure BDA00033996893800000414
Sea plug matrix
Figure BDA00033996893800000415
Figure BDA00033996893800000416
Figure BDA00033996893800000417
Step 2-7) calculating parameter estimation
Figure BDA00033996893800000418
Figure BDA00033996893800000419
Step 2-8) calculation
Figure BDA00033996893800000420
Figure BDA00033996893800000421
Step 2-9) t is increased by 1, whether the maximum recursion times are reached is judged, if not, the program jumps to step 2-5), and if so, the program enters step 2-10);
and 2-10) outputting a result to finish identification.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, a parameter identification model of the initiating explosive device in the initiating process is established, the parameters of the initiating process are identified by using a Levenberg-Marquardt recursion algorithm, and the convergence rate and the estimation precision are improved.
(2) Compared with a gradient descent method, the Levenberg-Marquardt recursion algorithm has higher convergence rate, and compared with a Newton-Gaussian method, the Levenberg-Marquardt recursion algorithm also has higher estimation accuracy.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a block diagram of the overall architecture of the present invention;
FIG. 2 is a diagram of a charging type ignition circuit of the electric initiating explosive device according to the present invention;
FIG. 3 is a general flow diagram of the Levenberg-Marquardt recursion algorithm of the present invention;
FIG. 4 is a schematic diagram of the error between the identification parameter and the true value according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
Fig. 2 shows a schematic diagram of a charging type ignition circuit of an electric initiating explosive device used in this example. Wherein U (t) is a power supply U s I.e. a given voltage in the charging circuit; y (t) is the current in the discharge circuit; r s For charging the resistor, diode prevention in the charging circuitThe current flows backwards; r is 1 The current limiting resistor in the discharge circuit prevents the current in the circuit from being overlarge; r is f Is an electrical initiator resistor; c is a capacitor, and the initiating explosive device is discharged to realize the detonation of the initiating explosive device; s. the 1 、S 2 Respectively, the control switches of the charging circuit and the discharging circuit.
Referring to fig. 1 to 4, the technical scheme provided by the invention is that the method for identifying the initiating explosive device detonation process parameters comprises the following specific steps:
step 1) establishing a Volterra model of the initiating explosive device detonation process;
and 2) constructing an identification process of a Levenberg-Marquardt recursion algorithm.
As a method for identifying parameters of the initiating explosive device detonation process provided by the invention, the step 1) specifically comprises the following steps:
step 1-1), constructing a Volterra model of the initiating explosive device initiating process:
the model of the priming process of the initiating explosive device can be expressed by Volterra series
Figure BDA0003399689380000061
Figure BDA0003399689380000062
Wherein h is n (τ 1 ,τ 2 ,…,τ n ) Is an n-order Volterra kernel function of a nonlinear system, u (t) is input, and y (t) is output;
identifying a Volterra model, providing a discrete nonlinear Volterra model, and adding noise, wherein the expression is shown as a formula (3), and h is n (τ 1 ,τ 2 ,…,τ n ) A Volterra kernel function for a non-linear system, with u (t) as input, y (t) as output, and v (t) as system noise, where n represents the nth order, M n Representing the corresponding memory length;
Figure BDA0003399689380000063
wherein D (z) is the back-shift operator z -1 Polynomial of
Figure BDA0003399689380000064
Step 1-2) according to the formula (3), the relation between output y (t) and input u (t) and system noise v (t) can be deduced as shown in the formula (11);
a Volterra kernel vector h of the nonlinear system, a parameter vector d of the noise part, and a parameter vector θ of the nonlinear system are defined as follows:
Figure BDA0003399689380000065
Figure BDA0003399689380000066
Figure BDA0003399689380000067
information vector
Figure BDA0003399689380000068
And
Figure BDA0003399689380000069
are respectively defined as
Figure BDA00033996893800000610
Figure BDA0003399689380000071
Figure BDA0003399689380000072
Figure BDA0003399689380000073
With the Volterra model mentioned above, the following second order Volterra model can be built for this example:
Figure BDA0003399689380000074
