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Prediction of fire resistance of concrete filled tubular steel columns using neural networks
Fire Safety Journal 37 (2002) 339–352
Prediction of fire resistance of concrete filled tubular steel columns using neural networks Abdullateef M. Al-Khaleefia,*, Mohammad J. Terroa, Alex P. Alexb, Yong Wangc a
Civil Engineering Department, College of Engineering & Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait b Engineering Systems Group, P.O. Box 5336, Safat 13054, Kuwait c UMIST, Manchester University, UK Received 17 August 2000; received in revised form 21 August 2001; accepted 20 October 2001
Abstract A functional relationship between the fire resistance of a concrete filled steel column and the parameters which cause the fire resistance is represented using an artificial neural network. Experimental data obtained from previous laboratory fire tests are used for training the neural network model. The model predicted values are compared with actual test results. The results indicate that the model can predict the fire resistance with adequate accuracy required for practical design purpose. The developed neutral network can be used to predict the fire resistance of similar columns under fire by observing various factors influencing the resistance such as: (a) structural factors, (b) material factors, and (c) loading conditions. The structural engineer is required to provide the magnitude of these influencing factors as inputs to the neural network and the network will predict the fire resistance, based on the combined effect of these factors. This system can be used by structural engineers to predict the resistance of fire in similar concrete filled steel columns without conducting costly fire tests, by using the known parameters such as column dimensions, column height, and loading conditions. r 2002 Published by Elsevier Science Ltd. Keywords: Artificial neural networks; Construction; Fire resistance; Structural analysis
*Corresponding author. Tel.: +965-4817240; fax: +965-4817524. E-mail address: khaleefi@civil.kuniv.edu.kw (A.M. Al-Khaleefi). 0379-7112/02/$ - see front matter r 2002 Published by Elsevier Science Ltd. PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 6 5 - 0
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1. Introduction Concrete and structural steel constructions are exposed to elevated temperature in many types of structural loading. Most evident examples of such structures/loading are nuclear power stations and accidental fires in residential buildings. Growing concerns about the safety of structures in general and under elevated temperature conditions, in particular, have been witnessed during the last few decades [1–6]. The theory of the behaviour of the structure in the event of a fire is still not fully developed due to the complexity of the problem and the large number of parameters controlling this behaviour. The prediction of the fire resistance of a concrete/steel construction under accidental fire is important for the design of the structure so that it resists load for a period of time sufficient for the rescue operations. It is also important for subsequent assessment of the residual capacity of the members of the structure for its rehabilitation in the aftermath of the fire. This research paper considers the use of artificial neural networks (ANN) in predicting the fire resistance of concrete-filled tubular steel columns. The choice of this type of structural member was based mainly on three reasons: *
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Concrete-filled steel columns are used in constructions as fire-resistant members as such sections are very efficient in resisting compressive loads. Due to the confining action of the steel on concrete and protection from direct contact with flame (there is no spalling in such sections), fire resistance data available in the literature are more coherent and suitable for use in ANN models. Fire resistance data on concrete-filled steel columns have been well studied and are abundant in the literature.
The proposed prediction method utilises neural networks, an AI-based technique that emulates the human ability to learn from the past experience and derive quick solutions to new situations. The developed neural network based prediction model can be used by structural engineers to predict the fire resistance of similar structural members.
2. Artificial neural networks Artificial neural networks, also known as connectionist systems, are a class of modelling tools inspired by the workings of biological neural systems. ANN are composed of neurons or processing elements (PE) and connections which are organised in layers: an input layer, middle or hidden layer(s), and output layer, as illustrated in Fig. 1. It is clear from the figure that the input parameters (neurons) are connected to the output parameters (neurons) through the hidden layer (neurons). The signals entering the input layer flow to the output layer through the middle layer(s), with the input signals detailing the problem to be solved and the output signals representing the network’s solution to that problem. The connections between the neurons are associated with numerical values called connection weights which determine the influence of one neuron on another. The connection weights
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Fig. 1. (a) An artificial neural network with three layers, (b) activities at the neural network node.
modify the output signal on each of the connection paths making some connections stronger and other connections weaker. The neurons in the input layer receive their activation from the environment, while the activation levels of neurons in the middle and output layers are computed as a function of the activation levels of the neurons feeding into them. Typically, this involves the summation of all incoming signals (along with a bias associated with the middle layer neuron) followed by the application of a non-linear function termed the activation function or transfer function. Artificial neural networks allow self-learning, self-organisation and parallel processing, and are well-suited for problems involving matching of input patterns to a set of output patterns where deep reasoning is not required. A good introduction to the general field of ANNs can be found in [7] or [8]. ANNs have been successfully used in many fields of engineering. Ref. [9] provides a detailed description about the fundamentals of neural networks along with their potential applications in civil and construction engineering. It has also been recently used as a predictive tool in civil engineering research work [10,11]. During the training process, the connection weights are learned by the network as training examples are presented repeatedly. The training process can be supervised or unsupervised. In supervised training (the approach adopted for the work presented here) the connection weights are modified continuously until the error between the desired output and the actual output is minimised. The neural network modifies the weights between layers in successive iterations until the network is able to generate the desired output of the system to within a specified accuracy or until the user-specified number of iterations has been performed. Knowledge is effectively learned and stored by the weights on the connections between the neurons. Once
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training has been completed, it is anticipated that the neural network will be able to generate the required output for example problems not considered during training. The back propagation algorithm is the most widely used training technique for continuous function mapping, has been shown to be theoretically sound [12], performs well in modelling non-linear functions, and is simple to code. Back propagation algorithm training develops the input to output mapping by minimising a sum squared error cost function measured over a set of training examples. The transfer function computes the activation level of a neuron from the sum of input values. The function adopted for the current problem was a sigmoidal curve, given by Transfer function ðxÞ ¼
1 1 þ ex
ð1Þ
where ‘‘x’’ is the sum of the inputs to the neuron. The sigmoidal function generates output values between 0 and 1. Another important network design variable is the learning rate coefficient (Z) which represents the degree by which the weights are changed when two neurons are excited. Each time a pattern is presented to the network, the weights leading to a neuron are modified slightly during learning in the direction required to produce a smaller error at the outputs the next time the same pattern is presented. The amount of weight modification is proportional to the learning rate. The value of Z ranges between 0.0 and 1.0, where a value closer to 1 indicates significant modification in weight while a value closer to 0 indicates little modification.
