Application of artificial neural network to forecast

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Engineering, Construction and Architectural Management Application of artificial neural network to forecast construction duration of buildings at the predesign stage SDHABHON BHOKHA STEPHEN O. OGUNLANA

Article information: To cite this document: SDHABHON BHOKHA STEPHEN O. OGUNLANA, (1999),"Application of artificial neural network to forecast construction duration of buildings at the predesign stage", Engineering, Construction and Architectural Management, Vol. 6 Iss 2 pp. 133 144 Permanent link to this document: http://dx.doi.org/10.1108/eb021106

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Engineering, Construction and Architectural Management 1999 6 | 2, 133-144

Application of artificial neural network to forecast construction duration of buildings at the predesign stage

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S D H A B H O N B H O K H A & STEPHEN O. O G U N L A N A School of Civil Engineering, Asian Institute of Technology, P.O.Box 4, Khlong Luang, Pathumthani 12120, Thailand

Abstract The application of an artificial neural network (ANN) to forecast the construction duration of buildings at the predesign stage is described in this paper. A three-layered back-propagation (BP) network consisting of 11 input nodes has been constructed. Ten binary input nodes represent basic information on building features (i.e. building function, structural system, foundation, height, exterior finishing, quality of interior decorating, and accessibility to the site), and one real-value input represents functional area. The input nodes are fully connected to one output node through hidden nodes. The network was implemented on a Pentium-150 based microcomputer using a neurocomputer program written in C + + . The Generalized Delta Rule (GDR) was used as learning algorithm. One hundred and thirty-six buildings

built during the period 1987-95 in the Greater Bangkok area were used for training and testing the network. The determination of the optimum number of hidden nodes, learning rate, and momentum were based on trial-and-error. The best network was found to consist of six hidden nodes, with a learning rate of 0.6, and null momentum. It was trained for 44700 epochs within 943 s such that the mean squared error (judgement) of training and test samples were reduced to 1.17 x 1 0 - 7 and 3.10 x 1 0 - 6 , respectively. The network can forecast construction duration at the predesign stage with an average error of 13.6%. Keywords artificial neural network (ANN), back-propagation, duration estimating, Generalized Delta Rule (GDR), predesign stage, supervised training and testing

INTRODUCTION

dra%vbacks. With increased competition in the con­ struction industry, the essence of forecasting, there­ fore, emphasizes not only its accuracy but also attempts to minimize the associated effort. Few re­ searchers have addressed the problem of forecasting project duration. Examples include forecasting of pre­ design construction duration (Sadashiv 1979), and the relationship between value and duration of construc­ tion projects (Kaka & Price 1991). These two studies introduce approaches, methodologies and frameworks for best utilizing historical information on completed projects to aid duration forecasting. Applications of the methods suggested are made difficult by the complex­ ity of projects. This paper addresses the forecasting of construction duration at the early stage of project development when only a few project parameters are known and designs are not yet well developed.

The number of high-rise buildings constructed in the Greater Bangkok area has increased dramatically in the last two decades. This has transformed both the con­ struction industry and the real-estate business in the city. The buildings have specific features and charac­ teristics. Post-tensioned slab has become the most popular system as the absence of beams maximize the number of floors in a given building. Basements are considered necessary to facilitate parking and the ac­ commodation of systems and utilities. Exterior walls tend to be changing from brick or cement block walls to curtain walls. The need for high quality decorating has gradually increased. Some building sites have poor accessibility, which creates difficulties in construction, design, as well as construction duration forecasting, especially at the early stages of project development. Forecasting construction duration at the predesign stage uses only basic and available information, e.g. schematic plans, basic engineering systems, and design criteria. A planner should have the ability to anticipate design decisions and assumptions. He or she should also have full knowledge of construction activities and sequencing. The procedure is heuristic, intuitive, fast, and valuable in solving the problems but is not without

© 1999 Blackwell Science Ltd

LITERATURE R E V I E W Construction duration forecast Construction duration is the time required to complete a specified task or activity which is determined by the owner's needs to occupy, utilize, or rent the completed space in a project (Callahan et al. 1992; Nkado 1995).

