An
Application of Fuzzy Modeling
In Construction Engineering
Abstract
The focus of this paper is the development of a model to measure the constructability of concrete construction systems. Fuzzy Set Theory (FST) is used to quantify the importance of the primary constructability characteristics: quality, safety, cost, and scheduling. Linguistic rules are also developed to provide a verbal measure of project constructability. The developed model is a constructability assessment tool that is generic enough to allow the company to encompass the particular criteria of the project at hand and to select the construction system best suited for project execution.
Keywords: Constructability, Construction Systems, Fuzzy rules, Modus Ponens, Fuzzy Quantifier, Truth Value
Introduction
Constructability is the application of sequencing, scheduling and constraint evaluation to the building of physical structures (Pepper, 1994). This is a broad term and applies widely across the construction industry. In spite of the variation in the types of structures, the criteria for evaluating the feasibility of construction projects is highly consistent. The criteria for successful construction projects include adherence to cost, schedule, safety and a variety of other factors. These issues are the core concepts of constructability (Russel & Gugel,1993). In recent years, constructability has brought the construction industry driven scheduling, construction sequencing of design and procurement efforts, practical design. All of these factors have been instrumental in reducing cost and scheduling associated with construction projects. It is important that constructability begin in the conceptual phase of a project (Pepper, 1994). This research evaluates a constructability model that assesses the feasibility of projects while in the conceptual phase.
Constructability is a multifaceted issue in terms of finance, labor and scheduling. These characteristics can significantly impact the success of a construction project. The available literature provides a reasonable amount of material on the benefits of constructability (Malek, 1996). Previous researchers have defined constructability, analyzed it and different implementation procedures have been discussed. Other studies have been conducted to format structured methodologies which improve the constructability of the projects. However, despite the advance in the construction methods, there is an absence of tools to comprehensively measure constructability. The shortcomings in the literature appear to be in reaching an agreement on the discipline and/or the methodology used to assess and to quantify the constructability.
This paper introduces a methodology leading to a model using FST. This model will be capable of assessing the constructability issue, a task which so far has not been performed satisfactorily, if at all. The major criteria in constructability include cost, scheduling, quality and safety (Russel & Gugel,1993). "The general meaning of constructability involves construction-oriented input into the planning, design and field operations of a construction project”(Pepper, 1994). The success and importance of the constructability review team is measured by the extent to which they anticipate construction problems and their ability to solve them at the onset. A decision that will affect to a great extent, the constructability of a project is the choice of the construction system to be used for the execution of the project.
A construction system, as defined for the purpose of this paper, is a practical methodology that describes a series of steps to be implemented for the purpose of erecting a structure. The construction systems considered in this paper have already penetrated the market and showed innovation in at least one of the following issues: materials used, erection operation or manufacturing technique (NAHB Research Center, 1993). To date, assessment of construction systems has been primarily decision based on intuition and heuristic experience. Intuition, experience and judgment are precisely the ingredients needed to form a set of linguistic rules in which parameters are defined as fuzzy sets in constructability and this ability to manipulate non-crisp data provides great incentives for the application of fuzzy logic to determine the degree of constructability of a system for a particular project. Civil engineering is highly compatible with fuzzy set theory due to the inherent variability in this field. When compared to other engineering branches, construction is fundamentally different, especially from the design point of view. This is primarily because the structural theories are rarely a perfect match to the design problem. Also, from the execution aspect, each project is uniquely defined by its characteristics and situation. FST has the ability to accommodate this variability. This paper develops a methodology leading to a model for constructability assessment using FST. This model predicts constructability and provides numeric and linguistic outputs to suggest the overall constructability of the project.
Fuzzy Set Theory for Constructability Assessment
Fuzzy representation is a useful tool in defining and evaluating problems commonly encountered in construction andcivil engineering (Bousbaine, 1991). Civil Engineering differs from other engineering disciplines in that each civil engineering project is generally unique in its characteristics. Hence, there is little chance to test a prototype, as in some other engineering disciplines (Klir, 1995). Consequently, the uncertainty in applying theoretical solutions to civil engineering projects is large. The designer has to make decisions in spite of the high uncertainty he/she faces. Because the standards of safety required by the general public regarding civil engineering constructions (such as bridges, buildings, dams, etc.) are extremely high, the manner in which the designer deals with this uncertainty is crucial.
