Building Services Standard Solutions Variational Generation of Plant Room Layouts

B. Medjdoub1, P. Richens1 and N. Barnard2 1The Martin Centre, University of Cambridge, UK 2 Oscar Faber, St Albans, Hertfordshire, UK

Key words: constraints, layout configuration, topological solutions, optimisation, interactivity, plant room, pipe routing, 3D solution.

Abstract: Object-based CAD programming is used to take advantage of standardisation to handle the schematic design, sizing, layout and (potentially) pipe-routing for LPHW (Low Pressure Hot Water) plant rooms in buildings. From a simple specification of the plant room geometry, and the heating load in kw, our software proceeds through a number of steps. First the standard number and size of modular boilers, pumps etc. is determined from the heat load. Then a compatible optimising 3D variational solution is generated, using Constraint Logic Programming. Our approach is highly interactive. Modifying the topology of the solution is done directly through the graphic interface, e.g. modifying a boiler position is done by dragging; the system automatically updates the 3D model including the pipe-routing while maintaining all the constraints, and hence the validity of the design.

1. INTRODUCTION

If the design of any complex artefact is suitably restricted by adhering to a library of predefined components and assembly details, it becomes possible to automate a great deal of the design process. In the case of heating and ventilation plants there are in any case good value-engineering reasons to use standard components and details.

Currently, designers solve these problems "by hand". Starting from the heating load in kW, a schematic solution is defined. The engineers proceed to equipment selection, then its location, followed by pipe routing governed by objective requirements (minimum surface area, minimum pipe length, minimum bend number…). In summary plant room physical design amounts to layout configuration followed by pipe routing.

480 CAAD Futures 2001

Computer support for layout configuration has been studied for more than twenty years. Studies include techniques such as mathematical programming (Mitchell et al., 1976), expert systems (André, 1986; Flemming, 1988), genetic evolution (Jo and Gero, 1998; Gero and Kazakov, 1998; Rosenman, 1996) and constraint satisfaction (Baykan and Fox, 1991; Aggoun and Beldiceanu, 1992; Charman, 1994). These approaches typically enumerate all placement solutions. Similar solutions, differing only in the precise positioning of an element on the modular grid, are considered as two different geometrical solutions. Clearly, in preliminary design, it is wasteful to distinguish between geometrically close solutions, as this generates a high number of solutions (typically several thousands or millions) which cannot be distinguished in their global aspect by the designer. A recent approach based on constraint satisfaction has been presented by Medjdoub and Yannou (Medjdoub and Yannou, 2000) where the topology and the geometry are separated. This brings great flexibility in constraint utilisation since the constraint definition is separated from the resolution algorithms, and deals with high-order combinatorial problems.

Another disadvantage of most of the aforementioned approaches to space planning is that they attempt full automation of the process.

Our approach to plant room design combines automation and interactivity. From a simple specification of the plant room geometry (an orthogonal polygon with known obstructions, openings and external walls), and the heating load in kW, our software proceeds through a number of steps. First the number and size of standard modular boilers, pumps etc is determined from the heat load. Then a compatible optimising 3D variational solution is generated, using Constraint Logic Programming and particularly the arc-consistency1 (Smith, 1995) on integers. To do this we firstly enumerate a satisfactory topological solution, and then refine it to form a compatible geometrical solution. The final step generates pipe routes, using branch and bound optimisation to minimise the length of pipes and the number of bends. Heuristics are used to restrict the search to promising areas of the solution space. In this NP-complete problem, dynamic variable ordering (dvo) heuristics can have a profound effect on the performance of backtracking search algorithms (Bacchus et al., 1995; Gent et al., 1996;

1 If there is a binary constraint Cij between the variables xi and xj then the arc (xi; xj) is arc consistent if for every value a ∈ Di (Di is the Domain of xi), there is a value b ∈ Dj such that the assignments xi=a and xj=b satisfy the constraint Cij. Any value a ∈ Di for which this is not true, i.e. no such value b exists, can safely be removed from Di, since it cannot be part of any consistent solution: removing all such values makes the arc (xi; xj) arc consistent. Note that we have only checked the values of xi; there may still be values in the domain of xj which could be removed if we reverse the operation and make the arc (xj; xi) arc consistent.