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It can be derived from the critical path in which duration for items of work or activity in sequence cannot be reduced further (Barrie & Paulson 1992), or determined from an examination of one or more mediods of carrying out the works on the basis of minimum cost, and the forecast is usually done, in the first instance, for normal conditions (Nkado 1992; Pilcher 1992). In this research, construction duration is defined as the time-frame given by the owner for the contractor to complete the project under normal work conditions, and normal construction practice. Chan & Kumaraswamy (1995) noted that precon­ tract determination of construction duration is essen­ tial for proper cash flow forecasting by both the contractor and the client. It can facilitate optimal resource allocation, financial planning, profitability and efficiency of capital flow within a predetermined time limit. Based on the inputs required for schedul­ ing, all the current mediods of scheduling, i.e. Gantt or bar chart, the Critical Path Method (CPM), and the Program Evaluation and Review Technique (PERT), seem to be most applicable only when the detailed design is completed. Without sufficient information, the schedule can be prepared based only on the best guess, i.e. extrapolating using experience of similar projects (Pilcher 1992).

Factors affecting construction duration and their representation There are many factors affecting construction duration and its forecasting. The larger the building size (i.e. in m 2 ), the more complex the construction, thus needing longer time to complete (Sadashiv 1979; Ireland 1985; Ashworth 1988; Nkado 1992; Pilcher 1992). The function of a building implies the business target that the building serves, e.g. office, retail, and other build­ ings. It can be considered as a qualitative variable (Nkado 1992). The height of a building, represented by the number of floors, indicates the construction technique, major equipment needed, and construction sequence, all of which affect construction duration (Sadashiv 1979; Ireland 1985; Callahan et al. 1992). Complexity can be represented in the form of con­ struction equipment, mediod and sequence (Sadashiv 1979; Callahan et al. 1992; Chan & Kumaraswamy 1995). Quality can be classified by variables or at­ tributes, i.e. appearance, strength, stability, materials used, performance, finishes, etc. (Ashworth 1988). Sadashiv (1979) considered the number of major finishing works in his duration forecasting model in­ stead of a defined quality index. The location of a

building has a significant effect on construction dura­ tion, i.e. whether or not restrictions or easements exist, availability of services, supply of resources, use of major equipment, and productivity on site (Sadashiv 1979; Callahan et al. 1992; Chan & Kumaraswamy 1995). Construction technology changes slighdy with the passage of time (Ashworth 1988). Therefore, a model for forecasting the construction duration should be valid in application for a reasonably long period of time without the effects from changes in price level.

Artificial neural networks: definitions and basic concept Artificial neural networks (ANNs) may be called by different names: (1) connectionist models; (2) parallel distributed processing models; (3) neuromorphic sys­ tems; and (4) neural computing. ANN is a branch of artificial intelligence (Al) in which structures are based on the biological nervous system. It can exhibit a surprising number of the human brain's characteris­ tics, e.g. learn from experience and generalize from previous examples to new problems. ANN can provide meaningful answers even when the data to be pro­ cessed include errors or are incomplete, and can pro­ cess information extremely rapidly when applied to solve real world problems (Lippmann 1988; Smidi 1993). Neurocomputing architectures can be built into physical hardware (or neurocomputer, or machine) or neurosoftware languages (or programs) that can think and act intelligently like human beings. Among various architectures and paradigms, the back-propagation network is one of the simplest and most practicable network being used in performing higher level human tasks such as diagnosis, classification, decision-making, planning, and scheduling. The neural network based modelling process involves five main aspects: (1) data acquisition, analysis and problem representation; (2) architecture determination; (3) learning process deter­ mination; (4) training of the network; and (5) testing of the trained network for generalization evaluation, (Wu & Lim 1993). Fig. 1 shows how biological and artificial neural cells operate. BP networks have two main characteristics: (1) they are multilayered in structure; and (2) they incorporate transfer functions, e.g. sigmoid function for their pro­ cessing elements. Learning or training takes place in an iterative fashion. The summation function, which finds the weighted average of all input elements to each processing element, then, multiplies the input values (5,) by the weight (Wij) and totals them together for a weighted sum (a ω ) plus a bias (bj), thus:

