CN110321524B - Nuclear magnetic resonance echo data inversion method and system based on non-negative elastic network - Google Patents
Nuclear magnetic resonance echo data inversion method and system based on non-negative elastic network Download PDFInfo
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Abstract
The invention discloses a nuclear magnetic resonance echo data inversion method and a nuclear magnetic resonance echo data inversion system based on a non-negative elastic network, wherein the nuclear magnetic resonance echo data inversion method comprises the following steps: constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution; replacing the variable f by using a non-negative exponential function exp (x), and converting a non-negative elastic network objective function into an unconstrained objective function; solving a solution x of the unconstrained objective function; obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution. The nuclear magnetic resonance echo data inversion method based on the non-negative elastic network provided by the invention adopts a variable replacement method to realize the non-negative constraint of the non-negative elastic network, so that the non-negative elastic network is converted into a non-constraint elastic network, and then the non-negative elastic network can be simply and quickly solved by adopting a Levenberg-Marquardt method to obtain a solution, and the distribution amplitude of nuclear magnetic resonance T2 is inverted.
Description
Technical Field
The invention belongs to the technical field of geophysical inversion in oil and gas exploration, and particularly relates to a nuclear magnetic resonance echo data inversion method and system based on a non-negative elastic network.
Background
For the inversion of nuclear magnetic resonance echo data, truncated singular value decomposition and Tikhonov regularization methods are mainly used at present (Prammer, 1994; Dunn et al, 1994; Chen et al, 2009). The signal-to-noise ratio of the nuclear magnetic resonance logging echo string is low, and a truncated singular value decomposition method needs to adopt a larger truncated singular value, so that the inverted T2 distribution resolution is low; the Tikhonov regularization method smoothes the inverted T2 distribution so that coupling between the spectral peaks of the T2 distribution occurs, reducing resolution. Since the elastic network was proposed by Zou and Hastie (2005), the elastic network provided a new regularization method for people, which fuses L 1 Penalty sum L 2 The punishment characteristic is used for balancing the sparsity and the smoothness of the inversion result, the resolution of the inversion result can be improved, the method is more and more concerned and emphasized in various subject fields such as support vector machines, metric learning, combination optimization and the like, and the method has a very wide application prospect. However, the solution elastic network is a nonlinear inverse problem, and the solution process is difficult and complex. At present, people mainly adopt an LARS-EN method to solve the elastic network, and the method adopts the LARS method to solve after converting the elastic network into Lasso. In practical applications, sometimes to satisfy practical physical meanings, it is necessary to apply non-negative constraints to the solution of the elastic network, that is, to solve the non-negative elastic network, but the LARS method does not consider the case when the elastic network applies the non-negative constraints.
Therefore, it is necessary to provide a nuclear magnetic resonance echo data inversion method and system based on the non-negative elastic network.
Disclosure of Invention
The invention provides a nuclear magnetic resonance echo data inversion method and system based on a non-negative elastic network, wherein a non-negative elastic network target function is constructed based on nuclear magnetic resonance echo data, and a variable f of the non-negative elastic network target function is the distribution amplitude of transverse relaxation time T2; the non-negative constraint of the non-negative elastic network is realized by adopting a variable replacement method, so that the non-negative elastic network is converted into an unconstrained elastic network, the solution of the non-negative elastic network can be obtained simply and quickly by adopting a Levenberg-Marquardt method, and the amplitude of the distribution of the nuclear magnetic resonance T2 can be inverted, so that reservoir parameters such as the formation porosity, the permeability, the fluid type, the fluid saturation, the pore size distribution, the formation wettability, the crude oil viscosity and the like can be further evaluated.
According to one aspect of the invention, a nuclear magnetic resonance echo data inversion method based on a non-negative elastic network is provided, and the method comprises the following steps:
1) constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution;
2) replacing a variable f by using a non-negative exponential function exp (x), and converting the non-negative elastic network objective function into an unconstrained objective function;
3) solving a solution x of the unconstrained objective function;
4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution.
