Modeling workflow for a building model for control purposes

Barbara Mayer∗

FH JOANNEUM

Werk-VI-Strasse 46, 8605 Kapfenberg, Austria∗barbara.mayer@fh-joanneum.at,

Michaela Killian† and Martin Kozek‡

Vienna University of Technology

Wiedner Hauptstrasse 8-10/325/A5, 1040 Vienna, Austria

{†killian, ‡kozek}@impa.tuwien.ac.at

Abstract—Modeling of large multi-purpose buildings for con-trol design of building services is a complex and applicationspecific task. In this work a general modeling approach isproposed, which is based on a standardized work flow anda small rule base. It aims at establishing an industrial toolchain which eventually enables control engineers to model abuilding and design a control strategy in the most efficient way.The modeling workflow is clearly structured, and both datadriven and analytical modeling procedures are presented andcompared. Real data from a University building are utilized todemonstrate the efficiency of the proposed methods.

Index Terms—building modeling; system identification; sim-ulation; MPC;

I. INTRODUCTION

Saving energy has become a political and social issue

of concern worldwide. As buildings cause 40% of the total

final energy consumption [1] and due to the long lifespan of

buildings, an emphasis is put on the development of strategies

to operate the existing Heating, Ventilation, Air Conditioning

(HVAC) systems in an energy efficient way. Model Predicitve

Control (MPC) is a proven technology for optimizing dy-

namic systems with respect to their constraints which requires

a balanced model as simple as possible and as precise

as necessary to accurately reproduce real world conditions.

Unfortunately, large buildings are complex dynamic systems,

hence modeling and identification are demanding and time

consuming procedures. Recent papers [2], [6] present ex-

perimental, statistical, and simulation methods for building

identification aiming to a good and reasonably simple model

for MPC. Further, they present first applications of MPCs

for buildings with promising results. For stochastic MPC

an energy saving potential of 15% to 28% could be shown

[3] depending on the building parameters and the outside

conditions [4]. Nevertheless, considering the computational

effort and/or the required time and modeling knowledge,

these introduced methods are impractical for industrial usage.

This work focuses on the development of an industrial

tool chain for modeling methods for large buildings. This

intention raises additional requirements for building modeling

and identification. This paper initially motivates them and

presents an appropriate modeling workflow consisting of an-

alytical modeling and data driven identification. Furthermore,

the application on a demonstration building is shown, and the

uncertainty of model inputs and their effect on the desired

outputs are discussed.

II. REQUIREMENTS FOR AN INDUSTRIAL TOOL

CHAIN

If MPC is intended to be used for industrial building

automation some distinct requirements arise. Large modern

buildings are complex in several aspects. They differ con-

siderably in architecture, materials, thermodynamic behavior

and implemented HVAC systems. Thus, an identification

routine designed for general buildings has to be as generic

as possible to meet different settings.

Systems for optimization of the energy efficiency of large

buildings are industrially implemented either in the com-

missioning phase or retrofitted later in the operation phase.

The modeling tool’s input therefore is either plan data only,

or measured data generally gathered from the historic data

bases. Nevertheless, an industrial usage requires a quick

and robust modeling procedure, i.e. unknown parameters

such as occupancy schedules, must be well estimated or the

subsequent errors have to be accepted. Hence, the methods

chosen for identification routines are intended to yield the

most accurate model with the least effort possible.

Taking all requirements into accoun the resulting models

are possibly afflicted with a significant model error. The

design of a robust controller is, as a further tool of the chain,

subsequently planned to avoid a redesign of the controller

for every new application.

Summarized below are the listed requirements for the

model workflow presented in III-B which shows the steps

needed for the model identification of large buildings for a

robust MPC.

• The identification routine is as generic as possible and

can be applied to many buildings

• Quick and robust modeling methods needed for ob-

served and plan data

• Simple and clear guidelines how to partition the building

in smaller sub-systems (zoning)

III. MODELING METHODS

A. Pre-Processing

The Pre-Processing routine is necessary to prepare and col-

lect all information for a successive identification workflow.