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Smith et al., 1998). Tsang et al. (Tsang et al., 1995) show that there does not appear to be a universally best algorithm, and that certain algorithms may be preferred under certain circumstances.

The solution obtained can be modified or improved by the designer, when we provide further contribution by concentrating on interactivity. Modifying the topology of the solution or the geometry of the plant room is done directly through the graphic interface, e.g. modifying a boiler position is done by dragging; the system automatically updates the 3D model including the pipe-routing while maintaining all the constraints.

We describe the plant room design problem in section 2. The object model of the plant room and the plant room design rules are presented in sections 3 and 4. The enumeration algorithm is described in section 5. In section 6 the interactivity of the system is presented. Before concluding, the implementation and benchmarking are presented in sections 7.

2. PROBLEM DESCRIPTION

The selection of systems for the plant room is based on its function, e.g. heating, cooling, air handling, electrical etc. The selection of equipment for each system will then be a standard solution defining the number of plant items and the interconnection configuration required to perform the function (Barnard, 1999). These solutions are typically manifested in the form of schematics (see Figure 1). Sizing will generally require data in the form of loads, together with rules. The data may be calculated externally, generated on the basis of a rule-of-thumb or supplied from another plant item. For example, boilers will require a heat load for sizing that may initially be estimated using a rule-of-thumb based on the building area, to be replaced by a calculated value as the design evolves. When the number of plant items to perform the function is defined, two steps remain to reach the final solution: item location and pipe routing.

Figure 1. Example of schematic solution of plant room

Traditionally, the location of equipment is approached from two

extremes. One extreme is to devise a solution where the general arrangement of the (main) equipment is predetermined on the basis of a fairly rigid set of

482 CAAD Futures 2001 rules. This is appropriate for new buildings where there may be a degree of flexibility concerning the size and configuration of the plant room. The other extreme would be to allow the plant to be placed randomly within the space available. This would allow it to fit into plant rooms of various sizes. A number of possible configurations could be produced and the best selected according to a number of judgement criteria, e.g. spatial requirement, cost etc. Figure 2 shows some preferred layouts of modular boilers, based on general location rules: – The boiler room is usually in a separate space (must be separate from

chillers). – Each piece of equipment requires a minimum maintenance space around

it. – All equipment is on a plinth 100mm high. – Access routes are provided through plant areas: 2000mm is ideal,

1500mm is the minimum requirement. – Double doors leading to the plant room are required. – A single door for emergency escape must be located opposite to the main

door. – Boiler location is side by side – Boilers back against a wall.

Double doors(minimum 1.5 doors)

Single door foremergency exit

Figure 2. Favourite layout configuration of plant room

As soon as the plant room layout is defined we proceed to pipe routing. The priority is for horizontal orientation minimising the number of bends and the pipe length.

3. OBJECT MODEL OF THE PLANT ROOM

The plant room object model holds three main classes of objects representing the plant room geometry, equipment and pipework. Each defined class is characterised by attributes and class constraints.

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3.1 Plant room geometry

The plant room geometry can be an orthogonal polygon with known obstructions, openings and external walls. We can also provide columns (see Figure 3). The object structure of the plant room geometry includes three classes: Space, Door and Column. Each class is characterised by a reference point (x, y, z), a length l, a width w and a height h. In Figure 3 the plant room is an L-shape with two doors and one column. The L-shape corresponds to: space1−space2. The reference points, l, w and h, are integer-constrained variables. We use an arc-consistency on integers constraint programming technique which explains the need for a distance increment; but this is not too restrictive as the scale used is the millimetre.

Space1: (x,y,z), l, w, h.Space2: (x,y,z), l, w, h.Main door: (x,y,z), l, w, h.Emergency door: (x,y,z), l, w, h.column: (x,y,z), l, w, h.

Figure 3. Plant room geometrical representation

3.2 Equipment

The equipment is described in four sub-classes: Boiler, Pump, Pressurisation unit and Control panel. Each class is characterised by a reference point (x1, y1, z1), a length l, a width w, a height h, and an orientation ori. The reference point, l, w and h are integer-constrained variables. The orientation attribute is a constrained discrete variable defined over the domain {0°, 90°, 180°, 270°}, the length, the width and the height are fixed variables. As is indicated in Figure 4, each piece of equipment requires a minimum space for the maintenance.