It is an interesting paradox that data based on fuzzy variables provide more accurate evidence about real phenomena, than data based upon crisp variables. Since fuzzy variables capture measurement uncertainties as part of experimental data, they are more attuned to reality than crisp variables (Klir, 1995). The complexity in construction engineering often results in hesitation on the part of the decision maker in selecting specific alternatives. Moreover, FST provides approximate reasoning to better handle partly-defined, or incomplete, information as is often, the case in construction engineering. It is also a suitable technique to deal with the out of control factors: site, labor, equipment, climate, unforeseen circumstances, time dependence situations, and regulations. The quantification of these factors and the capturing of their uncertainty could be best represented by an approach based on subjectiveness and expertise, yet structured enough for the purpose.
Definition of a Construction System
For the purpose of this study, a construction system, is defined as a practical methodology that describes a series of steps to be implemented for the purpose of erecting a structure. The construction system that penetratesthemarketshows innovation in either materials used, erection operation or manufacturing technique.
Categorization of Construction Structures by Types
Multifamily and single family homes are the focus of this evaluation. Figure 1 categorizes the different types of structures ranging from multistory building to single family homes. The two extremes represented in this figure encompass most of the construction systems in the industry.
Multistory Building Systems
Knowledge acquisition was useful in identifying the most commonly used construction systems. Three of the most recognizable multistory construction systems are half tunnel, EFCO and flying form system mentioned in (Figure 1). The most recognizable construction systems were identified and assessed by the experts as being more widely used than other existing ones.
Fig.1: Examples of construction systems used in the industry.
The considered systems were categorized according to their inherent characteristics and functionality into five separate well-defined categories. The first category, namely the traditional concrete block system, is considered as the benchmark of the industry. For the second and third categories some of the most relevant examples of well-established newly-developed techniques, as identified by the experts, were chosen and described. The fourth and fifth categories deal with systems having a block as a basic module, similar to the traditional concrete block, but in these cases new properties enhancements were implemented. Again, for these categories as for the previous ones, only those systems considered the most relevant examples were considered.
Knowledge Representation
The characteristics of the model include quality, safety, cost, and schedule. These characteristics are presented in Figure 2. A comprehensive assessment of a construction project includes: the construction system used for the execution of the project, the layout of the site, the location of the project, the rules and regulations affecting the project. While other characteristics can be added to the list for the development of the prototype, the model was restricted to these essential factors. The assessment of these aspects of the project is done through an evaluation of the relevant primary assessment criteria. Again, these criteria are cost, quality, schedule and safety.
The methodology developed is applied to one branch of the construction system (Figure 2). This application of the methodology concentrates solely on this area. Through the analysis of this branch, the model methodology is explained.
As suggested by the Association of Civil Engineers (ASCE, 1991) and as established by the literature, the four criteria: cost, quality, schedule and safety are used to assess the constructability of the system. The same methodology could be extended for the other branches of the tree for further research and the final result is an assessment of the constructability of the whole project.
Examples of other construction systems are listed in Figure3. This list can be extended as new systems are being developed or as they become worth mentioning in the study. In view of the four mentioned criteria,
the constructability of each system can be assessed. The procedure by which it is assessed is explained in the following sections.
Fig.2: Constructability of the Construction System
Fig.3: Assessment of project constructability
The Development of the Fuzzy Rules and Linguistic Variables
The parameters affecting each of the criteria are expressed in the form of IF/THEN rules. The rule base reflectstherelationship the ability of a particular condition (i.e. weather) to impact more than one of the characteristics (i.e.scheduling and safety). To understand what factors impact each characteristics, the results of all of the knowledge acquisition phases were combined into an information pool. This information pool was categorized as permitted easy determination of consistencies and contradictions. It also illustrated the relationship of a factor in impacting more than one characteristic.
In the construction of the rule base, the sharing of the same parameters by different criteria is translated by applying the same rules as part of the information pool shaping the other criteria. In other words, the same rules are applied to the other criteria they affect besides the rules pertaining solely to this criteria. Again, the input from the experts was primarily used to construct the rules but the text analysis and survey were used to substantiate or refute the feasibility of the rules.
The Application and Constructability Assessment Based on Fuzzy Set Modeling
Step 1. As previously mentioned the inference rules are developed through the interviews of the experts. This was an ongoing process throughout model development where the rules are constantly developed and refined.
