GPR reinforcing steel bar interference suppression method based on unsupervised generative network

Abstract

The invention relates to the technical field of ground penetrating radar technology, in particular to a GPR reinforcing steel bar interference suppression method based on an unsupervised generative network, which comprises the following steps: S1, acquiring and preprocessing GPR data, including a first type of images including void defect echoes and reinforcing steel bar clutters and a second type of images only including void defect echoes; s2, an unsupervised generative network model is constructed, the model comprises a variational auto-encoder and a generative adversarial network (GANs), and image inter-domain mapping is realized by sharing a potential space; s3, introducing an attention module into the network model, and optimizing key information extraction and processing; and S4, training and verifying the model by using simulation data and real data, inhibiting reinforcement interference and reconstructing a cavity signal. According to the method, GPR multi-reflection interference signals generated by reinforcing steel bars are effectively eliminated, and cavity defect signals in the image are accurately reconstructed, so that radar data can be automatically explained, and the accuracy of an explaining result is improved.

Description

Technical Field

[0001] The present invention relates to the technical field, and in particular to a GPR steel bar interference suppression method based on an unsupervised generation network. Background Art

[0002] In the detection of tunnel linings, the presence of voids is a common and serious structural defect. They not only weaken the load-bearing capacity of the structure but may also lead to more serious structural damage. Accurately and quickly identifying and evaluating voids in tunnel linings is crucial. Ground Penetrating Radar, abbreviated as GPR, as an efficient non-destructive detection technology, can quickly scan the tunnel lining and provide detailed internal images of the tunnel lining and its surrounding environment. However, the steel bars widely used in tunnel linings often cause significant interference during GPR detection. The strong reflection of radar waves by the steel bars will form significant hyperbolic clutter on the image, and these clutters often mask the void signals located under the steel bars, making the detection of voids extremely difficult. In order to automatically interpret radar data and improve the accuracy of the interpretation results, it is necessary to suppress the steel bar signals in GPR data. Summary of the Invention

[0003] To solve the above problems, the present invention provides a GPR steel bar interference suppression method based on an unsupervised generation network, which effectively eliminates the GPR multiple reflection interference signals generated by steel bars and accurately reconstructs the void defect signals in the image, so as to be able to automatically interpret radar data and improve the accuracy of the interpretation results.

[0004] The technical implementation solution of the present invention is: a GPR steel bar interference suppression method based on an unsupervised generation network, including the following steps:

[0005] S1. Obtain and preprocess GPR data, including a first type of image containing void defect echoes and steel bar clutter and a second type of image containing only void defect echoes;

[0006] S2. Construct an unsupervised generation network model, the model includes variational autoencoders (VAEs) and generative adversarial networks (GANs), and realizes image domain mapping through a shared latent space;

[0007] S3. Introduce an attention module into the network model to optimize key information extraction and processing;

[0008] S4. Use simulation data and real data to train and verify the model, suppress steel bar interference and reconstruct void signals.

[0009] Optionally, in the step S1, forward numerical simulation is used to generate GPR simulation data, and two types of images are obtained through the interaction between electromagnetic waves and different media; the preprocessing includes zero-point correction, background removal, median filtering, time window setting, and geometric transformation operations.

[0010] Optionally, the unsupervised generation network model in the S2 includes: two domain image encoders E A and E B , two domain image generators G A and G B , two domain adversarial discriminators D A and D B ; the encoder-generator pairs {E A , G B} are used to map the first type of image to the second type of image, and the encoder-generator pairs {E B , G A} are used to map the second type of image to the first type of image.

