modeling blast wave propagation using artificial neural network methods

Advanced Engineering Informatics 23 (2009) 418–423

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Advanced Engineering Informatics

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Modeling blast wave propagation using artificial neural network methods

Ian Flood a,*, Bryan T Bewick b, Robert J Dinan b, Hani A Salim c

a University of Florida, Gainesville, FL 32611, USAb Air Force Research Laboratory, Tyndall AFB, FL 32403, USAc University of Missouri-Columbia, Columbia, MO 65211, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 27 November 2008Received in revised form 15 May 2009Accepted 12 June 2009Available online 16 July 2009

1474-0346/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.aei.2009.06.005

* Corresponding author.E-mail address: flood@ufl.edu (I. Flood).

The paper reports on work concerned with the development of artificial neural network approaches tomodeling the propagation of bomb blast waves in a built-up environment. A review of current methodsof modeling blast wave propagation identifies a need for a modeling system that is both fast and versatilein its scope of application. This is followed by a description of a preliminary study that used artificial neu-ral networks to estimate peak pressures on buildings protected by simple blast barriers, using data gen-erated from, first, an existing empirical model and, second, miniature bomb-barrier-buildingexperiments. The first of these studies demonstrates the viability of the approach in terms of producingaccurate results very rapidly. However, the study using data from live miniature bomb-barrier-buildingexperiments was inconclusive due to a poor distribution of the sample data. The paper then describes on-going research refining this artificial neural network approach to allow the modeling of the time-wiseprogress of the blast wave over the surfaces of critical structures, facilitating a three-dimensional visual-ization of the problem. Finally, the paper outlines a proposed novel method of modeling blast wave prop-agation that uses a coarse-grain simulation approach combined with artificial neural networks, which hasthe goal of extending modeling to complicated geometries while maintaining rapid processing.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

This paper reports on the development of methods of modelingthe propagation of blast waves in a built-up environment that isaccurate and can generate results rapidly (ideally in a matter ofseconds). Such a tool would allow engineers to optimize the designof new buildings in terms of blast-mitigation performance andcost-effectiveness, including retrofits of existing buildings, andthe design of protective structures such as blast walls.

Existing blast modeling tools involve a trade-off betweenthe complexity of the environment they can model and the timethey take to generate results. Modeling tools that can produceresults rapidly (the existing empirical models, see for example,Remennikov [12]) are limited in terms of the complexity of theenvironment they can consider. Often, the problem is simplifiedto one in which a blast wave propagates over a single blast barrieronto the face of a building, and acts across a vertical line over theface of that building, such as the configuration shown in Fig. 1.Blast waves propagating through more complex environments,and acting in two or three spatial dimensions, can usually onlybe modeled using CFD techniques (Computational Fluid Dynamics)(such as ANSYS [1]). Unfortunately, three-dimensional CFD models,even when limited to a single barrier and building configuration

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and run on a supercomputer, can take several days or more to com-plete a single simulation run.

One approach for simplifying the difficulty in blast load predic-tions is to use ray tracing. This uses an algorithm that identifies themost significant paths (the shortest) that a blast wave can followfrom the point of detonation to specific target points, taking intoaccount reflection and diffraction. The time-based forms of thewaves arriving along each path are determined using the semi-empirical TNT Standard Methodology and are then superimposedusing the LAMB Shock Addition rules [11]. Enhancements to theapproach have been used by Frank et al. [7,8] to predict behaviorin environments with complex geometries. The approach certainlyprovides a highly versatile method of modeling complex internalgeometries, and the authors claim that the results are of reasonableaccuracy and that the model runs fast. However, a comprehensiveset of case studies is required to determine more precisely theaccuracy and processing speed relative to established approachesto the problem. The algorithm required to determine all significantpaths for the blast wave appears to be too complex to allow resultsto be generated in a matter of seconds for all target points acrossall relevant surfaces of the environment that would be requiredfor the application proposed in this paper.

An alternative approach to these issues, considered by Löhneret al. [9], was to test the sensitivity of processing time and accuracyon the coarseness of the modeling mesh for three-dimensional CFDsimulations of blast wave propagation through complex building

Fig. 1. Simple bomb-barrier-building configuration, with blast wave acting along a vertical line on the target building.

