This invention relates to a method and system for the three-dimensional reconstruction of material properties of a target using remotely located physical sensors. The sensors can illuminate the target using an active transmitter source such as one of acoustic, electromagnetic, or some other origin, while recording the response from the target in receivers placed in suitable locations. Alternatively, the receivers can record the target response in the presence of a passive source such as gravitational attraction and its gradients, the geomagnetic field, the magneto telluric field and others. Utilizing the special technique disclosed here, the method can provide an order of magnitude improvement in computational speed and memory requirements over current state-of-the-art artificial intelligence-based systems. When compared against state-of-the-art methods that do not rely on artificial intelligence, the current method provides improvement in accuracy and resolution that enables high resolution imaging of buried infrastructure using above ground sensors mounted on drones and other devices possible. This level of improvement makes it feasible to perform several first order inspection tasks related to pipeline health, corrosion, integrity, and others that are currently only possible using inline inspection tools such magnetic flux leakage (MFL) and ultrasonic (UT) sensors.
Three-dimensional image reconstruction using remote sensing sensors is a ubiquitous practice that cuts across many applications and industries ranging from the medical, oil and gas, mining, military, civil and environmental engineering, among others. The method uses physics-based algorithms to simulate the response of the target and its surroundings in the presence of an inducing field of electromagnetic, gravitational, seismic, ultrasonic, or some other origin and uses data optimization algorithms to find the material properties that can simulate a response that matches the recorded response by the receivers most closely.
The number of receivers recording the response is usually far fewer than the number of elements required to successfully simulate the observed response, leading to an underdetermined system with a non-unique (more than one) material property distribution that could potentially simulate the response observed by the sensors. This requires the imposition of certain a priori constraints on the nature of distribution of the material properties that are used to “match” the observed sensor response. In many geologic situations of increasing commercial interest, such constraints often lead to poorly reconstructed images which may not represent the subsurface at reliable levels of accuracy and/or resolution.
A key benefit of introduction of machine learning approaches to such efforts is the removal of explicit mathematical constraints on the distribution of the target material properties. Machine learning methods aim to “train” the system to “learn” the response of various material property realizations of the subsurface and then determine the “best” distribution of material property given the input of the observed sensor response. It has been observed that where the deployment of machine learning algorithms is technically, logistically, and commercially feasible, there is a step change improvement in the resolution and accuracy of the reconstructed image/material properties.
The major bottlenecks to such methods are twofold: 1) the large volume of simulations that need to be generated to accurately represent a “universe” of potential candidates that may represent the subsurface material property distribution. 2) The large memory consumption of the simulated models when being called for “training” by the machine learning algorithm. This effectively prevents the usage of machine learning algorithms for many problems of practical interest.
Most state-of-the-art deep learning machine learning architectures used to address image reconstruction issues follow the blueprint of dividing the image domain into several small pixels which are mathematically represented as two- or three-dimensional matrices. The input data is also cast into a matrix whose format is similar to the target image domain. A series of machine learning layers are introduced between the input data and the target or output image. Each of these layers comprise a set of smaller matrices which are then mathematically combined with a set of weights that help transform the values of the input data matrix to the output image matrix.
The two- and three-dimensional nature of the input and output matrix combined with the similar dimensions of the smaller matrices in the intermediate layers make this process memory intensive and is a key barrier for the solution of very large-scale imaging problems in a commercially effective manner.
The conventional method of image reconstruction that does not deploy machine learning methods, frequently stores this matrix as a one-dimensional vector and can map the input data to the dimensions of the output image by utilizing an adjoint operator. Given this transformation occurs at an intermediate step of a process that does not utilize artificial intelligence, the concept of utilizing the data post adjoint transformation as the initial input for machine learning is novel and not practiced anywhere. By making this change, the computational footprint of the image reconstruction problem is dramatically reduced by one or two major dimensions which then translates into order of magnitude savings in computation time and cost without compromising the accuracy and resolution gains made with machine learning methods.
Additionally, the method provides an easy method for designing machine learning algorithms for unstructured meshes, where the description of the images into clear cut divisions of U-, V-, and W-pixel units along each of the coordinate axes, x-, y-, and z- are not possible.
When applied to above ground magnetic sensor data, the method was able to image the top of pipe confidently at 1-1.5 m below ground surface with variation in susceptibility along pipe axis suggestive of changes in thickness, corrosion, and other issues. The uncertainty in resolving the top of the structure is thus within 50 cm. In comparison, the conventional state-of-the-art least squares inversion algorithm was able to provide an uncertainty bound of location of a pipe-like body somewhere between 0-3 m and not much else. This implies an uncertainty in resolution of the top of the structure of 3 m. This observation suggests a conservative estimate of 6-fold and more improvement in resolution of the pipe-like structure using artificial intelligence compared to conventional state-of-the-art least squares inversion.
Referring to
In
While either approach is suitable for handling buried subsurface infrastructure like pipelines, the embodiment discussed in
A practical demonstration of the method using data acquired by Texas A & M university students under the guidance of Prof. Mark Everett using handheld magnetic sensors is disclosed.
After suitable processing of data as discussed above, the results of inversion using conventional least squares method is shown in
In
While the present invention has been described in terms of particular embodiments and applications, in both summarized and detailed forms, it is not intended that these descriptions in any way limit its scope to any such embodiments and applications, and it will be understood that many substitutions, changes and variations in the described embodiments, applications and details of the method and system illustrated herein and of their operation can be made by those skilled in the art without departing from the spirit of this invention.