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Predicting the effectiveness of blast wall barriers using neural networks
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International Journal of Impact Engineering 34 (2007) 1907–1923 www.elsevier.com/locate/ijimpeng
Predicting the effectiveness of blast wall barriers using neural networks Alex M. Remennikova,, Timothy A. Roseb a
School of Civil, Mining and Environmental Engineering, Faculty of Engineering, University of Wollongong, Wollongong, NSW 2522, Australia b Engineering Systems Department, Cranfield University, Defence College of Management and Technology, Shrivenham, Swindon SN6 8LA, UK Received 31 July 2006; received in revised form 10 November 2006; accepted 12 November 2006 Available online 16 January 2007
Abstract Blast damage assessment of buildings and structural elements requires an accurate prediction of the blast loads in terms of the peak pressures and impulses. Blast loadings on structures have typically been evaluated using empirical relationships. These relationships assume that there are no obstacles between the explosive device and the target. If a blast barrier is used to protect personnel or a structure behind it, the actual blast loading environment will be significantly reduced for some distance behind the barrier. This paper is concerned with an accurate prediction of the area of effectiveness behind the barrier using experimental data and a neural network-based model. To train and validate the neural network, a database is developed through a series of measurements of the blast environment behind the barrier. The principal parameters controlling the blast environment, such as wall height, distance behind the wall, height above ground, and standoff distance are used as the training input data. Peak overpressure and peak scaled impulse are used as the outputs in the neural network configuration. The trained and validated neural network is used to develop contour plots of overpressure and impulse adjustment factors to simplify the process of predicting the effectiveness of blast barriers. The developed model is also deployed in a stand-alone application that is used as a fast-running predictive tool for the blast overpressures and impulses behind the wall. r 2006 Elsevier Ltd. All rights reserved. Keywords: Neural networks; Blast loads; Blast walls; Explosion
1. Introduction Terrorism is evolving as a major threat to critical infrastructure and personnel throughout the world. In recent years car bomb attacks in which an explosive laden vehicle is detonated as close as possible to a target building have become a weapon of choice by some terrorist groups. The most common response to mitigate this threat has been to increase standoff distance (bollards, anti-ram walls, etc.) and retrofit existing buildings with blast protection measures. Increasing vehicle standoff distance could significantly increase real estate and Corresponding author. Tel.: +61 2 4221 5574; fax: +61 2 4221 3238.
E-mail address: [email protected] (A.M. Remennikov). 0734-743X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2006.11.003
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construction costs and could be very difficult to achieve in a dense urban environment. One cost-effective alternative is the installation of perimeter walls for blast effects reduction that would decrease the need for standoff and building blast retrofit requirements. However, only limited information is available on the blast loading environment behind a blast wall [1,2]. Research in the area of blast resistant design and retrofit of structures is currently receiving a great deal of attention by the engineering community. Although it is recognised that no civilian buildings can be designed to withstand any conceivable terrorist threat, it is possible to improve the performance of structural systems by better understanding the factors that contribute to a structure’s blast resistance. One such factor is the ability of the design engineer to predict accurately the blast loadings on structural components using analytical or numerical tools that take into account the complexity of the building, the presence of nearby structures and the surrounding environment. This paper reviews some available experimental in this area of research and presents a new approach to developing an engineering-level tool for predicting the effectiveness of blast perimeter walls. Such a tool could provide the opportunity to conduct a simplified and rapid analysis of the advantages of a blast protective barrier without the need for lengthy numerical simulations and feasibility studies. Improved predictive tools for the assessment of the blast environment behind a protective perimeter wall would allow urban site planners to account for any benefit from the wall in protecting structures and other critical facilities from vehicle bombs. The proposed engineering tool can also be employed for assessment of explosive storage and munition manufacturing facilities, where reinforced concrete dividing walls are used as shields for personnel protection and as physical barriers between explosive production steps. 2. Effects of blast walls on blast propagation Blast loads in simple geometries can be predicted using empirical or semi-empirical methods [3]. These can be used to calculate blast wave parameters for hemispherical surface charges or spherical free air explosive charges to predict blast effects on isolated structures and structural components. Events of the recent years have demonstrated that the most common source of unplanned explosions were terrorist devices in an urban environment. In complex geometries, consisting of multiple buildings or other obstacles capable of modifying blast propagation, the blast wave behaviour can only be predicted from first principles using such numerical tools as SHAMRC [4], FEFLO [5], Chinook [6], AUTODYN [7], Air3D [8], and others. Such tools solve the governing fluid dynamics equations and can be used to simulate threedimensional (3-D) blast wave propagation including multiple reflections, rarefaction and diffraction. In addition, computational fluid dynamics (CFD) techniques can capture such key effects as blast focussing due to the level of confinement and blast shielding by barriers or other buildings. A blast perimeter barrier serves to reflect back some portion of the explosive blast energy and thereby reduces the blast environment behind the wall. The effectiveness of the wall in suppressing the blast environment depends on the parameters of the wall and the explosive charge. When placed across the path of the blast wave, the barrier may reflect a portion of the incident wave and cause the remaining part of the blast to diffract over the wall, as illustrated in Fig. 1. The resulting diffracted pressure will be significantly reduced, and the distance behind the wall where the blast environment is significantly reduced may characterise the effectiveness of the barrier. The US Army Security Engineering Manual [9] contains a methodology for calculating the reduction in pressures and impulses behind a blast wall, but the manual is restricted for official use only and has a very limited availability to the non-military engineering community. The formulations in the manual are based upon small-scale tests conducted at US Army Engineer Waterways Experiment Station (WES) in the 1980s [10]. These formulations were never validated with full-scale experiments. The protective structures automated design system (PSADS) [2] provides some guidance on the effects of barriers and blast walls. PSADS was developed by the US Army Protective Design Centre to automate the procedures for blast-resistant design of structures. It provides methods for the design of protective structures in such areas as airblast, fragmentation, blast loads on structures, dynamic response of structures, as well as a suite of support computer codes. PSADS provides design charts for the peak
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Fig. 1. (a) Blast wave–blast wall interaction and blast environment behind blast wall and (b) expected reduction in overpressures behind wall [29].
pressures and impulses behind blast walls for two scaled wall heights (0.436 and 0.872 m/kg1/3). The design charts are based on experimental studies that had a limited range of burst positions, barrier heights, and measurement locations. As a result, the use of the design charts as a predictive engineering tool has very limited application. More recent research results for blast walls were reported by Humphreys and Piepenburg [11] in 2001 and Bogosian and Shi [12] in 2002 on the same series of explosive tests. In this 35-test series, the experiments included a number of barrier configurations, some of them rigid concrete walls, and others being frangible barrier designs. One of the major findings from this test series was that thin, frangible barriers could be almost as effective as their more massive rigid counterparts. To predict the reduced level of pressures and impulses behind a blast wall, a simple methodology is included in standard manuals (e.g. TM5-583) and uses the geometric configuration shown in Fig. 2. The perimeter wall, of height H and thickness K, is located a distance L2 from the explosive charge W kg TNT and a distance L3 from the face of the building. The standoff distance between the charge and the building, if there were no perimeter wall, would be a distance L1. The height at which reflected pressure and impulse are measured on the building is T. The same geometric configuration applies when side-on blast resultants in free air are required behind a blast wall for personnel protection outside the building.
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Fig. 2. Blast wall configuration used in TM5-583 [9].
The methodology involves determination of adjustment factors, for pressure (AFP) and impulse (AFi), which are defined as follows: AFP ¼
Pwith barrier I with barrier and AFi ¼ . Pno barrier I no barrier
(1)
The adjustment factors represent the ratio of the pressure and impulse behind the blast wall to its original value without the blast wall (i.e. assuming a standoff distance L1). Thus, an adjustment factor of 0.3 represents a 70% reduction in pressure and impulse behind a wall compared to a no-wall configuration. The adjustment factors are obtained from the blast load adjustment curves in the manuals [9] as a function of parameters W, L1, L2, H, and T. To use the curves, one needs first to generate the value of pressure and impulse that would be expected at the location of interest if there were no perimeter wall. Typically, the nobarrier blast loads can be estimated using simplified analytical relationships or design charts [13] as a function of scaled distance L1. They may also be evaluated using the computer programs such as ConWep or ATBlast (available from the US General Services Administration website [14]) that automate those calculations. As a second step, an adjustment factor is then obtained from the curves for a given perimeter wall, bomb size, and building placement. The no-wall pressure and impulse values are then multiplied by the adjustment factors to produce the values behind the blast barriers. In cases where blast loading is required for the area of interest on the building face, the adjusted pressure and impulse can be averaged over this area of interest to provide loading for analysis and design. Rose et al. [15] carried out a programme of research in which detailed measurements of the blast environment were made behind a 1/10th scale vertical barrier. For the set of parameters studied in that work, it was concluded that in the region between three and six wall heights behind a blast wall and over a vertical distance of three wall heights above the ground, pressures and impulses may be reduced to no more than 60% and 80%, respectively of those without a wall. The data sets of measured pressures and impulses from the experimental programme by Rose et al. [15] will be used in this study to develop a neural network-based system for prediction of the blast environment behind a blast wall. The blast environment behind the wall may be further suppressed by employing a canopy near the top of the wall on the loaded side, as shown in PSADS [2]. The use of a canopy assumes that blast wave would be focused in a direction away from the protected target. The canopy could be blown away by the forces of the explosion, but it would remain in place long enough to reduce the magnitude of blast wave diffracting over the wall. The effectiveness of a canopy is not considered further in this paper (Fig. 3). 3. Neural networks Artificial neural networks (ANNs) are computational models loosely inspired by the neuron architecture and operation of the human brain [16]. They are massively parallel; they can process not only clean but also
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Fig. 3. Typical blast wall scenario for development of neural network model.