[0011] Optionally, the loss function of the network model includes:

[0012] VAE loss, including reconstruction loss and KL divergence, where the first variational autoencoder loss, L VAE1 (E A , G A ) is used to measure the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the first domain image by the first domain image encoder EA and the first domain image generator GA. The calculation formula is:

[0013]

[0014] The second variational autoencoder loss L VAE2 (E B , G B ) is used to measure the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the second domain image by the second domain image encoder EB and the second domain image generator GB. The calculation formula is:

[0015]

[0016] Adversarial loss, the first adversarial loss L GAN1 (E B , G A , D A ) is used to measure the ability of the first domain adversarial discriminator DA to distinguish the image generated by the first domain image generator GA after being encoded by the second domain image encoder EB from the real first domain image. The calculation formula is:

[0017]

[0018] The second adversarial loss L GAN2 (E A , G B , D B ) is used to measure the ability of the second-domain adversarial discriminator DB to distinguish between the images generated by the second-domain image generator GB after being encoded by the first-domain image encoder EA and the real second-domain images. The calculation formula is:

[0019]

[0020] Cycle consistency loss: The first cycle consistency loss L cyc1 (E A , G A , E B , G B ) is used to constrain the degree of consistency of the first-domain images restored to the original images after being processed by the first-domain image encoder EA, the second-domain image generator GB, the second-domain image encoder EB, and the first-domain image generator GA. The calculation formula is:

[0021]

[0022] The second cycle consistency loss L cyc2 (E B , G B , E A , G A ) is used to constrain the degree of consistency of the second-domain images restored to the original images after being processed by the second-domain image encoder EB, the first-domain image generator GA, the first-domain image encoder EA, and the second-domain image generator GB. The calculation formula is:

[0023]

[0024] Optionally, the total loss function is:

[0025] L total = L VAE1 (E A , G A ) + L VAE2 (E B , G B ) + L GAN1 (E B , G A , D A ) + L GAN2 (E B , G A , D A )

[0026] + L cyc1(E A ,G A ,E B ,G B ) + L cyc2 (E A ,G A ,E B ,G B )

[0027] The weight values of the total loss for each part are: λ0 = λ3 = 0.01, λ1 = λ4 = 10, λ2 = 1

[0028] Optionally, in S3, the encoder generator incorporates a channel and spatial attention module (CSA) into {E A , G A}, {E A , G B}, {E B , G A}, {E B , G B}, and combines channel and spatial attention for use, optimizing the extraction and processing of information from both the feature channel and spatial layout dimensions simultaneously.

[0029] Optionally, the training process of S4 includes: S41, inputting the domain A image into E A， inputting the domain B image into E B ; S42, the generator G A reconstructs the domain A image based on the latent space z, and the generator G B generates the domain B image; S43, improving the image translation quality through adversarial training and cycle consistency constraints.

[0030] Optionally, the verification metrics of the model include root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), which are used to quantify the effect of reinforcing bar interference suppression and the accuracy of void signal reconstruction.

[0031] Compared with the prior art, the present invention has the following advantages: The present invention uses the finite-difference time-domain (FDTD) to perform forward numerical simulation on void defects to generate GPR simulation data, trains the network model, and validates it with the measured data set of tunnel lining GPR images. The method proposed by the present invention can effectively eliminate the reinforcing bar signal and accurately reconstruct the void signal, improving the interpretability of GPR data in tunnel linings and providing a new technical means for the safety detection of structures such as tunnels. Description of the Drawings

[0032] Figure 1 is the network structure diagram based on the VAE-GAN model;

[0033] Figure 2 It shows a schematic structural diagram of the CSA module;

[0034] Figure 3 It is a schematic diagram of the waveform superposition of the GPR multiple reflection interference signal generated by steel bars and the cavity signal;

[0035] Figure 4 It is a comparison chart of the processing results of real tunnel data. Specific implementation manners

[0036] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. It is hereby declared that the azimuth terms such as up, down, left, right, front, back, inner, and outer that appear or will appear in the text of the present invention are only based on the accompanying drawings of the present invention, and they do not specifically limit the present invention.