Preferably, the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | non-woven phosphor 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the magnitude of the nuclear magnetic resonance T2 distribution.
Preferably, step 3) comprises:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining the solution x of the unconstrained objective function by the Levenberg-Marquardt method.
Preferably, the gradient of the unconstrained objective function is represented as:
φ'＝(WAdiag(f)) T (WAf-Wb)+α(diag(f)) T f+βf (2)
wherein W is a diagonal matrix, A is a nuclear matrix, b is measured NMR echo data, α and β are both regularization parameters, and f is the magnitude of the NMR T2 distribution.
Preferably, the Hessian matrix of the unconstrained objective function is represented as:
φ”≈(WAdiag(f)) T (WAdiag(f))+α(diag(f)) T (diag(f)) (3)
where W is the diagonal matrix, a is the kernel matrix, b is the measured nmr echo data, α is the regularization parameter, and f is the magnitude of the nmr T2 distribution.
Preferably, the Levenberg-Marquardt method is an iterative method, and the iterative formula of the solution x of the unconstrained objective function is:
x n ＝x n-1 -(φ”+μI) -1 φ' (4)
wherein phi 'is the gradient of the unconstrained objective function, phi' is the Hessian matrix of the unconstrained objective function, I is the identity matrix,
Δx＝x n -x n-1 ，Δφ＝φ(x n )-φ(x n-1 ) N is the number of iterations, x n Is the solution, x, of the unconstrained objective function after the nth iteration n-1 Is the solution of the unconstrained objective function after the (n-1) th iteration, phi (x) n ) Is the value of the unconstrained objective function after the nth iteration, phi (x) n-1 ) Is the value of the unconstrained objective function after the (n-1) th iteration.
Preferably, the non-negative elastic network objective function is constructed based on elastic network Lasso and ridge regression regularization parameters α and β.
According to another aspect of the present invention, a nuclear magnetic resonance echo data inversion system based on a non-negative elastic network is provided, the system comprising: a memory storing computer-executable instructions; a processor that, when executing the computer-executable instructions on the memory, performs the steps of:
1) constructing nonnegative elasticity based on nuclear magnetic resonance echo dataA network objective function, wherein the variable f of the non-negative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution;
2) replacing a variable f by using a non-negative exponential function exp (x), and converting the non-negative elastic network objective function into an unconstrained objective function;
3) solving a solution x of the unconstrained objective function;
4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution.
Preferably, the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | non-woven phosphor 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the magnitude of the nuclear magnetic resonance T2 distribution.
Preferably, step 3) comprises:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining the solution x of the unconstrained objective function by the Levenberg-Marquardt method.
The invention has the beneficial effects that: constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein a variable f of the nonnegative elastic network objective function is the distribution amplitude of transverse relaxation time T2; the method realizes the non-negative constraint of the non-negative elastic network by using a variable replacement method, converts the non-negative constraint elastic network objective function into the unconstrained elastic network objective function for solving, solves the new objective function simply and quickly, overcomes the technical problems of difficulty and complexity in realizing the non-negative constraint and solving of the elastic network in the prior art, solves the solution x of the unconstrained objective function and finally obtains the transverse relaxation time T 2 The magnitude of the distribution.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
Fig. 1 shows a flow chart of a nuclear magnetic resonance echo data inversion method based on a non-negative elastic network according to the invention.
FIG. 2 shows a simulated transverse relaxation time T according to an embodiment of the invention 2 Schematic diagram of distribution model, where Amplitude is Amplitude, T 2 Is the transverse relaxation time.
FIG. 3 is a diagram illustrating simulated NMR echo data and NMR echo data after applying noise thereto according to an embodiment of the invention, where Amplitude is Amplitude and T is Amplitude 2 Is the transverse relaxation time, Raw Echo Train is the Raw Echo data and noise Echo Train is the Echo data after applying noise.