Fig. 4. (a) Basic operation of artificial neuron and (b) multi-layer perceptron neural network for predicting effectiveness of blast barriers.
noisy or incomplete data. ANNs can be used for the mapping of input to output data without knowing ‘a priori’ a relationship between those data. ANNs can be applied in optimum design, classification and prediction problems. An artificial neural network is an assembly (network) of a large number of highly connected processing units, the so-called nodes or neurons. The neurons are connected by unidirectional communication channels (‘‘connections’’). The strength of the connections between the nodes is represented by numerical values, which normally are called weights. Knowledge is stored in the form of a collection of weights. Each neuron receives a number of inputs and produces output as schematically shown in Fig. 4(a). The neural networks are capable of self-organisation and knowledge acquisition, i.e. learning. One of the characteristics of neural networks is the capability of producing correct, or nearly correct, outputs when presented with partially incomplete inputs. Further, neural networks are capable of performing an amount of generalisation from the patterns on which they are trained. Most neural networks have some sort of ‘‘training’’ rule whereby the weight of connections is adjusted on the basis of presented patterns. Training consists of providing a set of known input–output pairs to the network. The network iteratively adjusts the weights of each of the nodes so as to obtain the desired outputs within a requested level of accuracy. Error is defined as a measure of the difference between the computed pattern and the expected output pattern.
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3.1. Multi-layer perceptron network (MLP) The multi-layer perceptron (MLP) network trained by means of the back-propagating algorithm [16] is currently given the most attention by application developers. The MLP network belongs to the class of layered feed-forward nets with supervised learning [16]. A multi-layer neural network is made up of one or more hidden layers placed between the input and output layers. A neural network structure considered in this work for the blast barrier effectiveness prediction system is shown in Fig. 4(b). Each layer consists of a number of nodes connected in the structure of a layered network. The typical architecture is fully interconnected, i.e. each node in a lower level is connected to every node in the higher level. Output units cannot receive signals directly from the input layer. During the training phase activation flows are only allowed in one direction, a feed-forward process, from the input layer to the output layer through the hidden layers. The input vector feeds each of the first hidden layer nodes, the outputs of this layer feed into each of the second hidden layer nodes and so on. At the start of the training process the weights of the connections are initialised by random values. During the training phase, representative examples of input–output patterns are presented to the network. Each presentation is followed by small adjustments of weights and thresholds if the computed output is not correct. If there is any systematic relationship between input and output and the training examples are representative of this, and if the network topology is properly chosen, then the trained network will often be able to generalise beyond learned examples. Generalisation is a measure of how well the network performs on the actual problem once training is complete. It is usually tested by evaluating the performance of the network on new data outside the training set. Generalisation is most heavily influenced by three parameters: the number of data samples, the complexity of the underlying problem and the network architecture. Currently, there are no reliable rules for determining the capacity of a feed-forward multi-layer neural network. Generally, the capacity of a neural network is a function of the number of hidden layers, the number of processing units in each layer, and the pattern of connectivity between layers. 4. Use of ANNs for predicting non-ideal airblast loading Predicting non-ideal airblast loads is presently a complex computational art requiring many hours of highperformance computing to evaluate a single explosive scenario [17]. Prediction of blast loads in complex geometries is typically carried out with first-principle 3-D Euler CFD solvers. Accurate blast–structure interaction calculations require large number of cells, often in excess of 107, and use of high-performance computing facilities and massively parallel processors. Numerical simulations of this magnitude require approximately 10 Gbytes of memory [18], and can only be run on 64-bit operating systems. Given the high cost and low availability of these machines, fast and accurate engineering-level models are needed for predicting the effects of surrounding buildings and the effects of barriers on airblast pressures (for design, emergency planning, etc.). Simple engineering algorithms may avoid most of these issues by relying on experimental data to tune empirical predictive models using traditional methods of curve fitting, but still require the specification of algorithmic rules describing the dependence of the response parameters on the input variables. In recent years, the use of non-traditional tools based on artificial intelligence has received significant attention from civil engineering researchers in relation to systems that exhibit dynamic, multi-variate, and complex behaviours (e.g. wave forces, weather conditions, shock and impact problems). Dealing with such systems could be a difficult task and traditional tools might not be adequate to predict accurately the behaviour of such systems for design and analysis purposes. A non-traditional technique, artificial neural networks (ANNs), has been reported as efficient for accurately modelling a solution to a problem by considering actual previous situations for which results are known [19]. In addition, through their learning-by-example process, a neural network is able to generate the required results for a previously unseen situation with minimal computational efforts. One of the main advantages of the ANNs is that they extract the regularities in the data empirically, even if the relationship between the inputs and outputs of the system are known explicitly. This important feature makes the ANN a good candidate for modelling problems in the area of dynamics and
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control of multi-dimensional, highly non-linear systems, particularly systems that are difficult to model mathematically [20]. Artificial neural networks rely on sufficient number of reliable data points in order successfully to train the networks. These reliable data points have to be obtained either through experimental testing programmes or by high-fidelity physics modelling of the system, or both. It should be noted that the generalisation capabilities of the trained neural networks will be limited to the range of data used in the training process; outside the training range the predictions could be unreliable due to poor generalisation of the neural network. In the present research, artificial neural networks are developed and trained to store the explosively generated blast data. The main objective is to use the trained ANNs thereafter as a fast-running, standalone tool for predicting the blast resultants (pressure, impulse, fragmentation) in complex geometries with reasonable accuracy and cost. The developed neural network-based algorithms can easily be implemented in special anti-terrorist software (e.g. AT Planner Software, [21]) to assist planners in evaluating the hazard to building occupants associated with a given terrorist threat. At the moment, the airblast shielding provided by blast barriers and the effect of building groups on blast load predictions are not addressed satisfactorily in the AT Planner models [22]. 5. Predicting the blast environment behind a vertical wall barrier using ANNs A blast wall is a barrier placed between the location of a possible explosive threat and that which it is protecting (personnel, inhabited building, critical infrastructure facility, etc.). The problem of predicting blast effects behind the vertical barrier can be approached by conducting (a) small-scale experiments [15]; (b) fullscale experiments [11,12]; or (c) CFD simulations [23]. The first two approaches are the most expensive and time consuming, and typically limited in a number of blast wall scenarios and measurement locations. The use of 3-D CFD blast propagation calculations can generate data sets for a large area of space behind the wall, for a wide range of wall heights, and at practically unlimited numbers of target points to give a detailed picture of the blast environment behind a barrier. Despite the relatively simple geometry of a blast wall scenario, it has been demonstrated [24] that the blast wave–blast wall interaction is particularly difficult to analyse using CFD techniques. This difficulty is caused by the fact that the process of a blast wave diffracting over the wall is highly dependent on the pressure and duration (wavelength) which the blast possesses as it passes the top of the wall. In numerical simulations of a blast wall scenario, this process would primarily depend on the mesh discretisation. In real-life scenarios, the blast wall thickness would be just a small fraction of the computational domain dimensions which can result in the wall model being represented by only one or two computational cells across its width. Such mesh discretisation would be unrepresentative of the continuum, and one should expect degradation of the simulated blast effects behind the wall, depending on other problem parameters such as standoff distance, distance behind the wall, charge weight, and so on. Therefore, the experimental data sets containing values of pressures and impulses behind a blast wall are a more reliable source of data that can be used to calibrate the numerically based results. In this paper, the experimental data sets for a relatively wide range of scaled wall heights and a large area of scaled space behind the wall are employed to train and validate the neural networks. Three-dimensional CFD calculations can be used to extend the database by considering a number of additional blast wall scenarios. These will be presented in the subsequent publications by the authors. The goal of the present study is to develop a fast-running tool for predicting the blast environment behind a vertical barrier. This is accomplished by training an artificial neural network to approximate the overpressures and impulses from the experimental programme by Rose et al. [15]. The present study uses the blast scenario nomenclature as shown in Fig. 3. From Fig. 3, it can be seen that every blast wall scenario can be completely defined by the following independent scaled using cube root scaling [25] parameters: Parameter
Units: [m/kg1/3]
1. Scaled standoff distance 2. Scaled charge elevation 3. Scaled distance behind the wall
r/W1/3 z/W1/3 R/W1/3
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H/W1/3 h/W1/3
4. Scaled height of the wall 5. Scaled elevation of point of interest
These five parameters uniquely define the blast wall scenario. Therefore, these five parameters will be used as inputs to train and validate the neural network using the experimental data sets. The problem of characterising the blast environment behind a vertical barrier on the basis of existing experimental data is essentially a prediction (interpolation) problem. Since artificial neural networks are proving to be an effective tool for predicting values of blast loads [26], the basic idea in a neural network-based approach is to train a neural network with patterns of the blast wall scenario parameters describing the spatial distribution of blast wave parameters in the area behind the wall. This implies that each pattern represents the unique values of peak pressure and peak scaled impulse at each of the monitoring locations behind a blast wall with height H due to detonation of an explosive charge, W, at a particular location described by values of R and h. Therefore, the patterns of the quantities describing the blast environment are used as inputs and the peak pressure and peak scaled impulse as outputs to train the neural network. The training of a neural network with appropriate data containing the information about the cause and effect is a key requirement of a neural network approach. This means that the first step is to establish the training set which can be used to train a network in a way that the network can predict the blast effects within reasonable accuracy of the experimental results. In order to verify how well a trained network has learned the training cases, the trained network is tested by subjecting it to the training sets. The important generalisation capability of a neural network for predicting blast wave parameters is tested by subjecting the trained network to data not included in the training sets (the so-called validating sets). How well a trained network is to generalise depends on the adequacy of the selected network architecture (number of hidden nodes, number of hidden layers, and so on) and the information on the blast load environment included in the training sets.