[0037] Embodiment 1

[0038] A GPR steel bar interference suppression method based on an unsupervised generation network includes the following steps:

[0039] S1. Obtain and preprocess GPR data, including a first type of image containing cavity defect echoes and steel bar clutter, and a second type of image containing only cavity defect echoes;

[0040] S2. Construct an unsupervised generation network model, which includes a variational autoencoder (VAEs) and a generative adversarial network (GANs), and realizes image domain mapping through a shared latent space;

[0041] S3. Introduce an attention module into the network model to optimize key information extraction and processing;

[0042] S4. Use simulation data and real data to train and verify the model, suppress steel bar interference and reconstruct cavity signals;

[0043] In the S1 step, forward numerical simulation is used to generate GPR simulation data, and two types of images are obtained through the interaction of electromagnetic waves with different media; the preprocessing includes zero-point correction, background removal, median filtering, time window setting, and geometric transformation operations.

[0044] In the S1 step, first, the finite-difference time-domain (FDTD) is used to perform forward numerical simulation on cavity defects to generate GPR simulation data, and according to the different characteristics of different media, radar data of a simulated image with steel bar clutter and a simulated image without steel bar clutter are obtained through the mutual influence between electromagnetic waves and different media; second, as shown in the attached figure Figure 3As shown, the reflected signals of steel bars form regular hyperbolic patterns in GPR images, while the reflected signals of cavity diseases show pseudo-hyperbolic patterns. Again, preprocessing includes zero-point correction, background removal, median filtering, and setting of time windows. Finally, the radar data is processed to remove direct waves, and geometric and color transformations such as cropping, rotation, and stitching operation combinations are performed, and then divided into training data and test data for the deep learning network.

[0045] Example 2

[0046] The unsupervised generation network model in step S2 includes: two domain image encoders E A and E B , two domain image generators G A and G B , two domain adversarial discriminators D A and D B ; The encoder-generator pair {E A , G B} is used to map the first type of image to the second type of image, and the encoder-generator pair {E B , G A} is used to map the second type of image to the first type of image;

[0047] The loss function of the model includes:

[0048] VAE loss, including reconstruction loss and KL divergence. Among them, the first variational autoencoder loss, L VAE1 (E A , G A ) is used to measure the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the first domain image by the first domain image encoder EA and the first domain image generator GA. The calculation formula is:

[0049]

[0050] The second variational autoencoder loss L VAE2 (E B , G B ) is used to measure the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the second domain image by the second domain image encoder EB and the second domain image generator GB. The calculation formula is:

[0051]

[0052] Adversarial loss, the first adversarial loss L GAN1 (E B , G A , D A) It is used to measure the ability of the first domain adversarial discriminator DA to distinguish between the images generated by the first domain image generator GA after being encoded by the second domain image encoder EB and the real first domain images. The calculation formula is:

[0053]

[0054] The second adversarial loss L GAN2 (E A ,G B ,D B ) It is used to measure the ability of the second domain adversarial discriminator DB to distinguish between the images generated by the second domain image generator GB after being encoded by the first domain image encoder EA and the real second domain images. The calculation formula is:

[0055]

[0056] The cycle consistency loss The first cycle consistency loss L cyc1 (E A ,G A ,E B ,G B ) It is used to constrain the consistency degree of the first domain images to be restored to the original images after being processed by the first domain image encoder EA, the second domain image generator GB, the second domain image encoder EB and the first domain image generator GA. The calculation formula is:

[0057]

[0058] The second cycle consistency loss L cyc2 (E B ,G B ,E A ,G A ) It is used to constrain the consistency degree of the second domain images to be restored to the original images after being processed by the second domain image encoder EB, the first domain image generator GA, the first domain image encoder EA and the second domain image generator GB. The calculation formula is:

[0059]

[0060] The total loss function is:

[0061] L total =L VAE1 (E A ,G A )+L VAE2 (E B ,G B )+L GAN1 (E B ,G A ,D A )+L GAN2 (EB , G A , D A ) + L cyc1 (E A , G A , E B , G B ) + L cyc2 (E A , G A , E B , G B ) Formula 7

[0062] The weight values of the total loss for each part are: λ0 = λ3 = 0.01, λ1 = λ4 = 10, λ2 = 1