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geometries. In an example study of a concert hall, the authorsconsidered a range of resolutions ranging from main element sizesof 0.3–1.2 m in length. They found that moving to the coarser meshreduced processing time from 18 h to 7 min, although the predic-tions of the coarse mesh model were about 50% off compared tothe fine mesh model. While the speed of processing of the coarsemesh approach makes it accessible to users of desk-top computers,the authors of this paper believe greater accuracy in the predic-tions of the model is needed. Indeed, later the authors of this paperpropose a possible method for running coarse mesh models thathas the potential to overcome the accuracy problem.

Other attempts to overcome the above problems have led sev-eral researchers to consider using artificial neural networks(ANN’s) to model the effects of blast waves on buildings. ANN’sare, in essence, an empirical modeling method in that they are usu-ally developed directly from experimental data. They are, however,very versatile, capable of considering many input variables thathave non-linear relationships with the output (dependent) vari-ables [6]. This, in principle, gives them the potential to model morecomplex bomb-building configurations than considered to date byempirical methods. Remennikov and Rose [13], for example,considered five input variables that embraced all configurationsof the problem represented by Fig. 1 plus the height of the bombabove the ground (note, the size of the charge, W, was removedfrom their analysis using inverse cube-root scaling). The outputsconsidered in their study included peak pressure (kPa) and impulse(kPa–ms) which is the integral of the pressure–time envelope.Their network was trained using data from miniature bomb-bar-rier-building experiments [2]. Similar work has been undertakenby the authors of this paper, as detailed below, which includes asadditional parameters the lateral position on the face of the targetbuilding, and the time into an event, enabling visualization of thetime-wise evolution of the pressure wave over critical surfaces.

The above studies used the ANN’s as simple vector mappingdevices, that is, as models that map directly from a set of inputsto a set of outputs. Their scope of application represents aboutthe limit of what can be achieved using ANN’s in this way. Extend-ing these studies to include additional input variables wouldrequire an increase in the number of experimental data pointsbeyond what is reasonably attainable in a blast modeling environ-ment, where data must either be obtained from live experiments orexpensive CFD simulations.

This paper first describes progress using ANN’s as vector map-ping devices to solve the blast wave modeling problem, illustratingthe performance and limits of this approach. It then outlines a pro-posed radically new ANN-based approach, using the concept ofCGM (coarse-grain modeling). Other simulation applications ofthe CGM approach [4] suggest that it has the potential to simulaterapidly the propagation of blast waves through complicated builtenvironments, comprising many structures arranged within athree-dimensional space.

2. Study 1: direct mapping artificial neural networks trainedusing empirically derived data

The first study conducted was a proof of concept that consid-ered the configuration of input parameters shown in Fig. 1, whereZ (m) is the distance from bomb to building, d (m) is the distancefrom the bomb to the barrier, h (m) is the height of the barrier,and y (m) is the height at the building where the effect of the blastis estimated. The charge, W (kg-TNT), was removed from the prob-lem by scaling all distances by W�1/3, a scaling parameter that hasbeen shown to work well for a broad range of free field experi-ments (see, for example, Mays and Smith [10]). The output variableconsidered in this study was the peak pressure (kPa) measured atthe location ‘y’ on the face of the target building.

Data used for training this ANN was obtained using an existingempirical modeling system, PURWall (not available in the publicdomain) – the intention was to see if the ANN was capable ofreproducing its performance. A total of 1365 patterns were gener-ated at random for training the ANN and an additional 252 weregenerated at random for testing its accuracy. The RGIN (Radial-Gaussian Incremental Network) neural network system wasadopted for this study since it has been found to perform wellfor problems where training uses large data sets [5]. RGIN net-works represent a function as a compound of radial-Gaussian func-tions, within a three layer feedforward structure (an input layer, ahidden layer, and an output layer. Each hidden neuron implementsa single radial-Gaussian function, which may take the form ofeither a hill (if it is positive) or hollow (if it is negative); the ideais that an appropriate combination of these shapes can be com-bined to form any continuous mapping function. The parameterson each hidden neuron and its links determine the precise form

♦ = Test Patterns

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Fig. 4. Distribution of errors for test patterns versus scaled height of the barrier, ‘h’.

