Patent Description:
Metal components of structures are susceptible to defects, such as due to imperfect manufacture, corrosion, fatigue, wear, damage, etc. To prevent catastrophic failure of such structures, metal components may be visually inspected to identify defects before a failure occurs. However, many structures are not easily inspected due to being buried underground or beneath the sea, or due to being embedded within other materials such as concrete. For large infrastructure that contains metal components, visual inspection may be impractical or too costly to perform routinely.

Many ferromagnetic objects, including steel pipe, act as weak permanent magnets even when not intentionally magnetized; for example, magnetic dipoles in steel may partially orient to the Earth's magnetic field after cooling below the Curie temperature when cast or hot-rolled in the foundry. Magnetic fields present in ferromagnetic objects as stray byproducts of their manufacture are known herein as parasitic fields. The Earth's magnetic field also induces magnetic fields in ferromagnetic objects. These magnetic fields permit detection of ferromagnetic objects from a distance. Magnetic exploders for naval mines and torpedoes have been designed to detect magnetic fields from large ferrous objects, such as warships, since <NUM>, although both German and American magnetic exploders were problematic when used in combat on torpedoes in <NUM>-<NUM>. Magnetic exploders, however, are merely intended to detect the object from a distance, not to detect or analyze defects in that object.

Magnetic particle inspection is well known as a method for detecting cracks in objects. In this technique, a ferromagnetic object is placed in a magnetic field, and magnetic particles, such as iron filings, are applied to the object. The magnetic field may be provided by passing an electric current through the object, or by placing the object in a field provided by an electromagnet. If a crack is present, the magnetic particles cluster near the crack. Field strengths used for magnetic particle inspection are typically much greater than the Earth's magnetic field, or those parasitic fields that may be present in ferromagnetic materials.

It is known from <CIT> to use an array of magnetic field sensors and apply a threshold on the magnetic field gradient to detect an anomaly. Using theory of magnetostriction, a degree of stress experienced by the pipeline can be deduced from characteristics of the magnetic field of the pipeline.

In <CIT>, a method for measuring a magnetic field distribution in which the 3D profile of a magnetic field is measured. A map of magnetic field strength along a conductor can be used to detect defects such as cracks.

In <CIT>, a method for detecting corrosion of pipelines through measuring magnetic flux leakage. A wavelet neural network is trained on two-dimensional sections of magnetic leakage flux data of defects and non-defects to automatically detect defects.

According to an embodiment, a method for characterizing a ferromagnetic material according to claim <NUM> includes: receiving measured magnetic field data from a plurality of sensors adjacent the ferromagnetic material at a plurality of locations along the ferromagnetic material; deriving measured magnetic field features from the measured magnetic field data; comparing the derived magnetic field features with modeled or previously collected, verified magnetic field features to identify differences caused by a phenomenon in the ferromagnetic material.

According to another embodiment, a system for characterizing a ferromagnetic material according to claim <NUM> includes: memory capable of storing magnetic field data from at least one sensor configured to measure magnetic field data at a plurality of scan positions along the ferromagnetic material, and software including machine readable instructions. The system may further include a processor coupled with the memory, the processor configured to, in response to execution of the software, perform the steps of: derive magnetic field feature data from the magnetic field data at the plurality of scan positions, and compare the measured magnetic field features data with modeled magnetic field feature data to identify a phenomenon in the ferromagnetic material.

<FIG> schematically illustrates one system <NUM> for characterizing a ferromagnetic material <NUM>, in embodiments. System <NUM> non-intrusively and non-destructively detects local phenomena in an infrastructure, including defects and non-defects, based on ferromagnetic material <NUM>. System <NUM> includes a plurality of magnetic sensors <NUM>. Although <FIG> shows four magnetic sensors <NUM>, system <NUM> may have more or fewer sensors <NUM> without departing from the scope hereof. Sensors <NUM> couple to a data processing module <NUM> via communication paths <NUM>, which may include one or both of a wired and/or a wireless communication media. Data processing module <NUM> processes magnetic field measurements received from sensors <NUM> via communication paths <NUM> to characterize ferromagnetic material <NUM> as described below. Data processing module <NUM> has at least one processor <NUM> coupled with a memory <NUM>, and may in some embodiments have a global positioning system (GPS) receiver <NUM> and/or a digital-radio uplink <NUM>. Digital-radio uplink <NUM> may operate through a cell phone network, or other wireless network such as WiFi, for example, to transmit or receive information to a server <NUM>. Server <NUM> may include, in embodiments, a database <NUM> of anomalies.

Ferromagnetic material <NUM> exhibits magnetization based on its structure, composition, and fabrication history. At the same time, ferromagnetic material <NUM> may have a phenomenon <NUM> that perturbs the magnetic field from ferromagnetic material <NUM>, as illustrated by magnetic field lines <NUM> in <FIG>, wherein phenomenon <NUM> "disrupts" an otherwise spatially regular magnetic field of ferromagnetic material <NUM>. Phenomenon <NUM> is for example (a) a weld or junction between segments of ferromagnetic material <NUM>, (b) an unintentional irregularity of cracked, missing or otherwise faulty ferromagnetic material (hereinafter called a "defect" and typically due to corrosion, fatigue, wear, damage or imperfect manufacture; some defects may lead to infrastructure failure), or (c) an intentionally-designed gap or opening. Sensors <NUM> may be magnetometers arranged in an array to measure magnetic field <NUM> related to phenomenon <NUM>.

Identifying a defect in material <NUM> prior to failure in components such as reinforcing steel, pipelines, oil platform legs, ship hulls, etcetera buried underground or located underwater often requires inspecting beneath a visible surface. The embodiments disclosed herein may be suitable in evaluating ferromagnetic material of such infrastructure including, but not limited to: industrial vessels and pipes of plants and equipment, including power plants, refineries and heat exchangers; pipelines, such as oil and gas pipelines; railways, including rails and bridges of railroads, light-rail and subways; structures, such as buildings and bridges made with ferrous beams or rebar-reinforced concrete; and partially or fully submerged drilling rigs, ships and submarines.

During use of system <NUM> to inspect infrastructure, system <NUM> is positioned near, and moved along ferromagnetic material <NUM> while system <NUM> measures material-associated magnetic field <NUM>. Sensors <NUM> are arranged in a spatially distributed array that provides a spatial map of magnetic field <NUM>, at each traveled location along material <NUM>, with each sensor <NUM> measuring both magnetic direction and magnitude. Data processing module <NUM> in turn processes magnetic field measurements received from the array of sensors <NUM> via communication paths <NUM> to characterize magnetic field <NUM>, thereby providing a current scan of magnetic field along ferromagnetic material <NUM>.

In data processing system <NUM>, processor <NUM> may execute software (for example software <NUM> discussed in further detail below with respect to <FIG>), realized as machine readable instructions stored in memory <NUM>, to implement (a) scan routines to store the current scan of the magnetic field in memory <NUM>, and (b) analysis routines to analyze the scan of the magnetic field for anomalies such as phenomenon <NUM>. If an anomaly is located, processor <NUM> may further execute additional software (for example software <NUM> discussed in further detail below), also realized as machine readable instructions stored in memory <NUM>, to implement further analysis routines on the stored scan to identify the anomaly as a non-defect, such as a weld, flange, or intentionally-designed gap/opening, or identify the anomaly as a defect, such as a missing metal defect or other unintentional fault within the material <NUM>. It should be appreciated that various aspects of data processing system <NUM> may be performed remotely, such as in server <NUM>, without departing from the scope hereof. For example, the analysis routines, including analyzing the scan of magnetic field for anomalies such as phenomenon <NUM>, may be performed on a scan that is previously implemented by data processing module <NUM> (via scan routines) and then transmitted from data processing module <NUM> to server <NUM>.

