Distributed strain accuracy improvement method and system based on online transfer learning

Abstract

A method and system for improving the accuracy of distributed strain based on online transfer learning, the method comprising: first distributing multiple discrete fiber gratings in a long-distance optical cable bundle, measuring the distributed strain in the optical cable bundle by BOTDA, and at the same time, measuring the discrete FBG strains at multiple positions of the optical cable bundle by FBG, then smoothing and denoising the distributed strains as source domain data, and using the FBG strains as target domain data, and finally improving the accuracy of the distributed strains by an online transfer learning model according to the source domain data and the target domain data; the system is used to implement a method for improving the accuracy of distributed strains based on online transfer learning; the present invention transfers the distributed strains to the FBG strains, improves the accuracy of the distributed strains, and overcomes the measurement errors caused by random factors such as the Brillouin random scattering mechanism and light source fluctuations.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed strain measurement, and in particular to a method and system for improving distributed strain accuracy based on online transfer learning. Background Art

[0002] The unique ecological environment of the deep sea contains rich resources. Autonomous underwater vehicles (AUVs) have been widely used in marine scientific research, marine resource exploration, and marine safety assurance. The key to achieving underwater vehicle control and real-time return of high-definition video information lies in establishing fast communication between the vehicle and the ground. Unlike electromagnetic communication in the air, electromagnetic waves will decay rapidly in seawater, and the transmission depth is only a few meters. Compared with electromagnetic communication, optical fiber communication has outstanding advantages such as anti-electromagnetic interference, cross-media transmission, strong environmental adaptability, and large information transmission capacity.

[0003] According to certain process criteria, optical fibers are wound into optical cable bundles with complex geometric structures. During the navigation of the vehicle, the optical fibers are passively released from this precision structure layer by layer. The reliability of successful release of optical fibers is closely related to the initial strain state in the bundle structure. Fiber breakage will lead to failure of deep-sea exploration missions, inability to obtain real-time underwater video information, and inability to control the vehicle. Therefore, obtaining accurate and reliable strain distribution inside the entire bundle structure is crucial to assessing the safety risks of such precision structures.

[0004] At present, the main methods for measuring optical fiber strain are point sensing measurement, such as fiber Bragg grating (FBG); and distributed sensing measurement, such as Brillouin optical time domain analysis (BOTDA). Point sensors have the characteristics of high measurement sensitivity and high accuracy, but can only measure strain at discrete positions, and the capacity of sensors in the same optical fiber is limited by the bandwidth of the reflection spectrum; while distributed optical fiber sensors obtain distributed strain in optical fibers with high spatial resolution, and have the characteristics of many sensing points and low cost, but the strain measurement accuracy is low.

[0005] After careful theoretical and experimental research, it was found that although there is a certain gap in the amount of data and data values ​​obtained by the two measurement mechanisms, the two methods measure the same object, and the distribution law of distributed measurement data and point measurement data is similar. The distribution law of distributed measurement data is transferred to point measurement data to obtain distributed strain measurement data with high accuracy. Based on this idea, a distributed strain accuracy improvement method based on online transfer learning is proposed. Summary of the invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method and system for improving the accuracy of distributed strain based on online transfer learning. The distributed strain in the optical cable sheath is measured by BOTDA and smoothed as the source domain, and the discrete FBG strain at multiple positions of the optical cable sheath is measured by FBG as the target domain. Based on the source domain and target domain data, the accuracy of the distributed strain is improved through an online transfer learning model.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A distributed strain accuracy improvement method based on online transfer learning includes the following steps:

[0009] Step 1: Distribute multiple discrete fiber Bragg gratings in a long-distance optical cable bundle, measure the distributed strain in the optical cable bundle by BOTDA, and at the same time, measure the discrete FBG strain at multiple locations of the optical cable bundle by FBG;

[0010] Step 2: The distributed strain measured in step 1 is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data;

[0011] Step 3: Based on the source domain data and target domain data obtained in step 2, the accuracy of distributed strain is improved through the online transfer learning model. First, domain adaptation is performed through affine transformation to make the distributed strain curve close to the point strain. Then, the influence of each point strain in the target domain on the distributed strain curve is adjusted through adaptive weights to realize the online migration of distributed strain to point strain and obtain distributed strain with high accuracy.

