# Software-hardware FPGA-Based System for the solution of the 3D heat equationapplications on the non-destructive evaluation of minefields

- Diego Cabello Ferrer Director
- Marco Balsi Co-director

Universidade de defensa: Universidade de Santiago de Compostela

Fecha de defensa: 17 de decembro de 2008

- Francisco Javier López Aligué Presidente/a
- Paula López Martínez Secretaria
- Mauro Olivieri Vogal
- Ramón Ruiz Merino Vogal
- Francisco Javier Ríos Gómez Vogal

Tipo: Tese

## Resumo

Non-destructive Evaluation (NDE) is an interdisciplinary field of research integrating advances in measurement, analysis and information processing techniques for the quantitative characterization of materials and structures by non-invasive means. Applications are ubiquitous in fields such as medical diagnosis, clearance of minefields and on-line manufacturing process control, as well as the traditional NDE areas of flaw detection and materials characterization. Despite the broad range of applications, all NDE tests are characterized by the use of some form of energy (for instance, electromagnetic, ultrasonic, radiographic or thermographic) injected into the inspected material and the evaluation of the interaction between the energy and the material.\par In this work we are concerned with the non destructive evaluation of soils for the detection of buried landmines, particularly small plastic antipersonnel mines which are virtually undetectable by traditional methods. To this aim several techniques such as Ground Penetrating Radar (GPR) or infrared thermography (IRT)have been considered. The main drawback of GPR is the difficulty of detecting shallowly buried objects due to the large reflection coming form the air-ground interface, which tends to mask reflections from objects just underneath the surface. On the other hand, infrared thermography has been shown as an efficient technique to detect buried objects at a maximum depth of 10-15 cm. As antipersonnel mines are usually buried near the surface, we have chosen the infrared thermography as detection technique. Its use consists on subjecting the area under inspection to a source of natural or artificial heating/cooling process and studying the soil's response by means of the analysis of its thermal evolution given by a temporal sequence of infrared images. A satisfactory way of extracting information regarding the presence and exact location of the mines from such data based on the solution of the heat equation\index{heat equation} was presented in [1] . The process is divided in two steps. On the first one the soil is subjected to a heating process and a comparison between temperatures measured at the soil surface (through IR imaging) and those obtained by simulation using the model under the assumption of homogeneous soil and mine absence is made, the so called forward problem. The differences between measured and simulated data put into evidence the presence of unexpected objects on the soil. The second step is an inverse engineering problemwhere the thermal model must be run for multiple soil configurations representing different types of possible targets (mine, stone, ...) and depths of burial. The nearest configuration to the measured data gives us the estimated nature and location of the targets. This approach and, particularly, the inverse engineering process, makes an intensive use of the 3D thermal model that needs to be solved iteratively involving complex, coupled sets of partial differential equations. The extensive computing power required makes its software implementation impractical. The challenge in this case is on the efficient solution of the aforementioned model. To this aim, the Finite-Difference Time-Domain (FD-TD) method has been used in order to express the set of equations describing the model in a discrete way. FD-TD has been successfully used in a variety of fields, most notably on electromagnetic simulations, but its applicability has been traditionally limited due to its demanding requirements in terms of memory and computing power. This limitation can be, however, avoided by means of a hardware implementation. \par To illustrate the required computing power of the detection algorithm previously described, we will consider the analysis of a piece of soil of moderate dimensions, of 1 mx1 m. As explained, the scope of applicability of IR techniques for mine detection is restricted to a depth of barely 10-15 cm, but the depth of analysis must be set to at least 40-50 cm in order assume a constant temperature at such a depth. Using a uniform spatial discretization of dx = dy = dz = 0.8 cm and assuming a temporal discretization step of dt = 6.25 s, the simulation of the behavior of the soil during one hour using C++ on a Pentium IV 3GHz takes 5 minutes if single precision arithmetic is used to represent the temperatures (20 minutes if double precision is used). Taking into account that the proposed inverse procedures require the solution of the forward model for multiple soil configurations, the total computing assuming that only 100 iterations are needed (a soft approach) will add up to 8 hours (32 hours in double precision). As this time is excessive for on the field experiments arises the need to reduce it.\par %, for this reason, a hardware heat equation solver accelerator is proposed. In this way the processes involving the use of the 3D thermal model run on this accelerator, thus reducing the computing time. \par The aim of this work was to develop efficient techniques to reduce the computing time of the detection algorithm working in two different ways: -Development of a hardware solver for the thermal model. -Using non-uniform grids in the discretization scheme to reduce the number of nodes. We present a fully 3D FD-TD hardware solver of the heat equation applied, but not limited, to the thermal model simulation of the soil for the detection of buried landmines, with a significant speedup\index{speed-up} over a PC, using a commercial FPGA platform from Celoxica. The system was designed using VHDL and Handel-C; the processing core was developed using VHDL, whereas Handel-C was only used to perform the communications with the outside of the FPGA. Additionally, the use of non-uniform grids allows to reduce the number of layers of the thermal model, thereby reducing the computing time. \par The thesis is outlined as follows. In Chapter 1 a review of the main NDE techniques is done and we will also introduce the main NDE techniques used to detect buried landmines, centering our attention on the use of infrared thermography and ground penetrating radar. In this chapter we will also introduce the physical thermal model and a brief summary of the detection algorithm proposed in [1]. In Chapter 2 the applications where the FD-TD method has been used are introduced; we will also make a review of the FD-TD hardware implementations. Moreover, this chapter introduces the FD-TD algebraic equations for different situations: interface between two different materials, use of non-uniform grids and a combination of both situations. Chapter 3 addresses the hardware implementation of the thermal model. A detailed review of the system architecture and all aspects related to the implementation is made, including the description of the processing elements and the complete data flow of the system. In Chapter 4 the results are shown, where several simulations has been carried out to test the validity of the hardware implementation and the use of non-uniform grids. The hardware implementation speed ups the computations by a factor of 34 compared to a software solution, while with the use of non-uniform grids the nodes that need to be computed are reduced in a 30%. Finally, the main conclusions and future work are presented in the last chapter. [1] Paula López. "Detection of Landmines from measured infrared images using thermal mondeling of the soil". PhD Thesis, Universidad de Santiago de Compostela, 2003.