FIG. 4 shows transverse relaxation times T obtained by inversion of the nuclear magnetic resonance echo data of FIG. 3 with noise applied according to an embodiment of the invention 2 Transverse relaxation time T of the distribution and simulation in FIG. 2 2 Comparison of the distribution model, where Amplitude is Amplitude, T 2 Is the transverse relaxation time, T 2 Model is T 2 The distribution model, inversion Result, is the inverted T2 distribution.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below. While the following describes preferred embodiments of the present invention, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Example 1
In this embodiment, the method for inverting nuclear magnetic resonance echo data based on a non-negative elastic network according to the present invention may include: 1) constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution; 2) replacing the variable f by using a non-negative exponential function exp (x), and converting a non-negative elastic network objective function into an unconstrained objective function; 3) solving a solution x of the unconstrained objective function; 4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution.
Elastic network simultaneous application of L 1 And L 2 Punishment, it merges L 1 Penalty sum L 2 And the punishment characteristic is used for balancing the sparsity and the smoothness of the solution and is applied to the field of data inversion of various disciplines. The solution elastic network is a nonlinear inverse problem, the solution of the objective function is complex and difficult, and the objective function is usually solved by combining a quasi-Newton method with a complex linear search method. In practical application, in many cases, in order to satisfy the practical physical significance, non-negative constraints need to be applied to the solution of the objective function, and the complexity and difficulty in understanding the objective function are further increased.
The embodiment provides a nuclear magnetic resonance echo data inversion method and system based on a non-negative elastic network, a non-negative elastic network target function is constructed based on nuclear magnetic resonance echo data, and a variable f of the non-negative elastic network target function is the amplitude of transverse relaxation time T2 distribution; the non-negative constraint of the non-negative elastic network is realized by adopting a variable replacement method, so that the non-negative elastic network is converted into an unconstrained elastic network, the solution of the non-negative elastic network can be obtained simply and quickly by adopting a Levenberg-Marquardt method, and the amplitude of the distribution of the nuclear magnetic resonance T2 can be inverted, so that reservoir parameters such as the formation porosity, the permeability, the fluid type, the fluid saturation, the pore size distribution, the formation wettability, the crude oil viscosity and the like can be further evaluated.
Fig. 1 shows a flow chart of a nuclear magnetic resonance echo data inversion method based on a non-negative elastic network according to the invention. The following describes in detail specific steps of the inversion method of nuclear magnetic resonance echo data based on non-negative elastic network according to the present invention with reference to fig. 1.
in one example, given the elastic network Lasso and ridge regression regularization parameters α and β, a non-negative elastic network objective function of the non-negative elastic network is constructed.
In one example, the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | non-woven phosphor 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the amplitude of the nuclear magnetic resonance T2 distribution.
102, replacing a variable f by a non-negative exponential function exp (x), and converting a non-negative elastic network objective function into an unconstrained objective function;
specifically, according to the objective function of the non-negative elastic network as shown in formula (1), let
f＝exp(x)， (5)
Constructing an unconstrained objective function, wherein the unconstrained objective function is shown in formula (6):
in the embodiment, the solution of the non-negative elastic network objective function is converted into the solution of a new unconstrained objective function by replacing the solution variable f with the non-negative exponential function exp (x), so that the non-negative constraint of the solution is realized.
103, solving a solution x of the unconstrained objective function;
in one example, step 3) includes:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining the solution x of the unconstrained objective function by a Levenberg-Marquardt method.
In one example, the gradient of the unconstrained objective function, as shown in equation (6), is solved, with the gradient being expressed as:
φ'＝(WAdiag(f)) T (WAf-Wb)+α(diag(f)) T f+βf (2)
wherein, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data, alpha and beta are both regularization parameters, and f is the amplitude of nuclear magnetic resonance T2 distribution.
In one example, a Hessian matrix of the unconstrained objective function as shown in equation (6) is solved, where the Hessian matrix is expressed as:
φ”≈(WAdiag(f)) T (WAdiag(f))+α(diag(f)) T (diag(f)) (3)
where W is the diagonal matrix, a is the nuclear matrix, b is the measured nmr echo data, α is the regularization parameter, and f is the magnitude of the nmr T2 distribution.
