Kinematics chain based dimensional variation analysis of construction assemblies using building information models and 3D point clouds

Automation in Construction 75 (2017) 33–44

Contents lists available at ScienceDirect

Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Kinematics chain based dimensional variation analysis of construction assemblies using building information models and 3D point clouds Christopher Rausch, Mohammad Nahangi ⁎, Carl Haas, Jeffrey West Ralph Haas Civil Infrastructure Sensing Laboratory, Department of Civil and Environmental Engineering, University of Waterloo, Canada.

a r t i c l e

i n f o

Article history: Received 21 July 2016 Received in revised form 27 November 2016 Accepted 8 December 2016 Available online xxxx Keywords: Dimensional variability Kinematics chains Robotics Laser scanning Building information model Tolerance Discrepancy and deviation

a b s t r a c t As modern methods of construction progressively incorporate more facets of manufacturing, design optimization tools used in manufacturing can be adopted into construction to solve complex challenges. The specification and control of dimensions and geometry of construction assemblies is one such challenge that can be solved using tools from manufacturing. Even with building information models (BIM) to assist with clash detection for identifying potential dimensional problems, or the use of tolerances to control critical features in an assembly, dimensional variability is still a complex challenge to address in construction. This paper explores the use of a dimensional variation analysis (DVA), which is a design optimization tool from the manufacturing industry. This paper presents a DVA approach which is based on kinematics theory in robotics to define the assembly equation (how components are dimensionally related to each other). A case study is used to validate the proposed framework through two distinct approaches: (1) an as-designed (model-based) DVA and (2) an as-built (laser-based) DVA. Comparison of these two methods resulted in a percent difference less than 1% which demonstrates the reliability of using the model-based method for designing critical construction components. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The inherent variability associated with the geometry of as-built construction assemblies can create serious problems if not properly managed. This type of variability often has a direct impact on how well components can be constructed and assembled together. Constructability is one method that can be used to ensure problems associated with the construction and assembly of components is minimized. Constructability is the use of strategic knowledge during planning, design and execution to achieve project objectives, and requires an investment in front-end planning in order to anticipate and solve potential problems [1,2]. Some of the most prevalent problems that constructability analysis addresses are rework, design errors, change orders, low product quality, project delays, tolerance problems, physical interface problems, and not meeting client expectations [3]. What all of these problems have in common is that they can stem from the dimensional or geometric properties of components or construction assemblies. The ability to model the geometry of components in a virtual three-dimensional space has enabled the use of building information models (BIM) and computer-aided design (CAD) tools for facilitation in constructability reviews [4,5]. Use of these virtual design tools in construction places an emphasis on ensuring coordination between trades and detection of physical component clashes. The focus on both ⁎ Corresponding author. E-mail address: [email protected] (M. Nahangi).

http://dx.doi.org/10.1016/j.autcon.2016.12.001 0926-5805/© 2016 Elsevier B.V. All rights reserved.

constructability and use of BIM in the construction industry demonstrates that the proper management of component and system geometry is vital for overall project success. The importance of properly managing component and assembly geometry is generally well understood in the construction industry. Although designs specify the nominal (or intended) dimensions and locations of components in an assembly, dimensional variability is unavoidable; that is to say, the dimensions and configuration of components always vary somewhat from nominal specifications [6]. For this reason, the construction industry has traditionally adopted the use of standardized tolerances to ensure that acceptable limits are placed on dimensional variability [7,8]. Yet despite the use of tolerances, dimensional problems in construction still exist since tolerances can accumulate throughout assemblies resulting in component fit problems, delays, rework and increased costs [9]. The trend toward increasing industrialization in construction has further introduced a new demand for stricter dimensional variability management and a systematic approach to managing the interaction of offsite and onsite tolerances [10]. As the construction industry continues to utilize manufacturing approaches for project delivery (i.e., offsite construction, pre-assembly, prefabrication and modular construction), methodologies for managing dimensional variability from manufacturing can be used analogously [11]. In the aerospace and automotive manufacturing industries, systematic management of dimensions and tolerances is used extensively in practice [12]. Dimensional variation analysis (DVA) models production processes in order to predict expected component variations in

34

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

terms of their size, shape and location in an assembly. As such, DVA can be used to predict how minor dimensional variations in components can propagate through an assembly and impact overall functionality of a product [13]. DVA has not been used widely in construction applications, but has the potential to yield a successful dimensional variability management framework as the construction industry continues to adopt manufacturing methods of production. Previous research to implement manufacturing design and production practices in construction has focused on analytical methods of predicting tolerance accumulation in order to specify better tolerances [13,14]. One of the most popular analytical methods is called tolerance mapping which employs a combination of graph theory and manufacturing tolerance notation in order to define the relationship of components and component-features in an assembly [15] (note: a component-feature is a geometrical element of a component, such as a line, plane, or mathematically defined curve or surface). While the use of tolerance mapping can assist with better specification of tolerances [16], it is tedious to employ and requires an extensive understanding of Geometric Dimensioning and Tolerancing (GD&T) [17,18]. As such, there is still an opportunity for applying manufacturing production practices to construction in a way which can be generalized and which focuses on controlling only critical sources of variation. This paper presents a framework for dimensional variation analysis which utilizes kinematics theory in order to model the geometric relationship of components in construction assemblies. First, related background is investigated. An alternative form of dimensional variation analysis is then developed and its challenges and complexities are briefly discussed. The proposed framework (kinematics chain-based dimensional variation analysis) is then presented. A case study is provided for validating and verifying the performance of the dimensional variation analysis method. 2. Background This section presents background related to: (1) current approaches for dimensional control in construction, (2) current use of dimensional variation analysis in industry and (3) current use of kinematics chains for geometric modeling purposes. For clarity, this paper refers to variation as the continuous spectrum of variability of a dimension from its nominal (or intended) value, while deviation is used to represent a discrete variation value. 2.1. Existing methods for dimensional variation control in construction Existing methods for analyzing, detecting and controlling dimensional variation in construction can be done throughout the project life cycle (i.e., during design, fabrication, or assembly on site). Although variation control during fabrication and assembly on site can utilize proactive 3D analysis techniques such as spatial change analysis [19] or automated compliance checking [20], the majority of variation control techniques during construction are still performed in a reactive manner (i.e., problems related to dimensional variability are only solved once they have occurred). Proactive methods for dimensional variation control are typically only considered during the design stage through the use of BIM. Clash detection is an example of a proactive approach for detecting and resolving dimensional variation conflicts, as discussed earlier. Proactively resolving dimensional conflicts is superior to reactive methods, which is a large reason why approximately 90% of commercial contractors are currently using BIM-based clash detection on projects which utilize a building information model [21]. In a study by Leite et al. [22], it was shown that field-detected clashes are more costly than the extra time spent upfront in modeling a more detailed BIM. For this reason, spending more time during the design to detect and avoid clashes can offset the cost associated with field rework due to dimensional variations. Within clash detection, there are three types of clashes (or dimensional conflicts): (1) hard clashes, where two components occupy the same

