Cascade FBG array multi-vibration event identification method based on group sparse reconstruction

Abstract

The invention discloses a cascade FBG array multi-vibration event identification method based on group sparse reconstruction. The method comprises the following steps: 1) providing a cascade FBG grating array; 2) solving a sparse feature vector; 3) establishing a vibration event projection observation matrix; 4) obtaining and constructing a vibration event feature dictionary; and 5) identifying a vibration event. According to the cascaded FBG array multi-vibration event identification method based on group sparse reconstruction, based on the structured sparse characteristics of the reflection spectrum of each FBG and the structured sparse characteristics of the reflection spectrum of each FBG, a group sparse representation model that a single vibration event generates phase shift in adjacent FBGs is established for the reflection spectrum of a cascaded FBG grating array, and the multi-vibration event identification of the cascaded FBG array is realized. The multi-point vibration event synchronous recognition method based on the FBG group sparse representation model has the advantages that the coupling interference between the FBGs is suppressed, the synchronous recognition of the multi-point vibration event is obtained through the optimization solution of the group sparse representation model, the recognition accuracy and sensitivity are high, and the popularization and application value is high.

Description

Technical Field

[0001] The invention relates to a method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction. Background Art

[0002] In the actual application of grating detection systems, it is often necessary to simultaneously detect multiple parameters such as temperature, strain and vibration. Since a single grating sensor cannot separate the modulation of each parameter on the FBG central wavelength, it makes it difficult to distinguish the wavelength change of a single physical quantity.

[0003] To solve the above problems, the present invention adopts multi-point vibration sensing technology based on grating arrays, and realizes simultaneous detection at multiple points by connecting multiple FBGs in series on a single optical fiber. Each FBG is sensitive to vibrations at different positions. By analyzing the reflection spectrum of each FBG, vibration information of multiple points can be obtained simultaneously, thereby significantly improving the detection range and sensitivity of the system. However, in the actual implementation process, there will be coupling interference of the phase of the subsequent FBG reflected light from the transmitted light of the front FBG, and interference peaks will appear in the demodulated spectrum, reducing the accuracy of vibration event recognition. Summary of the invention

[0004] In order to solve the technical problems existing in the prior art, the object of the present invention is to provide a method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction.

[0005] In order to achieve the above purpose and the above technical effect, the technical solution adopted by the present invention is:

[0006] The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction includes the following steps:

[0007] 1) Providing a cascaded FBG grating array consisting of a plurality of FBGs;

[0008] 2) Solve for sparse feature vectors;

[0009] 3) Establishing vibration event projection observation matrix;

[0010] 4) Obtaining a dictionary of structural vibration event features;

[0011] 5) Identify vibration events.

[0012] 2. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 1, characterized in that, in step 1), the cascaded FBG grating array includes a plurality of FBGs arranged in sequence, which are respectively denoted as FBG 1, FBG 2, FBG 3, ... , FBG n;

[0013] Let the incident pulse light be expressed as:

[0014]

[0015] When the incident pulse light enters the cascaded FBG grating array, the reflected light pulse corresponding to the nth FBG is expressed as:

[0016]

[0017] When the transmitted light of the preceding FBG produces coupling interference on the subsequent FBG, the reflected light pulse corresponding to the interfered nth FBG is expressed as:

[0018]

[0019] Where E0 is the amplitude of the light source; f c is the incident light frequency; is the initial phase of the optical pulse modulation; T is the width of the modulated optical pulse; η is the amplitude modulation coefficient of the reflected light; τ n is the time delay corresponding to the nth FBG reflected light pulse; is the phase shift of the optical pulse caused by the vibration event observed by the nth FBG.

[0020] Furthermore, in step 2), the step of solving the sparse feature vector includes:

[0021] The phase search interval Ω of the phase domain dictionary is defined as:

[0022] Ω=[φ1,φ2,…,φ Q ] (4)

[0023] Search phase φ q The corresponding dictionary atoms are:

[0024]

[0025] Then the sparse dictionary Ψ corresponding to the phase search interval Ω is:

[0026] Ψ=[ψ1,ψ2,…,ψ Q ] (6)

[0027] The pulse light received by the signal processing end connected to the cascaded FBG grating array is the synthetic signal of the reflected light of each FBG, expressed as:

[0028]

[0029] Thus, according to the solution in equation (7), the sparse feature vector θ is obtained, and the index value of its non-zero element can represent the corresponding vibration event;

[0030] Where q, Q are the number of phases to be searched, q≦Q; E0 is the amplitude of the light source; f c is the incident light frequency; is the initial phase of optical pulse modulation; N is the number of FBGs in the cascaded FBG grating array.