In embodiments, the analysis routines operate by determining signature phenomena, of the observed magnetic field (such as phenomena in, or functions of, the magnetic field gradients and derivatives thereof) as recorded from multiple locations in a sliding window of the scan. In an embodiment, the software (for example software <NUM> discussed in further detail below) implementing such analysis routines determines signature phenomena by fitting a superposition of predefined signature phenomena. The predefined signature phenomena may be derived from (a) computer models of magnetic dipoles to the observed magnetic field from the locations in the sliding window, (b) a non-dipole based model, (c) measurements, or (d) a combination thereof.

Information about anomaly types, including classifications of the anomaly types and pattern phenomena corresponding to each anomaly type, may be stored in memory <NUM> and/or database <NUM>. In an embodiment optimized for analysis of pipelines, the anomaly types include exemplary good welds and exemplary defective welds, as well as cracks, breaks, valves, taps, and corroded locations. The analysis routines may be configured to provide the classification that most closely matches each anomaly found during a scan.

A location read from GPS <NUM>, and/or other location sensors such as an odometer, may in some embodiments be associated with a portion of the scan associated with a defect, or in some embodiments portions of the scan associated with a non-defect, such as a weld or flange, and these locations and associated scan windows are reported through uplink <NUM> to server <NUM> and stored in database <NUM>. Since weld locations in a pipeline, or bolted joints in railroad track, are unlikely to change with time in infrastructure <NUM>, new phenomena, or phenomena that have significantly changed character since any prior scan, can indicate incipient failure such as cracks in a pipe or breaks in rail. Either processor <NUM> or server <NUM>, may correlate the current and prior scan to align phenomena, and then compare phenomena of anomalies detected in the current scan to observations made during a prior scan at the same location, as may have been previously recorded in database <NUM>, to determine whether the phenomenon is new, and identify it as new. New phenomena, as well as phenomena classified as defects, may warrant further investigation, such as by excavating a pipeline.

In particular embodiments, system <NUM> does not include a bias magnet for magnetizing the ferromagnetic material <NUM>. In these embodiments, the magnetic fields sensed by system <NUM> are parasitic magnetic fields and fields induced in the ferromagnetic material by the Earth's magnetic field.

<FIG> schematically illustrates a system <NUM> that characterizes ferromagnetic material. System <NUM> is a an embodiment of system <NUM> In system <NUM>, sensors <NUM>, of <FIG>, are implemented in a sensor array <NUM> that communicatively couples to data processing module <NUM>. System <NUM> implements data processing module <NUM> with at least one processor <NUM> in communication with memory <NUM>. Processor <NUM> is an embodiment of processor <NUM>. Memory <NUM> is an embodiment of memory <NUM> and may be transitory and/or non-transitory and in some embodiments includes one or both of (a) volatile memory such as RAM and (b) non-volatile memory such as, ROM, EEPROM, Flash-EEPROM, magnetic media including disk drives, optical media. Memory <NUM> stores software <NUM> and firmware <NUM> as machine readable instructions executable by processor <NUM> to process data from sensor array <NUM> and identify and/or characterize one or more phenomena <NUM> of ferromagnetic material <NUM>. It should be appreciated that various aspects of software <NUM> and firmware <NUM> may be implemented by server <NUM> shown in <FIG>, instead of, or in addition to, data processing module <NUM>. In embodiments, measurements from sensor array <NUM> are received by a receiver <NUM> that communicates measurements to data processing module <NUM>. In other embodiments, measurements are communicated directly from sensor array <NUM> to data processing module <NUM>. Receiver <NUM> is for example a data acquisition device. In embodiments, data from non-magnetic sensors <NUM> (e.g., accelerometers) are also received by receiver <NUM>, as more fully described below. Illustratively, data processing module <NUM> includes an interface <NUM> for communicating with other devices, including server <NUM> that processes and stores data. Server <NUM> is similar to server <NUM>, and therefore the discussion of server <NUM> applies equally to server <NUM>. Although data processing module <NUM> is shown as a single device, it should be appreciated that data processing module <NUM> may incorporate one or more devices such as computers, processors, memories, etc..

<FIG> schematically illustrates an exemplary magnetic sensor array <NUM> for characterizing ferromagnetic material <NUM> in the form of a pipe. Sensor array <NUM> includes ten magnetic sensors, including a first magnetic sensor <NUM>, a magnetic second sensor <NUM>, and so on up to a tenth magnetic sensor <NUM> arranged in a three-dimensional (3D) array. More or fewer magnetic sensors may be utilized without departing from the scope hereof. Sensor array <NUM> is an embodiment of sensor array <NUM>, <FIG>, and each sensor <NUM>-<NUM> is for example an embodiment of sensor <NUM> of <FIG>. <FIG> illustrates an exemplary "T" arrangement of sensors <NUM>-<NUM> positioned along three orthogonally oriented axes.

Although in <FIG>, sensor array <NUM> is shown in a "T" arrangement, the sensor array <NUM> may be configured in other patterns without departing from the scope hereof. For example, sensor array <NUM> may also be implemented in non-orthogonal arrangements, instead of the orthogonal arrangement shown in <FIG> without departing from the scope hereof. Moreover, sensor array <NUM>, in either a non-orthogonal or an orthogonal arrangement may be configured with more or fewer magnetic sensors, and could be deployed in positions and arranged in a pattern, such as in a cone- or sphere-shaped pattern. Furthermore, in embodiments, the sensor array may be synthesized with just a single magnetic sensor moved between known positions to make multiple measurements as a data array. Likewise, the locations of sensors <NUM>-<NUM> need not be restricted to locations along the axes of a 3D coordinate system. One- or two-dimensional arrays may also be beneficially employed as array <NUM>.

Magnetic sensor array <NUM> is positioned with a standoff distance <NUM> above ferromagnetic material <NUM> having a defect <NUM>. Ferromagnetic material <NUM> is an example of ferromagnetic material <NUM>, <FIG>, while defect <NUM> is an example of phenomenon <NUM>. Defect <NUM> is for example a missing metal defect, a corrosion-induced defect, or any other type of irregularity that is substantially different from an expected shape and structure of ferromagnetic material <NUM>. Defect <NUM> thus causes a magnetic field phenomenon with an exemplary magnetization direction indicated by arrow <NUM>. Standoff distance <NUM> may be known, estimated or measured, for example using ground penetrating radar.

The ability to sense magnetic fields with sensor arrays, such as sensor array <NUM>, depends on standoff distance <NUM>, the strength of magnetic field <NUM> from ferromagnetic material <NUM>, the sensitivity of magnetic sensors <NUM>-<NUM>, and spacing distances <NUM>, <NUM>, <NUM>, <NUM>, <NUM> between sensors <NUM>-<NUM> in sensor array <NUM>. In an embodiment, magnetic sensors <NUM>-<NUM> are magnetometers that measure magnetic fields. Magnetic sensors <NUM>-<NUM> may be one-axis magnetometers that measure magnetic fields along one axis, two-axis magnetometers that measure magnetic fields along two axes, or three-axis magnetometers that measure magnetic fields along three axes. The three axes are for example x, y, and z axes depicted in <FIG>. Note that sensor array <NUM> includes variable spacing distances between magnetic sensors <NUM>-<NUM>; for example, a first distance <NUM> between magnetic sensors <NUM> and <NUM> is greater than a second distance <NUM> between magnetic sensors <NUM> and <NUM>. Similarly along the z-axis, a fourth distance <NUM> may be greater than a fifth distance <NUM>. In an embodiment, first, second, third, fourth, and fifth distances <NUM>, <NUM>, <NUM>, <NUM>, <NUM> are optimized to measure dipole magnetic fields and determine magnetic field gradient peak signatures of defect <NUM> for a given standoff distance <NUM>. In an operational example, which the embodiments herein are not limited to, a third distance <NUM> between magnetic sensors <NUM> and <NUM> is about <NUM> for a standoff distance <NUM> of <NUM>. In another operational example, magnetic sensors <NUM>-<NUM> have adjustable positions within sensor array <NUM> such that sensor spacing distances <NUM>, <NUM>, <NUM>, <NUM>, <NUM> are adjusted to optimize measurement of magnetic fields having different field strengths for different standoff distances <NUM>.