space, (2) soft clashes, where there is limited or insufficient space for access, and (3) logical clashes, which include constructability problems [23]. While the automatic detection of dimensional conflicts in a construction assembly is extremely powerful and can save upwards of millions of dollars on a given project [24], BIM-based clash detection does not instruct construction crews on how to resolve dimensional conflicts. Accordingly, contractors often avoid dimensional conflicts by leaving adequate clearance envelopes around components in the BIM using standardized tolerances. This approach requires that contractors use their experience or a priori knowledge to adequately specify acceptable tolerances. As such, this approach can be problematic for the assembly of construction components, which often require direct contact between components, with little to no gaps. 2.2. Current state of dimensional variation analysis (DVA) In aerospace and automotive manufacturing industries, dimensional variation analysis (DVA) is used extensively to ensure that the effect of dimensional variability on parts and assemblies is properly controlled. A DVA requires both internal constraints to control the shape and form of a component and external constraints to control the location and orientation of a component [13]. Common mathematical models used in dimensional variation analyses include worst case, statistical or sampled mathematical models (Table 1) and can be modeled in 1D, 2D or 3D [25,26] There can be numerous challenges for using these mathematical models properly in a DVA. Using a worst case or root mean square model does not account for the practical assembly procedures. Using six sigma is challenging, since process capability data is not always available or accurate, while Monte Carlo simulation can be very computationally intensive [28]. One form of DVA which has proven to overcome many of the challenges associated with the traditional mathematical models is a vector loop-based model which is also commonly used in commercialized platforms. A key part of creating a vector loop-based DVA is the use of kinematic constraints (or chains) between components to account for the assembly sequence [12]. A kinematics chain based DVA is a robust solution since it can be used on simple or complex assemblies, and it reduces the number of errors associated with mathematical parameters [13]. For these reasons, a kinematics chain based DVA is an efficacious method to utilize in construction applications. The use of a dimensional variation analysis in construction applications has been limited to the industrial sector and power plants. One project which has utilized an extensive DVA is the ITER Tokamak machine in Cadarache France. In this project, a DVA was used to ensure that the manufacturing functional tolerances and assembly processes were adequate in terms of accommodating dimensional variations in critical areas [29]. A Monte Carlo simulation-based model was created in order to ensure that large prefabricated slices of the large vacuum vessel could be aligned and assembled correctly [30]. While this example of DVA was implemented in a construction application, the dimensional precision and level of detail required in the analysis closely resembles a mechanical assembly rather than a typical construction assembly. As such, this DVA cannot be easily implemented in more mainstream construction applications such as commercial or residential building projects. There is therefore a need to develop a DVA which can be easily used in construction applications, which is also generalized and does not require extensive understanding of manufacturing tolerance theory. 2.3. Kinematics chain for geometry modeling Using kinematics theory has opened up a wide and efficient range of solutions in engineering problems. For example, robotics concepts have been used for state modeling and sensing of construction equipment such as pipe manipulators and excavators [31]. A specific pose of the

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

35

Table 1 Mathematical models used in dimensional variation analysis (DVA), adapted from [12,25,27]. Mathematical model

Formula

Worst case T accum Root mean square

Six sigma Sampled data (i.e., Monte Carlo simulation)

T accum

T accum

Notation

Τaccum = tolerance accumulation of a chain of tolerances Τi = single tolerance in a chain ¼ ∑aT i α = ±1 (outer/inner bound) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ci = inflation factor (accounts for sensitivity between tolerances in a chain) ¼ ∑ðð1−ni Þci ai T i Þ2 ni = mean shift ratio (applicable for processes which have a tendency to shift the mean tolerance value) rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cp = process capability ratio (ratio of specified tolerance range to the process capability) 2 Ti ¼ ∑ðci 3C p ð1−n Þ iÞ Tj = tolerance accumulation value from simulation j