Step 2. The Modus Ponens rule inferencing is used in the Constructability model.
The Modus Ponens format is as follows:
Rule: If X is A, Then Y is B
Fact: X is A'
Conclusion: Y is B'
Where: * B' is calculated by the following equation:
B'(y) = supxµX min [A' (x), R (x,y)] for all yµY
* R is the fuzzy relationship and is defined (Klir, 1995) by:
R(x,y) = J [A(x), B(y)].
R is then calculated [2] through the following equation:
Rj (x,y) = min [Aj(x), Bj(y)]
where: j is the rule # of the fuzzy inference rule.
Step 3. Applying the above theory to the Constructability issue, consider the example where the first inference rule related to the Cost criteria is:
"If the acquisition cost of the construction system under consideration is low, then the
constructability is high."
Now, consider the construction system under consideration to be say; the half-tunnel system.
Fact: " The acquisition cost is high."
We then need to calculate the conclusion B'.
In other words, applying the Modus Ponens format
Rule 1: If acquisition cost (X) is low(A), Then Constructability is high (B)
Fact 1: Acquisition cost (X) is high (A')
Conclusion 1: Constructability (Y) is low (B1')
The task is now to calculate (B1').
Step 4. To demonstrate analytically and graphically (Klir, 1995) that:
B'= A' o R Where: o denotes the sup min composition.
So, applying the above to the constructability example and using the numeric base with the assigned membership as decided by the experts in the construction field, results in the following rating for the respective linguistic categories:
High = { .3/1,.6/2,.8/3, 1/4 }
Medium = { .5/1, ˝, .3/3, 0/4 }
Low = { 1/1,.5/2,.4/3, 0/4 }
The Modus Ponens format for the previously discussed rule for the acquisition cost of
the half-tunnel system is then expressed a follows:
Rule 1: X = { 1/1, .5/2,.4/3, 0/4 } Then, Y = {.3/1,.6/2,.8/3, 1/4 }
Fact 1: X = { .3/1,.6/2,.8/3, 1/4 }
Conclusion: Calculate B1’
As explained above and based on Klir’s proof (Klir, 1995):
B1’ = A’ o R
Where: A' = { .3/1,.6/2,.8/3, 1/4 }
R = min [A { 1/1, .5/2,.4/3, 0/4}, B { .3/1,.6/2, .8/3, 1/4 }]
Thus, R = {.3/1, .5/2, .4/3, 0/4 }
Having attained R we can calculate B1'.
B1' = max [min {.3/1,.6/2,.8/3, 1/4 }, {.3/1,.5/2, .4/3, 0/4 }]
B1' = .3
Step 5. The same is applied for every rule and B2', B3', B4', B5'......... Bn' are calculated.
Step 6. The constructability of the whole Cost criteria is then calculated by the following:
Bc’ = supxµX min [B1'(x1), B2'(x2), B3'(x3), B4'(x4)........ Bn'(xn)]
Where: Bc’ is the constructability of the cost criteria encompassing all the rules pertaining to cost. It is represented by a fuzzy set.
Step 7. Let's assume a fuzzy set for the Cost criteria to be:
Bc' = { .5/x1 .3/x2 .4/x3,..........,.8/xn}
Transposing Cross' rational (Cross,1994) to this situation would allow the firing of only those rules that meet or surpass a predetermined threshold. Below this threshold the rules will not fire. Application of this methodology introduces a threshold (Ä ) to specify the minimal degree of satisfaction of the antecedent for the rule to fire. The same principle is applied to the degree of membership required for the rule to fire, which is in other terms the application of the ±-cut concept (Klir, 1995). This concept specifies all the elements of a set whose membership grades are greater than or equal to a specified value.
Also,
at this point a linguistic value is attached to the obtained
truth value, which represents the Constructability of the Cost criteria.
Based on the identified criteria, the categories for the truth value are:
Very high If 0.8< Constructability Truth value < 1
High If 0.6 < Constructability Truth value < 0.8
Medium If 0.4 < Constructability Truth value < 0.6
Low If 0.4 < Constructability Truth value < 0.2
Very Low If 0.2 < Constructability Truth value < 0
Step 8. Now that the task of quantifying the Construct has been accomplished, the methodology proceeds to the assignment of linguistic variables.
· The task is now to use a sound aggregation technique to pick the most suitable construction system and to quantify its constructability.