<FIG> illustrates yet another system <NUM> for characterizing ferromagnetic material <NUM>. System <NUM> is an embodiment of system <NUM>. System <NUM> shows four sensor arms <NUM>, <NUM>, <NUM>, <NUM> each of which contains one or more sensors <NUM> (e.g., magnetometers) that measure magnetic field strength. Sensors <NUM> may be arranged in an array, such as the sensor array <NUM> of <FIG>, and attached to a frame <NUM> by sensor arms <NUM>, <NUM>, <NUM>, <NUM> or by other structure when moving the array of sensors <NUM> along ferromagnetic material <NUM>. Sensors <NUM> are an embodiment of sensors <NUM> and are arranged in an example of sensor array <NUM>. Ferromagnetic material <NUM> is an example of ferromagnetic material <NUM>. By way of example, frame <NUM> may be equipped with straps <NUM> or other means for a user to carry system <NUM>. In another embodiment, system <NUM> is mechanically coupled to a vehicle, such as an automobile, train, aerial vehicle, or underwater vehicle. Sensor arms <NUM>, <NUM>, <NUM>, <NUM> may be moveable up and down along frame <NUM> to account for variation in standoff distance <NUM>.

A power supply <NUM> electrically couples to sensors <NUM> to provide direct current (DC) electrical power. Power supply <NUM> may be wired to an electrical grid or have a battery pack that enables remote, off-grid use of system <NUM>. A receiver <NUM> couples to sensors <NUM> via communication path <NUM>, which is similar to communication path <NUM> of <FIG>, to receive data therefrom. Receiver <NUM> is for example an embodiment of receiver <NUM>, <FIG>. A computer <NUM> connects to receiver <NUM> via communication path <NUM> to process received sensor data. Computer <NUM> is for example an embodiment of data processing module <NUM> implementing processor(s) <NUM>, memory <NUM>, and optional interface <NUM>. Communication paths <NUM>, <NUM> may include one or both of a wired and/or a wireless communication media.

<FIG> shows an exemplary pipe <NUM> made of ferromagnetic material. Pipe <NUM> is an example of ferromagnetic material <NUM> and <NUM> and may be characterized using any of systems <NUM>, <NUM>, and <NUM>. Pipe <NUM> includes a weld <NUM>, which is a welded junction that joins a first segment <NUM> to a second segment <NUM> of pipe <NUM>. Weld <NUM> is an example of an intentional non-defect phenomenon that produces a characteristic magnetic field phenomenon providing a magnetic field signature that may resemble a magnetic dipole. For example, magnetic flux leakage may occur at weld <NUM> producing the magnetic field signature. In an embodiment, magnetic field signatures are determined in real-time and used for calibration and compensation of magnetic field measurements caused by variability such as platform motion or standoff distance <NUM>. Data processing module <NUM> compares magnetic field measurements obtained by sensors <NUM> to known magnetic field signatures to detect a defect, such as defect <NUM>, <FIG>. In <FIG>, memory <NUM> may thus include at least one magnetic field signature for this purpose.

<FIG> is a flowchart illustrating steps of an exemplary method <NUM> for measuring magnetic field <NUM> from infrastructure containing ferromagnetic material <NUM>. Method <NUM> is an example of a "scan routine" as discussed above with respect to <FIG>, <FIG>, and <FIG>. As such, method <NUM> may be performed by system <NUM> of <FIG>, system <NUM> of <FIG>, and system <NUM> of <FIG>, for example using data processing module <NUM> executing software <NUM>.

In an optional step <NUM>, the system for characterizing ferromagnetic material moves to a first scan position, such as an arbitrary location adjacent to infrastructure containing ferromagnetic material. In an example of step <NUM>, system <NUM> of <FIG> is moved to a position adjacent to first segment <NUM> of pipe <NUM> of <FIG>. In other examples, system <NUM> or <NUM>, of <FIG> and <FIG>, is moved to a position adjacent to a first segment of ferromagnetic material <NUM>.

In a step <NUM>, the system measures magnetic fields. In an example of step <NUM>, sensors <NUM> measure a magnetic field (e.g. magnetic field <NUM>) from first segment <NUM>. In other examples of step <NUM>, sensors <NUM> of <FIG>, possibly in the arrangement of array <NUM> of <FIG>, measure a magnetic field from ferromagnetic material <NUM>.

In a step <NUM>, the system for characterizing ferromagnetic material moves to a next scan position. In an example of step <NUM>, system <NUM> of <FIG> moves to a position adjacent weld <NUM> of pipe <NUM> of <FIG>. In another example of step <NUM>, system <NUM> or <NUM>, of <FIG>, is moved to a next scan position along ferromagnetic material <NUM>.

Step <NUM> is a decision. If in step <NUM> the end of the infrastructure is reached, or the end of a desired scan range is reached, method <NUM> ends. Otherwise, method <NUM> returns to step <NUM>. In this way, method <NUM> is carried out to scan an entire infrastructure or a desired portion of an infrastructure. The rate at which magnetic fields are measured between first scan position and the next scan position may depend on bandwidth of data acquisition such as receiver <NUM> of <FIG>. In an embodiment, system <NUM> is moved between locations at a rate of <NUM> meters per second. In another embodiment, system <NUM> or <NUM>, of <FIG>, is moved at a rate of <NUM> meters per second along ferromagnetic material <NUM>.

<FIG> shows a plot <NUM> of exemplary magnetic fields measured by one sensor, such as sensor <NUM> in array <NUM> or any of sensors <NUM> of <FIG> and <NUM> of <FIG>, versus scan position along pipe <NUM>. Specifically, plot <NUM> illustrates exemplary magnetic field <NUM> measured by this sensor during method <NUM> over multiple iterations of step <NUM>. Plot <NUM> includes magnitude of magnetic field, B, aligned in x, y, and z axes (Bx, By, Bz) versus scan position along pipe <NUM>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, versus scan position; a dataset <NUM> shows magnetic field strength along the y-axis, By, versus scan position; and a dataset <NUM> shows magnetic field strength along the z-axis, Bz, versus scan position. The scan direction is oriented along the x-axis and sensor <NUM> is centered above pipe <NUM> in the y-dimension. By way of comparison, at a scan position of zero in <FIG>, sensor <NUM> of <FIG> is positioned directly above defect <NUM>. As sensor <NUM> is moved along ferromagnetic material <NUM>, the scan position from defect <NUM> varies, corresponding to an increasing (positive values) or decreasing (negative values) scan position depending on the direction of movement.

Referring again to <FIG>, in an optional step <NUM>, magnetic field data measured from step <NUM> is processed to characterize ferromagnetic material <NUM>. In an example of step <NUM>, measured magnetic field data is compared, by data processing module <NUM> executing software <NUM> (or alternatively a remote server such as server <NUM> executing software similar to software <NUM>), with an empirically determined or physics-based model of magnetic fields to identify and characterize phenomena in the magnetic field data caused by a phenomenon of ferromagnetic material <NUM>. Measured data and modeled data are compared using for example matched filters or statistical-detection algorithms. One example of a physics-based model is a magnetic dipole model. Missing metal from ferromagnetic material produces predominantly magnetic dipole characteristics that are detected and matched with a magnetic dipole model. Missing metal defects, such as defect <NUM>, <FIG>, may have a dipole in reverse orientation to magnetization in ferromagnetic material <NUM>. The reverse dipole orientation may be used to help identify defect <NUM>. Similarly, welds forming junctions between segments of ferromagnetic material, such as weld <NUM> of <FIG>, produce predominantly magnetic dipole characteristics. For example, at weld <NUM> between pipe segments <NUM>, <NUM> dipoles may exist due to differences in magnetization direction and amplitude between pipe segments <NUM>, <NUM> together with magnetic reorientation due to heating when the weld was made.