Taccum = AVG(Tj)

end effector (i.e., the end of a kinematics chain, which is the critical feature of interest) can then be modeled using related inverse and forward kinematics. Kinematics theory, and more specifically robotics concepts can also be used for automating tasks associated with a high level of repetition or harsh tasks that are performed by workers in hazardous areas. For instance, a machine-vision-assisted system was developed by [32] for automating the task of bricklaying assembly in a prefabricated environment. Comparatively, kinematics theory was used for modeling the geometry of construction assemblies as a mathematical function [33]. Discrepancies of the as-built state of construction assemblies are therefore quantified (via forward kinematics) and required corrective actions are then calculated (via inverse kinematics) [34,35]. Using kinematics chains for identifying the geometric relationships has been found to be very effective for integrating parametric models for systematic and electronic monitoring of civil infrastructure. 3. Deviation mapping for dimensional variation analysis Tolerance mapping can be very challenging to use for analyzing the effect of dimensional variability in construction assemblies. In this section, the overall concept of tolerance mapping is presented in the context of a dimensional variation analysis to demonstrate how it can be tedious and complex to use. For this purpose, it is herein referred to as deviation mapping since the deviations of component-features and components are analyzed rather than their allowable tolerances, however it follows the exact same approach as used in tolerance mapping. Deviation maps are challenging, because without proper selection of only critical component-features and critical components in an assembly, they become extremely detailed and unnecessarily large. Secondly, the notation used in deviation maps requires an extensive knowledge about Geometric Dimensioning and Tolerancing (GD&T), which is not intuitive for engineers and designers in the construction industry. The general procedure for creating a deviation map can be described in three steps: (1) create an assembly network to define how all parts are geometrically related to each other in an assembly, (2) create component diagrams to define how all component-features are geometrically related to each other in each component, and (3) amalgamate all component diagrams in the assembly network to create the overall deviation map. To demonstrate the creation of a deviation map, a simple example is shown, which outlines the geometric relationships of all component-features for a steel component in a modular steel bridge (Fig. 1). Three variation categories are employed in deviation mapping to define the relationship between component-features and components within an assembly. These categories are based on GD&T notation: (1) orientation and location variations, which define a component-feature's spatial state, (2) form variation, which defines how straight, flat or round a component-feature is, and (3) size variations which define two-point measurements of a component-feature. For the assembly diagram, typically only orientation and location tolerances are used, since the assembly diagram defines how the sub-components or parts are spatially related (Fig. 2). The creation of component diagrams and the

overall deviation map (Fig. 3) follows the same approach taken for the assembly diagram (i.e., component-features are geometrically related using GD&T notation). Details related to these figures can be found in [36]. As shown in Fig. 3, the use of deviation mapping as a form of DVA is not practical, since it is tedious to setup, and without a proper selection of critical dimensional variations, it becomes extremely detailed, even for simple structural components. This justifies the need for a more systematic and generalized approach for modeling dimensional variations in construction assemblies. 4. Methodology In this paper, the geometric relationships between components in an assembly are modeled using the analogy of robotics and kinematics chain modeling. It is assumed that construction assemblies are similar to robot arms with mutual degrees of freedom until fixed and finally connected. The dimensional variations are modeled parametrically, and the critical component-features and their variations are controlled systematically. The analogy of construction assemblies with robot arms was first used by Nahangi et al. [33], in order to quantify incurred discrepancies in construction assemblies. It was then used to calculate the required changes for realigning defective assemblies [34] by solving the inverse kinematics problem. This paper is directed toward dimensional variation analysis, in order to investigate how deviations propagate in an assembly. The variations can then be monitored mathematically for efficient and systematic design of critical components. 4.1. Overview of the kinematics chain-based modeling An overview of the proposed method is shown in Fig. 4. Some critical information integrated in the BIM is required to develop the kinematics chain for analyzing dimensional variations. As shown in Fig. 4, critical interfaces and an assembly diagram are required for identifying the

(a)

(b)

Fig. 1. Structural component used as an example to demonstrate complexity of deviation mapping. (a) Structural assembly of component. (b) Location of component in overall modular bridge.

36

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

Xo Yo Zo XL YL ZL

Form Tolerance

F X

Location & Orientation Tolerances

Y

Z

Size Tolerances

Fig. 2. Example of steps involved with creating an assembly diagram for a single structural assembly. (a) A dimensioned drawing for an assembly is broken down into its sub-components using (b) Geometric Dimensioning and Tolerancing notation to create (c) an assembly diagram.

critical chains for variation analysis. The kinematics chain is then developed for the construction assembly. Fig. 5 illustrates the identification of the assembly plan as well as the critical chains required for developing the kinematics chain. As previously discussed, DVA can be used for efficient and systematic design of critical interfaces and connections. This section describes: (1) how kinematics chains are developed for construction assemblies (Section 4.2), and (2) how the developed chain can be applied for critical interface and connection design (Section 4.3).

4.2. Kinematics chain development For modeling the geometric relationships of different segments of an assembly, the kinematics chain is developed using the analogy of robotics discussed earlier. For developing the kinematics chain, a similar approach to [33] is employed. Transformations are then derived using the Denavit-Hartenberg (D-H) convention [37]. While it is possible to use any consistent convention for the derivation of the transformations, the D-H convention is a systematic method that can be programmed

1. Assembly Diagram

3. Deviation Map

2. Component Diagrams

Fig. 3. Example of steps involved for creating a deviation map: (1) create the assembly diagram, (2) create diagrams for each component and (3) amalgamate all component diagrams into the assembly diagram to obtain the overall deviation map.