Figure 1 shows the consecutive steps.

The central sub-process is the zoning zoomed out in

Figure 2.

To avoid modeling each single room of a large building,

rooms with similar attributes are aggregated to a bigger

zone. The partitioning is a multidimensional problem and an

iterative process, where thermodynamic behavior and specific

building physics, as well as the rooms’ usage, determine the

zones which are controlled individually. Before the multi-

zone structure is determined, it is essential to check whether

the approximation made is acceptable. If so, for all identified

zones, a corresponding variable structure is established to

declare control and manipulated variables, as well as distur-

bances. These structures give a clear picture which sensors

or measured data are needed for the black box identification.

If necessary input data is not available, some zones have

to be aggregated to bigger entities and the zone structure

has to be redefined. If all required data can be achieved,

the zoning iteration is complete and succeeded by the data

acquisition of the pre-processing routine. Additionally, all

zone usage profiles have to be defined generically, if no

occupancy plans are at hand. The Pre-Processing routine

concludes with gathering the weather data for the specific

building’s location.

Fig. 1. Workflow for the Pre-Processing routine

B. Modeling Workflow

Building modeling is the most time consuming and de-

manding task. In regard to the industrial requirements, proven

modeling approaches are not suitable. Physical detailed mod-

eling, e.g. represented as RC-networks [8], lead to infeasible

fitting of parameters of differential equations for large-scale

problems [9], [2].

Fig. 2. Workflow for the Zoning Iteration

This paper presents a combined explicit data-driven black

box and implicit white box modeling approach with the aim

of creating an industrially deployable modeling workflow

(Figure 3).

Fig. 3. Workflow for the identification of a multi-zone building

The preceding Pre-Processing routine (see III-A) provides

modeling data for both sub-processes, the analytical modeling

and the data driven identification. To continue the workflow

some necessary criteria have to be met (see Table I).

TABLE INECESSARY CRITERIA FOR THE MODELING AND IDENTIFICATION

ROUTINE

Criteria Simulation Data drivenModeling Identification

architectural plans yes noconstruction of walls/floors/roofs/windows yes noweather data (radiation, outside temperature) yes yesobserved data of zones’ temperature yes yesInput-Output structure for all zones no yesoccupancy plans (real data or generic) good yes

For the black box identification, local linear model (LLM)

networks are an efficient means of modeling complex nonlin-

ear dynamic systems such as large buildings. One of the main

advantages is the existing theory of system identification

[12], [13] which is extended to globally nonlinear system

behaviors. In addition the algorithm is easy to implement

and fast in execution.

Within the analytical modeling step an (implicit) white box

model can also be set up based on plan data with the aim

of fitting parameters of the data driven model, if any data is

missing or additional excitation is needed without generating

additional costs. Figure 3 shows the interaction.

The validation of the analytical simulation model is based

on a sensitivity analysis by calculating the difference quotient

multiplied with the ratio of the standard deviation of the

specific parameter xi to the output y as shown in (1).

Sσi =

∆y

∆xi

∗σxi

σy

∀i (1)

The validation of the identified model is done by cal-

culating the model performance in terms of coefficient of

determination (R2) and the Mean Squared Error (MSE).

MSE =1

n∑(Yi −Yi)

2, (2)

where (Yi−Yi)2 is the squared error between the global model

output Yi and the measurements Yi.

1) Analytical System Modeling with Simulation

Many software tools for building simulation are on

the market, but only some of them are appropriate for

control purposes. Among them are hardly any provid-

ing explicit models in terms of mathematical formulas

in the form of differential or difference equations. [5]

gives an overview of building simulation tools and their

general capabilities.