[0031] Furthermore, the sparse feature vector θ is obtained according to equation (7), which includes the following steps:

[0032] Step 1: Initialize the search count j = 1, define the correlation threshold ζ and the residual value ρ (0) = 0, event atom set Θ = [], atom offset value σ = 0;

[0033] Step 2: Calculate ω j =ψ T (j+σ) y;

[0034] Step 3: Make a threshold judgment;

[0035] Step 4: Update the event atomic set Θ = [Θ∪ψ j ], define the atomic offset value σ = j;

[0036] Step 5: Calculate the sparse feature vector θ.

[0037] Furthermore, in step 3, the step of performing threshold determination includes:

[0038] If j <ζ, then set j=j+1 and jump to step 2;

[0039] If j >ζ, then update the residual ρ (j) =ρ (j-1) -ω j And proceed to step 4.

[0040] Furthermore, in step 5, the step of calculating the sparse feature vector θ includes:

[0041] If j<N, set j=j+1 and jump to step 2;

[0042] If j = N, stop searching and calculate

[0043] Furthermore, in step 3), in order to further identify the local vibration events received by each FBG, a vibration event projection observation matrix as shown in formula (8) is established:

[0044]

[0045] Among them, λ n , κ n , Ln represent the wavelength, effective refractive index and length of the nth FBG respectively.

[0046] Furthermore, in step 4), the step of obtaining and constructing a vibration event feature dictionary includes:

[0047] Since the sparse domain eigenvector is a characterization of the phase offset of the cascaded FBG grating array at a certain moment, let θ (t) represents the measurement result at time t. If the entire vibration event monitoring process includes M observation times, that is, the time vector is [t1, t2, …, t M ], then the sparse domain feature matrix obtained by complete monitoring is expressed as:

[0048]

[0049] It can be seen that Ξ is sparse. In order to further use the vibration event projection observation matrix to complete time projection and recognition, Ξ needs to be transformed into a non-sparse matrix and defined as nonzeros(·) is a non-zero element extraction function, which extracts the non-zero elements in the vector and reconstructs the new vector in the original index order. The feature matrix after non-sparse transformation is:

[0050]

[0051] Then, the strain characteristic matrix is ​​calculated:

[0052]

[0053] Finally, in the vibration event recognition process, a vibration event feature dictionary is constructed based on prior information and empirical information. Its vibration event feature dictionary is expressed as:

[0054]

[0055] in, represents the pth vibration event at the observation time t m strain characteristics.

[0056] Further, in step 5), the step of identifying the vibration event includes:

[0057] Establish a sparse representation model as shown in formula (13):

[0058] Z=EΛ (13)

[0059] Then solve the following optimization problem:

[0060]

[0061] The vibration event feature vector Λ can be reconstructed, and the vibration event can be identified from the index value of the non-zero element. If the vibration event is an event set Unknown events other than the above are further identified through modal decomposition technology.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] The present invention discloses a method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction. Based on the structured sparse characteristics of the reflection spectrum of each FBG, a group sparse representation model of a single vibration event generating a phase shift in adjacent FBGs is established through the reflection spectrum of the cascaded FBG grating array, thereby suppressing the coupling interference between the FBGs. By optimizing and solving the group sparse representation model, synchronous identification of multi-point vibration events is obtained, and the identification accuracy and sensitivity are high, which has great promotion and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram of the structure of the cascaded FBG grating array of the present invention. DETAILED DESCRIPTION

[0065] The present invention is described in detail below so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0066] A brief summary of one or more aspects is given below to provide a basic understanding of these aspects. This summary is not an exhaustive overview of all conceived aspects, and is neither intended to identify the key or critical elements of all aspects nor to define the scope of any or all aspects. Its only purpose is to give some concepts of one or more aspects in a simplified form as a prelude to a more detailed description that will be given later.

[0067] Glossary:

[0068] FBG: Fiber Bragg Grating.

[0069] The present invention discloses a method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction, comprising the following steps:

[0070] Use Figure 1 The cascaded FBG grating array shown in FIG. 1 includes a plurality of FBGs arranged in sequence, which are respectively denoted as FBG 1, FBG 2, FBG 3, . . . , FBG n; the incident pulse light is expressed as:

[0071]

[0072] Where E0 is the amplitude of the light source, f c is the incident light frequency, is the initial phase of optical pulse modulation, and T is the width of the modulated optical pulse.