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

Create Assembly Diagram

Critical Aggregation Interfaces

Kinematic Relationships

Isolate Critical Dimensional Chains

Develop System Kinematic Equation

37

Integrated in BIM Process

Determine Critical Sources of Variabilty

Quantify Expected Variability

Dimension Allocation

Tolerance Allocation

Complete Design of Connection Dimensions

Fig. 4. Overview of the proposed method for kinematics chain-based dimensional variation analysis.

and integrated with other components of the proposed framework. D-H parameters represent any homogeneous transformation as a combination of four transformations, as illustrated in Fig. 6. Of these four transformations (illustrated in Fig. 6), two are rotational and two are translational transformations as:      Ti 2 ¼ Rot z;θi Transz;di32Transx;ai Rotx;α i 32 32 cθi −sθi 0 0 1 0 0 0 1 1 0 0 ai 6 sθi 76 6 76 cθi 0 07 76 0 1 0 0 76 0 1 0 0 76 0 ¼6 4 0 0 1 0 54 0 0 1 di 54 0 0 1 0 54 0 0 0 0 1 0 0 0 1 0 0 0 31 2 0 cθi −sθi cα i sθi sα i ai cθi 6 sθi cθi cα i −cθi sα i ai sθi 7 7 ¼6 4 0 sα i cα i di 5 0 0 0 1

0 cα i sα i 0

0 −sα i cα i 0

3 0 07 7 05 1

ð1Þ in which, θi, di, ai, and αi are parameters associated with link i and joint i (Fig. 7). cβ and sβ denote cosβ and sinβ, respectively. The four parameters θi, di, ai, and αi are also known as “link length”, “link twist”, “link offset”, and “joint angle”, respectively. End Node (Critical Feature) Joints with variable parameters (1 DoF)

Generally, two types of joints can define the characteristics of an assembly connection (Fig. 7): 1- Rotational joints: are considered where dimensional variation can occur in the form of rotation. Rotational joints are also known as revolute joints. 2- Translational joints: are considered where dimensional variation can occur in the form of translation or offset. Such joints are also known as prismatic joints. In order to model variation of connections and joints, θi is the design variable used for rotational joints, and di is the design variable used for translational joints. For modeling the geometric relationship between different segments of an assembly and considering the dimensional variations that may occur, the appropriate joint type is considered and incorporated in the kinematics chain. In some cases, a combined joint comprised of many ‘typical’ joints (which are all coinciding at one point) may be modeled. For example, the connection illustrated in Fig. 7 is combined of one translational and one rotational joint in parallel, meaning that the order of their transformation can be reversed. However, in rare cases where a connection is complex (e.g., exterior cladding connection systems), it may have to be modeled as a series of joints. Also, placement of the origin for structural assemblies must follow a standard convention (typically at one corner or along an outer edge at the center of the assembly). The position of the critical interface or node is therefore modeled as a mathematical function with the potential dimensional variations as design variables.

Moment Constrained joints

Start Node (Datum)

Fig. 5. A typical structural frame and a hypothetical assembly diagram (highlighted path). The joints with variable parameters are identified in the assembly path. The position of the critical feature is therefore modeled as a function of the joint parameters and variables.

Fig. 6. Illustration of D-H parameters for a typical connection. D-H parameters are used for developing the kinematics chain to relate the geometric relationships of an assembly.

38

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

Combined joint: 1 translational joint + 1 rotational joint

Architectural Rendering

Building Structural Configuration 2 modules long

Fig. 7. Schematic of a hypothetical joint. The joint is comprised of one translational joint and and one rotational joint in parallel (mathematically). The value δi is variable for translational joints, and θi is variable for rotational joints. 8 modules wide

4.3. Dimensional variation analysis using kinematics chains Typical Module Structural Configuration

Once the assembly and potential dimensional variations are modeled mathematically by developing the kinematics chain, variation analysis of a critical feature becomes systematic and algorithmic. The assembly diagram which is integrated with the building information model identifies how various components are assembled. The potential variation as well as the acceptable tolerance values are therefore identified and the kinematics chain can then be developed. The kinematics chain identifies the position of the critical feature or connection as a function of the potential variations incorporated in the chain. The variation of the critical feature can then be modeled and analyzed for design and further considerations. A hypothetical example is shown in Fig. 8. As seen in Fig. 8, the position P of the hypothetical critical feature is identified as a function of the potential design variables θ and δ: P = f(θ, δ). Perfectly fabricated state is associated with θ = 0 and δ = 0. By changing the design variables within the acceptable tolerance limit assigned to each component and comparing the resulting positions with the perfectly aligned state, dimensional variation of the critical feature can be analyzed for design and further considerations. The deviation from the perfectly fabricated state is calculated as: Dev = f(θ, δ) − f(θ = 0,δ = 0). Since the dimensional variation is modeled mathematically, a wide range of analyses become possible for systematic monitoring or design of construction components. For instance, the rate of variation propagation in the critical region can be calculated by differentiating the kinematics chain with respect to the design variables. Components with

3.4 m

3.0 m

Fig. 9. The module used in the case study. Structural and building configurations are shown to identify how the modules are assembled.

large contributions to the dimensional variation of a critical feature can be identified systematically, and required actions for tolerance and variation control can then be planned automatically. These potential analyses are performed on the case study investigated for validating and verifying the explained framework. Furthermore, inverse kinematics can be used for tolerance allocation at each component for desired location of the critical feature. The analogy of robotics has been recently used in the same research group for automatic realignment of defective pipe assemblies and structural frames [33,34]. 5. Experiments and results In order to investigate the proposed framework and measure its performance, a case study on a modular construction assembly is

Critical Feature

Prismatic Joint

Perfectly fabricated state: Rotational Joint

(a)

(b)

Fig. 8. Hypothetical example for dimensional variation analysis using kinematics chain. (a) An assembly with 2 DOF's, one rotational and one translational, is shown. (b) The position of the critical feature is therefore modeled as mathematical function of the two variables and constant links' length identifying the geometry. The critical feature's position function is shown as: P=f(θ,δ).