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Application of artificial neural network to forecast construction duration of buildings

A continuous, nonlinear, and differentiable logistic function is used as a transformation function (or trans­ fer function, or local memory). It yields output of real value between 0 and 1. When a node in the hidden or output layer receives its inputs from other nodes im­ pinging on it, the activation levels will be computed. Based on this activation level, the node may or may not produce output by means of transformation. The learning rate, ;;, the constant of proportionality, pro­ vides dynamic access to the rate at which weights may be changed. A high learning rate corresponds to rapid learning which might push the training towards a local minimum or cause oscillation while small learning rates need a longer time to reach a global minimum (Khan et al. 1993; Smith 1993). The remedy for the problem of balancing the learning rate is to apply a momentum factor, which is multiplied by the previous weight change so that while the learning rate is con­ trolled the changes are still rapid.

Applications of ANNs in construction A number of researchers have applied ANNs in con­ struction management, principally for decision-mak­ ing, forecasting, and optimization. Kamarthi et dl. (1992) used a two-layered BP network for selecting vertical formwork systems. Murtaza & Deborah (1994) used an unsupervised neural network with the Khonen algorithm for decision-making on construction modu­ larization. Soemardi (1996) used two fuzzy neural networks for solving group decision-making in select­ ing a wall system under multiple criteria. William (1993) developed back-propagation networks for pre­ dicting changes in the construction cost index. Chao & Skibniewski (1994) used neural network and an obser­ vation-data-based approach to estimate construction

operation productivity. Hegazy & Moselhi (1994) used back-propagation artificial neural networks to develop an optimum markup estimation model that derived solutions to new bid situations. Li (1996) used an ANN to model construction cost estimation. McKim et al (1996) used a neural network to predict effective­ ness of a construction firm. Elazouni et al. (1997) used ANNs to estimate the required resources of concrete silo walls at the conceptual design stage. ANNs can also be applied for design, planning, and management. Mawdesley & Carr (1993) investigated the possibility of using ANNs to produce project planning networks to substitute the shortage of skilled planners and the ever increasing complexity of projects. Chua et al. (1997) used ANNs to identify the key management factors affecting budget performance in a project. AlTabtabai et al. (1997) used a BP network to capture the decision-making procedure of project experts in­ volved in schedule monitoring and prediction for mul­ tistorey building projects under construction. Adeli & Wu (1998) developed a regularization neural network to estimate the cost of reinforced concrete pavement. Hegazy & Ayed (1998) used the neural network ap­ proach to develop a parametric cost-estimating model for highway projects. Thus, ANNs are being increas­ ingly used for construction management research. A notable gap is that none of the aforementioned works is concerned with duration forecasting at the predesign stage.

O B J E C T I V E S A N D SCOPE This paper applies ANN to forecast the construction duration (in months) of buildings at the predesign stage. The subobjectives are: (1) to design and build an ANN for construction duration forecasting; (2) to test the accuracy of estimates made by using the ANN in terms of the mean squared error (MSE); (3) to test

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whether the forecasting errors using the network is related to project duration; and (4) to make recom­ mendations regarding how to implement the ANN for duration forecasting. Buildings which are higher man 23 m and with a functional area not less than 10000 m 2 are taken into consideration in this work. In Thailand, the Ministry of Interior requires buildings conforming to these two criteria to provide a fire extinguisher system. These prescreened criteria prevent large variations in the features of the buildings covered.