[0063] It should be noted that for the KL divergence term coefficient (i.e., λ0 in the formula) in the first variational auto - encoder loss L VAE1 (E A , G A ) and the second variational auto - encoder loss L VAE2 (E B , G B ), the value is 0.01, which is used to constrain the distribution of the latent variables output by the encoder to be close to the prior distribution. The coefficient of the reconstruction loss expectation term (i.e., λ1 in the formula) is 10, which is used to measure the difference between the reconstructed image and the original image, prompting the generator to better reconstruct the image; for each coefficient in the first adversarial loss L GAN1 (E B , G A , D A ) and the second adversarial loss L GAN2 (E A , G B , D B ), the value (i.e., λ2 in the formula) is 1. This parameter is used to balance the ability of the discriminator to distinguish between real images and generated images, ensuring the quality and authenticity of the generated images; for the KL divergence term coefficient (i.e., λ3 in the formula) in the first cycle - consistency loss L cyc1 (E A , G A , E B , G B ) and L cyc2 (E B , G B , E A , G A ), the value is 0.01, ensuring the rationality of the latent variable distribution during the cycle process; the coefficient of the cycle reconstruction loss expectation term (i.e., λ4 in the formula) is 10, ensuring that the image can be restored to the original image as much as possible after cross - domain transformation and cycling, enhancing the cycle - consistency of the model.

[0064] In step S2, first, an unsupervised generation network model consisting of variational autoencoders (VAEs) and generative adversarial networks (GANs) is constructed to achieve mapping between image domains through a shared latent space, effectively eliminating the GPR multiple reflection interference signals generated by steel bars. Second, the network model consists of a generation network and a discriminative network based on variational autoencoders (VAEs), including two domain image encoders E A and E B , two domain image generators G A and G B , and two domain adversarial discriminators D A and D B .

[0065] Second, the encoder generators {E A , G B} are used to learn the mapping AtoB between the two image domains. The encoder E A is responsible for mapping the ground penetrating radar image with steel bar clutter to the shared latent space z, and the generator G B maps z back to the output data space to generate a ground penetrating radar image without steel bar clutter. The discriminator D B is used to ensure the generation of a more realistic ground penetrating radar image without steel bar clutter. The network generates an image without steel bar clutter from the ground penetrating radar image with steel bar clutter interference to eliminate the interference of steel bar clutter on the void signal.

[0066] Third, the overall loss function of the model includes VAE loss, adversarial loss, and cycle consistency loss. The VAE loss includes reconstruction loss and KL divergence. The goal of the reconstruction loss is to maintain the content consistency between the generated image and the input image. By using a pixel-level loss function to measure the difference between images, the generated image is made to retain the content features of the input image as much as possible. The goal of the KL divergence loss is to minimize the difference between the posterior distribution of the generated latent variables and the standard normal distribution, prompting the encoder to learn a good representation for mapping the input image to the latent space, enabling the generator to generate realistic images. The calculation formulas for the VAE loss are shown in Formulas 1 and 2 respectively.

[0067] The adversarial loss constrains the model to learn the mapping relationship between the source domain and the target domain, making the generated image more in line with the distribution characteristics of the target domain. During training, the discriminator attempts to maximize the probability of correctly classifying real images and generated images, while the generator attempts to minimize the probability of the discriminator for the generated image, so that the generated image looks visually the same as the real image. The calculation formulas for the adversarial losses of the discriminators D A and D B are shown in Formulas 3 and 4 respectively.

[0068] The cycle consistency loss ensures that when an image is transformed from one domain to another and then back to the original domain, it should be restored to the original image as much as possible, preserving the important features and structures of the original image, and improving the quality and stability of the image translation effect. The calculation formulas for the cycle consistency loss are shown in Formulas 5 and 6 respectively.

[0069] Finally, the total loss function is obtained, as shown in Formula 7.

[0070] It should be further noted that the model in the loss function of the above-mentioned model refers to an unsupervised generation network model, and its design purpose is to achieve steel bar interference suppression and cavity signal reconstruction through joint optimization of multiple components.