[0073] When the incident pulse light enters the cascaded FBG grating array, the reflected light pulse corresponding to the nth FBG can be expressed as:

[0074]

[0075] Where η is the amplitude modulation coefficient of the reflected light, τ n is the time delay corresponding to the nth FBG reflected light pulse, is the phase shift of the optical pulse caused by the vibration event observed by the nth FBG.

[0076] When the transmitted light of the preceding FBG produces coupling interference on the subsequent FBG, the reflected light pulse corresponding to the interfered nth FBG can be expressed as:

[0077]

[0078] For the sake of simplicity, the present invention only considers the transmitted light coupling interference between two adjacent FBGs. When the coupling interference spans multiple FBGs, it can be expanded according to the design concept of the present invention.

[0079] From formula (3), we can see that if the existing method is used to Perform phase offset demodulation and obtain the phase offset as The vibration event estimated by the phase offset is necessarily inaccurate. Therefore, the present invention, starting from the sparse characteristics of the phase feature domain, establishes a group sparse representation model of the phase offset generated by a single vibration event in adjacent FBGs to suppress the above coupling interference.

[0080] The phase search interval of the phase domain dictionary is defined as:

[0081] Ω=[φ1,φ2,…,φ Q ] (4)

[0082] Where Q is the number of phases to search. Search phase φ q The corresponding dictionary atoms are:

[0083]

[0084] Then the sparse dictionary corresponding to the phase search interval Ω is:

[0085] Ψ=[ψ1,ψ2,…,ψ Q ] (6)

[0086] The pulse light received by the signal processing end is the composite signal of the reflected light from each FBG, which can be expressed as:

[0087]

[0088] Where N is the number of FBGs in the FBG array, and θ is a sparse feature vector, the index value of its non-zero element can characterize the corresponding vibration event.

[0089] The process of solving equation (7) to obtain the sparse feature vector θ can be summarized into the following steps:

[0090] Step 1: Initialize the search count j = 1, define the correlation threshold ζ and the residual value ρ (0) = 0, event atom set Θ = [], atom offset value σ = 0;

[0091] Step 2: Calculate ω j =ψ T (j+σ) y;

[0092] Step 3: Make a threshold judgment. If ω j <ζ, then let j=j+1 and jump to step 2; if ω j >ζ, then update the residual ρ (j) =ρ (j-1) -ω j And proceed to the next step;

[0093] Step 4: Update the event atomic set Θ = [Θ∪ψ j ], define the atomic offset value σ = j;

[0094] Step 5: If j < N, set j = j + 1 and jump to step 2; if j = N, stop searching and calculate

[0095] In the above optimization and reconstruction process, the present invention uses an atomic offset compensation method to obtain an optimal solution with an offset, thereby obtaining an estimated value of the true sparse feature vector θ.

[0096] Subsequently, in order to further identify the local vibration events to which each FBG is subjected, the present invention establishes the following vibration event projection observation matrix:

[0097]

[0098] Among them, λ n , κ n , L n represent the wavelength, effective refractive index and length of the nth FBG respectively.

[0099] The sparse domain feature vector estimated by the above steps is the phase offset representation of the FBG array at a certain moment. Let θ (t) represents the measurement result at time t. If the entire vibration event monitoring process includes M observation times, that is, the time vector is [t1, t2, …, t M ], then the sparse domain feature matrix obtained by complete monitoring can be expressed as:

[0100]

[0101] It can be seen that Ξ is sparse. In order to further use the vibration event projection observation matrix to complete time projection and recognition, Ξ needs to be transformed into a non-sparse matrix and defined as Among them, nonzeros(·) is a non-zero element extraction function, that is, the non-zero elements in the vector are extracted and reconstructed into a new vector in the original index order. The feature matrix after non-sparse transformation is:

[0102]

[0103] Then, the strain characteristic matrix is ​​calculated:

[0104]

[0105] Finally, in the vibration event recognition process, a vibration event feature dictionary is constructed based on prior information and empirical information. Its vibration event feature dictionary can be expressed as:

[0106]

[0107] in, represents the pth vibration event at the observation time t m strain characteristics.

[0108] The following sparse representation model is further established:

[0109] Z=EΛ (13)

[0110] By solving the following optimization problem:

[0111]

[0112] The vibration event feature vector Λ can be reconstructed, and the vibration event can be identified from the index values ​​of the non-zero elements. Unknown events other than those detected can be further identified through techniques such as modal decomposition.

[0113] Parts or structures not specifically described in the present invention may adopt existing technologies or existing products and will not be described in detail here.

[0114] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for identifying multiple vibration events in a cascaded FBG array based on group sparse reconstruction, characterized in that: The following steps are involved: 1) Providing a cascaded FBG grating array consisting of a plurality of FBGs; 2) Solve for sparse feature vectors; 3) Establishing vibration event projection observation matrix; 4) Obtaining a dictionary of structural vibration event features; 5) Identify vibration events.

2. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 1, characterized in that: In step 1), the cascaded FBG grating array includes a plurality of FBGs arranged in sequence, which are respectively denoted as FBG 1, FBG 2, FBG 3, ... , FBG n; Let the incident pulse light be expressed as: When the incident pulse light enters the cascaded FBG grating array, the reflected light pulse corresponding to the nth FBG is expressed as: When the transmitted light of the preceding FBG produces coupling interference on the subsequent FBG, the reflected light pulse corresponding to the interfered nth FBG is expressed as: Where E0 is the amplitude of the light source; f c is the incident light frequency; is the initial phase of the optical pulse modulation; T is the width of the modulated optical pulse; η is the amplitude modulation coefficient of the reflected light; τ n is the time delay corresponding to the nth FBG reflected light pulse; is the phase shift of the optical pulse caused by the vibration event observed by the nth FBG.

3. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 1, characterized in that: In step 2), the steps of solving the sparse feature vector include: The phase search interval Ω of the phase domain dictionary is defined as: Ω=[φ1,φ2,…,φ Q ] (4) Search phase φ q The corresponding dictionary atoms are: Then the sparse dictionary Ψ corresponding to the phase search interval Ω is: Ψ=[ψ1,ψ2,…,ψ Q ] (6) The pulse light received by the signal processing end connected to the cascaded FBG grating array is the synthetic signal of the reflected light of each FBG, expressed as: Thus, according to the solution in equation (7), the sparse feature vector θ is obtained, and the index value of its non-zero element can represent the corresponding vibration event; Where q, Q are the number of phases to be searched, q≦Q; E0 is the amplitude of the light source; f c is the incident light frequency; is the initial phase of optical pulse modulation; N is the number of FBGs in the cascaded FBG grating array.

4. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 3, characterized in that: The sparse feature vector θ is obtained by solving equation (7), which includes the following steps: Step 1: Initialize the search count j = 1, define the correlation threshold ζ and the residual value ρ (0) = 0, event atom set Θ = [], atom offset value σ = 0; Step 2: Calculate ω j =ψ T (j+σ) y; Step 3: Make a threshold judgment; Step 4: Update the event atomic set Θ = [Θ∪ψ j ], define the atomic offset value σ = j; Step 5: Calculate the sparse feature vector θ.

5. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 4, characterized in that: In step 3, the steps of threshold determination include: If j <ζ, then set j=j+1 and jump to step 2; If j >ζ, then update the residual ρ (j) =ρ (j-1) -ω j And proceed to step 4.

6. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 4, characterized in that: In step 5, the steps of calculating the sparse feature vector θ include: If j<N, set j=j+1 and jump to step 2; If j = N, stop searching and calculate 7. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 1, characterized in that: In step 3), in order to further identify the local vibration events received by each FBG, a vibration event projection observation matrix as shown in formula (8) is established: Among them, λ n , κ n , L n represent the wavelength, effective refractive index and length of the nth FBG respectively.

8. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 1, characterized in that: In step 4), the step of obtaining and constructing a vibration event feature dictionary includes: Since the sparse domain eigenvector is a characterization of the phase offset of the cascaded FBG grating array at a certain moment, let θ (t) represents the measurement result at time t. If the entire vibration event monitoring process includes M observation times, that is, the time vector is [t1, t2, …, t M ], then the sparse domain feature matrix obtained by complete monitoring is expressed as: It can be seen that Ξ is sparse. In order to further use the vibration event projection observation matrix to complete time projection and recognition, Ξ needs to be converted into a non-sparse matrix. Define nonzeros(·) is a non-zero element extraction function, which extracts the non-zero elements in the vector and reconstructs the new vector in the original index order. The feature matrix after non-sparse transformation is: Then, the strain characteristic matrix is ​​calculated: Finally, in the vibration event recognition process, a vibration event feature dictionary is constructed based on prior information and empirical information. Its vibration event feature dictionary is expressed as: in, represents the pth vibration event at the observation time t m strain characteristics.

9. The method for identifying multiple vibration events of a cascaded FBG array based on group sparse reconstruction according to claim 8, characterized in that: In step 5), the step of identifying the vibration event includes: Establish a sparse representation model as shown in formula (13): Z=EΛ (13) Then solve the following optimization problem: The vibration event feature vector Λ can be reconstructed, and the vibration event can be identified from the index value of the non-zero element. If the vibration event is an event set Unknown events other than the above are further identified through modal decomposition technology.

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