THE D E V E L O P M E N T OF THE A N N M O D E L One hundred and thirty-six building samples situated in Greater Bangkok were obtained either by direct interview or through examination of historical records from various sources, e.g. former research, contractors, owners, consultants, designers, quantities surveyors,

and suppliers. Preanalysis of the obtained samples was carried out for six reasons: (1) to ensure the sufficiency and completeness of samples; (2) to know the charac­ teristics of each variable; (3) to select only variables that have a major effect on the output; (4) to exclude ineffective or redundant variables; (5) to determine the most efficient way of representing the variables; and (6) to split the samples into training and testing sets. The samples were equally divided into two parts for the purposes of training and testing. Fig. 2 shows the construction duration of buildings during 1987-95. It is evident from the figure that a ceiling value of 60 months is sufficient to complete a high-rise building which has an average height of 25 floors. This value is considered valid for some years to come and has been adopted in this work. Moreover, the single output node is easy to train as it is understandable to practi­ tioners. Therefore, all the values of construction dura­ tion (Tm) are normalized by the minimum and

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Application of artificial neural network to forecast construction duration of buildings

Table 1 Covariance for 11 input variables

Variable no. Variable no. Variable no. 1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

6

7

8

9

10

11

-0.133

-0.133 -0.198

-0.133 0.046 0.250

-0.133 -0.050 -0.050 0.168

-0.133 -0.005 0.053 -0.157 0.195

-0.133 -0.007 0.007 -0.004 0.005 0.250

-0.133 -0.024 0.052 -0.042 0.068 0.131 0.191

-0.133 0.137 0.057 -0.063 0.101 -0.084 -0.096 0.245

-0.133 -0.133 -0.152 0.041 -0.071 0.088 0.094 -0.241 0.246

-0.133 0.042 0.149 -0.040 0.069 0.012 0.017 -0.033 0.028 0.228

-0.133 0.023 -0.058 0.013 0.005 0.038 0.015 -0.010 0.012 0.043 0.216

-0.198 0.046 -0.050 -0.005 -0.007 -0.024 0.137 -0.133 0.042 0.023

0.250 -0.050 0.053 0.007 0.052 0.057 -0.152 0.149 -0.058

0.168 -0.157 -0.004 -0.042 -0.063 0.041 -0.040 0.013

0.195 0.005 0.068 0.101 -0.071 0.069 0.005

0.250 0.131 -0.084 0.088 0.012 0.038

0.191 -0.096 0.094 0.017 0.015

0.245 -0.241 -0.033 -0.010

0.246 0.028 0.012

0.228 0.043

0.216

-

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Covariance between the two variables (x and y) is: Cov(x, y) = E(xy) — E(x)E(y), where E(x) and Ely) are the expected values (means) of x and Y-

maximum values (12 and 60 months) such that only a single real-value output (7**) between 0 and 1 is provided. The normalization is performed using equa­ tion (2) below: T*m = (Tm -

Tmin)

/(Tmax

-

Tmin)

(2)

where Tm = target or actual output of the mth sample; T min = minimum target output found from all the sam­ ples; and Tmax = maximum target output found from all the samples. Eleven independent variables were selected which are: (1) building function (two nodes); (2) structural system (two nodes); (3) functional area (one node); (4) height index (one node); (5) complexity of foundation works (one node); (6) exterior finishing (two nodes); (7) decorating quality (one node); and (8) site accessibility (one node). Ten of the variables are binary while only the functional area is a real-value variable. The two nodes for building function can have the values (1,0) for residential construction; (0, 1) for an office; (1, l)for a building with dual functions; and (0, 0) for other buildings. Buildings classified under the category 'other buildings' include hospitals, shopping malls, and multi­ purpose buildings. The two nodes for structural system indicate whether a building is of conventional or cast-inplace reinforced concrete (1 and 0), or RC frame with post-tensioned slab (0 and 1), or other systems (0 and 0), e.g. RC frame with precast slab, and RC-steel composites. A single real-value node is used to represent functional area (in fractions of 10 6 m 2 ). One node represents the height of building (in number of floors) when compared to the mean height found in the whole sample (25 floors). Therefore, medium height is given the value 0 when the number of floors is less than or