3. Fire resistance prediction Fire resistance has been predicted mainly, to date, by the following three methods: (a) Use of recommendations concerned with parameters such as the cover to main reinforcement (in concrete structures) and thickness of the member concerned. (b) Similarity with experimental results of fire tests performed on similar structures. (c) Use of predictive analytical/computational tools to calculate the fire resistance. The costs involved in setting up and testing structures under fire are very high and the number of research centres around the world capable of reliably conducting such projects is not large. Such tests are also very hazardous. The remarkable advances in the computer technology and tools have created new horizons for solving many sophisticated engineering problems including structural behaviour under fire [6,13,14]. However, analytical/computational tools used to predict fire resistance are still not fully reliable and are dependent on many thermal/structural parameters/ variables that are usually tuned and fiddled by the researchers to fit experimental results. The literature contains many studies concerned with the fire behaviour covering a wide variety of steel and concrete structures [15–24]. The experimental research and data are independent, in general, and each study is used by the researcher to study a
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certain phenomena and not as a predictive tool by itself. The subject of this paper involves the collection and implementation of such experimental data on the fire behaviour of structures and the development of predictive mathematical models using the theory of ANNs. The behaviour of concrete at elevated temperature has also been studied using ANNs [25]. The researchers collected data from the literature on the residual compressive strength of concrete after heating to elevated temperatures. These data were then used to develop the ANN model, which succeeded in predicting concrete strengths to within 10–15%. The reason for the error in the results obtained could be attributed to the multitude of sources for the collection of data, when it is known that no two concrete mixes are alike. It should also be emphasised that the term ‘‘fire resistance’’ is defined as the time elapsed before an element of structure violates a limit state when exposed to a standard fire test [26]. The work by Chan et al. [25] only considers the residual compressive strength of concrete samples and not the prediction of fire resistance. To the best knowledge of the authors, the prediction of the fire resistance of structural members has not been yet studied using ANNs and hence worthy of investigation.
4. Knowledge representation The procedure adopted to model the fire resistance prediction of concrete filled tubular steel columns consists of the following steps: 1. Identification of the major factors that influence the fire resistance of concrete filled tubular steel columns. 2. Collection of a set of experimental cases with values for these identified factors along with the respective fire resistance. 3. Coding of the laboratory test cases and corresponding value of fire resistance obtained based on experiments. 4. Development of ANN model, from the coded cases, which is capable of predicting the fire resistance of other similar concrete filled tubular steel columns. 4.1. Factors affecting fire resistance Tests on the fire resistance of hollow steel columns filled with plain concrete have been studied in Ref. [27]. Circular hollow steel tube and square hollow steel tubes were tested and reported in this research (Fig. 2). Refs. [15–24] specifically indicate the results of tests on different types of structural components such as unprotected structural steel-1, circular steel columns filled with bar-reinforced concrete, steel hollow structural section columns filled with plain concrete, etc. The objective of this paper is not to generate ANNs model for all these different components, rather the intention is to use a homogenious set of research data to explore how this new and emerging modelling technique could be used for fire research problems. Further the authors chose to study concrete filled tubular steel columns because these
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Fig. 2. An artificial neural network to predict the fire resistance of hollow steel columns filled with concrete.
components are widely used in construction and more test data were available for their experiment. The authors chose to use a data set with an adequate number of specimen data available for satisfactory development of the model using ANNs. The authors found that Ref. [27] gave them enough data as required for this paper compared to other references. The test specimens are described in detail in [27]. Measurable factors affecting the fire resistance of concrete filled tubular steel columns were identified from this study. The eight self-explanatory factors that influence the fire resistance of the concrete filled tubular steel columns were obtained from [27] are as follows: (i) water cement ratio, (ii) type of aggregate, (iii) concrete 28 days cylinder strength, (iv) steel yield strength, (v) external dimension, (vi) steel thickness, (vii) column height, and (viii) test load.
5. Development of neural network Having identified the factors that influence the fire resistance of concrete filled tubular steel columns, it is necessary to establish the training samples to develop the neural network model. Cases were obtained from the experimental study conducted by Lie and Chabot [27] as given in Table 1. The experimental data were transformed into a numerical scale and coded to generate a set of training data. If the fire resistance and the factors affecting fire resistance are known, then it is possible to develop an empirical model of this prediction process. The number of experimental data used is of course limited. As far as the neural network is concerned, it is fitting a continuous function to the training data. The number of training points that are needed to develop an accurate continuous function model depends on other factors, most notably: the complexity of the solution surface being modelled (i.e., how many hills and valleys it contains); the
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Table 1 Tests on fire resistance of hollow steel columns filled with plain concrete [27] Case # w/c
Aggregate
Concrete Steel yield External Steel Column Test Fire 28 days strength dimension thickness height load resistance cylinder (Mpa) (mm) (mm) (mm) (KN) (min) strength (Mpa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
0.49 0.49 0.49 0.49 0.49 0.51 0.51 0.51 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.37 0.49 0.49 0.37 0.37 0.37 0.37 0.36 0.49 0.37 0.27
28.6 28.6 28.6 28.6 28.6 24.3 24.3 24.3 26.3 26.3 26.3 26.3 23.5 23.5 23.5 23.5 23.5 35.9 33 33 43 35.9 43 43 49.3 33 35.9 90.5
350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 300 300 300 300 350 350 350 350 350 350 350
141.3 141.3 168.3 168.3 168.3 219.1 219.1 219.1 273.1 273.1 273.1 273.1 323.9 323.9 355.6 355.6 406.4 141.3 141.3 219.1 219.1 219.1 273.1 273.1 273.1 273.1 273.1 273.1
6.55 6.55 4.78 4.78 6.35 4.78 4.78 8.18 5.56 5.56 5.56 12.7 6.35 6.35 6.35 12.7 12.7 6.55 6.55 4.78 4.78 8.18 6.35 6.35 6.35 6.35 6.35 6.35
3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810
110 131 150 218 150 492 384 525 574 525 1000 525 699 1050 1050 1050 1900 80 143 500 560 560 1050 1050 1050 715 712 1050
55 57 76 56 81 80 102 82 112 133 70 143 145 93 111 170 71 82 64 111 108 102 106 76 90 178 144 48
29 30 31 32 33 34 35
0.37 0.37 0.37 0.37 0.37 0.49 0.37
Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carb.+flyash Carbonate Carbonate Carb. +sil. Fume Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate
43 43 40.8 40.8 40.8 33 43
300 300 300 300 300 300 300
323.9 323.9 355.6 355.6 406.4 406.4 406.4
6.35 6.35 6.35 12.7 6.35 12.7 12.7
3810 3810 3810 3810 3810 3810 3810
820 1180 1335 965 1400 1900 1900
234 114 149 274 294 125 152
stochastic content of the data (i.e., one needs enough training points to prevent bias due to random fluctuations); and the number of input variables. The capability of neural networks to generalise on limited number of training data combined with the randomness in the training set will reduce the chance of bias due to the limited number of training cases.