Gaining certain building predictions with simulation

requires some principle proceedings, applicable for all

tools. The following steps are identified to build up a

proper simulation model:

• Extracting conductivity and heat transfer coeffi-

cients from the building physical construction of

walls, floor, windows

• Identification whether there are thermally activated

floors or ceilings

• Reading in the weather data, i.e. at least outside

temperature and radiance, from the observed loca-

tion

• Building up the simulation environment and feed-

ing it with the building specific data

• Assumption of profile for internal gains such as

occupancy and equipment

• Parametrization for dynamic modeling

2) Data Driven System Identification

The LOLIMOT algorithm combines a heuristic strategy

for partition space decomposition with weighted least

squares optimization [7]. It therefore provides a LLM

approximation of globally nonlinear dynamic systems.

In LOLIMOT, Gaussian kernel functions are fitted to

a rectangular partitioning of the m-dimensional input

or partition space performed by a decision tree with

axis-orthogonal splits at the internal nodes (Figure 4).

Each local model belongs to one hyper-rectangle in

whose center the fitting point is placed. New hyper-

rectangles are found by testing the possible splits in

all dimensions and taking the one with the highest

performance improvement. The algorithm stops when

it reaches a predetermined modeling error or maximum

size of the tree. Note that the partition space does not

need not be identical to the input space of the local

models, and that the choice of partition variables allow

the incorporation of expert knowledge.

Though the algorithm is fast in execution, the axis-

orthogonal splits in the partition space limit the

model fit considerably. Consequently, algorithms using

axis-oblique splits (hinging hyper-planes) have been

proposed [11]. In contrast to these computationally

more involved methods in [10], two methods for pre-

processing of the partition space are proposed, which

reduce the number of necessary LLMs, while improv-

ing the global performance.

One output of the identification algorithm is a set

of locally linear state-space models for a multiple-

input multiple-output (MIMO) or multiple-input single-

output (MISO) system. For each model a set of transfer

functions is given, one for each pair of input and output

variable. The function’s or model order l is predefined

by the user. The number of transfer functions received

is therefore l ∗m∗n, given m inputs and n outputs.

An essential requirement for this identification method

is the knowledge of the input output structure and the

availability of the corresponding measured data over a

representative period of time.

3) Fitting of parameters

Missing data leads to unsatisfactory black box identifi-

cation results. Using generated data from the simulated

building is a convenient method to compensate this lack

of information. A second identification iteration, using

better input data, can achieve improved or simplified

models concerning their order and number.

x1

x2

x1

x2

x1

x2

x1

x2

x1

x2

1I

2I

3I

x1

x2

x1

x2

4I1−1

2−1

2−2

3−1

3−2

3−3 4−1

4−2 4−3

4−4

Fig. 4. First four iterations of LOLIMOT algorithm for a two-dimensionalpartition space

IV. IDENTIFICATION RESULTS FOR

DEMONSTRATION BUILDING

A. Description of the building

The 27.000 m2 university building in the center of

Salzburg, Austria, has five floors above ground containing

several large and numerous smaller meeting rooms, offices

and lecture rooms. There are six atriums within the building

complex. For this study, the second floor is considered,

compiled of about 250 rooms almost all used as offices. The

facade of this floor has a glass ratio of about 70% and wooden

outside blinds.

The building contains five main shafts nearby the side

staircases. Through these shafts, the pipe circuits for the

cooling and heating supply are physically rooted from the

cellar to all floors. At the entrance to each floor, butterfly

valves regulate the acceptance rate of either the cooling or

the heating flow, depending on the demand of the zone.

Additional energy input is provided by a concrete activated

floor distributing supply water in a second circuit.

Several HVAC systems are used for the generation of

the demanded conditioning and distribution of water supply.

Both district heating and heating pumps ensure the heating

supply temperature (HS), whereas for cooling (CS), free

cooling towers as well as cooling machines are employed.

Additionally, geothermal energy is provided.

B. Pre-Processing

The procedure for aggregating the approximately 250

office rooms together was done iteratively as introduced

in III-A. The building construction is specific concerning

the shafts, atria and the amount of glass used. Due to the

thermodynamic behavior, the floor is split into five parts. The

first four group of rooms, oriented at the outside-edges, are at

the four cardinal points, with the fifth remaining in the center.