[0071] It should be further noted that in the definition of the λ series as the weight parameters of each part of the loss function, as shown in Formula 4:

[0072] The basis for the value is elaborated through experimental verification. Multiple groups of comparative experiments show that when the values are λ0 = 0.01, λ1 = 10, etc., the model can balance the reconstruction accuracy and the fidelity of the generated image in the tasks of steel bar interference suppression and cavity signal reconstruction, with the lowest total loss and the optimal performance. These are the data values cited in the experiment, and this value is the optimization result obtained by strictly controlling experimental variables and repeating the experiment multiple times, providing an accurate basis for the weight parameters of model training.

[0073] Example 3

[0074] In the step S3, a channel and spatial attention module (CSA) is introduced into the encoder generator for {E A , G A}, {E A , G B}, {E B , G A}, {E B , G B}, and the channel and spatial attention are combined for use, optimizing the extraction and processing of information from both the feature channel and spatial layout dimensions.

[0075] It should be noted that refer to the appendix Figure 2, a channel and spatial attention module (CSA) is introduced into the model to help the network better focus on the key information in GPR images, improve the model's recognition ability of void defect signals, and combine channel and spatial attention. Secondly, the module takes features in two directions as input, including the high-level semantic information containing complex structures such as steel bars and voids from the encoder, and the spatial information reflecting the gradually restored process in the reconstruction from the generator. Finally, simultaneously processing and integrating the features from the encoder and the generator helps the network more accurately identify and eliminate steel bar clutter, and further maintain the reconstruction integrity of key structures such as voids.

[0076] Example 4

[0077] The training process in the step S4 includes: S1. Input the domain A image into E A， Input the domain B image into E B ; S2. The generator G A Reconstructs the domain A image based on the latent space z, and the generator G B Generates the domain B image; S3. Improve the image translation quality through adversarial training and cycle consistency constraints; The verification metrics of the model include root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), which are used to quantify the steel bar interference suppression effect and void signal reconstruction accuracy.

[0078] It should be noted that, first of all, the simulated image training data with steel bar clutter is used as the input of the encoder E A 's input, and the simulated image training data without steel bar clutter is used as the input of the encoder E B 's input. For a ground penetrating radar image x ∈ A with steel bar clutter, the encoder E A is responsible for mapping x into the shared latent space z, and then two groups of generators decode z; Secondly, the generator G A Reconstructs a ground penetrating radar image with steel bar clutter that is as similar as possible to the original image x So that the reconstructed image has a high degree of consistency with the image in the original domain A, and the generator GB generates a clear ground penetrating radar image without steel bar clutter interference Finally, as shown in the attached Figure 4 figure, the collected measured radar data is used as the test set to input the deep learning model saved after being trained with simulation data for the effect diagram of steel bar suppression. The results show that the method of the present invention effectively improves the visibility of void defects and enhances the interpretability of ground penetrating radar data of tunnel linings.

[0079] To illustrate the effectiveness of the present invention, the method proposed in the present invention is compared with three widely used unsupervised learning methods. The root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM) metrics commonly used in the field of image denoising are used for evaluation. The experimental results are shown in Table 1.

[0080] Table 1 Comparison of evaluation metrics for different models

[0081]

[0082] As can be seen from the table, the three evaluation metrics of the method proposed in the present invention are higher than those of other methods. The results of these evaluation metrics indicate that when dealing with ground penetrating radar images of void defects with steel bar clutter interference, the method proposed in the present invention can effectively remove the steel bar clutter and retain the details and structural information of the void defects, effectively improving the visibility of the void defects and enhancing the interpretability of the ground penetrating radar data of tunnel linings.

[0083] In the description of this specification, the description with reference to terms such as "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0084] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art in the relevant technical field can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A GPR steel bar interference suppression method based on an unsupervised generation network, characterized in that, It includes the following steps: S1. Obtain and preprocess GPR data, including a first type of image containing echo of void defects and steel bar clutter and a second type of image containing only echo of void defects; S2. Construct an unsupervised generation network model, which includes a variational autoencoder and a generative adversarial network, and realizes image domain mapping through a shared latent space; S3. Introduce an attention module into the network model to optimize key information extraction and processing; S4. Use simulation data and real data to train and verify the model, suppress steel bar interference and reconstruct void signals.