In a particular embodiment, modeled data is determined from a finite element model. In embodiments, model-based analysis, for example performed by data processing module <NUM> executing software <NUM>, of magnetic dipoles detected by the system includes one or more of: applying interpolation on the magnetic field signature sphere to obtain the magnetic field at planes above and parallel and near-parallel to the pipe at different distances, and angles; extracting magnetic field spatial phenomena from the magnetic field, such as gradient, directional derivative, divergence or Laplacian, curl, magnitude and neighborhood local statistical moments of these phenomenon fields; obtaining daughter magnetic field phenomena from the field, such as a Spatial Fast-Fourier Transform (FFT) phase field, power spectral density (PSD), and Wavelet coefficients; separately analyzing each phenomenon statistically, for example using the t-test and the Wilcoxon Rank test; and selecting phenomena by collectively satisfying, or optimally satisfying, multiple criteria such as p-values, correlation to size and height, and orthogonality (non-correlation among phenomena). Nearby pairs and triplets of the above phenomena are fused for FFT and Wavelet analysis. Extracted phenomena are compared to a library of model-derived phenomena, such as welds and defects.

<FIG> show exemplary plots of measured and modeled magnetic field strength, respectively, as a function of scan position. <FIG> shows a plot <NUM> of exemplary magnetic fields measured by a single sensor (e.g. one of sensors of array <NUM>) for a range of scan positions using method <NUM> of <FIG> implemented by system <NUM> of <FIG>. Plot <NUM> may thus illustrate magnetic fields at a plurality of scan positions for weld <NUM> of <FIG> such as measured with sensor <NUM> for example. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz, over a range of scan positions along the x-axis at a position centered over the pipe in the y-dimension. Magnetic field strength of pipe segments as determined at weld <NUM>, such as that illustrated in plot <NUM>, may be used for scaling magnetic field measurements from pipe segments <NUM>, <NUM> to normalize data for improved detection of defects.

<FIG> shows a plot <NUM> of exemplary magnetic field strength versus scan position from a dipole model used in characterizing a ferromagnetic material phenomenon, such as weld <NUM> that joins first and second pipe segments <NUM>, <NUM> of <FIG>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz, versus scan position along the x-axis at a position centered over the pipe in the y-dimension.

According to an embodiment, data processing module <NUM> compares measured magnetic field plots, such as plot <NUM> of <FIG>, with modeled magnetic field plots, such as plot <NUM> of <FIG> to distinguish a weld signature from a defect signature in step <NUM> of method <NUM>, thereby detecting whether a defect has occurred. While both weld and defect signatures have dipole characteristics, magnetic field changes along the pipe may differ in magnitude from those expected at a weld. Further, field gradients at a weld will tend to taper from a field orientation in one segment of the pipe to a potentially-different orientation in another segment of the pipe, rather than returning to the same orientation beyond the defect as to be expected in a single section of pipe. This may be due to a broad transition zone between magnetic polarization of pipe sections produced as the metal was heated and cooled during welding, this transition zone being broader than typical missing metal defects.

In an embodiment, a scalar likelihood, L, indicates the presence of a defect determined from gradients in all axes in a scan position window near the phenomenon, and from other statistical processing; if L is greater than a threshold, the phenomenon or anomaly is reported as a defect. <FIG> illustrate L plotted versus scan window position with a threshold of one; <FIG> are associated with weld signatures and L<<NUM> indicating non-defect, for <FIG>, L><NUM> indicating a defect. The window size may be varied and the gradient data rescanned repeatedly with different window sizes depending on the sizes of ferromagnetic material, phenomenon (e.g. defects, weld, or anomaly) as discussed further below with respect to <FIG>.

Magnetic fields calculated from dipole models for x, y and z-axes, such as those plotted versus scan position in <FIG>, depend on orientation of the magnetic dipole. For example, a dipole may have an axial orientation along the scanning direction, for example along the x-axis of <FIG>, a lateral orientation sideways from the scanning orientation, for example along the y-axis of <FIG>, or a vertical orientation that is up and down from the scanning direction, for example along the z-axis of <FIG>. A combination dipole has magnetization components of all three orientations, Cx, Cy, and Cz. Three-axis magnetic fields are calculated for a dipole model using Equation <NUM>, below.

Equation <NUM> is the magnetic field equation for an arbitrary dipole orientation where Cx, Cy, and Cz are combination magnetic fields proportional to magnetization along the x, y, and z-axes, respectively, and r is the absolute distance that includes standoff distance <NUM> from the sensor to the magnetic field source. In order for a magnetic signature to resemble a dipole, sensor distance from a magnetic source, r, is for example about two to three times longer than the magnetic source itself, although shorter sensor distances contain dipole characteristics that may be matched to Equation <NUM> if r is known.

<FIG> shows a plot <NUM> of exemplary modeled magnetic fields versus scan position for an axial dipole model, aligned with the x-axis, which may be used by data processing module <NUM> (or server <NUM> implementing analysis functions) to identify phenomena of ferromagnetic material <NUM>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz, for a magnetic dipole source oriented axially. Cx is a constant, Cy and Cz are zero. Each of datasets <NUM>, <NUM>, and <NUM> show the magnetic field as a function of x at a position centered over the magnetic dipole source in the y-direction.

<FIG> shows a plot <NUM> of exemplary modeled magnetic field strength versus scan position for a lateral dipole model, aligned with the y-axis, which may be used by data processing module <NUM> (or server <NUM> implementing analysis functions) to identify phenomena of ferromagnetic material <NUM>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz for magnetic dipole source oriented laterally. Cy is a constant, Cx and Cz are zero. Each of datasets <NUM>, <NUM>, and <NUM> show the magnetic field as a function of x at a position centered over the magnetic dipole source in the y-direction.

<FIG> shows a plot <NUM> of exemplary modeled magnetic field strength versus scan position for a vertical dipole model which may be used by data processing module to identify phenomena of ferromagnetic material <NUM>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz for a magnetic dipole source oriented vertically. Cz is a constant, Cx and Cy are zero. Each of datasets <NUM>, <NUM>, and <NUM> show the magnetic field as a function of x at a position centered over the magnetic dipole source in the y-direction.

<FIG> shows a plot <NUM> of exemplary combination magnetic field strength versus scan position, which combines axial, lateral, and vertical dipole orientations of <FIG>. A dataset <NUM> shows magnetic field strength along the x-axis, Bx, a dataset <NUM> shows magnetic field strength along the y-axis, By, and a dataset <NUM> shows magnetic field strength along the z-axis, Bz. Cx, Cy and Cz are constants adjusted for model fitting, based on factors including the strength of measured magnetic fields.

Other than comparing models and measurements of magnetic fields over scan position, such as step <NUM> of method <NUM>, magnetic field gradients may be used to further identify phenomena of ferromagnetic material <NUM>. According to an embodiment, magnetic field gradients are calculated from a plurality of sensors arranged in an array, such as sensor array <NUM> of <FIG>. Specifically, <FIG> is a flowchart illustrating steps of one method <NUM> to detect a phenomenon of a ferromagnetic material and characterize the ferromagnetic material based upon magnetic field data obtained using one or more sensors. Each sensor (e.g. sensors <NUM>, <NUM>, <NUM>) is configured to measure the magnitude and direction of the local magnetic field. Method <NUM> uses models and measurements of magnetic fields over scan position to detect and characterize phenomenon <NUM> of ferromagnetic material <NUM>. Data processing module <NUM> (or server <NUM> implementing analysis functions) may perform method <NUM> based upon magnetic field data obtained from sensor array <NUM>. Method <NUM> may be implemented in data processing module <NUM> (or server <NUM>) as at least a portion of software <NUM> and/or firmware <NUM>, <FIG>. Accordingly, it should be appreciated that method <NUM> may also be implemented using system <NUM>, of <FIG>. Aspects of method <NUM> are for example an embodiment of step <NUM> of method <NUM>.