ANN TrainingHybrid-ANN Training

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of its radial-Gaussian function, that is, its position within the prob-lem space, its spread, and its amplitude. Development of thesenetworks proceeds one hidden neuron at a time, each time deter-mining a position, spread, and amplitude for the radial-Gaussianfunction that will remove (as much as possible) the residual errorin the output from the network.

Fig. 2 shows the progress of training, measured as mean abso-lute error versus the number of Gauss units – note that in the RGINsystem the network is developed one Gauss unit (hidden neuron)at a time. The graph shows separate progress curves for the train-ing patterns and the testing patterns. Training was allowed to pro-ceed until there was little further improvement in performancemeasured for the testing patterns, which occurred at around 100Gauss units. The mean absolute error for the testing patterns at thisstage was 6.27 kPa, about 3%.

Fig. 3 is a scatter plot of actual versus the ANN predicted peakpressure for the 252 test patterns. If the ANN was a perfect model,all points would fall along the indicated 45� line. Inspection of thisplot indicates the model is highly accurate, and performs consis-tently well across the range of peak pressure values. This is con-firmed by the correlation between the predicted and actual peakpressures which had a value of 0.9959. Similar performance resultswere found by Remennikov and Rose [13] in their ANN studytrained using scaled live experiments.

The performance of the model was further analyzed to see ifthere was any correlation between the magnitude of the errorsand the location in the problem domain – that is, whether theerrors are dependent on the values of the independent variables.Ideally, the model should perform consistently well across the en-tire problem domain. Fig. 4 shows the distribution of the errors forthe testing patterns plotted against the input variable ‘h’ (theheight of the barrier scaled using the inverse cube method). Fromthis figure it can be seen that the model performed equally wellacross the entire range for this variable, indicating that the modelhas no bias in this context. Plots of the distribution of errors for allother input variables yielded similar results, confirming that theANN performed consistently well across the entire problemdomain.

An attempt to refine this ANN was made by training it so thatthe first unit would act as a linear function (specifically imple-menting a hyper-plane since there were four input variables)rather than as a Gauss function. The intent was to see if this wouldallow the ANN to achieve the same degree of accuracy but withfewer Gauss units, based on the idea that a large part of the func-tion could be explained linearly. Fig. 5 compares the progress intraining for the 252 test patterns, for both the original ANN andthe hybrid-ANN (containing the linear unit). The graph demon-strates that there is no benefit to including the linear function unitin terms of reducing the size of the network required to achieve the

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

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Fig. 2. Training progress for the RGIN-based model of bomb blast pressures onbuildings.

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Fig. 5. Training progress for ANN and hybrid-ANN.

specified level of accuracy. Indeed, the learning for the hybrid-ANNlags behind the regular ANN up to the 20th unit, and thereafterlearns at a similar rate. This indicates that there is no significantlinear component to the problem.

3. Study 2: direct mapping artificial neural networks trainedusing miniature live bomb blast experiments

The next set of experiments was concerned with the develop-ment and evaluation of a neural network trained and tested using

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Fig. 7. Training progress for the ANN developed using the miniature bomb-barrier-building experiments data.

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Fig. 8. Scatter plot of predicted pressure (by the neural network) versus actualpressure, for the five test points.

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data from a series of miniature-scaled bomb-barrier experimentsprovided by the US Army Engineer Research Development Center[14]. The independent variables extracted from this data werethe charge W (kg-TNT), and the following distances: bomb to build-ing, Z (mm); bomb to barrier, d (mm); barrier height, h (mm); andheight at the building’s front face, y (mm). The dependent variableconsidered was the peak pressure (kPa). Data from 40 scaledexperiments was used in this study, each representing a differentbomb-barrier-building configuration. These 40 configurations arerepresented by the points in Fig. 6. Each experiment provided fivepeak pressure readings measured at locations on the front of thescaled-building. Thus, it was possible to extract five data patterns(mapping between the independent and dependent variables)from each experiment, giving a total of 200 patterns.

In this trial, the 200 data patterns were divided into two groups:the first group was used for training the neural network and com-prised 195 of the data patterns (selected at random); and the sec-ond group was used for testing the trained neural network andcomprised the remaining five data patterns.