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

39

Fig. 10. Schematic representation of the key fabrication processes involved with construction of module structural system (with additional processes outlined for fit-up and fastening of tie-in plates). Kinematics chains and transformations are developed based on this schematic assembly diagram integrated in the BIM (see Fig. 4).

performed. The described method for kinematics chain-based dimensional variability analysis is demonstrated.

this construction assembly: the tie-in plates between modules. The DVA is carried out in order to analyze the variations of tie-in plates in 3D (a sample deviation from the actual project in one direction is shown in Fig. 11).

5.1. Case study The case study investigated in this paper relates to the fabrication of the structural system of a single story modular building (Fig. 9). This case study comes from a recent project where there were numerous dimensional fit-up issues during erection, resulting in misalignments between module connection points (at the tie-in plates). In order to address these issues, a dimensional variation analysis using the proposed kinematics chain based methodology was developed. This DVA analyzed the key fabrication processes for the steel frame structure (Fig. 10). The focus of this case study is to develop a kinematics-chain based dimensional variation analysis on the critical aggregation features of

Misalignment between tie-in plates in direction of interest

5.2. Implementation of the kinematics-chain based dimensional variation analysis Using the assembly diagram (Fig. 10), kinematics chains are developed for analyzing the dimensional variation of critical features (i.e., tie-in plates). The transformation required for analyzing the tie-in plates is represented as a chain of transformations between various local coordinate systems. These local coordinate systems are located where either a deviation might occur or where a tolerance has been specified. The kinematics chain for analyzing each tie-in plate in this case study is shown in Fig. 12.

Adequate alignment between tie-in plates in direction of interest

Fig. 11. Depiction of misalignment of tie-in plates (left), and adequate alignment (right). Red arrows indicate deviation associated with misalignment, while blue arrows indicate direction of interest.

40

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

TP1

TP2

TP3

TP4

TP5

Fig. 12. Kinematics chain and transformations for representing critical features in the local {li} and global {G} coordinate systems.

As seen in Fig. 12, each tie-in plate is identified with a corresponding transformation [Ti] = [10T][i1T] consisting of a chain of transformations that relate the local coordinate system [li] of the critical feature i to the global coordinate system [G]. The local and global coordinate systems are then related to each other as: fP i g ¼ ½T i fpi g

ð2Þ

where, {Pi} and {pi} are the positions of critical features in the global and local coordinate systems respectively. The kinematics chain (transformation [Ti]) is the link for relating the global and local coordinate systems together. Fig. 13 shows how the kinematics chain is used to relate the local and global coordinate systems. As such, the dimensional variation can be analyzed from two perspectives: 1- From local to global coordinate systems: when the coordinates of critical points in a critical feature are known and the kinematics chain is used to calculate the coordinates of the critical points in the global coordinate system. 2- From global to local coordinate systems: when the local coordinates of critical points in a critical feature is measured in the global coordinate system, and the local coordinates are then identified for analyzing the variabilities and comparing to the acceptable tolerance ranges. In addition, two types of dimensional variation analyses can be performed: (1) as-designed (model-based) dimensional variation analysis, and (2) as-built (laser-based) dimensional variation analysis. Analyses are explained in the following sections.

1- How the tie-in plate is installed and assembled with respect to the roof frame, and 2- How the roof frame is installed with respect to the floor frame (global coordinate system) The variation of the tie-in plate and the impact of tolerance propagation can then be modeled by developing the kinematics chain relating the global to the local coordinate system, as shown in Fig. 12. The allowable tolerance impact can then be measured in the global coordinate system in order to investigate the propagation of the tolerances. Based on the explanation provided in the methodology section, the D-H parameters of the systems of coordinates of the case study (Fig. 13) can be defined as shown in Table 2 In Table 2, the values of l1 and l2 are constant and are extracted as the as-designed dimensions from the 3D CAD drawings integrated with the building information models. θ1 and θ2 are the design variables to be analyzed for dimensional variability of the tie-in plates. The ranges are chosen from the allowable tolerances identified in the design specifications. However, a typical range is chosen here for demonstrating the results. As discussed earlier, allowable tolerances on each part can be modeled with one rotational and one translation joint. For simplifying the illustration of the results (Figs. 14 and 15), we assume that the roof frame can only rotate about the perpendicular axis to the frame

local coordinate system

Arbitrary point

5.3. Model based DVA As-designed (model-based) analysis is performed, when acceptable tolerances and variations are investigated based on information provided in the building information model. In other words, this analysis identifies how acceptable tolerances propagate through fabrication processes. Typical analyses on the case study used in this paper are shown and discussed in this section. For investigating the case study (see Fig. 12), two stages of tolerance propagation can identify the variation of the tie-in plates:

Global coordinate system Fig. 13. Relationship between positions in the local (pi) and global (Pi) coordinate systems. Coordinate systems are defined based on D-H convention.

C. Rausch et al. / Automation in Construction 75 (2017) 33–44 Table 2 D-H parameters to identify and analyze the dimensional variation of tie-in plates for the case study and the associated assembly diagram extracted from the building information model (Fig. 10). i

α

a

d

θ

1

0

0

l1

2

90

l2

0

90 + θ1 θ2

plane (i.e., an axis parallel to the columns direction). In other words, the translational DOF's and rotational DOF's about other axes are ignored. Although all DOF's can be considered and modeled using the kinematics analogy explained here, this simplification is made to better illustrate the results. Considering more DOF's will result in highly multi-variate functions as the design variable functions, which are difficult to illustrate. The analysis results show that as the tie-in plates are spaced further away from the datum, the potential deviations are prone to increase. This is due to the fact any rotations of the beam with respect to the global datum will cause linearly increasing absolute deviations in the tie-in plates (this is with respect to the global datum). The input for the model-based design includes allowable tolerances which were either provided by the contractor in the design drawings or were taken from provisions listed in AISC Code of Standard Practice [38]. The tolerances used in the kinematics model-based DVA are for orientation and location deviations. As such, form tolerances (which are used to control the profile of a line or surface and are typically referred to in terms of straightness of an edge or flatness of a surface) are not considered in a kinematics chain based DVA. The results of the model-based DVA show that for the critical features in this assembly (i.e., tie-in plates 1, 2, 3, 4, and 5) that the absolute deviations in 3D range between 1.6 mm and 53 mm. Interestingly, there were no specifications of tolerances to control the dimensional variation of tie-in plates in this project. Conducting a kinematics model-based DVA before the geometric design and allowable tolerances were

Assembly assumption

BH1

BH2

41

finalized would have revealed that the deviations in the tie-in plates would have created large challenges for fit-up and erection of modules on site.