In step <NUM>, magnetic field data are received for a plurality of scan positions. In an example of step <NUM>, processor <NUM> executes software <NUM> and/or firmware <NUM> stored in memory <NUM> to parse data from sensor array <NUM>, which is received either directly from sensor array <NUM> or optionally via receiver <NUM>.

In step <NUM>, magnetic field derived features are derived from the magnetic field data of step <NUM>. Exemplary magnetic field derived features comprise numerics that are derived from the raw sensor data, or a denoised version thereof, including but not limited to: the field measurements, their Fourier, Wavelet or any other transform, their magnetic field gradients; the gradient Fourier transform, wavelet transform or any other transform; <NUM>nd derivative matrices or Hessians, their Fourier transforms or any of their transforms, fractal dimension of the field, gradients, Hessians, or features recovered by data mining or machine learning/ deep learning methods.

In an example of step <NUM>, the magnetic field derived features that are calculated are magnetic field gradients. In such example, the magnetic field gradients are calculated, by data processing module <NUM> (or server <NUM>), from differences in magnetic fields between sensors <NUM>-<NUM> of sensor array <NUM>, <FIG> for a plurality of scan positions. In one embodiment, a single sensor such as sensor <NUM> measures magnetic fields at a plurality of scan positions, and one or more gradients are calculated, using for example data processing module <NUM> (or server <NUM>), from the plurality of measurements. In another embodiment, magnetic field gradients between different sensors are calculated for each scan position. Equation <NUM>, below, shows an exemplary calculation for magnetic field gradients between fourth sensor <NUM> and eighth sensor <NUM> along the x-axis of <FIG>.

In Equation <NUM>, ΔBxyz/Δx is the difference between three-axis magnetic fields between sensor <NUM> (abbreviated S4) at position xS4 and sensor <NUM> (abbreviated S8) at position xss. BxS4 is the x-axis magnetic field at fourth sensor <NUM>, BxS8 is the x-axis magnetic field at eighth sensor <NUM>, and so on for y-axis and z-axis magnetic fields, By, Bz. xS4-S8 is the spacing distance between sensors <NUM> and <NUM>.

Three-axis magnetic field gradients are calculated from dipole models of magnetic fields for additional select pairs of sensors in the same manner. For example, three-axis magnetic field gradients (ΔBxyz) are calculated using Equation <NUM>, below, between fourth sensor <NUM> and ninth sensor <NUM>, between fourth sensor <NUM> and tenth sensor <NUM>, and between ninth sensor <NUM> and tenth sensor <NUM> along the z-axis, as depicted in <FIG>.

In Equation <NUM>, ΔBxyz/Δz is the difference between three-axis magnetic fields along the z-axis, zS4-S9 is the spacing distance between fourth sensor <NUM> (abbreviated S4) and ninth sensor <NUM> (abbreviated S9), BxS4 is the x-axis magnetic field at fourth sensor <NUM>, BxS9 is the x-axis magnetic field at ninth sensor <NUM>, and so on for other sensor pairs and for y-axis and z-axis magnetic fields, By, Bz.

Similarly, select three-axis magnetic field gradients (ΔBxyz/Δy) are calculated along the y-axis using Equation <NUM>, below.

In Equation <NUM>, ΔBxyz/Δy is the difference between three-axis magnetic fields along the y-axis, yS1-S2 is the spacing distance between first sensor <NUM> (abbreviated S1) and second sensor <NUM> (abbreviated S2), BxS1 is the x-axis magnetic field at first sensor <NUM>, BxS2 is the x-axis magnetic field at second sensor <NUM>, and so on for other sensor pairs and for y-axis and z-axis magnetic fields, By and Bz.

In an example of step <NUM>, x-axis magnetic field gradients (ΔBxyz/Δx) are calculated using Equation <NUM> from differences between three-axis magnetic fields (Bx, By, Bz) measured with fourth sensor <NUM> (S4) and eighth sensor <NUM> (S8) along the x-axis as depicted in <FIG>. Similarly, select z-axis magnetic field gradients (ΔBxyz/Δz) are calculated using Equation <NUM> for magnetic fields measured with fourth sensor <NUM> (S4), ninth sensor <NUM> (S9), and tenth sensor <NUM> (S10), along the z-axis, as depicted in <FIG>. Similarly, select y-axis magnetic field gradients (ΔBxyz/Δy) are calculated using Equation <NUM> for magnetic fields measured with first sensor <NUM> (S1), second sensor <NUM> (S2), third sensor <NUM> (S3), fourth sensor <NUM> (S4), fifth sensor <NUM> (S5), sixth sensor <NUM> (S6), and seventh sensor <NUM> (S7), along the y-axis, as depicted in <FIG>. Exemplary measured magnetic field gradients are plotted in <FIG>.

<FIG> shows a plot <NUM> of exemplary measured magnetic field gradients in the x-axis versus scan position. Plot <NUM> is determined by data processing module <NUM> from magnetic field <NUM> of defect <NUM> measured using sensor array <NUM> of <FIG> for example. Dataset <NUM> shows a first gradient ΔBx between first sensor <NUM> and second sensor <NUM>. Dataset <NUM> shows a second gradient ΔBx between first sensor <NUM> and third sensor <NUM>. Dataset <NUM> shows a third gradient ΔBx between first sensor <NUM> and fourth sensor <NUM>. Dataset <NUM> shows a fourth gradient ΔBx between third sensor <NUM> and fourth sensor <NUM>. Dataset <NUM> shows a fifth gradient ΔBx between third sensor <NUM> and fifth sensor <NUM>.

Although step <NUM> is described above including measured magnetic field gradients, it should be appreciated that other measured magnetic field derived features (other than gradients) could be utilized in step <NUM>. For example, instead of gradients, step <NUM> may calculate measured magnetic field hessians, wavelets, power spectral density, or fractal dimension without departing from the scope hereof. As such, it should be appreciated that, although equations <NUM>-<NUM> above show the formula for gradients, step <NUM> may be implemented based on similar formulas for many other magnetic field derived features that are derived from the magnetic field sensor data, such as those magnetic field derived features discussed above.

In an embodiment, method <NUM> includes optional step <NUM>, wherein at least one model of magnetic field derived features is calculated from modeled magnetic fields for a plurality of scan positions. In an example of step <NUM>, modeled magnetic field gradients shown in <FIG> are calculated by data processing module <NUM> (or server <NUM>) using Equations <NUM>-<NUM> from model magnetic fields calculated using Equation <NUM> for select pairs of sensors and a plurality of scan positions. In an alternative embodiment, modeled magnetic field features are calculated from historical data as found in database <NUM> for the same location. For example, if the same ferromagnetic material <NUM> was previously scanned using method <NUM>, the measured magnetic field features are used as a model for comparison with repeat measurements. This approach enables (a) monitoring a small anomaly that may be a defect over time to determine if it is growing in size; growth in size is more likely associated with a developing defect than with a weld or flange.

<FIG> shows a plot <NUM> of exemplary magnetic field gradients in the x-axis versus scan position calculated by data processing module <NUM> (or server <NUM>) for a dipole model of a defect, such as defect <NUM> of <FIG>. Dataset <NUM> shows a first gradient ΔBx between first sensor <NUM> and second sensor <NUM>. Dataset <NUM> shows a second gradient ΔBx between first sensor <NUM> and third sensor <NUM>. Dataset <NUM> shows a third gradient ΔBx between first sensor <NUM> and fourth sensor <NUM>. Dataset <NUM> shows a fourth gradient ΔBx between third sensor <NUM> and fourth sensor <NUM>. Dataset <NUM> shows a fifth gradient ΔBx between third sensor <NUM> and fifth sensor <NUM>. Again, it should be appreciated that step <NUM> is not limited to magnetic field gradients, but can be implemented based on other magnetic field derived features such as those discussed above.

