Defect depth is an essential indicator in magnetic flux leakage (MFL) detection and estimation. The quantification errors for defect depth are closely related to length and width errors, and this feature has always been used to support the operator's judgment in defect identification. However, the existing defect quantification algorithms based on shallow and deep neural networks only employed simple general network structures inspired by the field of artificial intelligence; consequently, these network structures lack the support of physical concepts and result in large quantification errors regarding defect size, especially depth. In this article, to describe and integrate the above theory into a deep neural network, we propose a physics-informed doubly fed cross-residual network (DfedResNet) suitable for MFL defect detection based on deep learning. Physics-based MFL defect quantification theory is studied and integrated into loss functions during the neural network training. DfedResNet quantifies defects in MFL data and automatically extracts deep features of defects. The experimental results show that it effectively achieves high-precision quantification of defect length, width, and depth simultaneously, especially defect depth. Moreover, it considers data from all three dimensions during network training, and use the originally measured magnetic signal data in place of recognized images to avoid defect information loss and further improve the quantification accuracy. The deep DfedResNet model proposed in this article reduces defect length and width quantification errors to within 0.3 mm and defect depth quantification errors to within 0.4% t . In addition, compared with other network structures and traditional algorithms, DfedResNet improves defect quantification accuracy by 1–2 orders of magnitude and thus achieves a high quantification performance.

Cracks that may cause pipeline cracking and leakage become the main risk of in-service pipelines after conventional metal loss defects have been detected. Therefore, it is imperative to develop ultra-high-definition magnetic flux leakage (MFL) detection for cracks. Due to the larger spatial sampling interval of conventional MFL inspections than the crack defect width, sparse sampling will result in problems such as missed detection of crack defects or insufficient signal sampling of crack defect MFL signals. To address the problem, this paper presents a detection topology in which the magnetic field signal is integrated first and then sampled, and it can effectively sample the leakage magnetic field of cracks. Furthermore, a magnetic field spatial integration (MFSI) method is proposed based on the magnetic dipole model, which develops an analytical solution for the depth quantification of crack defects. Using the multi-MFL spatial integral values under different lift offs, iterative equations are constructed, and the numerical solution for the width quantification of crack defects is provided. The finite element simulation and physical experiment are constructed. And, the results show that the proposed MFSI method can realize the quantification of crack size. When the crack defect aspect ratio is greater than 4, the quantization error of the crack depth and width does not exceed 0.7 mm and 0.1 mm, respectively. The robustness of the MFSI method for crack quantification is also discussed and verified. Moreover, based on theoretical analysis and simulation data, this paper concludes that the distribution of cracks MFL signal is width-insensitive, which would cause that classic MFL opening profile recognition methods for metal loss defects are no longer applicable to crack defects. Therefore, the proposed MFSI method is useful and meaningful for crack defect quantification in ultra-high-definition MFL detection.

Defect opening profile recognition is a common problem in magnetic flux leakage (MFL) detection, while the traditional defect edge detection methods are not accurate enough. Starting from the basic principle of the electromagnetic field, this article discusses the model of the corresponding relationship between defect MFL signal and defect opening profile and analyzes the errors of traditional defect edge detection methods. Furthermore, the approximation characteristic of the MFL signal is proposed, and a characteristic approximation approach (CAA) is developed to detect the defect edge. The rectangular opening profile, circular opening profile, and arbitrary opening profile in FEM simulation and the experiments all proved the opening profile recognition capability of the proposed CAA. Compared with traditional defect edge detection methods, CAA reduces the error of profile recognition from 6.00% to 2.00%, which can facilitate the defect sizing in MFL detection. CAA also has high accuracy in the recognition of the tangential profile, which improves the capability of traditional MFL to detect tangential recognition.

For in-line inspection of ferromagnetic materials, magnetic flux leakage (MFL) detection is one of the most common nondestructive testing methods. In practical applications of conventional MFL inspection, random mechanical vibration can cause the detection gesture of the probe, in particular, the lift-off and tilt detection angle, to continuously fluctuate throughout the inspection process, which introduces measurement errors to MFL signals. To address the problem and realize ultra-high-definition MFL detection, this paper proposed a new type of probe with dual diagonal distributed magnetic sensors for MFL detection. Based on the dual magnetic sensor probe structure and magnetic dipole model, this paper further developed analytical solutions of the real-time sensor lift-off, tilt detection angle, and defect depth. Additionally, this paper presented a compensation algorithm for MFL measurement errors caused by random lift-off and tilt detection angles. A practical implementation for the dual magnetic sensor probe in the actual MFL testing tool was given. The finite element simulation and physical experiments were designed to verify the feasibility of probe gesture compensation algorithm. Even under abnormal probe detection gesture case, MFL signals measured and compensated by the dual magnetic sensor probe were also in line with the engineering application, and measurement errors of MFL signals were reduced from more than 30 % to less than 10 %, which is conducive to the realization of ultra-high-definition MFL testing.

Pipeline inspection gauges (PIGs) are widely used for nondestructive testing of oil and natural gas pipelines, while above ground markers (AGMs) can locate and track the PIG through a variety of methods, including magnetic flux leakage signals, acoustic signals, and extremely low-frequency (ELF) magnetic signals. Traditional AGMs have the disadvantages of low positioning accuracy and only one-dimensional tracking capability. In this paper, a newly-designed PIG tracking system based on the ELF magnetic field is proposed by assembling dual receivers. Moreover, this paper develops a magnetic field sign-integration algorithm to achieve high-precision and four-dimensional (4-D) tracking of PIG. The simulation and experiment results demonstrate that the tracking system has the capability of 4-D tracking. In comparison with the previously published work, the designed tracking system improves the positioning accuracy and orientation tracking accuracy by more than 50%. The dual receivers tracking system also has the characteristic of high-robustness. Even in the state of lateral offset or tilt, it can still achieve accurate tracking of PIG. The realization of PIG’s high-precision 4-D tracking can improve the accuracy of defect location. Moreover, it can also provide the latest pipeline network layout and facilitate pipeline maintenance and pipeline surveying applications.

An appropriate modeling technique is critical for the quick analysis of alternating current (ac) field measurements destined for qualitative or quantitative studies of surface defects in conductive materials. Traditional modeling techniques often use the finite-difference method to solve the governing Laplace equation in the crack region, which gives a closed-form solution in the Fourier domain for regions outside the crack. However, these models are complex and only useful for cracks with extremely narrow openings. This article proposes an approximate analytical model that is based on current shunting of parallel circuits and the Biot–Savart law. We assume that the current induced by a high-frequency current-carrying coil is evenly distributed within a very thin layer at the surface of a conductor. In the presence of a defect, the current flows only along the edges and the bottom of the defect. Under these assumptions, the model simplifies the induced current by treating it as due to many current sources of equal amplitude. The magnetic field above the defect can be mathematically described by the linear superposition of these current sources. The proposed model can thus be used to analyze cracks with wider openings. We compare the magnetic-field signals of flat-bottomed cracks of various sizes as obtained by the proposed model and the finite-element method and also explore cracks with complex bottom profiles. The results show that the proposed model produces accurate quantitative and qualitative results for a wider range of defects.