In one example, the new objective function is solved using a Levenberg-Marquardt method, which is an iterative method, and the iterative formula for the solution x of the unconstrained objective function is:
x n ＝x n-1 -(φ”+μI) -1 φ' (4)
wherein phi 'is the gradient of the unconstrained objective function, phi' is the Hessian matrix of the unconstrained objective function, I is the identity matrix,
Δx＝x n -x n-1 ，Δφ＝φ(x n )-φ(x n-1 ) N is the number of iterations, x n Is the solution, x, of the unconstrained objective function after the nth iteration n-1 Is the solution of the unconstrained objective function after the (n-1) th iteration, phi (x) n ) Is the value of the unconstrained objective function after the nth iteration, phi (x) n-1 ) Is the value of the unconstrained objective function after the (n-1) th iteration.
The solution x of the unconstrained objective function is obtained using equation (4) in conjunction with equations (2) and (3).
Specifically, a non-negative elastic network objective function solution f, i.e., a transverse relaxation time T, is obtained using equation (5) from the solution x of the unconstrained objective function 2 The magnitude of the distribution.
In this embodiment, a non-negative elastic network objective function is constructed based on nuclear magnetic resonance echo data, and a variable f of the non-negative elastic network objective function is a distribution amplitude of transverse relaxation time T2; the method realizes the non-negative constraint of the non-negative elastic network by using a variable replacement method, converts the non-negative constraint elastic network objective function into the unconstrained elastic network objective function for solving, solves the new objective function simply and quickly, overcomes the technical problems of difficulty and complexity in realizing the non-negative constraint and solving of the elastic network in the prior art, solves the solution x of the unconstrained objective function and finally obtains the transverse relaxation time T 2 The magnitude of the distribution.
Application examples
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
FIG. 2 shows a simulated transverse relaxation time T according to an embodiment of the invention 2 Schematic diagram of distribution model. As shown in FIG. 2, T 2 The distribution preselects 128 components and has minimum and maximum values of 0.1ms and 10000ms, respectively. Wherein the inversion result f of the NMR echo data is about the transverse relaxation time T 2 The magnitude of the distribution.
FIG. 3 shows simulated nuclear magnetic resonance echo counts according to an embodiment of the inventionThe diagram shows the data of the nuclear magnetic resonance echo after the noise is applied, wherein the echo interval is 0.9ms, and the number of the echoes is 1666. The specific acquisition process of the nuclear magnetic resonance echo data in fig. 3 is as follows: simulated transverse relaxation time T in FIG. 2 2 And forward modeling the distribution model to obtain nuclear magnetic resonance echo data, wherein the obtained nuclear magnetic resonance echo data does not contain noise, namely the original nuclear magnetic resonance echo data simulated in the figure 3, and applying white gaussian noise with the standard deviation of 0.25pu to the nuclear magnetic resonance echo data to obtain the nuclear magnetic resonance echo data with the noise applied in the figure 3.
First, given that α is 2 and β is 0.1, a nonnegative elastic network objective function is constructed as shown in equation (1) based on the nmr echo data, and a variable f of the nonnegative elastic network objective function is a transverse relaxation time T 2 The magnitude of the distribution;
secondly, replacing a variable f by a non-negative exponential function exp (x), and converting a non-negative elastic network objective function shown in a formula (1) into an unconstrained objective function shown in a formula (6);
then, the gradient and the Hessian matrix of the unconstrained objective function shown in formula (6) are respectively calculated, and the solution x of the unconstrained objective function is obtained by a Levenberg-Marquardt method.
Finally, the non-negative elastic network solution f, i.e. the transverse relaxation time T, is obtained from the solution x of the unconstrained objective function using equation (5) 2 The magnitude of the distribution.