In step <NUM>, measured magnetic field derived feature data are compared to modeled magnetic field feature data for a plurality of scan positions to identify one or more phenomena in magnetic field features caused by welds, defects, or anomalies in the ferromagnetic material. In an example of step <NUM>, multiple measured magnetic field gradients from sensor array <NUM>, such as those shown in <FIG>, are compared, using data processing module <NUM> (or server <NUM>), to modeled magnetic field gradients, such as those shown in <FIG>, to identify a phenomenon in magnetic field gradients caused by defect <NUM> of ferromagnetic material <NUM> of <FIG>. As part of step <NUM>, measured and modeled data may be analyzed for correct dipole orientation based on dipole model gradients.

According to an embodiment, select magnetic field phenomena containing a defect signature are used to identify defect <NUM>. According to another embodiment, step <NUM> includes an optional step <NUM> of incorporating data from non-magnetic sensors <NUM> of <FIG> to further enhance characterization of ferromagnetic material <NUM>. In one example, non-magnetic sensors <NUM> provide ground penetrating radar used to measure standoff distance <NUM>. In another example, data processing module <NUM> utilizes GPS location information provided by GPS <NUM> for each magnetic field measurement, which may be augmented by one or both of Wide Area Augmentation System (WAAS) data and odometer data.

In an optional step <NUM>, one or more defects or irregularities of a ferromagnetic material are characterized, and their locations and classifications may be reported in step <NUM>. In an example of step <NUM>, defect <NUM> of <FIG> is identified and characterized. In an example of step <NUM>, location of defect <NUM> is reported to server <NUM> and stored in database <NUM>, <FIG>. Reporting location of defects and irregularities includes displaying two and three-dimensional plots on interface <NUM> of data processing module for example. Depending on the type of phenomenon identified, a more intrusive inspection, such as digging out an underground pipe for visual inspection, may be performed in the identified locations.

Characterization of a defect by data processing module <NUM> in step <NUM> may include determining its size and orientation, and may further include classifying a type of missing metal defect. Characterization includes distinguishing between a defect and a non-defect such as a weld, flange, coupled branch line, bend, or other normal or intentional anomaly. Identification and characterization of defects and irregularities may be assisted using information from different sensor types and prior magnetic sensor data for the same location. Method <NUM> provides advantages for identifying and characterizing phenomena in ferromagnetic material including that the method may be automated and is repeatable.

<FIG> shows an exemplary method <NUM> for determining a model, and thus a signature, for observed magnetic field gradients. Method <NUM> is an embodiment of aspects of <FIG>.

In one embodiment, method <NUM> includes a step <NUM> of plotting magnetic field data for a plurality of locations and a plurality of sensors via interface <NUM> for analysis by a user to determine a nearest sensor to a magnetic field source. For example, plot <NUM> of <FIG> may be analyzed for a weld signature from measurements made of weld <NUM> of <FIG> using method <NUM> of <FIG>. Step <NUM> may occur in method <NUM> prior to step <NUM>.

In a step <NUM>, a nearest sensor of the sensor array to a phenomenon of the ferromagnetic material is determined. In one embodiment, data processing module <NUM> determines the nearest sensor. In an example of this embodiment of step <NUM>, processor <NUM> executes a portion of software <NUM> and/or firmware <NUM> to process magnetic field data generated by sensors <NUM>-<NUM> of <FIG> to determine that sensor <NUM> of <FIG> is nearest defect <NUM>. In another embodiment, a user identifies sensor <NUM> as the nearest sensor to defect <NUM> by visually inspecting magnetic field plots displayed in step <NUM>. Step <NUM> may occur in method <NUM> between steps <NUM> and <NUM>.

In a step <NUM>, magnetic field data from the nearest sensor, measured over a plurality of scan positions, are analyzed for known signatures. In an example of step <NUM>, using data processing module <NUM>, magnetic field data from nearest sensor <NUM> of <FIG> are analyzed for signatures of one or more known phenomena in ferromagnetic material, such as weld <NUM> of <FIG>. In an embodiment of step <NUM>, measured magnetic fields versus scan position along the ferromagnetic material, such as in plot <NUM> of <FIG>, are compared to a magnetic dipole model versus scan position, such as in plot <NUM> of <FIG>. In an embodiment of step <NUM>, known signatures are analyzed via data processing module <NUM> using matched filters and statistical-detection algorithms.

If a signature is found in step <NUM>, a step <NUM> isolated a portion of the magnetic field data that matches a known signature. In an example of step <NUM>, using data processing module <NUM>, magnetic field data corresponding to a weld signature from weld <NUM> of <FIG> are isolated from magnetic field data of first and second pipe segments <NUM>, <NUM>. According to an embodiment, a user crops magnetic field data using data processing module <NUM> to isolate a weld signature. For example, plot <NUM> of <FIG> may be cropped between scan positions to a narrower window ranging from -<NUM> to <NUM> to isolate the weld signature.

Steps <NUM> and <NUM> may occur in method <NUM> between steps <NUM> and <NUM>. For example, if steps <NUM> and <NUM> are used in method <NUM>, step <NUM> may act to filter out known non-defects (such as welds) from the phenomenon identified in step <NUM>. Steps <NUM> and <NUM> may utilize non-magnetic sensors, such as GPS, and ground penetrating radar, as discussed above with respect to step <NUM> to further enhance identification of known non-defects in method <NUM>.

In a step <NUM>, a characterization is determined for the segment of ferromagnetic material having a phenomenon. Step <NUM> acts to identify the phenomenon as defects, and then potentially characterize said identified phenomenon as a specific type of defect. The characterization and phenomenon location are then reported in step <NUM>, <FIG>. In an example of step <NUM>, using data processing module <NUM>, magnetic flux leakage at weld <NUM> of pipe <NUM>, <FIG> is analyzed to determine a magnetization direction and a magnetization amplitude (or strength) for first and second segments <NUM>, <NUM>.

In an embodiment, using data processing module <NUM> (or server <NUM>), modeled magnetic data is modeled as a linear subspace of components of the magnetic signal over scan position, such as gradients, wavelets, and power spectral density. The magnetic signal components are extracted from a physics-based model, such as a dipole model, and corrupted with noise and interference from one or more magnetic sources to make the model more realistic. Magnetic sensor measurements are then projected onto the subspace spanned by dipole moments, or any function of the magnetic dipole moments, such as gradients, Hessians, wavelets, power spectral density, or fractal dimension of other magnetic field derived features discussed above. Equation <NUM>(a) shows an example linear subspace model.

In Equation <NUM>(a), X is a gradient measurement vector across scan positions, S is a feature subspace basis matrix across scan positions in terms of gradients, F is a known magnetic interference subspace such as a bias or flange, U is an unknown magnetic interference subspace matrix, n is a noise vector, and θ, φ, and ψ are scaling parameter vectors determined from measurements. U may be constructed as the matrix orthogonal to a concatenation of S and F.

Again, it should be appreciated that X may represent feature measurement vectors other than gradient. For example, within Equation <NUM>(a), the subspace basis matrix S is based on gradients, but it should be appreciated that the subspace basis matrix S may be based on other magnetic field measurements such as those magnetic field derived features discussed above. In an embodiment, subspace basis matrix S is physics dipole moment based. In this embodiment, the phenomena of interest within the measured magnetic field data are made of dipoles (geometric shapes discussed above), with a varying magnitude (small vs. large defects, defects vs. weld, etc.) In another embodiment, the subspace basis matrix S is constructed based on learning techniques such as Singular Value Decomposition (SVD), Espirit, and Music algorithms.