the parameters to be identified according to step 1 can be obtained as follows:
h＝[2.50,-1.49,1.59,-0.61,3.73,-1.93,3.29,-0.69,0.01] T (13)
d＝[1.16,-2.52] T (14)
Figure BDA0003399689380000075
as a method for identifying parameters of the initiating explosive device detonation process provided by the invention, the step 2) specifically comprises the following steps:
step 2-1), the initiating explosive device detonation circuit is divided into a charging circuit and a discharging circuit for initiating explosive devices, the initiating explosive devices are detonated through circuit discharging, the power supply voltage of the charging circuit is set as the input of a system, and the discharging current in the discharging circuit is set as the output of the system;
step 2-2) deriving a Levenberg-Marquardt recursion algorithm:
order to
Figure BDA0003399689380000076
And
Figure BDA0003399689380000077
respectively representing the estimation of Volterra kernel vector h, the estimation of parameter vector d of noise model and the estimation of parameter vector theta of nonlinear system, which are respectively defined as
Figure BDA0003399689380000078
Figure BDA0003399689380000079
Figure BDA00033996893800000710
Figure BDA00033996893800000711
And
Figure BDA00033996893800000712
are respectively information vectors
Figure BDA00033996893800000713
And
Figure BDA00033996893800000714
by estimating of
Figure BDA00033996893800000715
Replacement information vector
Figure BDA00033996893800000716
And
Figure BDA00033996893800000717
can be obtained from the unknown variable v (t-i)
Figure BDA0003399689380000081
And
Figure BDA0003399689380000082
the following were used:
Figure BDA0003399689380000083
Figure BDA0003399689380000084
defining a criterion function as
Figure BDA0003399689380000085
The gradient and the hessian matrix can be obtained by calculation as
Figure BDA0003399689380000086
Figure BDA0003399689380000087
According to the LM recursive algorithm,
Figure BDA0003399689380000088
and
Figure BDA0003399689380000089
satisfy the following recurrence expression
Figure BDA00033996893800000810
According to formula (11), obtaining
Figure BDA00033996893800000811
Using estimated values
Figure BDA00033996893800000812
Substitution
Figure BDA00033996893800000813
An estimate of v (t) is available
Figure BDA00033996893800000814
Is composed of
Figure BDA00033996893800000815
The combination of equations (8), (16) - (20) and (22- (25) form the Levenberg-Marquardt recursion algorithm for identifying the Volterra system;
step 2-3) let t =1, set p 0 Is a very large number, e.g. p 0 ＝10 6 Is provided with
Figure BDA00033996893800000816
u(t)＝0，y(t)＝0，
Figure BDA00033996893800000817
for t is less than or equal to 0, wherein I l Refers to a column vector of dimension l, whose elements are all 1;
step 2-4) collecting input data u (t) and output data y (t);
step 2-5) construction of respective
Figure BDA00033996893800000818
And
Figure BDA00033996893800000819
Figure BDA00033996893800000820
Figure BDA00033996893800000821
Figure BDA00033996893800000822
step 2-6) construction of gradient
Figure BDA00033996893800000823
Sea plug matrix
Figure BDA00033996893800000824
Figure BDA00033996893800000825
Figure BDA00033996893800000826
Step 2-7) calculating parameter estimation
Figure BDA0003399689380000091
Figure BDA0003399689380000092
Step 2-8) calculation
Figure BDA0003399689380000093
Figure BDA0003399689380000094
Step 2-9) t is increased by 1, whether the maximum recursion times are reached is judged, if not, the program jumps to step 2-5), and if so, the program enters step 2-10);
and 2-10) outputting a result to finish identification.
When the damping coefficient is small, the method can be similar to a Gauss-Newton method, and at the moment, the convergence speed is high, but the method is unstable in convergence and the estimation precision is not high; when the damping coefficient is larger, the method can be similar to a gradient descent method, and at the moment, convergence is stable, estimation accuracy is higher, but convergence speed is slow, so that the convergence speed and the estimation accuracy are ensured by selecting a proper damping coefficient.
The parameter identification result of the initiating explosive device detonation process based on the Levenberg-Marquardt recursion algorithm is shown in FIG. 4. It can be seen that the method has high identification precision, the estimated value of the parameter to be identified is very close to the true value, and the convergence rate is high; meanwhile, the identification method has better applicability to parameter identification in the initiating explosive device detonation process.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.