FIG. 4 shows the transverse relaxation time T obtained by inverting the NMR echo data of FIG. 3 with the method for inverting NMR echo data of the above application example 2 Transverse relaxation time T of the distribution and simulation in FIG. 2 2 Comparative plot of distribution model. As can be seen from fig. 4, the inversion result and the simulated transverse relaxation time T obtained by the non-negative elastic network solution method according to the embodiment of the present invention 2 The distribution models are almost overlapped, which shows the effectiveness of the method for solving the nonnegative elastic network, and the nonnegative elastic network can be effectively solved to obtain the solution, so that the nuclear magnetic resonance T2 distribution is inverted.
The application example is based on nuclear magnetic resonance echo data to construct a nonnegative elastic networkThe variable f of the target function of the non-negative elastic network is the amplitude of the distribution of transverse relaxation time T2; the method realizes the non-negative constraint of the non-negative elastic network by using a variable replacement method, converts the non-negative constraint elastic network objective function into the unconstrained elastic network objective function for solving, solves the new objective function simply and quickly, overcomes the technical problems of difficulty and complexity in realizing the non-negative constraint and solving of the elastic network in the prior art, solves the solution x of the unconstrained objective function and finally obtains the transverse relaxation time T 2 The magnitude of the distribution.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Example 2
According to an embodiment of the invention, a nuclear magnetic resonance echo data inversion system based on a non-negative elastic network is provided, and the system comprises: a memory storing computer executable instructions; a processor that, when executing the computer-executable instructions on the memory, performs the steps of:
1) constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution;
2) replacing the variable f by using a non-negative exponential function exp (x), and converting a non-negative elastic network objective function into an unconstrained objective function;
3) solving a solution x of the unconstrained objective function;
4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution.
The embodiment provides a nuclear magnetic resonance echo data inversion method and system based on a non-negative elastic network, a non-negative elastic network target function is constructed based on nuclear magnetic resonance echo data, and a variable f of the non-negative elastic network target function is the distribution amplitude of transverse relaxation time T2; the non-negative constraint of the non-negative elastic network is realized by adopting a variable replacement method, so that the non-negative elastic network is converted into an unconstrained elastic network, the solution of the non-negative elastic network can be obtained simply and quickly by adopting a Levenberg-Marquardt method, and the amplitude of the distribution of the nuclear magnetic resonance T2 can be inverted, so that reservoir parameters such as the formation porosity, the permeability, the fluid type, the fluid saturation, the pore size distribution, the formation wettability, the crude oil viscosity and the like can be further evaluated.
In one example, the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | non-woven phosphor 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the amplitude of the nuclear magnetic resonance T2 distribution.
In one example, step 3) includes:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining the solution x of the unconstrained objective function by a Levenberg-Marquardt method.
In this embodiment, a nonnegative elastic network objective function is constructed based on nuclear magnetic resonance echo data, and a variable f of the nonnegative elastic network objective function is a distribution amplitude of transverse relaxation time T2; the method realizes the non-negative constraint of the non-negative elastic network by using a variable replacement method, converts the non-negative constraint elastic network objective function into the unconstrained elastic network objective function for solving, solves the new objective function simply and quickly, overcomes the technical problems of difficulty and complexity in realizing the non-negative constraint and solving of the elastic network in the prior art, solves the solution x of the unconstrained objective function and finally obtains the transverse relaxation time T 2 The magnitude of the distribution.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
While embodiments of the present invention have been described above, the above description is illustrative, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (3)
1. A nuclear magnetic resonance echo data inversion method based on a non-negative elastic network is characterized by comprising the following steps:
1) constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution;
2) replacing a variable f by using a non-negative exponential function exp (x), and converting the non-negative elastic network objective function into an unconstrained objective function;
3) solving a solution x of the unconstrained objective function;
4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution;
wherein the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | non-woven phosphor 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the T sought 2 The magnitude of the distribution;
the step 3) comprises the following steps:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining a solution x of the unconstrained objective function by a Levenberg-Marquardt method;
the gradient of the unconstrained objective function is represented as:
φ'＝(WAdiag(f)) T (WAf-Wb)+αdiag(f)) T f+βf (2)
hessian matrix of the unconstrained objective function
Expressed as:
φ”≈(WAdiag(f)) T (WAdiag(f))+α(diag(f)) T (diag(f)) (3)
the Levenberg-Marquardt method is an iterative method, and the iterative formula of the solution x of the unconstrained objective function is as follows:
x n ＝x n-1 -(φ”+μI) -1 φ' (4)
wherein phi 'is the gradient of the unconstrained objective function, phi' is the Hessian matrix of the unconstrained objective function, I is the identity matrix,
Δx＝x n -x n-1 ，Δφ＝φ(x n )-φ(x n-1 ) N is the number of iterations, x n Is the solution, x, of the unconstrained objective function after the nth iteration n-1 Is the solution of the unconstrained objective function after the (n-1) th iteration, phi (x) n ) Is the value of the unconstrained objective function after the nth iteration, φ (x) n-1 ) Is the value of the unconstrained objective function after the (n-1) th iteration.