5.4. Laser based DVA As-built (laser based) analysis is performed when the built status of a construction assembly has been acquired. Feeding the built status information (via 3D point cloud from a laser scan) into the dimensional variation analysis framework developed here provides accurate information that can be used for as-built modeling, updating the BIM and for understanding contributions of out-of-tolerances. In this type of DVA, the actual constructed dimensions are extracted from point cloud models of the construction components, and the kinematics chain is then populated. The variation and deviations are therefore analyzed using the actual constructed dimensions. Typical analyses for laser based DVA in the case study are shown and discussed in this section. Using the kinematics chains that were developed for the model-based DVA, input of the actual as-built dimensions yields results which show 2D deviation surfaces for the two design variables used (Fig. 16) and the propagation of dimensional variation for all tie-in plates along the length of the module (Fig. 17). The results of the laser-based DVA are extremely close to that of the model-based DVA. In this case, input into the DVA was provided in the form of extracted dimensions from a 3D point cloud. The laser scanner used in this case study was a FARO LS 840HE which has an accuracy of ± 2 mm for the distance used [39]. Commercial software called PolyWorks® was used to extract the as-built dimensions through use of a simple feature which computes the point-to-point Euclidean distance between two user-selected points (Fig. 18) [40]. Since this approach was performed in a semi-automated fashion, extraction of all critical dimensions was somewhat time consuming and required careful selection of points. Furthermore, minor point cloud cleaning was employed in order to reduce slight noise around edges of components in the model. The results of the laser-based DVA show that for the

BH3

BH1 BH2 BH3

Fig. 14. Typical results for model-based DVA. Deviation surfaces and contour lines for the bolt holes (BH) are illustrated. The results are shown for the tie-in plate 2 (TP2) illustrated in Fig. 12.

42

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

Fig. 15. Propagation of dimensional variation along the roof frame of the case study in different tie-in plates. As seen, tie-in plates further from the datum have higher impacts. Using kinematics chains thorough analyses are possible using mathematical relationships between different components.

critical features in this assembly (i.e., tie-in plates 1, 2, 3, 4, and 5) that the absolute deviations range between 1.7 mm and 53 mm. 5.5. Comparison between model-based and laser-based DVA Comparison of results from the model-based and laser-based methods reveal nearly identical final deviation values for the tie-in plates (Table 3). The fact that the model-based DVA results closely match that of the laser-based DVA indicates that the accumulation of tolerances in the model-based DVA match the accumulation of deviations in the laser based DVA. Although the individual tolerances for links in the kinematics chain in the model-based method did not match every corresponding deviation for links in the kinematics chain, the overall

accumulations are nearly identical. For instance, the as-built column placement deviation was + 5 mm from the nominal specification, while the placement of the roof frame had a deviation of − 4 mm. These two deviations offset each other such that the effective out-ofplane deviation is only +1 mm. If the deviations in this case did not offset each other and in fact accumulated, then the results of the modelbased and laser-based DVA would be much different. In contrast with other dimensional variability methods (primarily in tolerance mapping), the main difference in the proposed method lies in the fact that form variations are not modeled in kinematics chains. This is because kinematics chains assume rigid body transformation, and do not account for distorted geometries. As such, it needs to be clearly stated that a kinematics chains DVA cannot be used when excessive distortions in geometry exist. An example of this in the context of

BH1 BH2 BH3

Fig. 16. Results for laser-based DVA of the case study. Deviation surfaces and contour lines for the bolt holes (BH) are illustrated. The results are shown for the tie-in plate 2 (TP2) illustrated in Fig. 12.

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

43

Fig. 17. Propagation of dimensional variation along the roof frame of the case study in different tie-in plates. As seen, tie-in plates further from the datum have higher impacts. Using kinematics chains and input from point cloud data yields output in the form of absolute deviations.

construction would be if the effects of welding distortion in a large steel structure were significantly larger than the variations associated with fit-up (i.e., position and orientation deviations). This leads into a discussion about rework minimization and adaptive fabrication process control. By modeling the kinematic systems of components in a construction assembly, it is possible to analyze each source of variability as it occurs during the progression of fabrication activities. Then using as-built data (laser scans), it is possible to quantify and determine how to optimally correct (or adapt) fabrication and assembly approaches to offset deviations such that the critical features are within tolerance. 6. Conclusions and recommendations for future work The objective of this paper is to explore the use of dimensional variation analysis (DVA) for modeling the effect of dimensional variability

3042.35

in construction assemblies. To do this, robotics theory in the form of kinematics chains are used to derive the spatial relationship between components in an assembly. The proposed method for DVA assumes rigid body transformation, where deviations are in the form of rotational and translational degrees of freedom. In comparison with other analytical DVA methods, the proposed method does not account for form variation. DVA has not been extensively used in construction, however similar methods such as tolerance mapping have been developed based on the need to understand the effect of the accumulation of dimensional variability. The case study presented in this paper demonstrates how to derive assembly equations in order to model the accumulation of dimensional variability. Two approaches are used in the case study in order to validate the proposed methodology. The first approach is an as-built DVA which utilizes tolerances and the assembly configuration contained in a BIM model (thus, it is referred to as a model-based DVA). The second

15721.38

Fig. 18. Sample extracted dimensions (in mm) from 3D point cloud model using PolyWorks®.