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In this research, a continuous function-mapping network has been adopted since the values of certain output variables and the input variables are continuous. Continuous mapping functions can represent both continuous and discrete data, whereas discrete mapping functions are limited in their ability to represent continuous data. A small learning rate of 0.15 was arbitrarily chosen for the current problem since larger learning rates have often been found to lead to oscillations in weight changes resulting in a never ending learning process. One way to allow faster learning without oscillations is to make the weight change, in part, a function of the previous weight change. A momentum coefficient represents this portion of the weight change. In this study, a coefficient of 0.7 was found to perform well. The eight factors (attributes) that are considered for the prediction of fire resistance become the input variables. The number of hidden layer(s) and the number of hidden neurons in the hidden layers, provide the power of internal representation in capturing the non-linear relationship between the input and output vectors. Hence, a larger number of hidden layers and hidden neurons provides the potential for developing a more effective network. However, the addition of more hidden neurons increases the number of undetermined parameters (weights and biases) associated with the network. A large number of training examples is then needed to solve these parameters and get a good approximation of the problem domain. When too few training examples are provided, the network will try to memorise, resulting in poor generalisation. In Ref. [28] it is determined that to provide a good approximation over the problem domain, one should have overdetermined approximations, that is, the number of training pairs should be greater than the number of undetermined parameters. Undetermined parameters in neural network approximations are the weights and biases associated with the network. To capture and represent the features within a set of data there should usually be one to two hidden layers. One hidden layer with 14 hidden neurons constitutes the present network arrangement.
6. Results and discussions The generated input–output data pairs (35 cases) were divided into a training set and a test set. The test set was derived from the data set by selecting 10–20% of data pairs randomly. Table 1 indicate the whole data set for all 35 cases out of which 27 cases are used for training and 8 for testing. A neural network development software, NeuroShellt [29] was employed to train and develop the neural network. Eight input neurons and one output neuron with 14 hidden neurons constitute the neural network arrangement for the problem. Since our training data were limited in number, (the reasons of the limited number of experiment results were mentioned in the beginning of the problem) we chose the most reasonable arrangement of one hidden layer with a set of 14 neurons. We reached this number based on our extensive experience with ANNs modeling. A detailed explanation about choosing the values of these ANNs components is presented by various ANNs researchers as indicated in Refs. [7,8,12,28]. Network development was performed on an IBM
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compatible Pentium class machine (200 MHz, 96 MB RAM). The training of a neural network is stopped when the error falls below a user-specified level, or when the user-defined number of training iterations has been reached. In this case, 10,000 iterations were planned for the final training process, as this was found adequate in a series of test runs. Training took less that 5 min and the minimum mean squared error of the network, which was accumulated over all the training sample cases, reached 0.001 (Fig. 3). The network computes the mean (average) squared error between the actual and predicted values for all outputs over all patterns. The network computes the squared error for each output in a pattern (in our case, there is only one output per pattern), then the network computes the mean of that number over all the patterns in the training set. The mean squared error is computed as follows: The mean squared error for a pattern ¼
ðYiact Yipred Þ2 þ ? þ ðYnact Ynpred Þ2 ; Number of outputs per pattern ð2Þ
where Yiact is the actual (experimental) results, i ¼ 1; 2; y; n; Yipred the predicted (neural network) results and, n the number of cases. The mean squared error for a training set P Mean squared error of patterns : ¼ Number of patterns in a training set
ð3Þ
Eq. (3) yields the minimum (least) mean (average) squared error which is the minimum reached while training the network. Table 2a provides a comparison between the experimental output, and the ANN generated output for the training set, while Table 2b provides a comparison between
Fig. 3. Reduction in error over training time.
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348 Table 2 Case #
Experimental fire resistance
ANN generated fire resistance
(a) Comparison of neural network generated output vs. experimental fire resistance on training cases 1 55 57 2 57 55 3 76 79 5 81 74 6 80 79 7 102 92 9 112 117 10 133 124 11 70 67 12 143 145 13 145 146 15 111 126 16 170 161 17 71 75 19 64 68 20 111 111 21 108 89 22 102 99 23 106 83 24 76 83 26 178 172 27 144 147 29 234 244 30 114 141 31 149 166 33 294 257 34 125 127 (b) Comparison of neural network generated output vs. experimental fire resistance on test cases 4 56 71 8 82 70 14 93 97 18 82 72 25 90 90 28 48 45 32 274 281 35 152 150 Average operational error ¼1=n
X ½ððb aÞ=aÞ100 ¼ 8:5%:
the experimental output, and the ANN generated output for the test set, Table 2 shows the application of the model and the result on how best the unseen data were evaluated by the ANNs to generate the output. It can be observed that the ANN model could capture the decision process very closely. Fig. 4 plots the actual (experimental) and the predicted (neural network) fire resistance for the complete
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Fig. 4. Comparison of experimental fire resistance vs. neural network generated fire resistance.
data set. It can be observed that the predictions made by neural network closely matches with the experimental data. Fig. 4 provides the overall fit of the whole data available for the generated model. The percentage of average operational error for the test case was found to be 8.5%, which show the ability of the network to predict the change in fire resistance values with moderate to high precision. The relative weights of each input parameter for the developed ANNs model are as follows: 0.25177 0.23284 0.14700 0.13061 0.08466 0.08101 0.07212
test load external dimension steel yield strength aggregate type w=c steel thickness concrete 28 days cylinder strength
Fig. 5 shows the experimental results on the horizontal axis and the predicted results on the vertical axis. The model is limited by the data used for training such as the extent of the scatter in the value of input parameters within themselves. By using more widely varied data for training, (for example, columns of different height) the model could capture the variety in real life cases. Thus, this limitation is implied by the limitation in conducting fire experiments and the limitation in conducting large scale test in many countries and not by the proposed modelling process itself. The ANN model by itself is limited to the computer processing power available for model development. With large number of input parameters and large training data, the process requires good computing resources as large number of processing steps during each iterations.
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Fig. 5. Pair wise comparison of experimental fire resistance vs. neural network generated fire resistance.