[0012] The distributed strain smoothing and denoising described in step 2 is specifically as follows: retaining the distributed strain peak value, filtering the remaining data for smoothing, and then sampling the smoothed data at equal intervals to form the source domain data with the retained peak data, and the number of data after equal interval sampling is not less than 1 / 20 of the original data.

[0013] The online transfer learning model described in step 3 consists of two parts: domain adaptation and adaptive weights:

[0014] The characteristics of domain adaptation are:

[0015] X sou Represents the source domain, which contains the position information along the fiber length P 1i and the corresponding strain information ε along the length of the optical fiber 1i ;

[0016] Y tar Represents the target domain, which contains the location information of multiple discrete points P 2i And the strain information ε corresponding to the discrete point position2i ;

[0017] Define the affine matrix as W and the transformed data set as X sou W, the goal of the affine transformation is to make X sou W and Y tar The distance between them is minimal:

[0018] min|X sou WY tar | (1)

[0019] Among them, X sou ∈R n×3 , Y sou ∈R m×3 ,

[0020] Source domain X sou Simplify and use the discrete FBG measurement point locations and the strains at these locations in the source domain as the new data set X sou_1 , at this time X sou_1 and Y tar With the same dimension space, equation (1) is transformed into the following equation:

[0021] min|X sou_1 WY tar | (2)

[0022] The solution of the affine matrix W is expressed as:

[0023] W=(X sou_1 T X sou_1 ) -1 X sou_1 T A (3)

[0024] in,

[0025] That is, X sou Migrate to X' sou :

[0026] X' sou =[p 1i ,X sou W] (4)

[0027] After affine transformation, X' sou and Y tar The distribution of is closer in macroscopic terms;

[0028] Adaptive weights are characterized by:

[0029] X' sou and Y tarCombined together to form the training space:

[0030]

[0031] Each strain in the target domain controls the distributed strain half the distance to its left and right sides, expressed as Y tar The position of each strain in the X' sou The distributed strain radiation in the middle is weighted by exponential decay from the center to both sides. tar The weighted sum of the distances between the positions of each strain and each distributed strain is calculated and the minimum value is calculated to determine the weight of the position. Let P 2i With P 2i-1 , P 2i With P 2i+1 The distance between them is l, X' sou With P 2i The point with the same position is P 1i , in the two sets of strain curves, the distance d between these two points i It is expressed as:

[0032]

[0033] In P 1i The distance weights of the points on both sides are:

[0034]

[0035] Among them, a is the weight coefficient, which is determined by the following formula:

[0036]

[0037] According to equations (6)-(8), the weight coefficient a and strain ε of each strain-controlled distributed strain in the target domain are determined in turn.

[0038] A distributed strain accuracy improvement system based on online transfer learning, comprising:

[0039] Data measurement module: multiple discrete fiber Bragg gratings are distributed in the long-distance optical cable package, and the distributed strain in the optical cable package is measured through BOTDA, and the discrete FBG strain at multiple positions of the optical cable package is measured through FBG;

[0040] Data accuracy improvement module: The distributed strain is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data; based on the source domain data and the target domain data, the accuracy of the distributed strain is improved through the online transfer learning model.

[0041] A distributed strain accuracy improvement device based on online transfer learning, comprising:

[0042] Memory: used to store a computer program for implementing the distributed strain accuracy improvement method based on online transfer learning;

[0043] Processor: used to implement the distributed strain accuracy improvement method based on online transfer learning when executing the computer program.

[0044] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method for improving distributed strain accuracy based on online transfer learning are implemented.

[0045] Compared with the prior art, the beneficial effects of the present invention are:

[0046] 1. The present invention proposes a method for improving the accuracy of distributed strain based on online transfer learning. Combining the advantages of high accuracy of FBG strain measurement and high spatial resolution of distributed strain measurement, the online transfer learning model is used to migrate the regularity of distributed data to accurate point data, thereby quickly improving the accuracy of distributed strain online.