equal to 25, and a high building is given the value 1 when the number of floors is more than 25. One input indicates the complexity of foundation work, i.e. whether construction is simple (0) or complex (1). Examples of complex foundation works are multistorey basements, raft foundations, and diaphragm walls. Two nodes represent exterior finishings. Brick or cement block wall with plastering is represented as (1, 0) and frame with glass or curtain wall is represented as (0, 1). The two nodes can take the value 0 when other kinds of exterior finishings are used (e.g. prefabricated panel) are used. One input represents normal (0) or excellent decorating (1). An excellently decorated building must conform to four criteria: (1) have premium class of sanitary fixtures and accessories; (2) use luxury electrical accessories; (3) have premium class of carpet, floor tiles, wall paper or specially decorated walls; and (4) have premium class of built-in furniture. The term 'premium class' means that the products are not widely available in the market but are produced or manufactured accord­ ing to specific orders by the customer, and the costs are much higher than the cost of regular products. The last node indicates good (0) or poor (1) accessibility to the building site. Two criteria for poor accessibility are: (1) limited freedom for selecting the types of pile; and (2) traffic constraints on delivery of materials to the site. Whereas ANNs are distribution-free models, it is perhaps helpful to verify the covariance of the variables. Table 1 shows the relative low covariance of all the variables indicating that they are not correlated. The predictiveness of each variable is verified through prun­ ing of the network. The 136 samples were split into two equal sets for training and testing. Table 2 summarizes the percent-

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Table 2 Preanalysis and statistics of building samples for duration forecasting

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Item and Description

Input node

Building feature

Training set Projects (%)

Testing set Projects (%)

Total samples Projects (%)

1.

Building function

1 2

Residence only Office only Dual (resident+office) Others

26(19.1) 35 (25.7) 3 (2.2) 4 (2.9)

37 (27.2) 24 (17.6) 3 (2.2) 4 (2.9)

63 (46.3) 59 (43.4) 6 (4.4) 8 (5.9)

2.

Structural system

3 4

Cast-in-placed RC RC frame + PC slab Others

15 (11.0) 51 (37.5) 2(1.5)

14 (10.3) 49 (36.0) 5 (3.7)

29(21.3) 100 (73.5) 7 (5.1)

3.

Functional area (m) (x10 6 m2)

5

Min./Max. Average

4.

Height index

6

Nos. of floor > 25 Nos. of floor ≤ 25

40 (29.4) 28 (20.6)

29(21.3) 39 (28.7)

69 (50.7) 67 (49.3)

5.

Foundation index

7

Complex Simple

56(41.2) 12 (8.8)

45 (33.1) 23 (16.9)

101 (74.3) 35 (25.7)

6.

Exterior finishing (walls)

8 9

Brick/cement block Curtain wall/glass Others

24 (17.6) 43 (31.6) 1 (0.7)

34 (25.0) 34 (25.0%) 0 (0.0)

58 (42.6) 77 (56.6) 1 (0.7)

7.

Decorating quality

10

Excellent Normal

19 (14.0) 49 (36.0)

29 (21.3) 39 (28.7)

48 (35.5) 88 (64.7)

8.

Accessibility to site

11

Difficult Easy

21 (15.4) 47 (34.6)

22 (16.2) 46 (33.8)

43 (31.6) 93 (68.4)

9.

Nos. of floors

Min./Max. Average

10.

Area/floor ratio

Min./Max. Average

373/20 100 2240

743/6907 2160

373/21 100 2205

11.

Construction duration (months)

Min./Max. Average

12/60 27.7

12/60 27.9

12/60 27.8

12.