7. Conclusion and recommendations Several approaches have been adopted during the past few decades to predict the fire resistance of structural members. These approaches were either very costly and hazardous, as in experimental fire tests, or contained some inaccuracies due to the complex nature of fire, as in the case of analytical and computational methods. A preliminary study to predict the fire resistance of concrete-filled tubular steel columns using ANNs is presented. Neural networks eliminate the need for identifying the relationship manually and do not limit the number of variables involved in these kind of problems. Furthermore, neural network automatically weeds out the insignificant variables by the process of self-organization and learning capability by assigning less weight to non-significant factors. However, setting the parameters of neural networks is an arbitrary process and the training process can be time consuming. The following conclusions have been drawn from this study: *
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A multi-layer feed forward neural-network based learning algorithm has been adopted for the development of the model. An experimental knowledge representation scheme is adopted for the development of the neural network. Thirty-five past test results are coded and used as the training and test data for the neural network. The developed model is able to establish the relationship between fire resistance of the composite element and the characteristics of its material composition and the fire environment. The predicted results compare favourably with experimental values with an average operational error of 8.5%. Such error levels are considered positive and
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acceptable in the field of fire engineering due to the highly unpredictable nature of fire and the behaviour of elements exposed to high temperatures. Moreover, computational methods used for predicting fire resistance employ parameters used to fit their results to those of limited experimental data, sometimes without reference to a sound theoretical base. The developed ANNs model can be easily integrated with any windows-based spreadsheet system to assist in the generation of fire resistance prediction. The developed neural network can be inserted in to any cell of a spreadsheet, such as Microsoft Excelt, as a dynamic link library (DLL) and thus can easily be used in spreadsheet computations. This integration capability allows the use of trained neural networks to solve similar modelling problems in any typical construction office equipped with a microcomputer. The literature on fire resistance of structural members contains a sizeable number of experimental studies and data. However, it has been very difficult to collect and isolate a coherent set of values for the fire resistance of structural members. Most of these data are scattered and obtained under varying material and experimental conditions. The use of ANN could prove its superiority over all other methods in predicting resistance of structural members.
References [1] Nasser KW, Neville AM. Creep of concrete at elevated temperatures. ACI J Proc 1965;62(12): 1567–80. [2] Abrams M. Compressive strength of concrete at temperatures to 16001F. Temperature and concrete. ACI Special Publication, SP-25, American Concrete Institute, Detroit, MI, USA, 1968. p. 33–58. [3] Schneider U, editor. Strength losses of concrete at high temperatures, cause and effects. Mitteilungsblat fur die Amtliche Material Prufung Niedersachen, Jahrg. 18/19, Hochschule Goslar, S., 1979. p. 50–7. [4] Schneider U, editor. Properties of materials at high temperatures concrete, 2nd ed. RILEM Report, Kassel University, Kassel, 1986. [5] Anderberg, Y., Thelandersson, S., Stress and deformation characteristics of concrete at high temperatures. Bulletin 34, Division of Structural Mechanics and Concrete Construction, Lund Institute of Technology, Lund, Sweden, 1973. [6] Terro MJ. Numerical modelling of the behaviour of concrete structures in fire. ACI Struct J 1998;95(2):183–93. [7] Lippman RP. An introduction to computing with neural nets. IEEE ASSP Mag 4 1987;4(2):4–22. [8] Caudill M. Neural networks primerFPart I. AI Expert, December 1987. p. 46–55. [9] Moselhi O, Hegazy T, Fazio P. Neural networks as tools in construction. J Construct Eng Manage 1991;117(4):606–25. [10] Rahal K, Abu Kiefa M. Neural networks for calculation of shear strength of reinforced and prestressed concrete beams. Kuwait J Sci Eng 1999;26(2):239–51. [11] Mo YL, Lin SS. Investigation of framed shearwall behaviour with neural networks. Mag Concrete Res 1994;46(169):289–99. [12] Rumelhart DE, Hinton GE, Williams RJ. Learning internal representation by error propagation. In: Rumelhart DE, McClelland JL, PDP Research Group, editors. Parallel distributed processing. Cambridge, MA: MIT Press, 1986. p. 318–62.
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[13] Becker J, Breseler B. FIRES-RC, a computer program for the fire response of structures-reinforced concrete frames. Report No. UCB FRG 74-3, Fire Research Group, University of California, Berkeley, 1974. [14] Anderberg Y. Exposed hyperstatic concrete structuresFAn experimental and theoretical study. Bulletin 55, Institute of Technology, Lund, Sweden, 1976. [15] Wainman DE, Kirby BR. Compendium of UK standard fire test data: unprotected structural steel-1. Ref. No. RS/RSC/S10328/87/B, British Steel Corporation, Swinden Labs, Rotherham, 1987. [16] Lie TT. Fire resistance of circular steel columns filled with bar-reinforced concrete. J Struct Eng, ASCE 1994;120(5):1489–509. [17] Lie TT, Stringer DC. Calculation of the fire resistance of steel hollow structural section columns filled with plain concrete. Can J Civil Eng 1994;21(3):382–5. [18] Sakumoto Y, Okada T, Yoshida M, Tasaka S. Fire resistance of concrete-filled, fire-resistant steeltube columns. J Mater Civil Eng, ASCE 1994;6(2):169–84. [19] Chien-Hung Lin, Chiou-Shyong Tsay. Deterioration of strength, stiffness of reinforced concrete columns after fire. J Chin Inst Eng 1990;13(3):273–83. [20] Kodur VKR, Lie TT. Fire performance of concrete-filled hollow steel columns. J Fire Prot Eng 1995;7(3):89–98. [21] Lie TT, Kodur VKR. Fire resistance of steel columns filled with bar-reinforced concrete. J Struct Eng, ASCE 1996;122(1):30–6. [22] Kodur VKR. Behaviour of high strength concrete-filled steel columns exposed to fire. Proceedings of the 1997 Annual Conference of the Canadian Society for Civil Engineering, vol. 7, 1997. p. 183–92. [23] Kodur VKR. Design equations for evaluating fire resistance of SFRC-filled HSS columns. J Struct Eng, ASCE 1998;124(6):671–7. [24] Dotreppe JC, Franssen JM, Vanderzeypen Y. Calculation method of reinforced concrete columns under fire conditions. ASI Struct J 1999;96(1):9–18. [25] Chan YN, Jin P, Wang JS, Anson M. Fire resistance of concrete: prediction using artificial neural networks. Mag Concrete Res 1998;50(4):353–8. [26] Terro MJ. Numerical modelling of thermal & structural response of reinforced concrete structures in fire. Ph.D. thesis, Department of Civil Engineering, Imperial College, 1991. [27] Lie TT, Chabot M. Experimental studies on the fire resistance of hollow steel columns filled with plain concrete. Internal Report No. 611, Institute for Research in Construction, National Research Council of Canada, Ottawa, Canada, 1992. [28] Carpenter WC, Hoffman ME. Training backprop neural networks. AI Expert, March 1995. p. 30–3. [29] NeuroShell2s Release 4.0. Ward Systems Group, Inc., Frederick, MD, USA, 1998.