Furthermore, the physical structure of the piping system build

additional criteria for the zoning, i.e. there is one string

through each shaft which supplies rooms with orientation

to e.g. north and east and inner rooms. Subsequently, first a

structure with eight outer and one inner zones was defined.

The consideration of the input-output structure and the lack

of needed inputs, such as the position of the butterfly valves,

required an aggregation of predefined zones. Due to the

redefined structure there are now only four outer zones and

one inner zone. Figure 5 shows the zones identified for further

modeling.

Fig. 5. Zone structure of the first office floor

TABLE IILIST OF INPUT-, OUTPUT-, AND DISTURBANCE VARIABLES

ID Variable Description Unit Type

T zone Zone temperature ◦C outputToutside Outside temperature ◦C disturbance

Radiation Radiation W/m2 disturbanceOccupancy Occupancy profile W disturbanceHS Supply heating temperature ◦C inputHR Return heating temperature ◦C inputCS Supply cooling temperature ◦C inputCR Return cooling temperature ◦C inputTABSS Supply temperature for TABS ◦C inputTABSR Return temperature for TABS ◦C input

Based on this modeling simplification, a structure defining

the inputs, outputs and disturbances of the system was de-

fined for each zone as shown in Table II. For the application

of the modeling workflow presented in III-B, a time period

of a year (Nov.2011 - Oct.2012) was chosen. The measured

input data for the data driven identification were taken

from the automation system of evon GmbH, the company

that provided the building automation, whereas the outside

temperature and the radiance was bought from the ZAMG1

Austria.

The result is a MISO model, since the zone’s temperature

is the only control variable.

C. Modeling Workflow

For demonstrating the modeling workflow, the north-east

zone supplied by the shaft 3 is focused on in detail. The

modeling and identification procedures are conducted for this

building part as introduced in III-B.

1) Analytical System Modeling with Simulation

For the white box modeling, Trnsys 16 [14] was chosen

which is a transient system simulation tool. The model

generated is not available in explicit form and therefore

not directly usable for predictive control.

Within this tool a simulation environment is set up. The

Trnsys Simulation Studio allows the modeling of the

interaction of all used Types. Beside the Trnsys specific

1 Zentralanstalt fur Meteorologie und Geodynamik - The central institutefor meteorology and geodynamics

Type 56, which is the central component for a multi-

zone building, Type 9a and Type 16a were employed

to read in the weather data. The radiation processor

transforming the global radiance to the solar radiation

hit the vertical surfaces of the building.

The plan data used was taken from the catalogue

of building components provided by the building’s

installer.

The zone’s floor and ceiling is a thermally activated

system where a meandering pipe runs through the

concrete. The occupancy plan was estimated with one

person working on a PC and a monitor calculated with

140W for each room, which was multiplied by 38 for

the whole zone.

The adjustment between heating and cooling power,

and the energy supplied for the thermally activated

building system (TABS) was time consuming in order

to simulate the real building’s dynamics, since there

was no flow rate data available, neither of the heating,

nor the cooling, nor the TABS system. The simulation

results can be seen in Figure 6. The red line depicts

the zone’s temperature in comparison with the orange

line, which is the mean value of all room temperatures

over time. The purple line shows the data driven

identification, whereas the outside temperature is dark

blue. The green and light blue lines at the bottom

denote the heat and cooling demand over time. It can

be seen that the global simulation model does not fit the

dynamics very well at the transition from one season

to another, where heating, cooling, and the TABS are

active.

- T zone- T outside- T real data- T identification

- Heat demand- Cooling demand

Simulation Time [h]

Tem

per

ature

[◦C]

Hea

tdem

and[k

W]

40

31

22

13

4

-5

25

20

15

10

5

0

0 2190 4380 6570 8760

Fig. 6. Simulation of office floor zone north-east

Due to the challenging parametrization for the sim-

ulation of the investigated building, and to validate

the simulation results, the parameters’ influence on the

simulation output was analyzed. Therefore the scaled

sensitivity coefficients (Table III) were computed.