5.1. Preparation of the data sets The steps for developing ANN models typically include determination of model input and output variables; division of the available data into training, testing, and validation subsets; determination of the optimal network architecture; and model validation. In this study, the most comprehensive set of experimental data available to the authors [15] is used to develop the data subsets. This provides the opportunity to consider a relatively wide range of scaled wall heights (h/W1/3 ¼ 0.5–1.0 m/kg1/3) and a large area of scaled space (R/W1/3 ¼ 0.35–5.0 m/kg1/3) behind the wall. The experimental programme is summarised in Table 1.
Table 1 Blast walls experimental programme [15] Experiment number
Scaled wall height H/W1/3 (m/kg1/3)
Actual wall height, H (m)
Charge weight, W (g) TNTeqv.
1 2 3 4 5 6 Scaled standoff r/W1/3 ¼ 0.327 m/kg1/3 Scaled charge elevation z/W1/3 ¼ 0.258 m/kg1/3
0.50 0.60 0.71 0.80 0.90 1.00
0.221
75.0 43.5 75.0 52.7 75.0 54.9
0.300 0.380
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H/W 1/3=0.5 m/kg1/3, h = 0.0 m 500
500
Pressure - experiment
100
100
50
50
Impulse (kPa-msec)
Pressure (kPa)
Impulse - experiment
10
10 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Horizonal distance behind wall (m) Fig. 5. Example of experimental peak pressures and impulses.
Table 2 Data ranges used for developing ANN models Model variables
Mean
Standard deviation
Minimum
Maximum
Scaled wall height, H/W1/3 (m/kg1/3) Scaled distance behind wall, R/H1/3 (m/kg1/3) Scaled height above ground, h/W1/3 (m/kg1/3) Peak overpressure, Pso (kPa) Scaled peak impulse, is/W1/3 (kPa-ms/kg1/3)
0.75 2.44 1.13 76.8 56.7
0.17 1.34 0.77 92.51 18.36
0.5 0.0 0.0 15.7 29.5
1.0 5.1 2.56 1080 122.5
The experimental programme was designed to include blast walls of three different heights. The charges were Demex plastic explosive, and they were initiated by No. 8 detonators. The TNT equivalence used was 1.32. Each of the experiments utilised a grid of pressure measuring locations in the space behind the walls which extended from R ¼ 0.15–1.8 m, horizontally behind the wall, in intervals of 0.15 m and from h ¼ 0.0–0.9 m, vertically above the ground, also in intervals of 0.15 m. This provided a total of 84 measuring locations for each experimental configuration. Measurements were made using pressure transducers configured to measure side-on pressure-time records. Experimental peak pressures and peak impulses for the target locations at the ground surface are shown in Fig. 5. The database of the experimental results included a total of 517 individual cases. Ranges of the data used for the input and output variables are summarised in Table 2. It should be noted that not all experimental records were included in the database for the development of the ANN models. The experimental database
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Table 3 Input and output statistics based on data division to enforce statistical consistency Model variables and data sets
Statistical parameters Mean
Standard deviation
Minimum
Maximum
Scaled wall height, H/W1/3 (m/kg1/3) Training set Testing set Validation set
0.7 0.7 0.8
0.2 0.2 0.2
0.5 0.5 0.5
1.0 1.0 1.0
Scaled distance behind wall, R/W1/3 (m/kg1/3) Training set Testing set Validation set
1.7 1.7 1.6
1.3 1.3 1.4
0.3 0.4 0.4
5.1 5.1 4.3
Scaled height above ground, h/W1/3 (m/kg1/3) Training set Testing set Validation set
0.7 0.9 0.6
0.6 0.7 0.6
0.0 0.0 0.0
2.1 2.1 2.1
107.8 104.5 108.1
108.8 89.2 87.9
16.2 20.0 22.1
757.4 456.0 317.0
67.2 66.2 66.5
19.8 20.4 20.7
30.1 36.3 38.6
123.2 116.5 120.6
Peak overpressure, Pso (kPa) Training set Testing set Validation set Scaled peak impulse, is (kPa-ms/kg1/3) Training set Testing set Validation set
cases were visually inspected and some of the records that exhibited contradicting trends to the majority of the records in their group were removed from the database. The database used for the development of the ANN models comprises a total of 285 measurements. In the majority of the applications of ANNs in various areas of engineering, the data are divided into sets needed to develop ANN models (e.g. training, testing, and validation) on an arbitrary basis without giving adequate attention to the statistical consistency of the data subsets. The crossvalidation technique [27] in which the training set is used to adjust the connection weights, the testing set is used to check the performance of the network and to decide when to stop training, and the validation set is used to evaluate the performance of the model is considered to be the most effective method to avoid problems with overfitting and generalisation of the network. Consequently, the statistical properties of the data subsets used in the model development need to be similar to ensure that each subset represents the same statistical population. If this is not the case, it may be difficult to justify the validity of ANN models [27]. In this study, the available data are divided in a way that ensured that the statistical properties of the data subsets are close to each other and thus represent the same statistical population. The statistical parameters used include the mean, standard deviation, minimum, maximum, and range. As part of this approach, the 285 individual records are divided into three statistically consistent subsets. In total, 85% of the data are used for calibration and 15% of the data are used for validation. The calibration set is further divided into 70% for training and 30% for testing. The statistics of the training, testing, and validation sets, obtained by taking into account the statistical characteristics of the subsets, are shown in Table 3. It can be seen that the statistical consistency between the various data subsets can be achieved with the consequent improvement in the performance of the models developed using these data subsets.
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Table 4 Configuration and statistical performance of trial networks Correlation coefficient, r
Root mean square error (RMSE)
Mean absolute error (MAE)
Pressure ANN
Impulse ANN
Pressure ANN
Pressure ANN
Impulse ANN
Single hidden layer 3-(2)-1 3-(5)-1 3-(9)-1 3-(10)-1 3-(15)-1
0.802 0.972 0.988 0.947 0.986
0.933 0.960 0.992 0.994 0.995
61.2 24.5 15.6 32.9 17.5
7.22 5.60 2.50 2.09 1.91
34.2 15.4 10.0 20.8 10.6
5.43 4.28 1.82 1.56 1.39
Two hidden layers 3-(2-2)-1 3-(5-5)-1 3-(8-8)-1
0.945 0.996 0.998
0.961 0.995 0.999
33.5 8.90 5.90
5.51 1.96 1.03
21.7 6.02 3.86
4.13 1.54 0.68
Three hidden layers 3-(4-4-4)-1
0.971
0.842
24.3
17.5
8.51
Network architecture and data sets
Impulse ANN
10.8
Note: network configuration, e.g. 3-(2)-1, refers to an ANN with 3 inputs, 1 output, and 2 nodes in a single hidden layer.
6. Results and discussion 6.1. Neural network implementation As stated above, multi-layer perceptron networks trained by means of the back-propagating algorithm are used for the development of ANN models. The computer program Neuroshell2 [28], Release 4.0, was used in the present study to train the network. The program implements several types of neural networks and architectures, including the multi-layer backpropagation nets, the genetic adaptive general regression neural networks (GRNN), the polynomial nets (GMDH), the backpropagation nets with jump connections and some others. The optimum network architecture was obtained by evaluating the performance of ANNs with one, two, and three hidden layers and variable numbers of hidden layer nodes. In order to determine the optimal control parameters for the backpropagation algorithm, the networks were trained with different combinations of momentum and learning parameters. Values between 0.1 and 0.8 were used for the momentum and learning rate in order to find the best performing network configuration. Network configuration and statistical parameters of the trial networks are presented in Table 4. 6.2. Analysis of performance of the ANN blast wall model Based on the statistical analysis results for the trial networks shown in Table 4, the network model with two hidden layers and eight hidden layer nodes (3-(8-8)-1) was selected for the further development. This model performed better than other network configurations based on the least errors for both RMSE and MAE in the predictions for both peak pressures and scaled impulses. The mean errors of the model 3-(8-8)-1 in predicting the peak pressures are 5.9 and 3.9 kPa for RMSE and MAE, respectively. For the scaled impulse, the mean errors of the same model are only 1.03 and 0.68 kPa-ms/kg1/3 for RMSE and MAE, respectively, which is an indication of practically 100% confidence in the scaled impulses predicted by the selected network model. The selected network model was further validated by the comparison of the statistical indicators for training, testing, and validation data sets as shown in Table 5. It can be seen that statistical consistency in the predicted results for all datasets ensures reliable predictions by the developed neural network within the range of variation of the input parameters. Fig. 6 shows the experimental peak pressures versus predicted values of all data records. It can be seen that the predictions of the neural network produce little scatter, and thus provide very good prediction of peak pressures behind a blast wall. Graphs comparing experimental peak pressures
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Table 5 Performance of the selected ANN models Data sets
Training set Testing set Validation set
Predicted peak overpressures
Predicted scaled impulses
r
RMSE (kPa)
MAE (kPa)
r
RMSE (kPa-ms/kg1/3)
MAE (kPa-ms/kg1/3)
0.999 0.997 0.997
5.2 6.7 9.0
3.4 4.6 5.6
0.999 0.998 1.000