Claims (1)

1. A method for identifying parameters of initiating explosive device detonation process is characterized by comprising the following steps:
step 1) establishing a Volterra model of the initiating explosive device detonation process;
step 2) constructing an identification process of a Levenberg-Marquardt recursion algorithm;
the step 1) specifically comprises the following steps:
step 1-1), constructing a Volterra model of the initiating explosive device initiating process:
model of initiating explosive device detonation process, expressed by Volterra series
Figure FDA0003890958760000011
Figure FDA0003890958760000012
Wherein h is n (τ 1 ,τ 2 ,…,τ n ) Is an n-order Volterra kernel function of a nonlinear system, u (t) is input, and y (t) is output;
identifying a Volterra model, providing a discrete nonlinear Volterra model, and adding noise, wherein the expression is shown as a formula (3), and h is n (τ 1 ,τ 2 ,…,τ n ) Is composed ofVolterra kernel function of nonlinear system, u (t) is input, y (t) is output, v (t) is system noise, wherein n represents nth order, M is n Representing the corresponding memory length;
Figure FDA0003890958760000013
wherein D (z) is the back-shift operator z -1 Polynomial of (2)
Figure FDA0003890958760000014
Step 1-2) according to the formula (3), the relation between output y (t) and input u (t) and system noise v (t) can be deduced as shown in the formula (11);
a Volterra kernel vector h of the nonlinear system, a parameter vector d of the noise part, and a parameter vector θ of the nonlinear system are defined as follows:
Figure FDA0003890958760000015
Figure FDA0003890958760000016
Figure FDA0003890958760000021
information vector
Figure FDA0003890958760000022
And
Figure FDA0003890958760000023
are respectively defined as
Figure FDA0003890958760000024
Figure FDA0003890958760000025
Figure FDA0003890958760000026
Figure FDA0003890958760000027
The step 2) specifically comprises the following steps:
step 2-1), the initiating explosive device detonation circuit is divided into a charging circuit and a discharging circuit for initiating explosive devices, the initiating explosive devices are detonated through circuit discharging, the power supply voltage of the charging circuit is set as the input of a system, and the discharging current in the discharging circuit is set as the output of the system;
step 2-2) deriving a Levenberg-Marquardt recursion algorithm:
order to
Figure FDA0003890958760000028
And
Figure FDA0003890958760000029
respectively representing the estimation of a Volterra kernel vector h, the estimation of a parameter vector d of a noise model and the estimation of a parameter vector theta of a nonlinear system, which are respectively defined as
Figure FDA00038909587600000210
Figure FDA00038909587600000211
Figure FDA00038909587600000212
Figure FDA00038909587600000213
And
Figure FDA00038909587600000214
are respectively information vectors
Figure FDA00038909587600000215
And
Figure FDA00038909587600000216
by estimating of
Figure FDA00038909587600000217
Replacement information vector
Figure FDA00038909587600000218
And
Figure FDA00038909587600000219
can be obtained from the unknown variable v (t-i)
Figure FDA00038909587600000220
And
Figure FDA00038909587600000221
the following were used:
Figure FDA00038909587600000222
Figure FDA00038909587600000223
defining a criterion function as
Figure FDA0003890958760000031
The gradient and the hessian matrix can be obtained by calculation as
Figure FDA0003890958760000032
Figure FDA0003890958760000033
According to the LM recursive algorithm,
Figure FDA0003890958760000034
and
Figure FDA0003890958760000035
satisfy the following recurrence expression
Figure FDA0003890958760000036
According to formula (11), obtaining
Figure FDA0003890958760000037
Using estimated values
Figure FDA0003890958760000038
Substitution
Figure FDA0003890958760000039
Available estimates of v (t)
Figure FDA00038909587600000310
Is composed of
Figure FDA00038909587600000311
The combination of equations (8), (12) - (16) and (18) - (21) constitutes the Levenberg-Marquardt recursion algorithm that recognizes the Volterra system;
step 2-3) let t =1,p 0 ＝10 6 Is provided with
Figure FDA00038909587600000312
u(t)＝0，y(t)＝0，
Figure FDA00038909587600000313
for t is less than or equal to 0, wherein I l Refers to a column vector of dimension l, whose elements are all 1;
step 2-4) collecting input data u (t) and output data y (t);
step 2-5) construction of respective
Figure FDA00038909587600000314
And
Figure FDA00038909587600000315
Figure FDA00038909587600000316
Figure FDA00038909587600000317
Figure FDA00038909587600000318
step 2-6) construction of gradient
Figure FDA00038909587600000319
Sea plug matrix
Figure FDA00038909587600000320
Figure FDA00038909587600000321
Figure FDA00038909587600000322
Step 2-7) calculating parameter estimation
Figure FDA00038909587600000323
Figure FDA00038909587600000324
Step 2-8) calculation
Figure FDA00038909587600000325
Figure FDA00038909587600000326
Step 2-9) t is increased by 1, whether the maximum recursion times are reached is judged, if not, the program jumps to step 2-5), and if so, the program enters step 2-10);
and 2-10) outputting a result to finish identification.
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