44

C. Rausch et al. / Automation in Construction 75 (2017) 33–44

Table 3 Comparison of maximum deviation values for model-based and laser-based DVA. Tie-in plate

Model-based DVA: maximum deviation (mm)

Laser-based DVA: maximum Percent deviation (mm) difference

TP1 TP2 TP3 TP4 TP5

1.64 13.86 26.96 40.05 53.20

1.65 13.85 26.95 40.05 53.22

−1.0% 0.1% 0.4% 0.0% −0.4%

approach is an as-built DVA, which uses data pertaining to the actual constructed assembly in the form of point clouds from laser scans (thus, it is referred to as a laser-based DVA). This case study analyzes the variation in position of tie-in plates between modules for a steel frame modular building. The results of both DVA approaches yielded remarkably similar deviation values, with percent differences less than 1%. This accuracy demonstrates that it is often not necessary to select ‘perfect’ tolerances for each component using the model-based DVA because even if one particular as-built deviation exceeds its tolerance, the overall accumulation of as-built deviations will likely be equal to or less than the tolerance accumulation value. This demonstrates that the importance of using a kinematics chain based DVA lies with the final position of the ‘end-effector’ (i.e., the critical feature at the end of the kinematics chain), rather than on the transformations of individual links. The limitations of the proposed methodology need to be clearly understood. The proposed method does not function adequately in cases where a rigid body transformation assumption is invalid; in other words, where there are large form deviations (e.g., bending, bowing, warping of steel components or assemblies). If large form deviations do exist, the proposed method can be adapted by modeling the local coordinate system of a component to adequately account for rigid body transformation. This process is not explored in this paper, and would be tedious to employ. In the case where large form deviations exist, an alternative DVA approach is preferable in order to account for additional degrees of freedom. Future works of this research include numerous applications of kinematics chain based DVA for construction assemblies. Among the list of proposed applications to be explored include: risk-based connection design, adaptive assembly (adjusting fabrication processes to control deviations of critical features), rework minimization and a simulationbased DVA method. Another direction for future research could be the investigation of best tolerance strategy for fitting up defective assemblies. This becomes possible fusing the kinematics chain modeling developed here and inverse kinematics analogy. This is currently being investigated by the authors. Acknowledgement The authors of this research would like to acknowledge the financial support of the Natural Science and Engineering Research Council (NSERC) and PCL-Permanent Modular Construction. References [1] E.H. Oh, N. Naderpajouh, M. Hastak, S. Gokhale, Integration of the construction knowledge and expertise in front-end planning, J. Constr. Eng. Manag. 142 (2015) 04015067. [2] M.H. Pulaski, M.J. Horman, Organizing constructability knowledge for design, J. Constr. Eng. Manag. 131 (8) (2005) 911–919 (911) 10.1061/(ASCE)0733-9364. [3] J. O'Connor, Constructability Implementation Guide, Construction Industry, 2006. [4] S. Azhar, M. Khalfan, T. Maqsood, Building information modelling (BIM): now and beyond, Constr. Econ. Build. 12 (2015) 15–28 (ISSN 1837-9133). [5] T. Hartmann, M. Fischer, Supporting the constructability review with 3D/4D models, Build. Res. Inf. 35 (2007) 70–80, http://dx.doi.org/10.1080/09613210600942218. [6] D.K. Ballast, Handbook of Construction Tolerances, John Wiley & Sons, 2007. [7] M. Jingmond, T. Lindberg, A. Landin, Identifying causes of additional costs in tolerance compliances failure in buildings, TG65 & W065-Special Track 18th CIB World Building Congress May 2010 Salford, United Kingdom 2010, p. 554.