Construction cost (Baht/m2)

Min./Max. Average

6034/14 000 10513

6364/14 643 10 391

6034/14 643 10 452

0.011/0.201 0.060

7/61 28.1

0.010/0.221 0.054

7/63 25.0

0.010/0.221 0.057

7/63 26.5

Values in parentheses show the percentage belonging to a category as compared to the total 136 samples.

age for each category (building function, structural system, height index, foundation index, exterior finish­ ing, decorating quality, and accessibility to the site) when compared to the whole 136 samples, the mini­ mum, the maximum, the average values for the func­ tional area, number of floors, area/floor ratio, construction cost and duration. Therefore, a network with 11 input nodes, one hidden layer, and one output node was built. Fig. 3 shows the topology of the three-layered BP network. This study uses the sigmoid transformation function:

Learning rate and momentum are applied based on trial-and-error at 0, 0.6, 0.7, 0.8, and 0.9, respectively. Each iteration cycle involves a forward propagation step for which activation level is computed, then the transformation function may or may not produce the output to the node in the next layer. The outputs produced by the network (O m ) and the desired output (T m ) of n samples are compared, the sum of squared error (SSE) between both is minimized:

f(N) = l / [ l - e x p - ( N - 6 ) ] where iV=the computed net input result from activa­ tion levels or function; and b = internal threshold (or offset or bias).

where n = number of samples used; Tkm = target or actual output at node k of the mth sample; and Okm = computed output (by the network) at node k of the mth sample.

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Application of artificial neural network to forecast construction duration of buildings

The mean squared error (MSE) can be determined as follows:

Training and testing stopped when either of two criteria were met: (1) SSE was less than the specified value, i.e. 0.001 (or MSE is less than 0.00001); or (2) the number of epochs reach 25000. Subsequently, the successfully trained network is trained again with a different number of epochs. The final set of weights and biases is obtained when two criteria are met: (1) SSE of the training set is less than the specified value; and (2) SSE of the test set is minimum. The best network was chosen by using the latter criterion. The SSE of training set converged orderly without oscillation.

RESULTS A N D D I S C U S S I O N The best network was found to consist of six hidden nodes and one output node. The learning rate and momentum are 0.6 and 0 respectively. The sum of squared error (SSE) on the test samples has a mini­ mum value 2.11 x l O - 4 (MSE = 3.10 x 1 0 - 6 ) at 44700 epochs of training whereas the SSE on training samples is 7.97 x l 0 - 6 ( M S E = 1.17 x 1 0 - 7 ) . The learning process takes 943 s. Fig. 4 presents the final weights and biases of the {11, 6, 1} network. It could not be pruned further. The calculated outputs of the 68 test samples can be grouped into two categories. Twenty-five projects (36.8%) are underestimated, while 43 projects (63.2%) are overestimated. The underestimates range from —73.3% to —1.7%, with an average value of

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— 8.0%. The overestimates range from 3.7% to 150.0%, with an average value of 26.2%. The average error for the 68 test samples is 18.2%. The results obtained show that the network overestimates more than it underestimates. Fig. 5 presents errors of predesign construction du­ ration forecasting on the tested samples. With the average error of 18.2%, the forecasted minimum, max­ imum, and average construction durations are 14.2, 70.9, and 32.9 months instead of 12, 60, and 27.8 months as per the design. In practice, apart from the actual duration spent for construction activities, the contractor may lose time for slow start-off, e.g. preparing the site office, mobilizing equipment and manpower, and delivering materials. Time lost can also be caused by late finish of activities, e.g. cleaning the site, remedial works, and completing the landscap­ ing. Two other major factors affecting the construction duration are unforeseen circumstances or situations

and change orders. The former may be caused by: (1) delivery of materials; (2) shortage of manpower; (3) geographic conditions; and (4) weather. The latter may require the contractor to alter the work plan, schedule, and procedure. Even though there is no range of accuracy for construction duration forecasting given in construction literature, forecasting by the ANN is considered acceptable for serving the feasibil­ ity study, planning, financing, decision-making, and bidding purposes. T o verify the relationship between forecasting error and construction duration, all the 136 training and test samples were examined. Forty projects (29.4%) were underestimated, i.e. errors range from — 73.3% to — 1.7%, with the average at —4.6%. Ninety-six projects (70.6%) are overestimated with errors ranging from 2.4% to 150.0%, with an average of 18.2%. The average error of the 136 samples is 13.6%. However, regression curves between forecasting error and con-