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and impulses with the neural network-predicted values for the horizontal arrays of target points at different heights above ground are given in Fig. 7. These graphs also demonstrate the good quality of the predicted blast pressures and impulses in the region behind the blast walls both in the horizontal and vertical directions. 6.3. Validation of the ANN blast wall model It is known that the generalisation capabilities of the trained ANNs are limited to the range of the training data points; outside the training range the ANNs usually have poor performance and should not be trusted to afford reliable predictions. In order to validate the developed ANN model for predicting the blast pressures and impulses behind a vertical barrier, the model’s performance should be tested on new, previously unseen data. Beyer [29] presents blast wall design criteria derived from a series of high explosive trials. The experimental program was performed at one-sixth scale, and some of the results from the ten trials can be compared with the present ANN model. Strictly, none of Beyer’s data is directly comparable because different values of r and z were employed. However, both r/W1/3 and z/W1/3 in the Beyer’s tests were 0.378 m/kg1/3, which are reasonably close to the corresponding values in Table 1 used in the development of the neural network-based blast wall model presented in this paper. Beyer’s data for H/W1/3 ¼ 0.857 m/kg1/3 are used to validate the ability of the neural network to generalise to new data not included in the training set. The graphs comparing peak pressures and scaled impulse with data from Beyer [29] are shown in Fig. 8. A reasonably good
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correlation is obtained with the ANN blast wall model, taking into consideration the fact that some parameters of the blast wall scenarios are close but not identical. 6.4. ANN blast wall model as a tool for rapid prediction of effectiveness of blast barriers The ANN blast wall model can be utilised for rapid prediction of the benefit of having a blast wall for a specified scenario. One way to achieve this is to plot the overpressures and impulses which occur in the area behind the blast barrier in terms of the percentage of the free-field pressures and impulses when the barrier is not present. So-called ‘benefit plots’ can be presented as contours of the adjustment factors for pressure (AFP) and impulse (AFi) based on the following formulas: AFP ¼
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(2)
It should be noted that for the free-field pressures and impulses to be consistent with the predicted quantities, the scaled range or horizontal distance to the point of interest behind the wall
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must be calculated as Rfreefield =W 1=3 ¼ r=W 1=3 þ d=W 1=3 þ R=W 1=3 ,
(3)
where r, d, and R are the blast wall scenario parameters shown in Fig. 3. Fig. 9 illustrates an example of rapid determination of the effectiveness of blast walls of different height for a specific point of interest behind the wall. In this blast wall scenario, the charge W kg is located at the scaled distance of r/W1/3 ¼ 0.327 m/kg1/3 from the wall and z/W1/3 ¼ 0.258 m/kg1/3 above the ground. For a vehicle bomb with W ¼ 230 kg, this scenario may be equated to a 2.0-m standoff from the wall and 1.5 m above the ground. The point of interest is placed 2.0 m/kg1/3 behind the barrier and at a scaled height of 0.5 m/kg1/3 above the ground. Three contour plots in Fig. 9 are generated for the walls with H/W1/3 ¼ 0.5, 0.75, and 1.0 m/kg1/3 using the blast wall ANN model. An initial ‘unobstructed’ estimate of the peak overpressure is obtained from the contour plot of free-field overpressures and is given as Pso ¼ 180 kPa. The ‘‘benefit plots’’ shown below the free-field contour plot in Fig. 9 give a rapid prediction of the effectiveness of the vertical barriers with the specified heights in suppressing the blast environment behind the wall. As it will be seen, the pressure adjustment factors for the blast wall heights H/W1/3 ¼ 0.5, 0.75, and 1.0 m/kg1/3 can be estimated as AFP ¼ 0.32, 0.27, and 0.20, respectively. This, in turn, allows for quantitative prediction of the peak overpressures at the point of interest as 57.6, 48.6, and 36.0 kPa. Based on this information, the design engineer or site planner can rapidly assess the benefit from the wall and adjust its location and height to achieve the optimal results with respect to the required reduction in pressures and impulses at the point of interest. It should be noted that the blast wall ANN model developed in this paper could predict the effectiveness of a blast wall scenario for any blast wall with scaled height between 0.5 and 1.0 m/kg1/3. This equates to heights of 3.0–6.0 m (the most typical range of blast wall heights) for a vehicle bomb size of W ¼ 230 kg. 7. Conclusion The main objective of this study was to evaluate a new approach of using artificial neural network for predicting the blast environment behind a vertical blast wall barrier. A database of overpressures and impulses in the region behind the wall was established from the measurements of the blast environment during a series of small-scale blast wall experiments. This database was used to train and test the neural network to serve as a prediction tool for various blast wall scenarios. The main advantage of this approach is its ability to predict the effectiveness of a blast wall configuration in a matter of minutes whereas the numerical CFD simulation of the problem could take hours or days to complete. Analysis of the network’s performance shows the feasibility of using ANN models for predicting non-ideal airblast loading in situations where the blast environment is modified by the presence of such rigid obstacles as protective walls and multiple buildings. It has been demonstrated that the effectiveness of a blast wall can be quantified using the so-called ‘benefit’ contour plots of overpressure and impulse adjustment factors that are generated by the trained neural network model. The developed blast wall neural network model has also been deployed as a standalone application that could be used as a fast-running engineering-level tool within an expert system capable of predicting information about the likely injury and damage levels in blast environments where shielding by barrier walls is present. References [1] Mayor RP, Flanders R. Technical manual, simplified computer model of air blast effects on building walls. US Department of Transportation, Research and Special Programs Administration, Transportation Systems Center, Cambridge, 1990. [2] DAHSCWEMAN. Technical manual—design and analysis of hardened structures to conventional weapons effects; PSADS (Protective Structures Automated Design System), version 1.0. Washington, DC: US Army Corps of Engineers; 1998. [3] Remennikov AM. A review of methods for predicting bomb blast effects on buildings. J Battlefield Technol 2003;6(3):5–10. [4] Crepeau JE. SHAMRC, second-order hydrodynamic automatic mesh refinement code, vol. 1: Methodology. Albuquerque, NM: Applied Research Associates; 1999. [5] Lo¨rner R, Yang C, Baum JD, Mestreau E. Advances in FEFLO. AIAA-02-1024, American Institute of Aeronautics & Astronautics, 2002.
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[6] Ripley RC, Donahue L, Zhang F. Modelling complex blast loading in streets. In: Proceedings of the sixth Asia-Pacific conference on shock & impact loads on structures, Perth, Australia, December 7–9, 2005. [7] Century Dynamics. AUTODYN-2D & 3D version 6.0 user documentation, 2005. [8] Rose TA. Air3D user’s guide. 7.0: RMCS. UK: Cranfield University; 2003. [9] Security engineering manual. US Army TM5-583-3, vol. 3. Washington, DC: Department of the Army. [10] Dove R, Hamilton J, Coltharp D. Perimeter walls for blast reduction. In: Proceedings of the ASCE specialty conference on structures for enhanced safety and physical security, 1989. p. 142–53. [11] Humphreys E, Piepenburg D. Assessing effectiveness of blast walls: final report for the period 1 January 2000–31 December 2000. SAIC-01/1003, Science International Corporation, 2001. [12] Bogosian D, Shi Y. Assessment of and prediction methodology for blast barrier effectiveness, Karagozian & Case, Report TR-01-34, 2002. [13] US Department of Army Technical Manual (TM5-1300). Design of structures to resist the effects of accidental explosions, Washington, DC, 1990. [14] Office of the Chief Architect. ATBlast 2.2, General Services Administration, /http://www.oca.gsa.gov/mainpage.phpS. [15] Rose TA, Smith PD, Mays GC. The effectiveness of walls designed for the protection of structures against airblast from high explosives. Proc Instn Civil Engrs Struct Bldg 1995;110:78–85. [16] Dayhoff JE. Neural network architectures: an introduction. New York: Van Nostrand Reinhold; 1990. [17] Remennikov AM, Rose TA. Modelling blast loads on buildings in complex city geometries. Int J Comput Struct 2005;83:2197–205. [18] Lo¨hner R, Baum JD. Comparison of coarse and fine mesh 3-D Euler predictions for blast loads on generic building configuration. In: Proceedings of the 18th international symposium on the military aspects of blast and shock (MABS-18), Bad Reichenhall, Germany, 2004. [19] Garett JH. Neural networks and their applicability within civil engineering. In: Proceedings of the eighth conference of computing in civil engineering. New York, NY: ASCE; 1992. p. 1152–62. [20] Omar TA. Artificial neural networks for modelling dynamics of impacting bodies and vehicles. Proc Instn Mech Engrs 2000;214 (Part K):133–42. [21] US Army ERDC. AT Planner Software 2001, Vicksburg, MS. [22] Bevins TL, Armstrong BJ, Baylot JT, Rickman DD. Multiple building simulations and effects of berms behind blast barrier walls. In: Proceedings of the 2003 user group conference (DoD UGC’03). New York: IEEE; 2003. [23] Rice DL, Giltrud ME, Luo H, Mestreau E, Baum JD. Experimental and numerical investigation of shock diffraction about blast walls. In: Proceedings of the 16th international symposium on the military aspects of blast and shock (MABS-16), Keble College, Oxford, UK, 2000. [24] Rose TA. An approach to the evaluation of blast loads on finite and semi-finite structures. PhD thesis, Cranfield University, Royal Military College of Science, 2001. [25] Mays GC, Smith PD. Blast effects on buildings. Thomas Telford; 1995. [26] Remennikov AM, Mendis P. Prediction of airblast loads in complex environments using artificial neural networks. In: Jones N, Brebbia CA, editors, Proceedings of the ninth international conference on structures under shock and impact (SUSI 2006), 3–5 July 2006, The New Forest, UK: WIT Press; 2006. p. 269–78. [27] Shahin MA, Maier HR, Jaksa MB. Data division for developing neural networks applied to geotechnical engineering. J Comput Civil Eng ASCE 2004;April:105–14. [28] NeuroShell2. Release 4.0. User’s manual. Frederick, MD: Ward Systems Group Inc.; 2000. [29] Beyer ME. Blast loads behind vertical walls. In: Proceedings of the 22nd explosives safety seminar. Anaheim, CA: Department of Defence, Explosives Safety Board, 1986.