The type of neural network and training system adopted wasthe same RGIN system used in study 1 above. Fig. 7 shows thelearning progress for the neural network, measured in terms ofthe mean absolute error for the training patterns. Training wasallowed to occur until there was no improvement in the perfor-mance of the neural network measured for the five test patterns;this occurred when around 250 hidden neurons had been added.It can be seen from this figure that the neural network learnedthe training data sets effectively, bringing the mean absolute errordown to just 0.4 kPa.

However, when it came to a validation of the network using thetesting data (the set of five patterns not used for training), theperformance was found to be relatively poor. This is shown graph-ically in Fig. 8 which plots predicted pressure against actual pres-sure for the five test patterns. Note, two sets of results are shown inthis figure: the first (the test results) represents the case where thetest patterns were not used during training; the second set (thetraining results) represent the case where the test patterns were

Fig. 6. Configuration of 40 Miniature bomb-barrier-building experiments with TNT-equivalent (g) factored-out by scaling to 100 g of TNT.

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used during training. The first case, the test patterns, provides themost accurate measure of validity. If the model was a perfect pre-dictor, these test points would all fall along the diagonal line.Clearly, however, they diverge significantly from the line implyinga relatively poor performance. These results are summarizednumerically in Table 1, where the error is shown to range from6.4% to 41.8%, having a mean value of 26.1%. The correlationbetween the predicted values (for the test results) and the actualvalues indicates a similar conclusion, having a value of 0.83.

The accuracy of the network trained using the scaled data is sig-nificantly less than that trained in study 1 using data extractedfrom PURWall. For the PURWall trained neural network, the aver-age absolute error for a set of test patterns was 3.1% (cmpf. 26.1%for the current experiments) and the correlation coefficient was0.996 (cmpf. 0.83 for the current experiments). One reason for thisis that fewer data points were available for training from the min-iature-scaled experiments. More importantly, however, is the factthat the data points provided by the scaled experiments were verypoorly distributed across the problem space, leaving large tracts ofthe problem space void of examples, as is apparent from Fig. 6. Incontrast, the training patterns extracted from PURWall wereevenly distributed across the entire problem space. Moreover,Remennikov and Rose’s study (2007) demonstrated that ANN’scan be trained satisfactorily using live data from miniatureexperiments.

The above neural network training experiment was repeatedtwo more times, each occasion randomly selecting a differentgroup of training and testing patterns from the miniature bomb-barrier-building experimental data set. For both additional experi-ments, similar results were found to those reported above.

4. Study 3: predicting the time-wise evolution of pressure usingdirect mapping artificial neural networks

This third study is on-going, and has the goal of predicting howpressure changes over time across the surfaces of the barrier, thefront and top of the building, and the ground between the barrierand building. In this case, it was decided not to scale distance mea-sures against the inverse cube-root of the charge size due to a lackof evidence that scaling works for situations other than free fieldsetups (that is, setups with no obstacles in the path of the blastwave, such as barriers). The input variables under consideration,therefore, are: Z (m) the distance from the bomb to the building,d (m) the distance from the bomb to the barrier, h (m) the heightof the barrier, y (m) the height on the face of the building wherethe effect of the blast is estimated, x (m) the lateral distance fromthe centerline on the face of the building, and W (kg-TNT) the bombcharge.

The output from the ANN will be estimates of the peaks in thepressure wave, the time to these events, and their decay rate.The training and testing patterns for these experiments are beinggenerated using a three-dimensional CFD model.

The advantage of this approach is that it will allow the user toview the time-wise progress of the blast wave over the criticalsurfaces of the building and barrier and ground between thesestructures. This will allow the user to visualize more clearly howa barrier interacts with a blast wave propagating towards a build-ing, and thus make more informed judgments concerning theorientation and design of the barrier.

Table 1Percentage error between predicted pressure (by the neural network) and actualpressure, for the five test points.

Test error 41.8% 6.4% 32.7% 39.8% 9.7% Mean 26.1%

5. Study 4: modeling blast wave propagation in complicatedbuilt environments using an ANN-based course-grain method(CGM)

This fourth study is a proposed approach that has the goal ofdeveloping a simulation modeling system that has the versatilityof CFD simulations (namely, an ability to model complex three-dimensional geometries) but with a speed of processing that isorders of magnitude faster. The basis of the approach is thecoarse-grain method (CGM) already proven to work for modelingdynamic heat-transfer in buildings [4].