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Application of artificial neural network to forecast construction duration of buildings

struction duration yielded very low values of R2 which indicate poor relationship. Therefore, forecasting er­ rors are independent of construction duration. Rather, they are dependent on factors which have been mod­ elled as the independent variables (or inputs) of the network. Relatively high errors were obtained on few samples which had extreme building features, e.g. minimum height ( 7 - 8 floors or 23.0 m), nearly mini­ mum or maximum functional area. Other factors are quality of interior decorating and site accessibility which possibly caused additional delay, e.g. material shortage, lack of special equipment and skilled work­ ers, transportation on site and other constraints.

CONCLUSIONS The forecasting of construction duration at the predesign stage, when very little project information is available, is mainly based on the knowledge and expe­

rience of the estimator. The procedure is heuristic, intuitive, fast, and valuable in solving problems. How­ ever, modern projects are becoming larger and more complex and information may increase in quantity but time for estimating may not increase proportionally. Therefore, any technological aid to the duration fore­ casting function will greatly benefit the duration forecaster. ANN structures are based on the biological nervous system which can exhibit the human brain's character­ istics, e.g. learn from experience, generalize from pre­ vious examples, infer solutions to problems beyond those to which they are exposed during training, and provide meaningful answers even when the data to be processed include errors or are incomplete. ANNs do not attempt to replace human experience and judge­ ment. Instead, they introduce the possibility to apply new approaches, methodologies and framework for the best utilization of historical duration records of com-

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Bhokha. S. & Ogunlana. SO.

pleted projects aided by computer technology, so that the planner can forecast the construction duration with high productivity and efficiency. Designing and building a network is not a straight forward process. All the inputs cannot be fed directly into the network. Instead, they need careful represen­ tation and transformation into an appropriate number of nodes and forms, e.g. binary, or normalized real value. The network's architecture, including learning paradigm and algorithm need, to be determined. The number and form of output need to be designed. The network needs training and testing for generalization capability. The number of parameters to be estimated must be minimized, especially when samples are limited. An ANN designed and built to forecast the con­ struction duration of building at the predesign stage has been described in this paper. The 11 independent variables of building features were selected based on their low covariance among one another. Training the duration forecasting networks started with 11 inputs consisting of: 1) building function (two nodes); 2) structural system (two nodes); 3) height index (one node); 4) foundation index (one node); 5) exterior finishing (two nodes); 6) interior decorating (one node); 7) site accessibility (one node); and 8) func­ tional area (one node). Even though there is no exact rule for determining the optimum number of hidden nodes, it was found from the trial-and-error that it should be between the average and sum of the input and output nodes. The most satisfactory network con­ sists of six hidden nodes, learning rate of 0.6, and null momentum. The single output node of the real num­ ber ranges from 0 to 1 representing the construction duration (months) which is normalized by the mini­ mum and maximum duration found in the samples (12 and 60 months). The {11, 6, 1} duration forecasting network yielded satisfactory results on the 68 test samples. The average error for duration forecasting is 18.2%, with standard deviation of 44.2 while the average error in the 136 projects is 13.6% with the standard deviation of 32.7. Based on the results, the network is more likely to overestimate than underestimate. An attempt was made to establish a relationship between forecasting errors from the network and pro­ ject duration. The comparison yielded low value of R2 suggesting that there is no relationship between fore­ casting errors from the network and project duration. This shows that the network is equally good at fore­ casting the duration of both long and short duration projects.