· In preliminary model development, a direct measure of factor importance was used to assign factor weight with the experts. The experts were given the scale [0, 1] where 0 represents no importance and 1 represents extreme importance. The experts were asked to assign weight values from ( 0, 1 ) to the four mentioned criteria given requirements of a particular project and a given geographic location.
Table 1.
|
Range of weightWi
W<.3 .3<W<.8 W>.8 |
Linguistic Interpretation
Low importance Moderate/medium importance Very/high importance |
* A fuzzy weighted mean is used as the approach (Klir, 1995), (Bonissone, 1982) for aggregation resulting in the following equation:
FWM = Sni=1 = Wi Rij / Sni=1Wi
Where: FWM = Fuzzy Weighted Mean and it expresses the combined factor inputs for
constructability of the construction system that is being evaluated.
Rij = The fuzzy relationship that appears in the depicted table of the assessing criteria and construction systems.
Table 2. Fuzzy Relationships
X1 X1 XI X1
C1 R11 R12 ---- R1n
C2 R21 R22 ---- R2n
Cn Rn1 Rn2 ---- Rnn
Wi = are weights to indicate the relative importance of the criteria.
* The Rij expressed in the above equation, when applied to the constructability example that was mentioned, will be replaced by the values of Tc’ , TQ', TSch', Tsaf ' for each construction system (j) and the constructability of the system under consideration (FWMj) is calculated.
Example and Results
As an experiment, three active construction projects of above $ 10 million were considered in the Central Florida area. Each project being considered is executed by a different construction company. The project managers of each construction company were interviewed and asked to develop relevant fuzzy rules and to assign weights or evaluation importance to each of the four constructability criteria as they relate to the circumstances of their respective project. The following (Table 3.) shows the Project Managers' assessment.
Table
3.
Project Cost Quality Schedule Safety
Project
.3 .2 .2
.3
1
Project
. 3 .2 .1 .4
2
Project
.1 .3 .3
.3
3
The following calculations quantify the constructability of the Half-Tunnel construction system. For practicality, a limitation was imposed on this example: only five rules corresponding to each criteria will be considered.
Applying the rule base, to generate a linguistic conclusion (the constructability of the rule) and collectively, the conclusions of each criteria will produce the Truth Value (the constructability of each criteria).
Then, considering only five rules and as demonstrated in the calculation already carried out in steps 1 to 6 of the model the Truth Values for each criteria are as follows:
The Cost criteria Truth Value = Constructability of the Cost
criteria = 0.4
The Quality criteria Truth Value = Constructability of the Quality
criteria= 0.6
The Schedule criteria Truth Value = Constructability of the
Schedule criteria= 0.8
The Safety criteria Truth Value = Constructability of the Safety
criteria = 0.5
Thus, based on step 7., the assessment of the constructability for each criteria in linguistic terms is:
· The Cost constructability is low.
· The Quality constructability is high.
· The Schedule constructability is very high.
· The Safety constructability is Medium.
The constructability of the Half-Tunnel construction system for the specific projects referred to based on the above expressed five rules limitation is quantified based on the equation.
FWM = Sni=1 = Wi Rij / Sni=1Wi
Thus, for Project # 1.
FWM = (0.3) (0.4) + (0.2) (0.6) + (0.2) (0.8) + (0.3) (0.5) = 0.55
For Project # 2
FWM = (0.3) (0.4) + (0.2) (0.6) + (0.1) (0.8) + (0.4) (0.5) = 0.52For Project # 3
FWM = (0. 1) (0.4) + (0.3) (0.6) + (0.3) (0.8) + (0.3) (0.5) = 0.61Taking into account the five rules limitation and the Project Managers weight assignments: the Half-Tunnel system is producing the best constructability for project # 3 and the least constructability for project #2.
Summary and Conclusion:
This paper presents a sequential application of fuzzy set theory to quantification of constructability. Though the model is considered preliminary, it provides the blueprint to achieve the overall goal of assessing the project constructability and illustrates the practicality of fuzzy rules in model development This also demonstrate the means of comparing the constructability of separate construction systems as applied to particular projects. The model could also be used for the purpose of project prioritization, determining the extent to which a particular project is constructable. Through this model construction companies, as well as owners, will be able to obtain feasibility of a project, and further determine the most advantageous construction system to be used for its implementation.
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