International Journal of Impact Engineering 34 (2007) 1907–1923 www.elsevier.com/locate/ijimpeng
Predicting the effectiveness of blast wall barriers using neural networks Alex M. Remennikova,, Timothy A. Roseb a
School of Civil, Mining and Environmental Engineering, Faculty of Engineering, University of Wollongong, Wollongong, NSW 2522, Australia b Engineering Systems Department, Cranfield University, Defence College of Management and Technology, Shrivenham, Swindon SN6 8LA, UK Received 31 July 2006; received in revised form 10 November 2006; accepted 12 November 2006 Available online 16 January 2007
Abstract Blast damage assessment of buildings and structural elements requires an accurate prediction of the blast loads in terms of the peak pressures and impulses. Blast loadings on structures have typically been evaluated using empirical relationships. These relationships assume that there are no obstacles between the explosive device and the target. If a blast barrier is used to protect personnel or a structure behind it, the actual blast loading environment will be significantly reduced for some distance behind the barrier. This paper is concerned with an accurate prediction of the area of effectiveness behind the barrier using experimental data and a neural network-based model. To train and validate the neural network, a database is developed through a series of measurements of the blast environment behind the barrier. The principal parameters controlling the blast environment, such as wall height, distance behind the wall, height above ground, and standoff distance are used as the training input data. Peak overpressure and peak scaled impulse are used as the outputs in the neural network configuration. The trained and validated neural network is used to develop contour plots of overpressure and impulse adjustment factors to simplify the process of predicting the effectiveness of blast barriers. The developed model is also deployed in a stand-alone application that is used as a fast-running predictive tool for the blast overpressures and impulses behind the wall. r 2006 Elsevier Ltd. All rights reserved. Keywords: Neural networks; Blast loads; Blast walls; Explosion
1. Introduction Terrorism is evolving as a major threat to critical infrastructure and personnel throughout the world. In recent years car bomb attacks in which an explosive laden vehicle is detonated as close as possible to a target building have become a weapon of choice by some terrorist groups. The most common response to mitigate this threat has been to increase standoff distance (bollards, anti-ram walls, etc.) and retrofit existing buildings with blast protection measures. Increasing vehicle standoff distance could significantly increase real estate and Corresponding author. Tel.: +61 2 4221 5574; fax: +61 2 4221 3238.
E-mail address: [email protected] (A.M. Remennikov). 0734-743X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2006.11.003
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construction costs and could be very difficult to achieve in a dense urban environment. One cost-effective alternative is the installation of perimeter walls for blast effects reduction that would decrease the need for standoff and building blast retrofit requirements. However, only limited information is available on the blast loading environment behind a blast wall [1,2]. Research in the area of blast resistant design and retrofit of structures is currently receiving a great deal of attention by the engineering community. Although it is recognised that no civilian buildings can be designed to withstand any conceivable terrorist threat, it is possible to improve the performance of structural systems by better understanding the factors that contribute to a structure’s blast resistance. One such factor is the ability of the design engineer to predict accurately the blast loadings on structural components using analytical or numerical tools that take into account the complexity of the building, the presence of nearby structures and the surrounding environment. This paper reviews some available experimental in this area of research and presents a new approach to developing an engineering-level tool for predicting the effectiveness of blast perimeter walls. Such a tool could provide the opportunity to conduct a simplified and rapid analysis of the advantages of a blast protective barrier without the need for lengthy numerical simulations and feasibility studies. Improved predictive tools for the assessment of the blast environment behind a protective perimeter wall would allow urban site planners to account for any benefit from the wall in protecting structures and other critical facilities from vehicle bombs. The proposed engineering tool can also be employed for assessment of explosive storage and munition manufacturing facilities, where reinforced concrete dividing walls are used as shields for personnel protection and as physical barriers between explosive production steps. 2. Effects of blast walls on blast propagation Blast loads in simple geometries can be predicted using empirical or semi-empirical methods [3]. These can be used to calculate blast wave parameters for hemispherical surface charges or spherical free air explosive charges to predict blast effects on isolated structures and structural components. Events of the recent years have demonstrated that the most common source of unplanned explosions were terrorist devices in an urban environment. In complex geometries, consisting of multiple buildings or other obstacles capable of modifying blast propagation, the blast wave behaviour can only be predicted from first principles using such numerical tools as SHAMRC [4], FEFLO [5], Chinook [6], AUTODYN [7], Air3D [8], and others. Such tools solve the governing fluid dynamics equations and can be used to simulate threedimensional (3-D) blast wave propagation including multiple reflections, rarefaction and diffraction. In addition, computational fluid dynamics (CFD) techniques can capture such key effects as blast focussing due to the level of confinement and blast shielding by barriers or other buildings. A blast perimeter barrier serves to reflect back some portion of the explosive blast energy and thereby reduces the blast environment behind the wall. The effectiveness of the wall in suppressing the blast environment depends on the parameters of the wall and the explosive charge. When placed across the path of the blast wave, the barrier may reflect a portion of the incident wave and cause the remaining part of the blast to diffract over the wall, as illustrated in Fig. 1. The resulting diffracted pressure will be significantly reduced, and the distance behind the wall where the blast environment is significantly reduced may characterise the effectiveness of the barrier. The US Army Security Engineering Manual [9] contains a methodology for calculating the reduction in pressures and impulses behind a blast wall, but the manual is restricted for official use only and has a very limited availability to the non-military engineering community. The formulations in the manual are based upon small-scale tests conducted at US Army Engineer Waterways Experiment Station (WES) in the 1980s [10]. These formulations were never validated with full-scale experiments. The protective structures automated design system (PSADS) [2] provides some guidance on the effects of barriers and blast walls. PSADS was developed by the US Army Protective Design Centre to automate the procedures for blast-resistant design of structures. It provides methods for the design of protective structures in such areas as airblast, fragmentation, blast loads on structures, dynamic response of structures, as well as a suite of support computer codes. PSADS provides design charts for the peak
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Fig. 1. (a) Blast wave–blast wall interaction and blast environment behind blast wall and (b) expected reduction in overpressures behind wall [29].
pressures and impulses behind blast walls for two scaled wall heights (0.436 and 0.872 m/kg1/3). The design charts are based on experimental studies that had a limited range of burst positions, barrier heights, and measurement locations. As a result, the use of the design charts as a predictive engineering tool has very limited application. More recent research results for blast walls were reported by Humphreys and Piepenburg [11] in 2001 and Bogosian and Shi [12] in 2002 on the same series of explosive tests. In this 35-test series, the experiments included a number of barrier configurations, some of them rigid concrete walls, and others being frangible barrier designs. One of the major findings from this test series was that thin, frangible barriers could be almost as effective as their more massive rigid counterparts. To predict the reduced level of pressures and impulses behind a blast wall, a simple methodology is included in standard manuals (e.g. TM5-583) and uses the geometric configuration shown in Fig. 2. The perimeter wall, of height H and thickness K, is located a distance L2 from the explosive charge W kg TNT and a distance L3 from the face of the building. The standoff distance between the charge and the building, if there were no perimeter wall, would be a distance L1. The height at which reflected pressure and impulse are measured on the building is T. The same geometric configuration applies when side-on blast resultants in free air are required behind a blast wall for personnel protection outside the building.
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Fig. 2. Blast wall configuration used in TM5-583 [9].
The methodology involves determination of adjustment factors, for pressure (AFP) and impulse (AFi), which are defined as follows: AFP ¼
Pwith barrier I with barrier and AFi ¼ . Pno barrier I no barrier
(1)
The adjustment factors represent the ratio of the pressure and impulse behind the blast wall to its original value without the blast wall (i.e. assuming a standoff distance L1). Thus, an adjustment factor of 0.3 represents a 70% reduction in pressure and impulse behind a wall compared to a no-wall configuration. The adjustment factors are obtained from the blast load adjustment curves in the manuals [9] as a function of parameters W, L1, L2, H, and T. To use the curves, one needs first to generate the value of pressure and impulse that would be expected at the location of interest if there were no perimeter wall. Typically, the nobarrier blast loads can be estimated using simplified analytical relationships or design charts [13] as a function of scaled distance L1. They may also be evaluated using the computer programs such as ConWep or ATBlast (available from the US General Services Administration website [14]) that automate those calculations. As a second step, an adjustment factor is then obtained from the curves for a given perimeter wall, bomb size, and building placement. The no-wall pressure and impulse values are then multiplied by the adjustment factors to produce the values behind the blast barriers. In cases where blast loading is required for the area of interest on the building face, the adjusted pressure and impulse can be averaged over this area of interest to provide loading for analysis and design. Rose et al. [15] carried out a programme of research in which detailed measurements of the blast environment were made behind a 1/10th scale vertical barrier. For the set of parameters studied in that work, it was concluded that in the region between three and six wall heights behind a blast wall and over a vertical distance of three wall heights above the ground, pressures and impulses may be reduced to no more than 60% and 80%, respectively of those without a wall. The data sets of measured pressures and impulses from the experimental programme by Rose et al. [15] will be used in this study to develop a neural network-based system for prediction of the blast environment behind a blast wall. The blast environment behind the wall may be further suppressed by employing a canopy near the top of the wall on the loaded side, as shown in PSADS [2]. The use of a canopy assumes that blast wave would be focused in a direction away from the protected target. The canopy could be blown away by the forces of the explosion, but it would remain in place long enough to reduce the magnitude of blast wave diffracting over the wall. The effectiveness of a canopy is not considered further in this paper (Fig. 3). 3. Neural networks Artificial neural networks (ANNs) are computational models loosely inspired by the neuron architecture and operation of the human brain [16]. They are massively parallel; they can process not only clean but also
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Fig. 3. Typical blast wall scenario for development of neural network model.