The approach has many similarities to conventional numericsimulation techniques, such as the Finite Difference Method, in thatthe environment is broken-down into a number of discrete spatialelements, the state of each of which is advanced in discrete time-steps. The difference, however, is that the spatial mesh in a CGMmodel is much coarser than traditional numeric simulations.Numeric simulations of processes such as blast wave propagationtypically use a mesh resolution of around 50 mm3, such that athree-dimensional model of a space 100 � 15 � 15 m wouldrequire in the order of 180 million spatial elements. In the proposedapproach, each element may be 1 m or larger in size, requiring just10,000 elements for the previous example, reducing mesh densityby a factor of 18,000. Moreover, the approach should also allow thesize of the time-steps to be increased significantly, further reducingthe amount of processing to be executed in a simulation run.

For fine-grain simulation models, such as the Finite DifferenceMethod, the propagation of a blast wave through the mesh is com-puted based on known fundamental physical laws. For a CGMmodel, however, the large size of each element and time-step ren-der these fundamental laws inapplicable. This problem can beovercome by training an ANN to implement the equations repre-senting behavior at this coarser level, based on observations fromfield experiments or, more conveniently, from CFD simulations.The loss of information that results from using large element sizes,which in turn would lead to a significant drop in modeling accu-racy, can be overcome by making the ANN-based functions samplethe state of the system in the time domain (specifically the recentpast) as well as spatially (the state of neighboring elements) [4].This additional input information comes at no extra cost computa-tionally since it is information that will have been generated at ear-lier steps in the simulation that is simply being recycled.

Using an ANN to calculate the change in state of a coarse-grainelement will be more involved computationally than solving thedriving equations on a regular fine-grain model, but this overheadshould be outweighed by several orders of magnitude by the mas-sive reduction in density of the mesh. In the dynamic heat-flowapplication of the CGM [4], the increase in processing speed rela-tive to a Finite Element Model was found to be more than threeorders of magnitude. A simulation that takes 1 day to completeusing a conventional CFD model would, by this expectation, becompleted in about 1 min using a CGM implementation. Finally,the potential complexity of these ANN’s may warrant the use ofgrowth algorithms, such as discussed by Flood [3], to allow the net-works to develop dedicated internal structures rather than justweights to solve a given problem. The potential advantage of thisapproach is a reduced size of the ANN to implement a given func-tion, thus increasing the speed of execution of a simulation.

6. Conclusions

Empirical methods of modeling the effects of bomb blast waveson buildings are fast and often accurate, but lack the flexibility toconsider anything other than the simplest of built environmentgeometries. ANN’s (artificial neural networks), when used as

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simple vector mapping devices, offer a means of extending thescope of application of empirically derived modeling. However,this is limited by the fact that the number of data points requiredto train an ANN increases geometrically with the number of inde-pendent variables in the problem. For this reason, it is not practicalto develop a vector mapping model of blast wave propagation thatcomprises more than about 5 or 6 independent variables. This ineffect limits the complexity of the geometry of the built environ-ment that can be modeled to configurations such as a blast barrierand a single building.

On the other hand, the CFD (computational fluid dynamic) mod-els, while potentially very versatile, can take several days to pro-cess a three-dimensional simulation model. As a consequence,CFD models cannot be used for interactive design, and do not allowthe engineer to consider more than a few alternative setups. Inresponse, this paper proposes a new method of modeling basedon simulating with a coarse-grained modeling mesh. Normallycoarse meshes result in significant reductions in the accuracy ofpredictions; the intent here, however, is to compensate for the lossof spatial information by sampling in the time domain. Previousstudies in the field of transient heat-transfer have shown this tobe viable if ANN’s are used to learn the functions that drive thesimulation. The approach has the potential to increase processingspeed by several orders of magnitude compared to conventionalCFD simulations without compromising accuracy.

Acknowledgements

The work reported in this paper was completed with the sup-port of USAF, contract FA4819-07-D-0001.

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