A class constraint is defined to ensure the four possible configurations corresponding to the four possible orientations. This constraint generates a choice point leading to four constrained sub-problems, these are shown in Figure 5.

484 CAAD Futures 2001

h

gasconnection

LPHW outletconnection

LPHW inletconnection

550

l

w

x

y

X

Y

600

600

maintenancespace

h

LPHW outletconnection

LPHW inletconnection

h

system fillconnection

mainssupply600

600

maintenancespace

l

w

x

y

X

Y

z300

725

615

400400

l

w

x

y

X

Y

150400

maintenancespace

z

400

h

50150

w

x

y

X

Y

610

460

maintenancespace

z

532

950

(a) boiler

(d) control panel(c) pressurisation unit

(b) pump

Figure 4. Geometrical representation of the plant room equipment

w

x

y

X

Y

z

l

orientation=0°

x

y

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w

orientation=90°

w

x

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l

orientation=180°

x

y

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w

orientation=270°

Figure 5. The four possible orientations of the boiler

3.3 Pipework

The Pipe class is defined by a set of points and a radius r (see Figure 6). Each pair of successive points defines a segment of the pipe (i.e. (P1,P2), (P2,P3) and (P3,P4) are the three segments of the pipe shown in Figure 6). An

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orientation ori is associated with each segment. All the attributes are integer-constrained variables except the orientation which is a constrained discrete variable defined over the domain {x°, y°, z°}. A class constraint is defined to ensure that two successive segments have different orientation.

P1P2

P3 P42×r

ori=z°ori=y°

ori=y°

Figure 6. Geometrical representation of a pipe with a set of four points (P1, P2, P3, P4) corresponding to two bends

4. PLANT ROOM DESIGN RULES

The plant room design rules are expressed by constraints. These constraints are applied implicitly by the system and can be divided into two categories: topological and dimensional. Topological constraints define continuity and neighbourhood in a building while dimensional constraints define distances and angles (Boudon et al. 1972).

4.1 Dimensional constraints

Dimensional constraints assign a minimal or a maximal value to the object constrained variables. This constraint is expressed by equality or inequality, i.e. boiler.l=532.

4.2 Topological constraints

Topological constraints comprise: – Inclusion constraint, i.e. all the objects are inside the plant room. – Non-overlapping constraint between the plant room components and

pipework. – Adjacency constraint, i.e. between the control panel and the walls.

486 CAAD Futures 2001 4.2.1 Inclusion in the plant room

This simple constraint consists of four conjunctive inequalities over x1, x1, z1, y2, y2, z2 in order to be inside of the current plant room. In the case of L-shape or T-shape (see Figure 3) equipment and pipework are inside space1 and do not overlap space2.

4.2.2 Non-overlapping

A non-overlapping constraint expresses the fact that two elements cannot overlap each other; it is automatically applied between all pairs of elements. Figure 7 shows the position permitted for e2.x2, e2.y2 and e2.z2 (e2.z2 represents the constrained variable z2 of element e2) by the non-overlapping constraint between two elements e1 and e2. The non-overlapping constraint introduces a new non-overlapping variable with six values {E,W,N,S,A,U}. This variable divides the space surroundings into six parts (see Figure 7) but not symmetrically. Indeed, we observe that the N and S values give more solutions than the E and W values. This asymmetry is made to avoid any redundant solution. It is the instantiation of these non-overlapping variables and the adjacency variables which, if proven consistent, gives a topological solution.

possible positions of (e2.x2, e2.y2, e2.z2)

e1 E (east)

S (south)

e2

e1.y1

e2.y2

e2.x2

W (west)

e1.x1

N (north)

Min(D(e2.l))

Min(D(e2.w))

e1 E (east)

U(under)

e2

e1.z2

e2.z1

e2.x2

W (west)

e1.x1

A (above)

Min(D(e2.l))

Min(D(e2.h))

e1.z1

(e2.z1<e1.z2 and e2.z2>e1.z1) (e2.z1>e1.z2 or e2.z2<e1.z1)

Figure 7. General non-overlapping constraint

The non-overlapping constraints between plant room equipment introduce variables with four values {E,W,N,S} as they are all on the same floor. Between the pipework and the equipment the variables generated have five values {E,W,N,S,A}, as the pipework can be located above the equipment.