Fig. 4. (a) Basic operation of artificial neuron and (b) multi-layer perceptron neural network for predicting effectiveness of blast barriers.
noisy or incomplete data. ANNs can be used for the mapping of input to output data without knowing ‘a priori’ a relationship between those data. ANNs can be applied in optimum design, classification and prediction problems. An artificial neural network is an assembly (network) of a large number of highly connected processing units, the so-called nodes or neurons. The neurons are connected by unidirectional communication channels (‘‘connections’’). The strength of the connections between the nodes is represented by numerical values, which normally are called weights. Knowledge is stored in the form of a collection of weights. Each neuron receives a number of inputs and produces output as schematically shown in Fig. 4(a). The neural networks are capable of self-organisation and knowledge acquisition, i.e. learning. One of the characteristics of neural networks is the capability of producing correct, or nearly correct, outputs when presented with partially incomplete inputs. Further, neural networks are capable of performing an amount of generalisation from the patterns on which they are trained. Most neural networks have some sort of ‘‘training’’ rule whereby the weight of connections is adjusted on the basis of presented patterns. Training consists of providing a set of known input–output pairs to the network. The network iteratively adjusts the weights of each of the nodes so as to obtain the desired outputs within a requested level of accuracy. Error is defined as a measure of the difference between the computed pattern and the expected output pattern.
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3.1. Multi-layer perceptron network (MLP) The multi-layer perceptron (MLP) network trained by means of the back-propagating algorithm [16] is currently given the most attention by application developers. The MLP network belongs to the class of layered feed-forward nets with supervised learning [16]. A multi-layer neural network is made up of one or more hidden layers placed between the input and output layers. A neural network structure considered in this work for the blast barrier effectiveness prediction system is shown in Fig. 4(b). Each layer consists of a number of nodes connected in the structure of a layered network. The typical architecture is fully interconnected, i.e. each node in a lower level is connected to every node in the higher level. Output units cannot receive signals directly from the input layer. During the training phase activation flows are only allowed in one direction, a feed-forward process, from the input layer to the output layer through the hidden layers. The input vector feeds each of the first hidden layer nodes, the outputs of this layer feed into each of the second hidden layer nodes and so on. At the start of the training process the weights of the connections are initialised by random values. During the training phase, representative examples of input–output patterns are presented to the network. Each presentation is followed by small adjustments of weights and thresholds if the computed output is not correct. If there is any systematic relationship between input and output and the training examples are representative of this, and if the network topology is properly chosen, then the trained network will often be able to generalise beyond learned examples. Generalisation is a measure of how well the network performs on the actual problem once training is complete. It is usually tested by evaluating the performance of the network on new data outside the training set. Generalisation is most heavily influenced by three parameters: the number of data samples, the complexity of the underlying problem and the network architecture. Currently, there are no reliable rules for determining the capacity of a feed-forward multi-layer neural network. Generally, the capacity of a neural network is a function of the number of hidden layers, the number of processing units in each layer, and the pattern of connectivity between layers. 4. Use of ANNs for predicting non-ideal airblast loading Predicting non-ideal airblast loads is presently a complex computational art requiring many hours of highperformance computing to evaluate a single explosive scenario [17]. Prediction of blast loads in complex geometries is typically carried out with first-principle 3-D Euler CFD solvers. Accurate blast–structure interaction calculations require large number of cells, often in excess of 107, and use of high-performance computing facilities and massively parallel processors. Numerical simulations of this magnitude require approximately 10 Gbytes of memory [18], and can only be run on 64-bit operating systems. Given the high cost and low availability of these machines, fast and accurate engineering-level models are needed for predicting the effects of surrounding buildings and the effects of barriers on airblast pressures (for design, emergency planning, etc.). Simple engineering algorithms may avoid most of these issues by relying on experimental data to tune empirical predictive models using traditional methods of curve fitting, but still require the specification of algorithmic rules describing the dependence of the response parameters on the input variables. In recent years, the use of non-traditional tools based on artificial intelligence has received significant attention from civil engineering researchers in relation to systems that exhibit dynamic, multi-variate, and complex behaviours (e.g. wave forces, weather conditions, shock and impact problems). Dealing with such systems could be a difficult task and traditional tools might not be adequate to predict accurately the behaviour of such systems for design and analysis purposes. A non-traditional technique, artificial neural networks (ANNs), has been reported as efficient for accurately modelling a solution to a problem by considering actual previous situations for which results are known [19]. In addition, through their learning-by-example process, a neural network is able to generate the required results for a previously unseen situation with minimal computational efforts. One of the main advantages of the ANNs is that they extract the regularities in the data empirically, even if the relationship between the inputs and outputs of the system are known explicitly. This important feature makes the ANN a good candidate for modelling problems in the area of dynamics and
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control of multi-dimensional, highly non-linear systems, particularly systems that are difficult to model mathematically [20]. Artificial neural networks rely on sufficient number of reliable data points in order successfully to train the networks. These reliable data points have to be obtained either through experimental testing programmes or by high-fidelity physics modelling of the system, or both. It should be noted that the generalisation capabilities of the trained neural networks will be limited to the range of data used in the training process; outside the training range the predictions could be unreliable due to poor generalisation of the neural network. In the present research, artificial neural networks are developed and trained to store the explosively generated blast data. The main objective is to use the trained ANNs thereafter as a fast-running, standalone tool for predicting the blast resultants (pressure, impulse, fragmentation) in complex geometries with reasonable accuracy and cost. The developed neural network-based algorithms can easily be implemented in special anti-terrorist software (e.g. AT Planner Software, [21]) to assist planners in evaluating the hazard to building occupants associated with a given terrorist threat. At the moment, the airblast shielding provided by blast barriers and the effect of building groups on blast load predictions are not addressed satisfactorily in the AT Planner models [22]. 5. Predicting the blast environment behind a vertical wall barrier using ANNs A blast wall is a barrier placed between the location of a possible explosive threat and that which it is protecting (personnel, inhabited building, critical infrastructure facility, etc.). The problem of predicting blast effects behind the vertical barrier can be approached by conducting (a) small-scale experiments [15]; (b) fullscale experiments [11,12]; or (c) CFD simulations [23]. The first two approaches are the most expensive and time consuming, and typically limited in a number of blast wall scenarios and measurement locations. The use of 3-D CFD blast propagation calculations can generate data sets for a large area of space behind the wall, for a wide range of wall heights, and at practically unlimited numbers of target points to give a detailed picture of the blast environment behind a barrier. Despite the relatively simple geometry of a blast wall scenario, it has been demonstrated [24] that the blast wave–blast wall interaction is particularly difficult to analyse using CFD techniques. This difficulty is caused by the fact that the process of a blast wave diffracting over the wall is highly dependent on the pressure and duration (wavelength) which the blast possesses as it passes the top of the wall. In numerical simulations of a blast wall scenario, this process would primarily depend on the mesh discretisation. In real-life scenarios, the blast wall thickness would be just a small fraction of the computational domain dimensions which can result in the wall model being represented by only one or two computational cells across its width. Such mesh discretisation would be unrepresentative of the continuum, and one should expect degradation of the simulated blast effects behind the wall, depending on other problem parameters such as standoff distance, distance behind the wall, charge weight, and so on. Therefore, the experimental data sets containing values of pressures and impulses behind a blast wall are a more reliable source of data that can be used to calibrate the numerically based results. In this paper, the experimental data sets for a relatively wide range of scaled wall heights and a large area of scaled space behind the wall are employed to train and validate the neural networks. Three-dimensional CFD calculations can be used to extend the database by considering a number of additional blast wall scenarios. These will be presented in the subsequent publications by the authors. The goal of the present study is to develop a fast-running tool for predicting the blast environment behind a vertical barrier. This is accomplished by training an artificial neural network to approximate the overpressures and impulses from the experimental programme by Rose et al. [15]. The present study uses the blast scenario nomenclature as shown in Fig. 3. From Fig. 3, it can be seen that every blast wall scenario can be completely defined by the following independent scaled using cube root scaling [25] parameters: Parameter
Units: [m/kg1/3]
1. Scaled standoff distance 2. Scaled charge elevation 3. Scaled distance behind the wall
r/W1/3 z/W1/3 R/W1/3
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H/W1/3 h/W1/3
4. Scaled height of the wall 5. Scaled elevation of point of interest
These five parameters uniquely define the blast wall scenario. Therefore, these five parameters will be used as inputs to train and validate the neural network using the experimental data sets. The problem of characterising the blast environment behind a vertical barrier on the basis of existing experimental data is essentially a prediction (interpolation) problem. Since artificial neural networks are proving to be an effective tool for predicting values of blast loads [26], the basic idea in a neural network-based approach is to train a neural network with patterns of the blast wall scenario parameters describing the spatial distribution of blast wave parameters in the area behind the wall. This implies that each pattern represents the unique values of peak pressure and peak scaled impulse at each of the monitoring locations behind a blast wall with height H due to detonation of an explosive charge, W, at a particular location described by values of R and h. Therefore, the patterns of the quantities describing the blast environment are used as inputs and the peak pressure and peak scaled impulse as outputs to train the neural network. The training of a neural network with appropriate data containing the information about the cause and effect is a key requirement of a neural network approach. This means that the first step is to establish the training set which can be used to train a network in a way that the network can predict the blast effects within reasonable accuracy of the experimental results. In order to verify how well a trained network has learned the training cases, the trained network is tested by subjecting it to the training sets. The important generalisation capability of a neural network for predicting blast wave parameters is tested by subjecting the trained network to data not included in the training sets (the so-called validating sets). How well a trained network is to generalise depends on the adequacy of the selected network architecture (number of hidden nodes, number of hidden layers, and so on) and the information on the blast load environment included in the training sets.
5.1. Preparation of the data sets The steps for developing ANN models typically include determination of model input and output variables; division of the available data into training, testing, and validation subsets; determination of the optimal network architecture; and model validation. In this study, the most comprehensive set of experimental data available to the authors [15] is used to develop the data subsets. This provides the opportunity to consider a relatively wide range of scaled wall heights (h/W1/3 ¼ 0.5–1.0 m/kg1/3) and a large area of scaled space (R/W1/3 ¼ 0.35–5.0 m/kg1/3) behind the wall. The experimental programme is summarised in Table 1.