2. The inversion method of nuclear magnetic resonance echo data based on a non-negative elastic network according to claim 1, wherein the non-negative elastic network objective function is constructed based on elastic network Lasso and ridge regression regularization parameters α and β.
3. A nuclear magnetic resonance echo data inversion system based on a non-negative elastic network, the system comprising:
a memory storing computer-executable instructions;
a processor that, when executing the computer-executable instructions on the memory, performs the steps of:
1) constructing a nonnegative elastic network objective function based on nuclear magnetic resonance echo data, wherein the variable f of the nonnegative elastic network objective function is transverse relaxation time T 2 The magnitude of the distribution;
2) replacing a variable f by using a non-negative exponential function exp (x), and converting the non-negative elastic network objective function into an unconstrained objective function;
3) solving a solution x of the unconstrained objective function;
4) obtaining a transverse relaxation time T based on the value of x 2 The magnitude of the distribution;
wherein the non-negative elastic network objective function is expressed as:
wherein φ (f) is a nonnegative elastic network objective function, W is a diagonal matrix, A is a nuclear matrix, b is measured nuclear magnetic resonance echo data,
is a ridge regression regularization term, | f | | calculation 1 For the Lasso regularization term, α and β are both regularization parameters, and f is the T of interest 2 The magnitude of the distribution;
the step 3) comprises the following steps:
3.1) calculating the gradient and Hessian matrix of the unconstrained objective function;
3.2) obtaining a solution x of the unconstrained objective function by a Levenberg-Marquardt method;
the gradient of the unconstrained objective function is represented as:
φ'＝(WAdiag(f)) T (WAf-Wb)+α(diag(f)) T f+βf (2)
hessian matrix of the unconstrained objective function
Expressed as:
φ”≈(WAdiag(f)) T (WAdiag(f))+α(diag(f)) T (diag(f)) (3)
the Levenberg-Marquardt method is an iterative method, and the iterative formula of the solution x of the unconstrained objective function is as follows:
x n ＝x n-1 -(φ”+μI) -1 φ' (4)
wherein phi 'is the gradient of the unconstrained objective function, phi' is the Hessian matrix of the unconstrained objective function, I is the identity matrix,
Δx＝x n -x n-1 ，Δφ＝φ(x n )-φ(x n-1 ) N is the number of iterations, x n Is the solution, x, of the unconstrained objective function after the nth iteration n-1 Is the solution of the unconstrained objective function after the (n-1) th iteration, phi (x) n ) Is the value of the unconstrained objective function after the nth iteration, phi (x) n-1 ) Is the value of the unconstrained objective function after the (n-1) th iteration.
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106199474A (en) * | 2016-07-21 | 2016-12-07 | 上海理工大学 | A kind of low-field nuclear magnetic resonance two-dimensional spectrum inversion algorithm |
| CN106291723A (en) * | 2016-07-25 | 2017-01-04 | 中国石油大学(北京) | Nuclear magnetic resonance, NMR echo data inversion method based on two-parameter regularization and device |
Non-Patent Citations (1)
| Title |
|---|
| 随钻核磁共振井下快速反演算法设计;孟铎等;《国外电子测量技术》;20140531(第5期);第35-39页 * |
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