2. The GPR steel bar interference suppression method based on an unsupervised generation network according to claim 1, wherein In the step S1, forward numerical simulation is used to generate GPR simulation data, and two types of images are obtained through the interaction of electromagnetic waves with different media; The preprocessing includes zero-point correction, background removal, median filtering, time window setting and geometric transformation operations.

3. A GPR rebar interference suppression method based on an unsupervised generation network according to claim 1, characterized in that, The unsupervised generation network model in S2 includes: Two domain image encoders E A and E B ,two domain image generators G A and G B ,two domain adversarial discriminators D A and D B ; The encoder generator pair {E A , G B} is used to map the first type of images to the second type of images, and the encoder generator pair {E B , G A} is used to map the second type of images to the first type of images.

4. A GPR rebar interference suppression method based on an unsupervised generation network according to claim 3, characterized in that, The loss function of the network model includes: The VAE loss, including the reconstruction loss and the KL divergence, where the first variational autoencoder loss, L VAE1 (E A , G A ) is used to measure the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the first-domain image by the first-domain image encoder EA and the first-domain image generator GA. The calculation formula is as follows: The second variational autoencoder loss L VAE2 (E B , G B ) The calculation formula for measuring the difference between the reconstructed image and the original image and the rationality of the latent space distribution during the encoding and decoding of the second-domain image by the second-domain image encoder EB and the second-domain image generator GB is as follows: Adversarial loss, the first adversarial loss L GAN1 (E B , G A , D A ) is used to measure the ability of the first domain adversarial discriminator DA to distinguish between the images generated by the first domain image generator GA after encoding by the second domain image encoder EB and the real first domain images. The calculation formula is as follows: The second adversarial loss L GAN2 (E A , G B , D B ) is used to measure the ability of the second domain adversarial discriminator DB to distinguish between the images generated by the second domain image generator GB after encoding by the first domain image encoder EA and the real second domain images. The calculation formula is as follows: Cycle consistency loss: The first cycle consistency loss L ctc1 (E A , G A , E B , G B ) is used to constrain the consistency degree that the first-domain image is restored to the original image after being processed by the first-domain image encoder EA, the second-domain image generator GB, the second-domain image encoder EB, and the first-domain image generator GA. The calculation formula is as follows: The second cycle consistency loss L cyc2 (E B ,G B ,E A ,G A ) is used to constrain the consistency degree that the second-domain image is restored to the original image after being processed by the second-domain image encoder EB, the first-domain image generator GA, the first-domain image encoder EA, and the second-domain image generator GB. The calculation formula is as follows:

5. A GPR steel bar interference suppression method based on an unsupervised generation network according to claim 1, characterized in that The total loss function is: L total = L VAE1 (E A , G A ) + L VAE2 (E B , G B ) + L GAN1 (E B , G A , D A ) + L GAN2 (E B , G A , D A ) + L cyc1 (E A , G A , E B , G B ) + L cyc2 (E A , G A , E B , G B )。 6. A GPR rebar interference suppression method based on an unsupervised generation network according to claim 1, wherein In S3, the channel and spatial attention modules are introduced into {E A , G A}, {E A , G B}, {E B , G A}, {E B , G B}, and the channel and spatial attention are combined for use, optimizing the extraction and processing of information from both the feature channel and spatial layout dimensions simultaneously.

7. A GPR rebar interference suppression method based on an unsupervised generation network according to claim 1, characterized in that, The training process of S4 includes: S41. Input the image of domain A into E A , input the image of domain B into E B ; S42. Generator G A Based on the latent space z, the generator G reconstructs the images in domain A B and generates images in domain B; S43. Improve the image translation quality through adversarial training and cycle consistency constraint.

8. The method according to any one of claims 1 to 7, characterized in that, The verification indexes of the model include root mean square error, peak signal-to-noise ratio and structural similarity index, which are used to quantify the steel bar interference suppression effect and the void signal reconstruction accuracy.

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