Prediction of fire resistance of concrete filled tubular steel columns using neural networks Abdullateef M. Al-Khaleefia,*, Mohammad J. Terroa, Alex P. Alexb, Yong Wangc a
Civil Engineering Department, College of Engineering & Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait b Engineering Systems Group, P.O. Box 5336, Safat 13054, Kuwait c UMIST, Manchester University, UK Received 17 August 2000; received in revised form 21 August 2001; accepted 20 October 2001
Abstract A functional relationship between the fire resistance of a concrete filled steel column and the parameters which cause the fire resistance is represented using an artificial neural network. Experimental data obtained from previous laboratory fire tests are used for training the neural network model. The model predicted values are compared with actual test results. The results indicate that the model can predict the fire resistance with adequate accuracy required for practical design purpose. The developed neutral network can be used to predict the fire resistance of similar columns under fire by observing various factors influencing the resistance such as: (a) structural factors, (b) material factors, and (c) loading conditions. The structural engineer is required to provide the magnitude of these influencing factors as inputs to the neural network and the network will predict the fire resistance, based on the combined effect of these factors. This system can be used by structural engineers to predict the resistance of fire in similar concrete filled steel columns without conducting costly fire tests, by using the known parameters such as column dimensions, column height, and loading conditions. r 2002 Published by Elsevier Science Ltd. Keywords: Artificial neural networks; Construction; Fire resistance; Structural analysis
*Corresponding author. Tel.: +965-4817240; fax: +965-4817524. E-mail address: khaleefi@civil.kuniv.edu.kw (A.M. Al-Khaleefi). 0379-7112/02/$ - see front matter r 2002 Published by Elsevier Science Ltd. PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 6 5 - 0
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1. Introduction Concrete and structural steel constructions are exposed to elevated temperature in many types of structural loading. Most evident examples of such structures/loading are nuclear power stations and accidental fires in residential buildings. Growing concerns about the safety of structures in general and under elevated temperature conditions, in particular, have been witnessed during the last few decades [1–6]. The theory of the behaviour of the structure in the event of a fire is still not fully developed due to the complexity of the problem and the large number of parameters controlling this behaviour. The prediction of the fire resistance of a concrete/steel construction under accidental fire is important for the design of the structure so that it resists load for a period of time sufficient for the rescue operations. It is also important for subsequent assessment of the residual capacity of the members of the structure for its rehabilitation in the aftermath of the fire. This research paper considers the use of artificial neural networks (ANN) in predicting the fire resistance of concrete-filled tubular steel columns. The choice of this type of structural member was based mainly on three reasons: *
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*
Concrete-filled steel columns are used in constructions as fire-resistant members as such sections are very efficient in resisting compressive loads. Due to the confining action of the steel on concrete and protection from direct contact with flame (there is no spalling in such sections), fire resistance data available in the literature are more coherent and suitable for use in ANN models. Fire resistance data on concrete-filled steel columns have been well studied and are abundant in the literature.
The proposed prediction method utilises neural networks, an AI-based technique that emulates the human ability to learn from the past experience and derive quick solutions to new situations. The developed neural network based prediction model can be used by structural engineers to predict the fire resistance of similar structural members.
2. Artificial neural networks Artificial neural networks, also known as connectionist systems, are a class of modelling tools inspired by the workings of biological neural systems. ANN are composed of neurons or processing elements (PE) and connections which are organised in layers: an input layer, middle or hidden layer(s), and output layer, as illustrated in Fig. 1. It is clear from the figure that the input parameters (neurons) are connected to the output parameters (neurons) through the hidden layer (neurons). The signals entering the input layer flow to the output layer through the middle layer(s), with the input signals detailing the problem to be solved and the output signals representing the network’s solution to that problem. The connections between the neurons are associated with numerical values called connection weights which determine the influence of one neuron on another. The connection weights
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Fig. 1. (a) An artificial neural network with three layers, (b) activities at the neural network node.
modify the output signal on each of the connection paths making some connections stronger and other connections weaker. The neurons in the input layer receive their activation from the environment, while the activation levels of neurons in the middle and output layers are computed as a function of the activation levels of the neurons feeding into them. Typically, this involves the summation of all incoming signals (along with a bias associated with the middle layer neuron) followed by the application of a non-linear function termed the activation function or transfer function. Artificial neural networks allow self-learning, self-organisation and parallel processing, and are well-suited for problems involving matching of input patterns to a set of output patterns where deep reasoning is not required. A good introduction to the general field of ANNs can be found in [7] or [8]. ANNs have been successfully used in many fields of engineering. Ref. [9] provides a detailed description about the fundamentals of neural networks along with their potential applications in civil and construction engineering. It has also been recently used as a predictive tool in civil engineering research work [10,11]. During the training process, the connection weights are learned by the network as training examples are presented repeatedly. The training process can be supervised or unsupervised. In supervised training (the approach adopted for the work presented here) the connection weights are modified continuously until the error between the desired output and the actual output is minimised. The neural network modifies the weights between layers in successive iterations until the network is able to generate the desired output of the system to within a specified accuracy or until the user-specified number of iterations has been performed. Knowledge is effectively learned and stored by the weights on the connections between the neurons. Once
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training has been completed, it is anticipated that the neural network will be able to generate the required output for example problems not considered during training. The back propagation algorithm is the most widely used training technique for continuous function mapping, has been shown to be theoretically sound [12], performs well in modelling non-linear functions, and is simple to code. Back propagation algorithm training develops the input to output mapping by minimising a sum squared error cost function measured over a set of training examples. The transfer function computes the activation level of a neuron from the sum of input values. The function adopted for the current problem was a sigmoidal curve, given by Transfer function ðxÞ ¼
1 1 þ ex
ð1Þ
where ‘‘x’’ is the sum of the inputs to the neuron. The sigmoidal function generates output values between 0 and 1. Another important network design variable is the learning rate coefficient (Z) which represents the degree by which the weights are changed when two neurons are excited. Each time a pattern is presented to the network, the weights leading to a neuron are modified slightly during learning in the direction required to produce a smaller error at the outputs the next time the same pattern is presented. The amount of weight modification is proportional to the learning rate. The value of Z ranges between 0.0 and 1.0, where a value closer to 1 indicates significant modification in weight while a value closer to 0 indicates little modification.