Table 1 Blast walls experimental programme [15] Experiment number
Scaled wall height H/W1/3 (m/kg1/3)
Actual wall height, H (m)
Charge weight, W (g) TNTeqv.
1 2 3 4 5 6 Scaled standoff r/W1/3 ¼ 0.327 m/kg1/3 Scaled charge elevation z/W1/3 ¼ 0.258 m/kg1/3
0.50 0.60 0.71 0.80 0.90 1.00
0.221
75.0 43.5 75.0 52.7 75.0 54.9
0.300 0.380
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H/W 1/3=0.5 m/kg1/3, h = 0.0 m 500
500
Pressure - experiment
100
100
50
50
Impulse (kPa-msec)
Pressure (kPa)
Impulse - experiment
10
10 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Horizonal distance behind wall (m) Fig. 5. Example of experimental peak pressures and impulses.
Table 2 Data ranges used for developing ANN models Model variables
Mean
Standard deviation
Minimum
Maximum
Scaled wall height, H/W1/3 (m/kg1/3) Scaled distance behind wall, R/H1/3 (m/kg1/3) Scaled height above ground, h/W1/3 (m/kg1/3) Peak overpressure, Pso (kPa) Scaled peak impulse, is/W1/3 (kPa-ms/kg1/3)
0.75 2.44 1.13 76.8 56.7
0.17 1.34 0.77 92.51 18.36
0.5 0.0 0.0 15.7 29.5
1.0 5.1 2.56 1080 122.5
The experimental programme was designed to include blast walls of three different heights. The charges were Demex plastic explosive, and they were initiated by No. 8 detonators. The TNT equivalence used was 1.32. Each of the experiments utilised a grid of pressure measuring locations in the space behind the walls which extended from R ¼ 0.15–1.8 m, horizontally behind the wall, in intervals of 0.15 m and from h ¼ 0.0–0.9 m, vertically above the ground, also in intervals of 0.15 m. This provided a total of 84 measuring locations for each experimental configuration. Measurements were made using pressure transducers configured to measure side-on pressure-time records. Experimental peak pressures and peak impulses for the target locations at the ground surface are shown in Fig. 5. The database of the experimental results included a total of 517 individual cases. Ranges of the data used for the input and output variables are summarised in Table 2. It should be noted that not all experimental records were included in the database for the development of the ANN models. The experimental database
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Table 3 Input and output statistics based on data division to enforce statistical consistency Model variables and data sets
Statistical parameters Mean
Standard deviation
Minimum
Maximum
Scaled wall height, H/W1/3 (m/kg1/3) Training set Testing set Validation set
0.7 0.7 0.8
0.2 0.2 0.2
0.5 0.5 0.5
1.0 1.0 1.0
Scaled distance behind wall, R/W1/3 (m/kg1/3) Training set Testing set Validation set
1.7 1.7 1.6
1.3 1.3 1.4
0.3 0.4 0.4
5.1 5.1 4.3
Scaled height above ground, h/W1/3 (m/kg1/3) Training set Testing set Validation set
0.7 0.9 0.6
0.6 0.7 0.6
0.0 0.0 0.0
2.1 2.1 2.1
107.8 104.5 108.1
108.8 89.2 87.9
16.2 20.0 22.1
757.4 456.0 317.0
67.2 66.2 66.5
19.8 20.4 20.7
30.1 36.3 38.6
123.2 116.5 120.6
Peak overpressure, Pso (kPa) Training set Testing set Validation set Scaled peak impulse, is (kPa-ms/kg1/3) Training set Testing set Validation set
cases were visually inspected and some of the records that exhibited contradicting trends to the majority of the records in their group were removed from the database. The database used for the development of the ANN models comprises a total of 285 measurements. In the majority of the applications of ANNs in various areas of engineering, the data are divided into sets needed to develop ANN models (e.g. training, testing, and validation) on an arbitrary basis without giving adequate attention to the statistical consistency of the data subsets. The crossvalidation technique [27] in which the training set is used to adjust the connection weights, the testing set is used to check the performance of the network and to decide when to stop training, and the validation set is used to evaluate the performance of the model is considered to be the most effective method to avoid problems with overfitting and generalisation of the network. Consequently, the statistical properties of the data subsets used in the model development need to be similar to ensure that each subset represents the same statistical population. If this is not the case, it may be difficult to justify the validity of ANN models [27]. In this study, the available data are divided in a way that ensured that the statistical properties of the data subsets are close to each other and thus represent the same statistical population. The statistical parameters used include the mean, standard deviation, minimum, maximum, and range. As part of this approach, the 285 individual records are divided into three statistically consistent subsets. In total, 85% of the data are used for calibration and 15% of the data are used for validation. The calibration set is further divided into 70% for training and 30% for testing. The statistics of the training, testing, and validation sets, obtained by taking into account the statistical characteristics of the subsets, are shown in Table 3. It can be seen that the statistical consistency between the various data subsets can be achieved with the consequent improvement in the performance of the models developed using these data subsets.
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Table 4 Configuration and statistical performance of trial networks Correlation coefficient, r
Root mean square error (RMSE)
Mean absolute error (MAE)
Pressure ANN
Impulse ANN
Pressure ANN
Pressure ANN
Impulse ANN
Single hidden layer 3-(2)-1 3-(5)-1 3-(9)-1 3-(10)-1 3-(15)-1
0.802 0.972 0.988 0.947 0.986
0.933 0.960 0.992 0.994 0.995
61.2 24.5 15.6 32.9 17.5
7.22 5.60 2.50 2.09 1.91
34.2 15.4 10.0 20.8 10.6
5.43 4.28 1.82 1.56 1.39
Two hidden layers 3-(2-2)-1 3-(5-5)-1 3-(8-8)-1
0.945 0.996 0.998
0.961 0.995 0.999
33.5 8.90 5.90
5.51 1.96 1.03
21.7 6.02 3.86
4.13 1.54 0.68
Three hidden layers 3-(4-4-4)-1
0.971
0.842
24.3
17.5
8.51
Network architecture and data sets
Impulse ANN
10.8
Note: network configuration, e.g. 3-(2)-1, refers to an ANN with 3 inputs, 1 output, and 2 nodes in a single hidden layer.
6. Results and discussion 6.1. Neural network implementation As stated above, multi-layer perceptron networks trained by means of the back-propagating algorithm are used for the development of ANN models. The computer program Neuroshell2 [28], Release 4.0, was used in the present study to train the network. The program implements several types of neural networks and architectures, including the multi-layer backpropagation nets, the genetic adaptive general regression neural networks (GRNN), the polynomial nets (GMDH), the backpropagation nets with jump connections and some others. The optimum network architecture was obtained by evaluating the performance of ANNs with one, two, and three hidden layers and variable numbers of hidden layer nodes. In order to determine the optimal control parameters for the backpropagation algorithm, the networks were trained with different combinations of momentum and learning parameters. Values between 0.1 and 0.8 were used for the momentum and learning rate in order to find the best performing network configuration. Network configuration and statistical parameters of the trial networks are presented in Table 4. 6.2. Analysis of performance of the ANN blast wall model Based on the statistical analysis results for the trial networks shown in Table 4, the network model with two hidden layers and eight hidden layer nodes (3-(8-8)-1) was selected for the further development. This model performed better than other network configurations based on the least errors for both RMSE and MAE in the predictions for both peak pressures and scaled impulses. The mean errors of the model 3-(8-8)-1 in predicting the peak pressures are 5.9 and 3.9 kPa for RMSE and MAE, respectively. For the scaled impulse, the mean errors of the same model are only 1.03 and 0.68 kPa-ms/kg1/3 for RMSE and MAE, respectively, which is an indication of practically 100% confidence in the scaled impulses predicted by the selected network model. The selected network model was further validated by the comparison of the statistical indicators for training, testing, and validation data sets as shown in Table 5. It can be seen that statistical consistency in the predicted results for all datasets ensures reliable predictions by the developed neural network within the range of variation of the input parameters. Fig. 6 shows the experimental peak pressures versus predicted values of all data records. It can be seen that the predictions of the neural network produce little scatter, and thus provide very good prediction of peak pressures behind a blast wall. Graphs comparing experimental peak pressures
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Table 5 Performance of the selected ANN models Data sets
Training set Testing set Validation set
Predicted peak overpressures
Predicted scaled impulses
r
RMSE (kPa)
MAE (kPa)
r
RMSE (kPa-ms/kg1/3)
MAE (kPa-ms/kg1/3)
0.999 0.997 0.997
5.2 6.7 9.0
3.4 4.6 5.6
0.999 0.998 1.000
0.9 1.4 0.7
0.6 0.9 0.6
Note: RMSE ¼ root mean square error; MAE ¼ mean absolute error
Prediced Peak Pressures (kPa)
1000 500
100 50
10 10
50 100 500 Experimental Peak Pressures (kPa)
1000
Fig. 6. ANN-predicted peak pressures versus experimental peak pressures.