Equation <NUM>(a) linearly models the phenomenon identified within the magnetic field raw data. Using equation <NUM>(a), data processing module <NUM> (or server <NUM>) can both identify and characterize a detected phenomenon within the measured magnetic field data. For example, within data processing module <NUM> (or server <NUM>) and using equation <NUM>(a), for a given phenomenon, a window size W is selected. Within that window, magnetic field derived features are determined. The window size W may be adjusted for sensitivity to features of different sizes. For example, a small window size W may be used to aim detection at small-scale features, whereas a larger window size W may be used to aim detection at larger-scale features. In another example, the same dataset may be analyzes using two or more different window sizes to be sensitive to features of a variety of sizes. In the above example of gradients, computations of equations <NUM>-<NUM>, over the determined window W, derived from all possible pairs of sensor measurements, provide the canonical shape of what a gradient of the magnetic field for any event looks like. Equation <NUM>(a)'s modulation by the vector θ determines whether a dipole moment based phenomenon is present. If the magnitude of θ is above a threshold, then the phenomena contains a defect (or in other words a defect is detected). The direction of the vector θ may be utilized to characterize the phenomena, as discussed below. <NUM>) The matrix F represents other known events that may be non-dipole moment based, or different. F is computed as in equation <NUM>.

It should be appreciated that non-linear models may be utilized instead of the linear model shown in equation <NUM>(a). For example, non-linear models would include an equation <NUM>(b).

S, F are a non-linear function of θ, ϕ. Under equation <NUM>(b), either S, F, or both, may be learned using non-linear curve fitting, neural networks, deep-learning algorithms, etc. For each phenomenon within the measured magnetic field data, S (or F) may have its own shape.

A hypothesis test may be used to determine whether the measured magnetic field data does not (null hypothesis, H0) or does (first hypothesis, H1) include a phenomenon signature that is a defect. Equations <NUM> and <NUM> state an exemplary hypothesis test based on equation <NUM>(a), but may be modified as understood by those of ordinary skill based on equation <NUM>(b), above.

Equation <NUM> shows null hypothesis, H0, which states that the gradient measurement vector across scan positions, X, is due to (a) known interference subspace, F, plus (b) a subspace N which is the subspace orthogonal to the projection of subspace S onto the subspace orthogonal to known interference subspace F, and (c) noise vector n. Herein, each of F, N, and S interchangeably refers to the respective matrix as well as the subspace spanned by the columns of the matrix.

Equation <NUM> shows first hypothesis, H1, which states that the gradient measurement vector across scan positions, X, is due to feature subspace basis matrix across scan positions in terms of gradients, S, plus known interference subspace, F, and noise vector n.

The output of the hypothesis test of Equations <NUM> and <NUM> is a statistic proportional to the likelihood, L, of a phenomenon being present. Equations <NUM> and <NUM> may be graphically understood with respect to <FIG>, where hypothesis H0 is shown in <FIG> because only welds are shown and the likelihood never crosses threshold. By contrast, <FIG> show hypothesis H1 because defects <NUM> and <NUM> are shown and the likelihood crosses the threshold.

Thus, it is shown that a defect may be identified in a binary manner (e.g. presence versus absence of defect, but not yet classified to determine the type of defect). The likelihood compares the observed value X of equation <NUM> to a threshold. This decision may be made by selecting the most likely event, which is the phenomenon in a dictionary of phenomena that most closely resembles the measurement X, preferably (but not necessarily) after accounting for noise in the data. This decision may utilize a hypothesis test, as shown in equations <NUM> and <NUM>, or alternatively/additionally, a nearest neighbor model, or any other pattern classification/machine learning/deep-learning algorithm. To compensate for noise, statistic used thereby may be a Chi-Square statistic, an F statistic, or non-Gaussian generalization of the Chi-Square or F statistic such as those discussed in: MN Desai, RS Mangoubi, "Robust Gaussian and non-Gaussian matched subspace detection," IEEE Transactions on Signal Processing, <NUM>.

It should be appreciated that functions other than the likelihood function may be utilized, such as the robust likelihood function which is a trimmed version of the likelihood function that protects against noise outliers. Moreover, the estimate of θ, ϕ, or θ̂, ϕ̂, may be obtained by inverting the matrix or functions (non-linear models) S, F, respectively. The magnitude and direction of these vectors may then be used instead of the likelihood function. Embodiments where the noise model is unknown and the non-parametric approach is used, may use non-parametric statistics such as the sign test, the rank sum test, rank histograms of the noise, etc..

The magnitude of phenomenon scaling parameter vector, θ, may be a statistic for determining the presence of a phenomenon, the size of the phenomenon, and the magnetization direction of the phenomenon.

In an embodiment, modeled magnetic data is modeled as a non-linear subspace of components of the magnetic signal versus scan position, such as a polynomial, neural network, or learning-based technique, fitted to a measured magnetic field data curve. The coefficients of the non-linear subspace may include components that determine the presence of phenomena and characterize the nature of those phenomena. In another embodiment, a fractal dimension of the measured magnetic field data is used to determine the presence of phenomena and to characterize the nature of those phenomena.

It should be appreciated that the models of Eq. <NUM>(a) and <NUM>(b) may be replaced by models not based on feature subspaces S and F.

<FIG> is a flowchart for a method <NUM> to identify a phenomenon within ferromagnetic material by comparing modeled and magnetic field data over a variable window of scan positions. In step <NUM>, method <NUM> compares modeled and magnetic field data, such as gradient data, from a small window of scan positions corresponding to a portion of a ferromagnetic material. In one example of operation of step <NUM>, data processing module <NUM> compares modeled magnetic field data to captured magnetic field data, captured using one or more of sensors <NUM> of <FIG>, corresponding to a window of scan positions along ferromagnetic material <NUM>. Method <NUM> is an example of steps <NUM>-<NUM> and <NUM> of <FIG> and <FIG>, respectively.

Step <NUM> is a decision. If step <NUM> determines that a likelihood, L, has crossed a predefined threshold indicating that a phenomenon is present in the ferromagnetic material, then method <NUM> proceeds with step <NUM>. Otherwise, method <NUM> proceeds with step <NUM> to increase window size. In an example of step <NUM>, L has crossed a predefined likelihood threshold of for example one (L><NUM>), as shown in <FIG>, indicating presence of a defect within a scan position window from zero to one along the x-axis. In another example of step <NUM>, L has not crossed the predefined threshold of one (L<<NUM>) in a scan window from zero to one, as shown in <FIG>, indicating absence of a defect. The predefined likelihood threshold may take on other values than one, without departing from the scope thereof. For example, the predefined likelihood threshold may depend on whether or not the likelihood L has been normalized and the nature of such normalization. Step <NUM> is an example of step <NUM> and <NUM> of methods <NUM> and <NUM>, respectively.

In optional step <NUM>, the window size is increased. In an example of step <NUM>, the window for comparing measured and modeled magnetic field data is increased to the entire range of zero to two shown in <FIG>. Window as used herein means the number of data points surrounding, or beginning from, a given scan position in the measured magnetic field data.

Step <NUM> is a decision. If, in step <NUM>, the window size has been increased to maximum, method <NUM> proceeds to step <NUM>, which determines that no defect is present in the corresponding portion of ferromagnetic material. Otherwise, method <NUM> returns step <NUM> to determine if the likelihood threshold has been crossed. In an example of step <NUM>, the window size corresponds to scan positions taken along first segment <NUM> of pipe <NUM>, <FIG>, which is not a maximum window and method <NUM> returns to step <NUM>. Steps <NUM> to <NUM> together form an example of step <NUM> of method <NUM>.

In step <NUM>, a magnetic field source is identified. In an example of step <NUM>, a magnetic field phenomenon is identified from defect <NUM>, <FIG>.