3. Fire resistance prediction Fire resistance has been predicted mainly, to date, by the following three methods: (a) Use of recommendations concerned with parameters such as the cover to main reinforcement (in concrete structures) and thickness of the member concerned. (b) Similarity with experimental results of fire tests performed on similar structures. (c) Use of predictive analytical/computational tools to calculate the fire resistance. The costs involved in setting up and testing structures under fire are very high and the number of research centres around the world capable of reliably conducting such projects is not large. Such tests are also very hazardous. The remarkable advances in the computer technology and tools have created new horizons for solving many sophisticated engineering problems including structural behaviour under fire [6,13,14]. However, analytical/computational tools used to predict fire resistance are still not fully reliable and are dependent on many thermal/structural parameters/ variables that are usually tuned and fiddled by the researchers to fit experimental results. The literature contains many studies concerned with the fire behaviour covering a wide variety of steel and concrete structures [15–24]. The experimental research and data are independent, in general, and each study is used by the researcher to study a
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certain phenomena and not as a predictive tool by itself. The subject of this paper involves the collection and implementation of such experimental data on the fire behaviour of structures and the development of predictive mathematical models using the theory of ANNs. The behaviour of concrete at elevated temperature has also been studied using ANNs [25]. The researchers collected data from the literature on the residual compressive strength of concrete after heating to elevated temperatures. These data were then used to develop the ANN model, which succeeded in predicting concrete strengths to within 10–15%. The reason for the error in the results obtained could be attributed to the multitude of sources for the collection of data, when it is known that no two concrete mixes are alike. It should also be emphasised that the term ‘‘fire resistance’’ is defined as the time elapsed before an element of structure violates a limit state when exposed to a standard fire test [26]. The work by Chan et al. [25] only considers the residual compressive strength of concrete samples and not the prediction of fire resistance. To the best knowledge of the authors, the prediction of the fire resistance of structural members has not been yet studied using ANNs and hence worthy of investigation.
4. Knowledge representation The procedure adopted to model the fire resistance prediction of concrete filled tubular steel columns consists of the following steps: 1. Identification of the major factors that influence the fire resistance of concrete filled tubular steel columns. 2. Collection of a set of experimental cases with values for these identified factors along with the respective fire resistance. 3. Coding of the laboratory test cases and corresponding value of fire resistance obtained based on experiments. 4. Development of ANN model, from the coded cases, which is capable of predicting the fire resistance of other similar concrete filled tubular steel columns. 4.1. Factors affecting fire resistance Tests on the fire resistance of hollow steel columns filled with plain concrete have been studied in Ref. [27]. Circular hollow steel tube and square hollow steel tubes were tested and reported in this research (Fig. 2). Refs. [15–24] specifically indicate the results of tests on different types of structural components such as unprotected structural steel-1, circular steel columns filled with bar-reinforced concrete, steel hollow structural section columns filled with plain concrete, etc. The objective of this paper is not to generate ANNs model for all these different components, rather the intention is to use a homogenious set of research data to explore how this new and emerging modelling technique could be used for fire research problems. Further the authors chose to study concrete filled tubular steel columns because these
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Fig. 2. An artificial neural network to predict the fire resistance of hollow steel columns filled with concrete.
components are widely used in construction and more test data were available for their experiment. The authors chose to use a data set with an adequate number of specimen data available for satisfactory development of the model using ANNs. The authors found that Ref. [27] gave them enough data as required for this paper compared to other references. The test specimens are described in detail in [27]. Measurable factors affecting the fire resistance of concrete filled tubular steel columns were identified from this study. The eight self-explanatory factors that influence the fire resistance of the concrete filled tubular steel columns were obtained from [27] are as follows: (i) water cement ratio, (ii) type of aggregate, (iii) concrete 28 days cylinder strength, (iv) steel yield strength, (v) external dimension, (vi) steel thickness, (vii) column height, and (viii) test load.
5. Development of neural network Having identified the factors that influence the fire resistance of concrete filled tubular steel columns, it is necessary to establish the training samples to develop the neural network model. Cases were obtained from the experimental study conducted by Lie and Chabot [27] as given in Table 1. The experimental data were transformed into a numerical scale and coded to generate a set of training data. If the fire resistance and the factors affecting fire resistance are known, then it is possible to develop an empirical model of this prediction process. The number of experimental data used is of course limited. As far as the neural network is concerned, it is fitting a continuous function to the training data. The number of training points that are needed to develop an accurate continuous function model depends on other factors, most notably: the complexity of the solution surface being modelled (i.e., how many hills and valleys it contains); the
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Table 1 Tests on fire resistance of hollow steel columns filled with plain concrete [27] Case # w/c
Aggregate
Concrete Steel yield External Steel Column Test Fire 28 days strength dimension thickness height load resistance cylinder (Mpa) (mm) (mm) (mm) (KN) (min) strength (Mpa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
0.49 0.49 0.49 0.49 0.49 0.51 0.51 0.51 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.37 0.49 0.49 0.37 0.37 0.37 0.37 0.36 0.49 0.37 0.27
28.6 28.6 28.6 28.6 28.6 24.3 24.3 24.3 26.3 26.3 26.3 26.3 23.5 23.5 23.5 23.5 23.5 35.9 33 33 43 35.9 43 43 49.3 33 35.9 90.5
350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 300 300 300 300 350 350 350 350 350 350 350
141.3 141.3 168.3 168.3 168.3 219.1 219.1 219.1 273.1 273.1 273.1 273.1 323.9 323.9 355.6 355.6 406.4 141.3 141.3 219.1 219.1 219.1 273.1 273.1 273.1 273.1 273.1 273.1
6.55 6.55 4.78 4.78 6.35 4.78 4.78 8.18 5.56 5.56 5.56 12.7 6.35 6.35 6.35 12.7 12.7 6.55 6.55 4.78 4.78 8.18 6.35 6.35 6.35 6.35 6.35 6.35
3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810 3810
110 131 150 218 150 492 384 525 574 525 1000 525 699 1050 1050 1050 1900 80 143 500 560 560 1050 1050 1050 715 712 1050
55 57 76 56 81 80 102 82 112 133 70 143 145 93 111 170 71 82 64 111 108 102 106 76 90 178 144 48
29 30 31 32 33 34 35
0.37 0.37 0.37 0.37 0.37 0.49 0.37
Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Siliceous Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carb.+flyash Carbonate Carbonate Carb. +sil. Fume Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate Carbonate
43 43 40.8 40.8 40.8 33 43
300 300 300 300 300 300 300
323.9 323.9 355.6 355.6 406.4 406.4 406.4
6.35 6.35 6.35 12.7 6.35 12.7 12.7
3810 3810 3810 3810 3810 3810 3810
820 1180 1335 965 1400 1900 1900
234 114 149 274 294 125 152
stochastic content of the data (i.e., one needs enough training points to prevent bias due to random fluctuations); and the number of input variables. The capability of neural networks to generalise on limited number of training data combined with the randomness in the training set will reduce the chance of bias due to the limited number of training cases.
