A Neural Network Approach to Modeling the Effects of Barrier Walls on Blast Wave Propagation

A practical means of reducing the impact of blast loads on buildings is to introduce a barrier wall between the explosive device and the building. The height and location of the barrier wall are key design variables in terms of effectively reducing the peak positive and negative overpressure and impulse on the building. Until recently, set-ups that included a barrier between the explosive device and the building could only be modeled with consistent accuracy by using numeric simulation techniques. Unfortunately, these models require many hours of processing time to complete a simulation run, even for the fastest of today’s computers. This has led several researchers to consider the use of advanced empirical modeling methods, specifically artificial neural networks, to overcome problems of computationally expensive simulations. Neural networks have the potential to make predictions of the influence of a barrier on blast propagation in a matter of seconds using a desktop computer, thus making it easier for designers to hone-in on an optimal solution. Artificial neural networks appear to be well suited to this application, performing well for problems that are strongly non-linear and comprise many independent variables. This paper reports on past and on-going research in this field at AFRL Tyndall, using both scaled-live experimental data and simulated data to develop the neural models. The design and validation of these models are presented, and their successes and deficiencies are discussed. The paper concludes with an overview of current and future research plans to take this work to a state suitable for use in the field, and to extend it to problems comprising significantly more complicated configurations of structures than a barrier positioned between the explosive device and a building. INTRODUCTION This paper is concerned with the development of a method of modeling the propagation of blast waves in a built-up environment that is accurate and can generate results rapidly (in a matter of minutes). Such a tool would allow engineers to optimize the design of new buildings in terms of blast-mitigation performance and cost-effectiveness, including retrofits of existing buildings, and the design of protective structures such as blast walls. Existing blast modeling tools involve a trade-off between the complexity of the environment they can model and the time they take to generate results. Modeling tools that can produce results rapidly (the empirical models, see for example, Remennikov [1]) are limited in terms of the complexity of the environment they can consider. Often, the problem is simplified to one in which a blast wave propagates over a single blast barrier onto the face of a building, and acts across a vertical line over the face of that building, such as shown in Figure 1. Blast waves propagating through more complex environments, and acting in two or three spatial dimensions, can usually only be modeled using CFD techniques (Computational Fluid Dynamics) (such as ANSYS[2]). Unfortunately, 3-dimensional CFD models, even when limited to a single barrier and building configuration and run on a supercomputer, can take several days or more to complete a single simulation run. In an attempt to overcome these problems, several researchers have considered using artificial neural networks (ANN’s) to model the effects of blast waves on buildings. ANN’s are, in essence, an empirical modeling method in that they are usually developed directly from experimental data. They are, however, very versatile, capable of considering many input variables that have a non-linear relationship to the output (dependent) variables [3]. This, in principle, gives them the potential to model more complex bomb-building configurations than considered to date. Remennikov and Rose [4], for example, considered five input variables that embraced all configurations of the problem represented by Figure 1 plus the height of the bomb above the ground (note, the size of the charge, W, was removed from their analysis using inverse cube-root scaling). The outputs considered in their study included peak pressure (kPa) and impulse (kPa-msec) (the integral of the pressure-time envelope), and the network was trained based on data from miniature experiments (Chapman et al., [5]). Similar work has been undertaken by the authors of this paper, as detailed below, which includes as additional parameters the lateral position on the face of the target building, and the time into an event, enabling visualization of the time-wise evolution of the pressure wave over critical surfaces. W (lb-TNT) Line of action of blast wave h (ft) y (ft) d (ft) Z (ft) Figure 1: Simple Bomb-Barrier-Building Configuration, with Blast Wave Acting along a Vertical Line on the Target Building The above studies used the ANN’s as simple vector mapping devices, that is, as models that map directly from a set of inputs to a set of outputs. Their scope of application represents about the limit of what can be achieved using ANN’s in this way. Extending these studies to include additional input variables would require an increase in the number of experimental data points beyond what is reasonably attainable in a blast modeling environment, where data must either be obtained from live experiments or expensive CFD simulations. This paper first describes progress using ANN’s as vector mapping devices to solve the blast wave modeling problem, illustrating the performance and limits of this approach. It then outlines a proposed radically new ANN-based approach, using the concept of CGM (coarse-grain modeling). Other simulation applications of the CGM approach [6] suggest that it has the potential to simulate rapidly the propagation of blast waves through complicated built environments, comprising many structures arranged within a 3-dimensional space. PREDICTING PEAK PRESSURE USING ARTIFICIAL NEURAL NETWORKS AS VECTOR MAPPING DEVICES The first study conducted was a proof of concept that considered the configuration of input parameters shown in Figure 1, where Z (ft) is the distance from bomb to building, d (ft) is the distance from the bomb to the barrier, h (ft) is the height of the barrier, and y (ft) is the height at the building where the effect of the blast is estimated. The charge, W (lb-TNT), was removed from the problem by scaling all distances by W, a scaling parameter that has been shown to work well for a broad range of free field experiments (see, for example, Mays & Smith [7]). The output variable considered in this study was the peak pressure (psi) measured at the location y on the face of the target building. Data used for training this ANN was obtained using an existing empirical modeling system, PURWall [8] – the intention was to see if the ANN was capable of reproducing its performance. A total of 1,365 patterns were generated at random for training the ANN and an additional 252 (approximately 16% of the total patterns) were generated at random for testing its accuracy. The values for the inputs for these patterns were generated at random from within the problem domain, the boundaries of which were constrained by the PURWall software, and are defined in Table I. Table I: Boundaries of Input Variables for Generating the Training and Testing Patterns Input Variable Minimum Value Maximum Value Scaled Z (ft·lb-TNT ) 4.0 12.0 Scaled d (ft·lb-TNT) 0.5 3.0 Scaled h (ft·lb-TNT) 0.8 4.0 Scaled y (ft·lb-TNT) 0.0 5.0 The RGIN neural network system was adopted for this study since it has been found to perform well for problems where training uses large data sets [9]. Figure 2 shows the progress of training, measured as mean absolute error versus the number of Gauss units that have been trained for the network. Note that in the RGIN system, the network is developed one Gauss unit (hidden neuron) at a time. Each Gauss unit is trained by focusing it in the section of the problem domain where the network is generated the largest errors. The Gauss unit is trained using an error-gradient technique to remove as much of this error as possible. Once a Gauss unit has been trained, the residual errors for the training patterns are recalculated, and are used to determine the focus for the next Gauss unit, and to train it. By this approach, the first Gauss units make the biggest contribution to solving the problem and are the most generalized across the problem domain. Successive Gauss units make less of a contribution to the solution and their spheres of influence are typically more localized within the problem domain. Figure 2 shows separate progress curves for the training patterns and the testing patterns. Training was allowed to proceed until there was little further improvement in performance measured for the testing patterns, which occurred at around 100 Gauss units. The mean absolute error for the testing patterns at this stage was 0.91 psi, about 3%. Training Pattern and Testing Pattern Training Progress