[0047] 2. The present invention proposes a distributed strain accuracy improvement method based on online transfer learning, which only relies on the distributed strain and FBG strain measured simultaneously. The migration relationship does not depend on historical data. The two sets of measured data are used as input to dynamically establish the migration relationship between the two sets of data. It is universal for variable distributed strains.

[0048] 3. The present invention adopts a method of simultaneously measuring distributed strain and FBG strain in the same optical fiber. The two measurement methods are carried out simultaneously without interfering with each other, which provides a new means for accurately characterizing the internal strain of the optical cable sheath, avoids sensor fixing errors, and greatly reduces the optical fiber wiring length. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of measuring optical cable bundles using BOTDA and FBG measurement systems, where 1 represents the FBG measurement system, 2 represents the fiber fixer, 3 represents the optical cable bundle, 4 represents the coupler, and 5 represents the BOTDA measurement system.

[0050] Figure 2 This is a diagram of the distributed Brillouin strain results of the optical cable sheath measured by BOTDA in an embodiment of the present invention.

[0051] Figure 3 This is the target domain FBG strain distribution diagram in an embodiment of the present invention.

[0052] Figure 4 This is the FBG strain distribution diagram of the verification domain in the embodiment of the present invention.

[0053] Figure 5 This is a Brillouin strain distribution diagram containing 12,500 Brillouin strains in the source domain in an embodiment of the present invention.

[0054] Figure 6 This is a Brillouin strain distribution diagram containing 7500 Brillouin strains in the source domain in an embodiment of the present invention.

[0055] Figure 7 This is a diagram showing the result of the migration of 12,500 Brillouin strains in the source domain in an embodiment of the present invention.

[0056] Figure 8 This is a diagram showing the result of the migration of 7500 Brillouin strains in the source domain in an embodiment of the present invention.

[0057] Fig. 9 This is a comparison diagram of relative errors before and after the source domain contains 12,500 Brillouin strains in an embodiment of the present invention.

[0058] Fig.10 This is a comparison diagram of relative errors before and after the source domain contains 7500 Brillouin strains in an embodiment of the present invention.

[0059] Fig.11 This is a statistical chart of the time consumed for transfer learning in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0061] This embodiment selects a 2.5 km long optical cable package for underwater vehicle communication to illustrate the distributed strain accuracy improvement method based on online transfer learning, which is not limited to this embodiment.

[0062] A distributed strain accuracy improvement method based on online transfer learning includes the following steps:

[0063] Step 1: Distribute multiple discrete fiber Bragg gratings in a long-distance optical cable bundle, measure the distributed strain in the optical cable bundle by BOTDA, and at the same time, measure the discrete FBG strain at multiple locations of the optical cable bundle by FBG;

[0064] Step 2: The distributed strain measured in step 1 is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data;

[0065] Step 3: Based on the source domain data and target domain data obtained in step 2, the accuracy of distributed strain is improved through the online transfer learning model. First, domain adaptation is performed through affine transformation to make the distributed strain curve close to the point strain. Then, the influence of each point strain in the target domain on the distributed strain curve is adjusted through adaptive weights to realize the online migration of distributed strain to point strain and obtain distributed strain with high accuracy.

[0066] The distributed strain smoothing and denoising described in step 2 is specifically as follows: retaining the distributed strain peak value, filtering the remaining data for smoothing, and then sampling the smoothed data at equal intervals to form the source domain data with the retained peak data, and the number of data after equal interval sampling is not less than 1 / 20 of the original data.