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In this research, a continuous function-mapping network has been adopted since the values of certain output variables and the input variables are continuous. Continuous mapping functions can represent both continuous and discrete data, whereas discrete mapping functions are limited in their ability to represent continuous data. A small learning rate of 0.15 was arbitrarily chosen for the current problem since larger learning rates have often been found to lead to oscillations in weight changes resulting in a never ending learning process. One way to allow faster learning without oscillations is to make the weight change, in part, a function of the previous weight change. A momentum coefficient represents this portion of the weight change. In this study, a coefficient of 0.7 was found to perform well. The eight factors (attributes) that are considered for the prediction of fire resistance become the input variables. The number of hidden layer(s) and the number of hidden neurons in the hidden layers, provide the power of internal representation in capturing the non-linear relationship between the input and output vectors. Hence, a larger number of hidden layers and hidden neurons provides the potential for developing a more effective network. However, the addition of more hidden neurons increases the number of undetermined parameters (weights and biases) associated with the network. A large number of training examples is then needed to solve these parameters and get a good approximation of the problem domain. When too few training examples are provided, the network will try to memorise, resulting in poor generalisation. In Ref. [28] it is determined that to provide a good approximation over the problem domain, one should have overdetermined approximations, that is, the number of training pairs should be greater than the number of undetermined parameters. Undetermined parameters in neural network approximations are the weights and biases associated with the network. To capture and represent the features within a set of data there should usually be one to two hidden layers. One hidden layer with 14 hidden neurons constitutes the present network arrangement.
6. Results and discussions The generated input–output data pairs (35 cases) were divided into a training set and a test set. The test set was derived from the data set by selecting 10–20% of data pairs randomly. Table 1 indicate the whole data set for all 35 cases out of which 27 cases are used for training and 8 for testing. A neural network development software, NeuroShellt [29] was employed to train and develop the neural network. Eight input neurons and one output neuron with 14 hidden neurons constitute the neural network arrangement for the problem. Since our training data were limited in number, (the reasons of the limited number of experiment results were mentioned in the beginning of the problem) we chose the most reasonable arrangement of one hidden layer with a set of 14 neurons. We reached this number based on our extensive experience with ANNs modeling. A detailed explanation about choosing the values of these ANNs components is presented by various ANNs researchers as indicated in Refs. [7,8,12,28]. Network development was performed on an IBM
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compatible Pentium class machine (200 MHz, 96 MB RAM). The training of a neural network is stopped when the error falls below a user-specified level, or when the user-defined number of training iterations has been reached. In this case, 10,000 iterations were planned for the final training process, as this was found adequate in a series of test runs. Training took less that 5 min and the minimum mean squared error of the network, which was accumulated over all the training sample cases, reached 0.001 (Fig. 3). The network computes the mean (average) squared error between the actual and predicted values for all outputs over all patterns. The network computes the squared error for each output in a pattern (in our case, there is only one output per pattern), then the network computes the mean of that number over all the patterns in the training set. The mean squared error is computed as follows: The mean squared error for a pattern ¼
ðYiact Yipred Þ2 þ ? þ ðYnact Ynpred Þ2 ; Number of outputs per pattern ð2Þ
where Yiact is the actual (experimental) results, i ¼ 1; 2; y; n; Yipred the predicted (neural network) results and, n the number of cases. The mean squared error for a training set P Mean squared error of patterns : ¼ Number of patterns in a training set
ð3Þ
Eq. (3) yields the minimum (least) mean (average) squared error which is the minimum reached while training the network. Table 2a provides a comparison between the experimental output, and the ANN generated output for the training set, while Table 2b provides a comparison between
Fig. 3. Reduction in error over training time.
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348 Table 2 Case #
Experimental fire resistance
ANN generated fire resistance
(a) Comparison of neural network generated output vs. experimental fire resistance on training cases 1 55 57 2 57 55 3 76 79 5 81 74 6 80 79 7 102 92 9 112 117 10 133 124 11 70 67 12 143 145 13 145 146 15 111 126 16 170 161 17 71 75 19 64 68 20 111 111 21 108 89 22 102 99 23 106 83 24 76 83 26 178 172 27 144 147 29 234 244 30 114 141 31 149 166 33 294 257 34 125 127 (b) Comparison of neural network generated output vs. experimental fire resistance on test cases 4 56 71 8 82 70 14 93 97 18 82 72 25 90 90 28 48 45 32 274 281 35 152 150 Average operational error ¼1=n
X ½ððb aÞ=aÞ100 ¼ 8:5%:
the experimental output, and the ANN generated output for the test set, Table 2 shows the application of the model and the result on how best the unseen data were evaluated by the ANNs to generate the output. It can be observed that the ANN model could capture the decision process very closely. Fig. 4 plots the actual (experimental) and the predicted (neural network) fire resistance for the complete
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Fig. 4. Comparison of experimental fire resistance vs. neural network generated fire resistance.
data set. It can be observed that the predictions made by neural network closely matches with the experimental data. Fig. 4 provides the overall fit of the whole data available for the generated model. The percentage of average operational error for the test case was found to be 8.5%, which show the ability of the network to predict the change in fire resistance values with moderate to high precision. The relative weights of each input parameter for the developed ANNs model are as follows: 0.25177 0.23284 0.14700 0.13061 0.08466 0.08101 0.07212
test load external dimension steel yield strength aggregate type w=c steel thickness concrete 28 days cylinder strength
Fig. 5 shows the experimental results on the horizontal axis and the predicted results on the vertical axis. The model is limited by the data used for training such as the extent of the scatter in the value of input parameters within themselves. By using more widely varied data for training, (for example, columns of different height) the model could capture the variety in real life cases. Thus, this limitation is implied by the limitation in conducting fire experiments and the limitation in conducting large scale test in many countries and not by the proposed modelling process itself. The ANN model by itself is limited to the computer processing power available for model development. With large number of input parameters and large training data, the process requires good computing resources as large number of processing steps during each iterations.
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Fig. 5. Pair wise comparison of experimental fire resistance vs. neural network generated fire resistance.