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4.2.3 Adjacency

The adjacency constraint is applied between the control panel and the plant room walls.

The application of this constraint creates a new discrete constrained variable named adjacency variable defined over the domain {E, W, N, S}, standing for east, west, north and south wall. In fact, each adjacency constraint and its consequent adjacency variable introduce a choice point in the tree search (see Figure 8). The adjacent constraint is a "dæmon" constraint for which an instantiation of the adjacency variable triggers a propagation and consequently a domain reduction thanks to the arc-consistency technique. During enumeration, corner solutions are only enumerated once.

Adjacent (cp, proom)⇒ Var ∈ {N, E, S, W}

Var

(cp.y1 = proom.y1)

(cp.x2 = proom.x2)(cp.y1 ≠ proom.y1)(cp.y2 ≠ proom.y2)

(cp.y2 = proom.y2)EN S W

(cp.x1 = proom.x1)(cp.y1 ≠ proom.y1)(cp.y2 ≠ proom.y2)

Figure 8. Adjacency between the control panel and the plant room walls

In our application, the following disjunctive form is supported: e1 (adjacent#1) e2 OR e1 (adjacent#2) e3 with e2≠ e3. It is applied in case of L-shape or T-shape plant room. In figure 2 the control panel is constrained to be adjacent to space1 walls or to space2 walls.

5. ENUMERATION ALGORITHM

To generate the solution we follow two steps. First, we generate the plant room layout which determines the equipment location. Then, we proceed to pipe routing minimising the length of pipes and the number of bends.

488 CAAD Futures 2001 5.1 Plant room layout generation

In this step our objective is to enumerate the first satisfactory topological solutions, and then refine it to form a 3D compatible geometrical solution.

The topological solution is based on Medjdoub and Yannou definition (Medjdoub and Yannou 2000):

Each space layout Constraint Satisfaction Problem (CSP) where the n(n−1)/2 (n being the number of items) non-overlapping variables and adjacency variables are instantiated and which remains geometrically consistent (i.e. for which at least one geometrical solution exists) is a topological solution.

Contrary to Medjdoub’s approach, we enumerate just the first satisfactory topological solution. Dynamic variable ordering (dvo) heuristics are used to restrict the search to promising areas of the space tree. These heuristics are not only used for a better performance of the backtracking search algorithms, but also to lead to a better topology solution if it exists. Thus, the designer can select from the user interface (by choosing between vertical or horizontal layout as indicated in Figure 2) which topology the search algorithm will investigate first.

To refine the topological solution to a 3D geometrical solution we instantiate the geometrical parameters of the plant room equipment. We use the classical dvo heuristic for ordering the geometrical variables, thus the priority is given to the variable with the smallest domain.

5.2 Pipe routing

The pipe routing is the last step of the enumeration. As soon as we have obtained a consistent 3D geometrical solution, we determine from our user interface the wall through which the LPHW mains pass. The algorithm proceeds in three steps. First the bends number variables are instantiated, the smallest values being chosen first. Then the non-overlapping variables between pipes and pipes/equipment are instantiated. Finally, we instantiate the pipe reference points minimising the length of each pipe using the “branch and bound” algorithm (Carpaneto et al., 1995). This is the most common approach used in constraint programming to find the optimal solution. First, we create a constrained variable representing the objective function and find an initial solution, then we introduce a new constraint that the value of the objective variable must be better than in the initial solution. We repeatedly solve the new problem and tighten the constraint on the objective variable until the problem becomes insoluble: the last solution

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found is then the optimal solution (Smith, 1995). Figure 9 shows three different solutions of two pipes with different z1 and z2.