and impulses with the neural network-predicted values for the horizontal arrays of target points at different heights above ground are given in Fig. 7. These graphs also demonstrate the good quality of the predicted blast pressures and impulses in the region behind the blast walls both in the horizontal and vertical directions. 6.3. Validation of the ANN blast wall model It is known that the generalisation capabilities of the trained ANNs are limited to the range of the training data points; outside the training range the ANNs usually have poor performance and should not be trusted to afford reliable predictions. In order to validate the developed ANN model for predicting the blast pressures and impulses behind a vertical barrier, the model’s performance should be tested on new, previously unseen data. Beyer [29] presents blast wall design criteria derived from a series of high explosive trials. The experimental program was performed at one-sixth scale, and some of the results from the ten trials can be compared with the present ANN model. Strictly, none of Beyer’s data is directly comparable because different values of r and z were employed. However, both r/W1/3 and z/W1/3 in the Beyer’s tests were 0.378 m/kg1/3, which are reasonably close to the corresponding values in Table 1 used in the development of the neural network-based blast wall model presented in this paper. Beyer’s data for H/W1/3 ¼ 0.857 m/kg1/3 are used to validate the ability of the neural network to generalise to new data not included in the training set. The graphs comparing peak pressures and scaled impulse with data from Beyer [29] are shown in Fig. 8. A reasonably good
ARTICLE IN PRESS A.M. Remennikov, T.A. Rose / International Journal of Impact Engineering 34 (2007) 1907–1923 Pressure - experiment Impulse -experiment
Pressure - ANN Impulse -ANN
100
50
50
1
1.2 1.4 1.6 1.8
10 2
100
100
50
50
10 0
Horizonal distance behind wall (m)
100
50
50
1
1.2 1.4 1.6 1.8
2
Pressure (kPa)
100
0.2 0.4 0.6 0.8
10
500
100
100
50
50
10
10 0
100
50
50
1.2 1.4 1.6 1.8
Horizonal distance behind wall (m)
10 2
Pressure (kPa)
100
1
1
1.2 1.4 1.6 1.8
2
H/W 1/3 = 0.5 m/kg1/3, h = 0.90 m
500
Impulse (kPa-msec)
Pressure (kPa)
H/W 1/3 = 0.5 m/kg1/3, h = 0.30 m
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
Horizonal distance behind wall (m)
500
0
10 2
500
Horizonal distance behind wall (m)
10
1.2 1.4 1.6 1.8
H/W 1/3 = 0.5 m/kg1/3, h = 0.75 m
500
Impulse (kPa-msec)
Pressure (kPa)
H/W 1/3 = 0.5 m/kg1/3, h = 0.15 m
0
1
Horizonal distance behind wall (m)
500
10
0.2 0.4 0.6 0.8
Impulse (kPa-msec)
0.2 0.4 0.6 0.8
500
500
500
100
100
50
50
10
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
Impulse (kPa-msec)
0
500
Impulse (kPa-msec)
100
Pressure (kPa)
H/W 1/3 = 0.5 m/kg1/3, h = 0.45 m
500
Impulse (kPa-msec)
Pressure (kPa)
H/W 1/3 = 0.5 m/kg1/3, h = 0.0 m
500
10
1919
10
Horizonal distance behind wall (m)
Fig. 7. Comparison of predicted and experimental pressures and impulses for H/W1/3 ¼ 0.5 m/kg1/3 at different heights above ground.
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Target on ground
Pressure (kPa)
500
H/W1/3 = 0.857
FREE-FIELD
100 50 Predicted pressure H/W1/3=0.857 Beyer's data H/W1/3=0.857
10 0.2 0.5 1 5 10 Scaled horizontal distance behind wall (m/kg1/3) Target on ground Peak scaled Impulse (kPa-ms/kg1/3)
500 FREE-FIELD
H/W1/3 = 0.857
100 50 Predicted impulse H/W1/3=0.857 Beyer's data H/W1/3=0.857
10 0.2
0.5 1 5 10 Scaled horizontal distance behind wall (m/kg1/3)
Fig. 8. Comparison of predicted peak pressure and scaled impulse data with other methods.
correlation is obtained with the ANN blast wall model, taking into consideration the fact that some parameters of the blast wall scenarios are close but not identical. 6.4. ANN blast wall model as a tool for rapid prediction of effectiveness of blast barriers The ANN blast wall model can be utilised for rapid prediction of the benefit of having a blast wall for a specified scenario. One way to achieve this is to plot the overpressures and impulses which occur in the area behind the blast barrier in terms of the percentage of the free-field pressures and impulses when the barrier is not present. So-called ‘benefit plots’ can be presented as contours of the adjustment factors for pressure (AFP) and impulse (AFi) based on the following formulas: AFP ¼
Ppredicted I predicted 100% and AFi ¼ 100%. Pfreefield I freefield
(2)
It should be noted that for the free-field pressures and impulses to be consistent with the predicted quantities, the scaled range or horizontal distance to the point of interest behind the wall
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Free-field Peak Pressure Contours
Point of interest
43 0
24 0
62
0
1 4 30
8 10
00
0.5
24 0
620
2
1.5
3
3.5
50
70
60
90
1 60
0.5
AFp=0.32
40
30
30
20
0.5
1
40
50
50
1.5
70 80
70
2
2.5
3
75
45 55
1.5
45
3.5
4
H/W 1/3=0.75 35
35
65
1
25
35
AFp= 0.27
15
45
0.5 25
0.5
1
1.5
2
2
2.5
3
50
75
3.5
4
40
60
70
80
55
65
50
1.5 1
90
55
2
Scaled Height Above Ground (m/kg1/3)
4
H/W 1/3=0.5
60
40
Scaled Height Above Ground (m/kg1/3)
2.5
80
Scaled Height Above Ground (m/kg1/3)
1.5
1
10 0
0.5 2
50
Pso= 180 kPa
10
Scaled Height Above Ground (m/kg1/3)
1.5
24 0
50
2
H/W1/3=1.0
30
30 20
10
AFp= 0.20 30
0.5 20
0.5
1
40
40
1.5 2 2.5 3 Scaled Distance Behind Wall (m/kg^1/3)
50
60
3.5
Fig. 9. Rapid assessment of blast wall effectiveness for several wall heights.
4
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must be calculated as Rfreefield =W 1=3 ¼ r=W 1=3 þ d=W 1=3 þ R=W 1=3 ,
(3)
where r, d, and R are the blast wall scenario parameters shown in Fig. 3. Fig. 9 illustrates an example of rapid determination of the effectiveness of blast walls of different height for a specific point of interest behind the wall. In this blast wall scenario, the charge W kg is located at the scaled distance of r/W1/3 ¼ 0.327 m/kg1/3 from the wall and z/W1/3 ¼ 0.258 m/kg1/3 above the ground. For a vehicle bomb with W ¼ 230 kg, this scenario may be equated to a 2.0-m standoff from the wall and 1.5 m above the ground. The point of interest is placed 2.0 m/kg1/3 behind the barrier and at a scaled height of 0.5 m/kg1/3 above the ground. Three contour plots in Fig. 9 are generated for the walls with H/W1/3 ¼ 0.5, 0.75, and 1.0 m/kg1/3 using the blast wall ANN model. An initial ‘unobstructed’ estimate of the peak overpressure is obtained from the contour plot of free-field overpressures and is given as Pso ¼ 180 kPa. The ‘‘benefit plots’’ shown below the free-field contour plot in Fig. 9 give a rapid prediction of the effectiveness of the vertical barriers with the specified heights in suppressing the blast environment behind the wall. As it will be seen, the pressure adjustment factors for the blast wall heights H/W1/3 ¼ 0.5, 0.75, and 1.0 m/kg1/3 can be estimated as AFP ¼ 0.32, 0.27, and 0.20, respectively. This, in turn, allows for quantitative prediction of the peak overpressures at the point of interest as 57.6, 48.6, and 36.0 kPa. Based on this information, the design engineer or site planner can rapidly assess the benefit from the wall and adjust its location and height to achieve the optimal results with respect to the required reduction in pressures and impulses at the point of interest. It should be noted that the blast wall ANN model developed in this paper could predict the effectiveness of a blast wall scenario for any blast wall with scaled height between 0.5 and 1.0 m/kg1/3. This equates to heights of 3.0–6.0 m (the most typical range of blast wall heights) for a vehicle bomb size of W ¼ 230 kg. 7. Conclusion The main objective of this study was to evaluate a new approach of using artificial neural network for predicting the blast environment behind a vertical blast wall barrier. A database of overpressures and impulses in the region behind the wall was established from the measurements of the blast environment during a series of small-scale blast wall experiments. This database was used to train and test the neural network to serve as a prediction tool for various blast wall scenarios. The main advantage of this approach is its ability to predict the effectiveness of a blast wall configuration in a matter of minutes whereas the numerical CFD simulation of the problem could take hours or days to complete. Analysis of the network’s performance shows the feasibility of using ANN models for predicting non-ideal airblast loading in situations where the blast environment is modified by the presence of such rigid obstacles as protective walls and multiple buildings. It has been demonstrated that the effectiveness of a blast wall can be quantified using the so-called ‘benefit’ contour plots of overpressure and impulse adjustment factors that are generated by the trained neural network model. The developed blast wall neural network model has also been deployed as a standalone application that could be used as a fast-running engineering-level tool within an expert system capable of predicting information about the likely injury and damage levels in blast environments where shielding by barrier walls is present. References [1] Mayor RP, Flanders R. Technical manual, simplified computer model of air blast effects on building walls. US Department of Transportation, Research and Special Programs Administration, Transportation Systems Center, Cambridge, 1990. [2] DAHSCWEMAN. Technical manual—design and analysis of hardened structures to conventional weapons effects; PSADS (Protective Structures Automated Design System), version 1.0. Washington, DC: US Army Corps of Engineers; 1998. [3] Remennikov AM. A review of methods for predicting bomb blast effects on buildings. J Battlefield Technol 2003;6(3):5–10. [4] Crepeau JE. SHAMRC, second-order hydrodynamic automatic mesh refinement code, vol. 1: Methodology. Albuquerque, NM: Applied Research Associates; 1999. [5] Lo¨rner R, Yang C, Baum JD, Mestreau E. Advances in FEFLO. AIAA-02-1024, American Institute of Aeronautics & Astronautics, 2002.
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