[0067] The online transfer learning model described in step 3 consists of two parts: domain adaptation and adaptive weights:

[0068] The characteristics of domain adaptation are:

[0069] X sou Represents the source domain, which contains the position information along the fiber length P 1i and the corresponding strain information ε along the length of the optical fiber 1i ;

[0070] Y tar Represents the target domain, which contains the location information of multiple discrete points P 2i And the strain information ε corresponding to the discrete point position 2i ;

[0071] Define the affine matrix as W and the transformed data set as X sou W, the goal of the affine transformation is to make X sou W and Y tar The distance between them is minimal:

[0072] min|X sou WY tar | (1)

[0073] Among them, X sou ∈R n×3 , Y sou ∈R m×3 ,

[0074] Since the spatial sizes of the two datasets are not equal n≠m, equation (1) is difficult to solve. sou The source data set is simplified and the discrete FBG measurement point locations and the strains at these locations in the source domain are used as the new data set X sou_1 , at this time X sou_1 and Y tar With the same dimension space, equation (1) is transformed into the following equation:

[0075] min|X sou_1 WY tar | (2)

[0076] The solution of the affine matrix W is expressed as:

[0077] W=(X sou_1 T X sou_1 ) -1 X sou_1 T A (3)

[0078] in,

[0079] That is, X sou Migrate to X' sou :

[0080] X' sou =[p 1i ,X sou W] (4)

[0081] After affine transformation, X' sou and Y tar The distribution of is closer in macroscopic terms;

[0082] Adaptive weights are characterized by:

[0083] X' sou and Y tar Combined together to form the training space:

[0084]

[0085] Each strain in the target domain controls the distributed strain half the distance to its left and right sides, expressed as Y tar The position of each strain in the X' sou The distributed strain radiation in the middle is weighted by exponential decay from the center to both sides. tar The weighted sum of the distances between the positions of each strain and each distributed strain is calculated and the minimum value is calculated to determine the weight of the position. Let P 2i With P 2i-1 , P 2i With P 2i+1 The distance between them is l, X' sou With P 2i The point with the same position is P 1i , in the two sets of strain curves, the distance d between these two points i It is expressed as:

[0086]

[0087] In P 1i The distance weights of the points on both sides are:

[0088]

[0089] Among them, a is the weight coefficient, which is determined by the following formula:

[0090]

[0091] According to equations (6)-(8), the weight coefficient a and strain ε of each strain-controlled distributed strain in the target domain are determined in turn.

[0092] Single-mode quartz optical fiber (Yangfei Optical Fiber, Bl1011-A) is uniformly engraved with 50 fiber gratings (FBGs) at intervals of 50 meters by masking. The central wavelengths of the FBGs do not overlap each other. The length of the optical fiber is 2.5 km. Then, a glass fiber-reinforced protective sheath is woven on the surface of the optical fiber to form a micro-optical cable containing FBG grating strings. The optical cable package is a complex and precise structure formed by winding a micro-optical cable with a diameter of 3 mm on a composite core tube.

[0093] The BOTDA measurement system 5 has a spatial resolution of 5 cm. Its measurement is double-ended input, that is, the two ends of the optical cable bundle 3 are connected to the detection light and the pump light at the same time. The FBG measurement system 1 is a single-ended input measurement. The BOTDA detection light and the fiber grating demodulator are connected to one end of the optical cable bundle 3 through the 2×1 coupler 4, and the BOTDA pump light is connected to the other end of the optical cable bundle 3. The bundle is fixed to the fiber fixer 2, as shown in FIG. Figure 1 As shown in Figure 1, the Brillouin distributed strain and multiple FBG point strains can be measured simultaneously. The Brillouin distributed strain measurement results in the wire package are shown in Figure 1. Figure 2 As shown in the figure, the spatial resolution of the BOTDA measurement system is 5 cm, so the number of original measurement data reaches 50,000. The strain peaks at the fiber winding cross-layer position, and the strain changes smoothly within the layer. The FBG strain demodulation results are shown in the figure. Figure 3 and 4 As shown, 35 FBG strains were used as target domains and the remaining 15 FBG strains were used as validation domains.

[0094] The characteristics of distributed strain smoothing and denoising are: the distributed strain retains the peak value, the remaining data is filtered and smoothed, and the peak data is sampled from the smoothed data at equal intervals to form the source domain. First, the peak feature is retained by the threshold screening strategy, and the Savitzky-Golay method is used to average the remaining data for 5-point smoothing and denoising; then, an equal-interval sampling strategy is used to take 25% of the original data, that is, 12,500 measurement data ( Figure 5 ) and 15% or 7500 measurements ( Figure 6 ), combined with the retained peak features, to form two source domains respectively.