ANN shows advantages over conventional methods of construction duration forecasting at the predesign stage that use the knowledge and experience of ex­ perts. ANN needs only basic information which is available at the predesign stage. The ANN does not require measuring or determining the exact values of building dimensions and quantity of work. The infor­ mation can be input by less experienced users. Unlike regression models, verifying the covariance among the variables is not necessary for an ANN model because nonpredictive or redundant variable can be removed by pruning. However, the selection of the variables is based on low values of covariance. This justifies their inclusion in the model and significantly shortened the training process because only the important variables are considered. An ANN with hidden layer can exhibit nonlinear relationship among inputs and output which is more beneficial and simpler than multilinear, and nonlinear regression models, respectively. Due to supervised training, the networks embedded the knowledge leamt from training samples in form of "adjusted weights and biases" at minimum errors. The system error were minimized by means of the General­ ized Delta Rule. The network processes simple calcu­ lations, i.e. simply multiply the inputs to the weights and sum them up. On the hidden layer, the transfor­ mation function calculates the outputs based on the amount of weight sums and biases. In the application phase, the process is very fast. ANNs are flexible because they can incorporate errors or imperfect in­ puts, and can give meaningful answers at acceptable accuracy. Therefore, the forecasting of predesign con­ struction duration of buildings is significantly im­ proved by means of ANN. However, there are few disadvantages of which one should be aware, i.e. using the built networks to fore­ cast the construction duration needs knowledge in two fields. First, the planners should have full knowledge of construction activities and sequence. They have to understand the nature of forecasting for construction duration at the predesign stage when only litde infor­ mation of the project is available. They must be capa­ ble of transforming such information into the proper forms required by the network. Second, they should have some knowledge of ANN. They have to know how to operate the networks on the microcomputer, mechanism of the networks, and to obtain outputs. This is because ANNs lack user friendliness and expla­ nation facilities but only perform calculations as they have been trained to do. Moreover, modification or changing the ANNs' topology and learning paradigm

© 1999 Blackwell Science Ltd, Engineering, Construction and Architectural Management 6 | 2, 133-144

Application of artificial neural network to forecast construction duration of buildings

m u s t be performed only by those having good c o m ­ p u t e r skills a n d knowledge in A N N . Users w h o have n o knowledge of A N N can apply t h e A N N in parallel with conventional m e t h o d s with which they are familiar. T h e y can c o m p a r e t h e o u t p u t s from b o t h approaches until they are confident to apply t h e networks. F o r long-term application, they n e e d t o evaluate t h e A N N a n d give feedback to improve t h e efficiency of t h e A N N b y several m e a n s , i.e. building t h e user interface, explanation facilities, database m a n ­ a g e m e n t , routine m a i n t e n a n c e . It is also possible to modify

or

change

the

architecture

or

learning

p a r a d i g m of t h e A N N .

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U s i n g t h e built networks to forecast the construction d u r a t i o n of buildings at the predesign stage n e e d s knowledge in two fields. First, users m u s t have good b a c k g r o u n d in construction p l a n n i n g a n d scheduling. S e c o n d , they should have s o m e knowledge of A N N . However, users without knowledge of A N N can apply t h e network in conjunction with other conventional m e t h o d s with which they are familiar. T h e y can c o m ­ p a r e the o u t p u t s from b o t h approaches so t h a t they are confident to apply t h e network. T h e developed n e t ­ work gives n o written explanation a n d it is n o t user friendly. F u r t h e r i m p r o v e m e n t s could provide m o r e facilities such as better user interfacing, database m a n ­ a g e m e n t system a n d explanation facilities. N e t w o r k s n e e d routine m a i n t e n a n c e . Information o n newly c o m ­ pleted buildings should b e recorded. T h e

network

could b e retrained with m o r e samples to increase its generalization capability. At this beginning stage, t h e topology of t h e supervised back-propagation network is limited by t h e availability of training a n d test s a m ­ ples a n d the o u t p u t . If m o r e building samples are obtained, networks with different forms of o u t p u t s can b e trained a n d tested.

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