[8] C.T. Milberg, I.D. Tommelein, Tolerance and constructability of soldier piles in slurry walls, J. Perform. Constr. Facil. 24 (2009) 120–127, http://dx.doi.org/10.1061/ (ASCE)CF.1943-5509.0000079. [9] M. Jingmond, R. Ågren, A. Landin, Use of cognitive mapping in the diagnosis of tolerance failure, 6th Nordic Conference on Construction Economics and Organisation 2011, pp. 305–313. [10] A. Landin, P. Kämpe, Industrializing the Construction Sector through Innovation–Tolerance Dilemma, Proc. CIB World Building Conference 2007-387, Cape Town, 2007. [11] J.S. Goulding, F. Pour Rahimian, M. Arif, M. Sharp, New offsite production and business models in construction: priorities for the future research agenda, Architect. Eng. Des. Manag. 11 (2015) 163–184, http://dx.doi.org/10.1080/17452007.2014.891501. [12] D.E. Whitney, Mechanical assemblies, Their Design, Manufacture, and Role in Product Development, 1, Oxford University Press on Demand, 2004. [13] L.C. Sleath, P. Leaney, The use of a kinematic constraint map to prepare the structure for a dimensional variation analysis model, Am. J. Veh. Des. 1 (1) (2013) 1–8, http:// dx.doi.org/10.12691/ajvd-1-1-1. [14] T. Acharjee, Investigating Accumulation of Tolerances and its Impact on Reliability of Job Site Installation, University of Cincinnati, 2007 (Print). [15] C. Milberg, I.D. Tommelein, Application of tolerance mapping in AEC systemsProceedings Construction Research Congress, 2005. [16] C. Milberg, I.D. Tommelein, Tolerance mapping–partition wall case revisitedProceedings of the 12th Annual Conference of the International Group for Lean Construction 2004, pp. 2–5. [17] ISO, ISO-1101: Geometrical Product Specifications (GPS)—Geometrical Tolerancing—Tolerances of Form, Orientation, Location and Run-out, International Organization for Standardization, Geneva, Switzerland, 2012. [18] ASME, Dimensioning and tolerancing, Engineering Drawing and Related Documentation Practices. Revision of ASME Y 2009, p. 14. [19] P. Tang, G. Chen, Z. Shen, R. Ganapathy, A spatial-context-based approach for automated spatial change analysis of piece-wise linear building elements, Comput. Aided Civ. Inf. Eng. 31 (2016) 65–80, http://dx.doi.org/10.1111/mice.12174. [20] M. Nahangi, C.T. Haas, Automated 3D compliance checking in pipe spool fabrication, Adv. Eng. Inform. 28 (2014) 360–369, http://dx.doi.org/10.1016/j.aei.2014.04.001. [21] C.B. Farnsworth, S. Beveridge, K.R. Miller, J.P. Christofferson, Application, advantages, and methods associated with using BIM in commercial construction, Int. J. Constr. Educ. Res. 11 (2015) 218–236, http://dx.doi.org/10.1080/15578771.2013.865683. [22] F. Leite, A. Akcamete, B. Akinci, G. Atasoy, S. Kiziltas, Analysis of modeling effort and impact of different levels of detail in building information models, Autom. Constr. 20 (2011) 601–609, http://dx.doi.org/10.1016/j.autcon.2010.11.027. [23] C. Eastman, C.M. Eastman, P. Teicholz, R. Sacks, BIM handbook, A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers and Contractors, John Wiley & Sons, 2011. [24] V. Software, Vico guest blogger series, How Swinerton Builders Deliver Virtual Design and Construction, 2016 http://www.vicosoftware.com/vico-blogs/guest-blogger/tabid/88454/bid/12659/How-Swinerton-Builders-Deliver-Virtual-Design-andConstruction.aspx (04/27, 2016). [25] K.W. Chase, A.R. Parkinson, A survey of research in the application of tolerance analysis to the design of mechanical assemblies, Res. Eng. Des. 3 (1991) 23–37, http:// dx.doi.org/10.1007/BF01580066. [26] Y. Hong, T. Chang, A comprehensive review of tolerancing research, Int. J. Prod. Res. 40 (2002) 2425–2459, http://dx.doi.org/10.1080/00207540210128242. [27] F. Scholz, Tolerance stack analysis methods, Research and Technology Boeing Information & Support Services, Boeing, Seattle 1995, pp. 1–44. [28] Z. Yang, S. McWilliam, A. Popov, T. Hussain, H. Yang, Dimensional variation propagation analysis in straight-build mechanical assemblies using a probabilistic approach, J. Manuf. Syst. 32 (2013) 348–356, http://dx.doi.org/10.1016/j. jmsy.2012.11.008. [29] F.J. Fuentes, V. Trouvé, J. Cordier, J. Reich, Methodology for dimensional variation analysis of ITER integrated systems, Fusion Eng. Des. (2016)http://dx.doi.org/10. 1016/j.fusengdes.2016.03.006. [30] F.J. Fuentes, V. Trouvé, E. Blessing, J. Cordier, J. Reich, Status of ITER dimensional tolerance studies, Fusion Eng. Des. 88 (2013) 597–601, http://dx.doi.org/10.1016/j. fusengdes.2013.01.061. [31] Y.K. Cho, C.T. Haas, S.V. Sreenivasan, K. Liapi, Position error modeling for automated construction manipulators, J. Constr. Eng. Manag. 130 (1) (2004) 50, http://dx.doi. org/10.1061/(ASCE)0733-9364. [32] C. Feng, Y. Xiao, A. Willette, W. McGee, V.R. Kamat, Vision guided autonomous robotic assembly and as-built scanning on unstructured construction sites, Autom. Constr. 59 (2015) 128–138, http://dx.doi.org/10.1016/j.autcon.2015.06.002. [33] M. Nahangi, J. Yeung, C.T. Haas, S. Walbridge, J. West, Automated assembly discrepancy feedback using 3D imaging and forward kinematics, Autom. Constr. 56 (2015) 36–46, http://dx.doi.org/10.1016/j.autcon.2015.04.005. [34] M. Nahangi, C.T. Haas, J. West, S. Walbridge, Automatic realignment of defective assemblies using an inverse kinematics analogy, ASCE J. Comput. Civ. Eng. (2015), 04015008. http://dx.doi.org/10.1061/(ASCE)CP.1943-5487.0000477. [35] M. Nahangi, T. Czerniawski, C.T. Haas, S. Walbridge, J. West, Parallel systems and structural frames realignment planning and actuation strategy, J. Comput. Civ. Eng. (2015), 04015067. http://dx.doi.org/10.1061/(ASCE)CP.1943-5487.0000545. [36] C. Rausch, Development of a Framework for the Strategic Management of Dimensional Variabilty of Structures in Modular Construction, University of Waterloo, 2016. [37] J. Denavit, R.S. Hartenberg, A kinematic notation for lower-pair mechanisms based on matrices, J. Appl. Mech. (1955) 215–221. [38] AISC, Code of Standard Practice for Steel Buildings and Bridges (AISC 303–10), 2010. [39] FARO, FARO Laser Scanner LS 840/880, http://www2.faro.com/FaroIP/Files/File/ Techsheets%20Download/IN_LS880.pdf2014 (April 8, 2014). [40] PolyWorks, InnovMetric PolyWorks, http://www.innovmetric.com/en2015.