Step <NUM> is a decision. If in step <NUM>, a large window is determined to have been used, then a non-defect is determined. In an example of step <NUM>, a window covering scan positions for first and second pipe segments <NUM>, <NUM> of <FIG> was used and the magnetic source identified in step <NUM> was from weld <NUM>. Otherwise, if a large window was not used, for example the window includes data from only first pipe segment <NUM>, method <NUM> proceeds to step <NUM>, which determines that a defect is present within the scan positions of the ferromagnetic material corresponding to the window. Steps <NUM> and <NUM> are examples of step <NUM> of <FIG>.

Method <NUM> uses data windows and may apply steps <NUM> to <NUM> repeatedly to identify phenomena having different sizes. For example, method <NUM> may repeat for each, or a portion, of scan positions within the measured magnetic field data received from sensors <NUM>, <NUM>, <NUM>. Method <NUM> may be implemented in a parallel or hierarchical manner, using multiple windows without departing from the scope hereof.

<FIG> shows a pairwise statistical comparison plot <NUM> for characterizing ferromagnetic material. Pairwise statistical comparison plot <NUM> may be utilized by methods <NUM>, <NUM>, and <NUM> to specifically characterize the type of phenomenon, and in some embodiments the type of defect. That is, in addition to determining that a phenomenon occurs within the measured magnetic field data, methods <NUM>, <NUM>, and <NUM> may utilize plot <NUM>, or the data therefrom, to determine what the phenomenon is (i.e. type of weld, type of defect, type of anomaly, etc.). Plot <NUM> can be stored in server <NUM> or data processing module <NUM> and can identify a library of phenomenon that can been seen in the field by systems <NUM>, <NUM>, <NUM>, as well as how different one known phenomenon is to another known phenomenon.

Pairwise statistical comparison plot <NUM> is built by comparing the measure of divergence for each pair of phenomena. Specifically, <FIG> shows pairwise statistical comparison plot <NUM> of features extracted from the measured magnetic field data <NUM> (such as the angle between the vector θ for different phenomena) versus modeled magnetic field <NUM> for ten different phenomena <NUM>-<NUM>. In another embodiment, a finite element based model is used in place of modeled magnetic field <NUM>. The ten phenomena include for example three welds <NUM>, <NUM>, <NUM>, which are examples of weld <NUM>, <FIG>; phenomenon <NUM> which is a small defect; phenomenon <NUM> which is a detectable defect, such as defect <NUM>, <FIG>; and, phenomena <NUM>-<NUM> which include other miscellaneous anomalies. Each value in the matrix represents a numerical divergence between pairwise comparisons of measured and modeled magnetic field data for each of the ten phenomena <NUM>-<NUM>. For example, column <NUM> "<NUM>", row <NUM> "<NUM>" represents a pairwise comparison of small defect <NUM> to weld <NUM>. A difference between measured and modeled data is shown with legend <NUM>. The entries in <FIG> are a measure of the statistical divergence between two phenomena, such as a weld and a defect. As such, in <FIG>, phenomena <NUM> and <NUM> are separated by a small divergence and are therefore relatively similar, when contrasted to phenomena <NUM> and <NUM>. Alternatively, phenomenon <NUM> is more similar to phenomenon <NUM>, than it is to phenomenon <NUM>.

The measure of divergence may be based on many variables, and more than one variable may be used to build the pairwise statistical plot of <FIG>. For example, for two phenomena, we have two estimates of the vector θ, or <MAT>. The angle between these vectors may be a measure of divergence. The larger the angles, the more distinct are the phenomena (e.g. the larger the divergence), and vice versa. If that angle is not above a threshold, then the phenomena pair is not distinguishable. The threshold may be based on the quality of the measurement, or the sensor noise variance or signal to noise ratio. Other divergences may also be utilized, for example, when non-parametric noise methods are preferred, divergence between histograms or rank histograms may be used. One example is the Kullback Leibler divergence. Divergences derived from machine learning methods are also possible.

To specifically characterize a detected phenomenon using plot <NUM>, data processing module <NUM> (or server <NUM>), implementing methods <NUM>, <NUM>, or <NUM> may utilize a statistic from the test of equations (<NUM>) or (<NUM>), for instance. Take the case where the matrix F is zero (which could also mean that the matrices S and F are aggregated). The likelihood ratio is compared to a threshold, determining that a phenomenon of interest is present, as discussed above. In turn, data processing module <NUM> may obtain the estimate of vector θ̂, and compare it to the value vector <MAT>, where e can be any of the events <NUM> thru <NUM>. The comparison is based on the angle between vector θ̂ and the given vector <MAT>. The comparison yielding the smallest angle indicates the observed phenomenon.

Pairwise statistical plot <NUM> may include a machine learning feature where, if the smallest angle between θ, and θ_e, for all events e is above a certain threshold, then the answer would be "event or phenomenon not seen before".

It should be appreciated that the plot <NUM> may be just one of many plots analyzed by data processing module <NUM> (or server <NUM>). For example, there may be multiple plots for each given window size. In such a case, data processing module <NUM> may obtain multiple divergences for the same pair and fuse at the higher decision level using decision fusion methods, which may be learned using machine learning. Moreover, the system could fuse at the divergence level, and obtain a single fused diversion method, prior to decision.

<FIG> show three diagrams of exemplary schemes for combining magnetic field data with data from other sensing modalities, such as ground penetrating radar, multimodal cameras, tomographic measurements, ultrasonic measurements, and active modulated magnetic signals for signal-to-noise ratio enhancement. <FIG> are for example diagrams of schemes implementing step <NUM> of <FIG>. Any details extracted from different measurements may be fused, at different levels, such as a measurement level, a data extraction level, or a determination of defect versus non-defect level. <FIG> shows a diagram for fusing data from first, second, third and fourth modalities <NUM>, <NUM>, <NUM>, <NUM> at a measurement level in step <NUM>, followed by extracting phenomenon data in step <NUM>, determining defect versus non-defect in step <NUM>, and optionally characterizing a defect and its location in step <NUM>.

<FIG> shows a diagram for fusing data at a phenomenon level. Specifically, phenomenon data are extracted for each of the four modalities in steps <NUM>, <NUM>, <NUM>, <NUM> and fused in step <NUM>, followed by determining defect versus non-defect in step <NUM> and optionally characterizing a defect and its location in step <NUM>.

<FIG> shows a diagram for fusing data at a defect determining level. Specifically, a defect versus non-defect is determined in steps <NUM>, <NUM>, <NUM>, <NUM> from the four modalities <NUM>, <NUM>, <NUM>, <NUM> and the determinations are fused in step <NUM> to determine defect versus non-defect, and optionally characterizing a defect and its location in step <NUM>.

Claim 1:
A method for characterizing a ferromagnetic material, comprising
- providing a plurality of magnetometers (<NUM>) in at least a one-dimensional array (<NUM>) to measure a magnetic field (<NUM>), the magnetometers (<NUM>) being coupled to a data processing module (<NUM>) having a processor (<NUM>) coupled with a memory (<NUM>),
- wherein the magnetometers (<NUM>) are mutually spaced apart and the array (<NUM>) being positioned with a stand-off distance above the ferromagnetic material (<NUM>),
- moving the array (<NUM>) to a plurality of scan positions along the ferromagnetic material (<NUM>),
- measuring, by the magnetometers (<NUM>), magnetic field (<NUM>) data at the plurality of scan positions,
- comparing the measured magnetic field data with a physics-based model of magnetic fields using a processor (<NUM>) to identify and characterize phenomena (<NUM>) in the magnetic field (<NUM>) caused by missing metal defects, wherein characterizing includes distinguishing between a defect and a non-defect such as a weld, flange, coupled branch line, bend, or other normal or intentional anomaly,
- wherein comparing the measured magnetic field data with a physics-based model of magnetic fields comprises
- calculating magnetic field gradients from differences in magnetic field data of a plurality of the magnetometer (<NUM>) within the array (<NUM>), modelling magnetic field gradients and
- comparing the calculated magnetic field gradients with the modelled magnetic field gradients,
- characterized in that
- modeled and magnetic field data are compared over a variable window of scan positions.