[0095] According to the formulas (1)-(4) in the content of the invention, domain adaptation is performed to make X' sou and Y tarThe distribution of is close to that of the point FBG strain in the macroscopic sense. Then, adaptive weights are applied according to equations (5)-(8) to achieve the migration of Brillouin distributed strain to point FBG strain. The source domain contains 12500 Brillouin strains after migration. Figure 7 As shown in the figure, the source domain contains 7500 Brillouin strains after migration. Figure 8 As shown. When the number of source domain data is 12500 and the number of target domain data is 35, the ratio of the number of source domain data to the target domain data is 357; when the number of source domain data is 7500 and the number of target domain data is 35, the ratio of the number of source domain data to the target domain data is 214; for these two sets of different strain distributions in the source domain and the target domain, the Brillouin distributed strain is successfully migrated to the point strain, indicating that the method of the present invention has high robustness. Figure 7 and Figure 8 From the local enlarged image, it can be seen that the distributed strain curve not only includes affine transformation but also local shape adjustment before and after migration.

[0096] The accuracy of the Brillouin strain is evaluated by the average measurement error Er, which is defined as the arithmetic mean of the relative measurement errors of the Brillouin strain with respect to the FBG strain in the validation domain:

[0097]

[0098] Among them, ε iFBGV To verify the i-th FBG strain in the domain, ε itransfer is the Brillouin strain of the corresponding position of the i-th FBG after migration, and M is the number of data in the verification domain. The source domain contains 12500 Brillouin strains. The relative error comparison before and after migration is as follows Fig. 9 As shown in the figure, at 15 locations in the validation domain, the Brillouin strain error at each location has dropped significantly compared to before migration. The average measurement error before migration was 10.5%, and the average measurement error after migration was 4.3%. The source domain contains 7500 Brillouin strains before and after migration. Fig.10 As shown, at the 15 locations in the verification domain, the Brillouin strain error at each location decreased significantly compared to before migration. The average measurement error before migration was 10.5%, and the average measurement error after migration was 6.0%.

[0099] Therefore, the method for improving the accuracy of distributed strain proposed in the present invention is used to migrate the distributed strain to the FBG point strain, which can significantly improve the accuracy of the distributed strain and overcome the measurement errors caused by random factors such as the Brillouin random scattering mechanism and light source fluctuations. This method only relies on the distributed strain and point strain measured simultaneously. The migration relationship does not depend on historical data. It uses the two sets of measured data as input to dynamically establish the migration relationship between the two sets of data. It is universal for variable distributed strains. For a source domain containing 12,500 Brillouin strains, it takes 443.8 seconds to complete the data accuracy improvement. For a source domain containing 7,500 Brillouin strains, it takes 178.7 seconds to complete the data accuracy improvement. Fig.11 The method proposed by the present invention is time-saving and can quickly improve the accuracy of the measured data for the Brillouin strain and point strain measured simultaneously after the measurement is completed.

[0100] A distributed strain accuracy improvement system based on online transfer learning, comprising:

[0101] Data measurement module: multiple discrete fiber Bragg gratings are distributed in the long-distance optical cable bundle, the distributed strain in the optical cable bundle is measured by BOTDA, and the discrete FBG strain at multiple positions of the optical cable bundle is measured by FBG, so as to implement step 1 of a distributed strain accuracy improvement method based on online transfer learning;

[0102] Data accuracy improvement module: The distributed strain is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data. Based on the source domain data and the target domain data, the accuracy of the distributed strain is improved through an online transfer learning model, which is used to implement steps 2 and 3 of a distributed strain accuracy improvement method based on online transfer learning.

[0103] A distributed strain accuracy improvement device based on online transfer learning, comprising:

[0104] Memory: used to store a computer program for implementing the distributed strain accuracy improvement method based on online transfer learning;

[0105] Processor: used to implement the distributed strain accuracy improvement method based on online transfer learning when executing the computer program.

[0106] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method for improving distributed strain accuracy based on online transfer learning are implemented.