7. Conclusion and recommendations Several approaches have been adopted during the past few decades to predict the fire resistance of structural members. These approaches were either very costly and hazardous, as in experimental fire tests, or contained some inaccuracies due to the complex nature of fire, as in the case of analytical and computational methods. A preliminary study to predict the fire resistance of concrete-filled tubular steel columns using ANNs is presented. Neural networks eliminate the need for identifying the relationship manually and do not limit the number of variables involved in these kind of problems. Furthermore, neural network automatically weeds out the insignificant variables by the process of self-organization and learning capability by assigning less weight to non-significant factors. However, setting the parameters of neural networks is an arbitrary process and the training process can be time consuming. The following conclusions have been drawn from this study: *
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A multi-layer feed forward neural-network based learning algorithm has been adopted for the development of the model. An experimental knowledge representation scheme is adopted for the development of the neural network. Thirty-five past test results are coded and used as the training and test data for the neural network. The developed model is able to establish the relationship between fire resistance of the composite element and the characteristics of its material composition and the fire environment. The predicted results compare favourably with experimental values with an average operational error of 8.5%. Such error levels are considered positive and
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*
*
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acceptable in the field of fire engineering due to the highly unpredictable nature of fire and the behaviour of elements exposed to high temperatures. Moreover, computational methods used for predicting fire resistance employ parameters used to fit their results to those of limited experimental data, sometimes without reference to a sound theoretical base. The developed ANNs model can be easily integrated with any windows-based spreadsheet system to assist in the generation of fire resistance prediction. The developed neural network can be inserted in to any cell of a spreadsheet, such as Microsoft Excelt, as a dynamic link library (DLL) and thus can easily be used in spreadsheet computations. This integration capability allows the use of trained neural networks to solve similar modelling problems in any typical construction office equipped with a microcomputer. The literature on fire resistance of structural members contains a sizeable number of experimental studies and data. However, it has been very difficult to collect and isolate a coherent set of values for the fire resistance of structural members. Most of these data are scattered and obtained under varying material and experimental conditions. The use of ANN could prove its superiority over all other methods in predicting resistance of structural members.
References [1] Nasser KW, Neville AM. Creep of concrete at elevated temperatures. ACI J Proc 1965;62(12): 1567–80. [2] Abrams M. Compressive strength of concrete at temperatures to 16001F. Temperature and concrete. ACI Special Publication, SP-25, American Concrete Institute, Detroit, MI, USA, 1968. p. 33–58. [3] Schneider U, editor. Strength losses of concrete at high temperatures, cause and effects. Mitteilungsblat fur die Amtliche Material Prufung Niedersachen, Jahrg. 18/19, Hochschule Goslar, S., 1979. p. 50–7. [4] Schneider U, editor. Properties of materials at high temperatures concrete, 2nd ed. RILEM Report, Kassel University, Kassel, 1986. [5] Anderberg, Y., Thelandersson, S., Stress and deformation characteristics of concrete at high temperatures. Bulletin 34, Division of Structural Mechanics and Concrete Construction, Lund Institute of Technology, Lund, Sweden, 1973. [6] Terro MJ. Numerical modelling of the behaviour of concrete structures in fire. ACI Struct J 1998;95(2):183–93. [7] Lippman RP. An introduction to computing with neural nets. IEEE ASSP Mag 4 1987;4(2):4–22. [8] Caudill M. Neural networks primerFPart I. AI Expert, December 1987. p. 46–55. [9] Moselhi O, Hegazy T, Fazio P. Neural networks as tools in construction. J Construct Eng Manage 1991;117(4):606–25. [10] Rahal K, Abu Kiefa M. Neural networks for calculation of shear strength of reinforced and prestressed concrete beams. Kuwait J Sci Eng 1999;26(2):239–51. [11] Mo YL, Lin SS. Investigation of framed shearwall behaviour with neural networks. Mag Concrete Res 1994;46(169):289–99. [12] Rumelhart DE, Hinton GE, Williams RJ. Learning internal representation by error propagation. In: Rumelhart DE, McClelland JL, PDP Research Group, editors. Parallel distributed processing. Cambridge, MA: MIT Press, 1986. p. 318–62.
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[13] Becker J, Breseler B. FIRES-RC, a computer program for the fire response of structures-reinforced concrete frames. Report No. UCB FRG 74-3, Fire Research Group, University of California, Berkeley, 1974. [14] Anderberg Y. Exposed hyperstatic concrete structuresFAn experimental and theoretical study. Bulletin 55, Institute of Technology, Lund, Sweden, 1976. [15] Wainman DE, Kirby BR. Compendium of UK standard fire test data: unprotected structural steel-1. Ref. No. RS/RSC/S10328/87/B, British Steel Corporation, Swinden Labs, Rotherham, 1987. [16] Lie TT. Fire resistance of circular steel columns filled with bar-reinforced concrete. J Struct Eng, ASCE 1994;120(5):1489–509. [17] Lie TT, Stringer DC. Calculation of the fire resistance of steel hollow structural section columns filled with plain concrete. Can J Civil Eng 1994;21(3):382–5. [18] Sakumoto Y, Okada T, Yoshida M, Tasaka S. Fire resistance of concrete-filled, fire-resistant steeltube columns. J Mater Civil Eng, ASCE 1994;6(2):169–84. [19] Chien-Hung Lin, Chiou-Shyong Tsay. Deterioration of strength, stiffness of reinforced concrete columns after fire. J Chin Inst Eng 1990;13(3):273–83. [20] Kodur VKR, Lie TT. Fire performance of concrete-filled hollow steel columns. J Fire Prot Eng 1995;7(3):89–98. [21] Lie TT, Kodur VKR. Fire resistance of steel columns filled with bar-reinforced concrete. J Struct Eng, ASCE 1996;122(1):30–6. [22] Kodur VKR. Behaviour of high strength concrete-filled steel columns exposed to fire. Proceedings of the 1997 Annual Conference of the Canadian Society for Civil Engineering, vol. 7, 1997. p. 183–92. [23] Kodur VKR. Design equations for evaluating fire resistance of SFRC-filled HSS columns. J Struct Eng, ASCE 1998;124(6):671–7. [24] Dotreppe JC, Franssen JM, Vanderzeypen Y. Calculation method of reinforced concrete columns under fire conditions. ASI Struct J 1999;96(1):9–18. [25] Chan YN, Jin P, Wang JS, Anson M. Fire resistance of concrete: prediction using artificial neural networks. Mag Concrete Res 1998;50(4):353–8. [26] Terro MJ. Numerical modelling of thermal & structural response of reinforced concrete structures in fire. Ph.D. thesis, Department of Civil Engineering, Imperial College, 1991. [27] Lie TT, Chabot M. Experimental studies on the fire resistance of hollow steel columns filled with plain concrete. Internal Report No. 611, Institute for Research in Construction, National Research Council of Canada, Ottawa, Canada, 1992. [28] Carpenter WC, Hoffman ME. Training backprop neural networks. AI Expert, March 1995. p. 30–3. [29] NeuroShell2s Release 4.0. Ward Systems Group, Inc., Frederick, MD, USA, 1998.