(a) (b) (c)

P1

P2

P1P1

P2P2

P2.z1=P2.z2P1.z1=P2.z1P1.z1=P1.z2

P2.z1=P2.z2P1.z1=P2.z1

P1.z1≠P1.z2

P2.z1=P2.z2

P1.z1≠P2.z1P1.z1=P1.z2

(x1,y1,z1)

(x1,y1,z1)(x2,y2,z2)

(x2,y2,z2)

Figure 9. Three different pipework solutions

6. INTERACTIVITY

Our approach is based on interactivity. As an example we are going to generate and modify a plant room of 1GW. The first step is to generate the first satisfactory solution (see Figure 10b) from the defined plant room geometry (see Figure 10a). In this example, the heuristic of a vertical layout has been selected. The second step is to generate pipework; to do this we select the wall where the LPHW and the flue pipe pass through and run the search algorithm by clicking on a button. As indicated in Figure 1c the LPHW pipes pass through the north wall and the flue pipe passes through the west wall. After obtaining a complete 3D solution it is possible to make any modification. To modify the pipes passing through walls, we just have to select them and drag them around the walls. The flue pipe is dragged from its initial position (see Figure 10c) to a new one as indicated in Figure 10d. The same search algorithm of pipe routing is used with fixed values for all the pipes except the flue pipe.

Other features are offered by the system: plant room geometry modification and topology modification. Through the user interface, it is possible to modify the shape or size of the plant room and to add, move or delete columns and doors. From the examples shown in Figure 10d, by simply dragging the plant room geometry, the system generates a new solution corresponding to the new updated plant room geometry. Thus it is very easy to minimise the plant room area while maintaining all the constraints, i.e. the solution shown in Figure 10e corresponds to the minimum plant room area for 1GW. If the designer would like to explore

490 CAAD Futures 2001 other topologies, he/she has simply to select the component and drag it to the desired position. The system generates a new solution with the desired new topology (see Figure 10f). If no solution exists, the previous one is maintained.

(a) room geometry (b) layout generation

(c) pipe route (d) flue pipe modification

(e) area minimisation (f) topology modification

Figure 10 (a,b,c,d,e,f). 1GW plant room solution and its modification

7. IMPLEMENTATION AND BENCHMARKING

This application is developed in JMDL (Java Modeling Language) as embedded in MicroStation/J, and ECLiPSe2 the constraint logic programming system. We use JNI3 (Java Native Interface) as the programming interface between ECLiPSe and JMDL. We use MicroStation/J4 to hold the object model and for 3D rendering.

The solutions generated by our prototype have been tested against

2 ECLiPSe is a trademark of IC-PARC at Imperial College, London. 3 JNI is a trademark of Sun Microsystems, Inc. 4 Microstation/J is a trademark of Bentley Systems.

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conventional solutions in a benchmarking exercise (Hejab et al., 1993; Burberry, 1986). Advantages has been underlined and some advice has been suggested for future development. The main advantages: – the interactive layout modification. – the interactive plant room area minimisation has been particularly

appreciated. – the 3D solution. The main suggestions for future development: – improving the pipe routing and more precisely the interactivity of pipe

modification. The designer should be able to modify interactively the position of bends inside the plant room.

– to solve large models over 2GW. Our approach is limited to middle-size problems (50 objects between pieces of equipment and pipes).

8. CONCLUSION

The approach presented in this paper shows an interactive system for plant room design, simple to use with high-level modification of plant room layout topology, pipework position and plant room space geometry. Several aspects were discussed: the constraints and the plant room item structure, the algorithm of solution enumeration and the interaction via the user interface.

Compared to previous approaches we have here a compromise between full automation and interactivity. This balance gives to the designer full control while assisting him to solve complex problems automatically.

ACKNOWLEDGEMENTS

This project is funded by EPSRC5 and DETR6 under the LINK7 Meeting Client Needs through Standardisation programme in UK. There are more than 10 partners including Oscar Faber, BSRIA, Hamworthy2, Pullen Pumps, Bentley Systems, Taywood Engineering Ltd, The SCI, Sainsburys, Sheppard Robson, Carrier, Woods, Waterloo, Delta, Biddles, CADAC, IES Facet The programming was carried out at the Martin Centre CADLAB (University of

5 The Engineering and Physical Sciences Research Council 6 The Department of the Environment, Transport and the Regions 7 The LINK scheme is the UK Government's principal mechanism for promoting

partnership in pre-competitive research between industry and the research base.

492 CAAD Futures 2001 Cambridge Department of Architecture), which is supported by Informatix Inc of Tokyo.

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