Claims

1. A distributed strain accuracy improvement method based on online transfer learning, characterized in that: The following steps are involved: Step 1: Distribute multiple discrete fiber Bragg gratings in a long-distance optical cable bundle, measure the distributed strain in the optical cable bundle by BOTDA, and at the same time, measure the discrete FBG strain at multiple locations of the optical cable bundle by FBG; Step 2: The distributed strain measured in step 1 is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data; Step 3: Based on the source domain data and target domain data obtained in step 2, the accuracy of the distributed strain is improved through the online transfer learning model. First, domain adaptation is performed through affine transformation to make the distributed strain curve close to the point strain. Then, the influence of each point strain in the target domain on the distributed strain curve is adjusted through adaptive weights to achieve online migration of distributed strain to point strain, and obtain distributed strain with high accuracy. The distributed strain smoothing and denoising described in step 2 is specifically as follows: retain the distributed strain peak value, filter and smooth the remaining data, then equally sample the smoothed data and the retained peak data to form the source domain data, and the number of data after equally sampled is not less than 1 / 20 of the original data; The online transfer learning model described in step 3 consists of two parts: domain adaptation and adaptive weights, specifically: The characteristics of domain adaptation are: X sou Represents the source domain, which contains the position information along the fiber length P 1i and the corresponding strain information ε along the length of the optical fiber 1i ; Y tar Represents the target domain, which contains the location information of multiple discrete points P 2i And the strain information ε corresponding to the discrete point position 2i ; Define the affine matrix as W and the transformed data set as X sou W, the goal of the affine transformation is to make X sou W and Y tar The distance between them is minimal: min|X sou WY tar |(1) Where X sou ∈R n×3 , Y sou ∈R m×3 , Source domain X sou Simplify and use the discrete FBG measurement point locations and the strains at these locations in the source domain as the new data set X sou_1 , at this time X sou_1 and Y tar With the same dimension space, equation (1) is transformed into the following equation: minX sou_1 W-Y tar |(2) The solution of the affine matrix W is expressed as: W=(X sou_1 T X sou_1 ) -1 X sou_1 T A (3) in, That is, X sou Migrate to X s ' ou : X s ' ou =[p 1i ,X sou W] (4) After affine transformation, X s ' ou and Y tar The distribution of is closer in macroscopic terms; Adaptive weights are characterized by: X s ' ou and Y tar Combined together to form the training space: Z=X s ' ou ∪Y tar :Z={(P i ,ε i )}, Each strain in the target domain controls the distributed strain half the distance to its left and right sides, expressed as Y tar The position of each strain in the X s ' ou The distributed strain radiation in the middle is weighted by exponential decay from the center to both sides. tar The weighted sum of the distances between the positions of each strain and each distributed strain is calculated and the minimum value is calculated to determine the weight of the position. Let P 2i With P 2i-1 , P 2i With P 2i+1 The distance between them is l, X s ' ou With P 2i The point with the same position is P 1i , in the two sets of strain curves, the distance d between these two points i It is expressed as: In P 1i The distance weights of the points on both sides are: Among them, a is the weight coefficient, which is determined by the following formula: According to equations (6)-(8), the weight coefficient a and strain ε of each strain-controlled distributed strain in the target domain are determined in turn.

2. A distributed strain accuracy improvement system based on online transfer learning based on the method of claim 1, characterized in that: include: Data measurement module: multiple discrete fiber Bragg gratings are distributed in the long-distance optical cable package, and the distributed strain in the optical cable package is measured through BOTDA, and the discrete FBG strain at multiple positions of the optical cable package is measured through FBG; Data accuracy improvement module: The distributed strain is smoothed and denoised as the source domain data, and the FBG strain is used as the target domain data; based on the source domain data and the target domain data, the accuracy of the distributed strain is improved through the online transfer learning model.

3. A distributed strain accuracy improvement device based on online transfer learning, characterized in that: include: Memory: used to store a computer program for implementing a distributed strain accuracy improvement method based on online transfer learning as claimed in claim 1; Processor: used to implement the distributed strain accuracy improvement method based on online transfer learning as described in claim 1 when executing the computer program.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the steps of the method for improving distributed strain accuracy based on online transfer learning as claimed in claim 1 are implemented.

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