TABLE IIIOVERVIEW OF THE SENSITIVITY COEFFICIENTS OF SIMULATION

PARAMETERS

Ranking Parameter Value σxiσy

1 infiltration 9.78 12.50 0.0142 ventilation 1.85 0.005 0.0513 occupancy 0.51 0.005 0.502

The identification of sensitivity coefficients of single

simulation parameters shows that unknown parameters,

like infiltration, can significantly shift the dynamics.

For industrial usage, this might be a problem because

it limits the simulation’s robustness considerably.

2) Data driven identification

For the partition space, the observations of supply tem-

perature for heating/cooling and outside temperature

were chosen. The resulting partition space (Figure 7)

shows the scattered observed data representing the

four seasons. A first logical consequence is to run the

algorithm with the objective of identifying the sys-

tem with four local linear models. The corresponding

identification of the desired output, namely the zone’s

temperature, with model order six, yields a very good

model performance measured by the R2 and the MSE.

The zone’s dynamics were depicted very well (see

Figure 8).

As the number of inputs is nine and the number of

outputs is one (see TableII), the algorithm provides

a set of nine transfer functions (k) for each model.

Equation (3) shows their form for the considered model

order six. For each local model (l) the denominator

polynomials are identical, and they differ only in the

numerator coefficient b j.

Gl,k(z−1) =

∑j

bl,k, jz− j

1+∑i

al,iz−i

(3)

where b j,ai ∈ R for i = 1, ...,6 and j = 1, ...,5Attempts to achieve comparably high quality results

with only three models were successful, whereas a

single global linear model performs poorly. Table IV

compares the identification results. Figure 9 depicts the

difference of the split of the partition space if three or

four models are considered.

0 50 100 150 200 250 300−20

−10

0

10

20

30

40

winter

spring

summer

autumn

Heat supply [◦C]

Touts

ide[◦

C]

Fig. 7. Partition space of LOLIMOT Algorithm

3) Fitting of parameters

For the considered zone of the demonstration building,

the LOLIMOT algorithm performed unexpectedly well

with the observed data from the automation system.

0 1000 2000 3000 4000 5000 6000 7000 8000 900020.5

21

21.5

22

22.5

23

23.5

24

24.5

data

model

Time [h]

Tzo

ne[◦

C]

Fig. 8. System identification with LOLIMOT

TABLE IVCOMPARISON OF THE FITTING PERFORMANCE WITH DIFFERENT

NUMBER OF LLMS AND MODEL ORDER SIX

#LLM MSE R2

1 0.06309 0.872413 0.019875 0.959814 0.01697 0.96568

No data was missing for the data driven identification

routine, so no interaction with the simulation model

was needed.

4) Comparison of identification results

Comparing the results of the modeling methods used,

it is easy to see that the black box model depicts the

buildings’ dynamics better than the white box model. A

possible explanation could be that a lot of parameters

and building physical data, like the TABS parameters,

had to be estimated for the simulation, or were assumed

with slightly wrong values, which effected the output

significantly.

V. CONCLUSIONS AND FURTHER

DEVELOPMENT

This paper has introduced a building modeling workflow

in order to meet the requirements for an industrial tool

chain for building predictive control. From this perspective, a

simulation environment and the black box modeling method

LOLIMOT was combined to achieve a robust workflow

based on observed data and buildings’ physical structure.

The workflow was applied to a zone of a large multi-zone

0 50 100 150 200 250

−20

−10

0

10

20

30

Heat supply [◦C]

Toutd

oor[◦

C]

0 50 100 150 200 250

−20

−10

0

10

20

30

Heat supply [◦C]

Toutd

oor[◦

C]

Fig. 9. Identification result with 3 LLMs and 4 LLMs, respectively

university building. The investigations showed that the data

driven modeling met the industrial requirements very well.

Assuming that the necessary input data can be achieved from

historic data bases of the automation system, LOLIMOT is

a robust, quick, and performing identification method. Based

on the recent results, it is rather unlikely to use Trnsys when

considering the implementation of the modeling workflow

as the first link of the industrial tool chain. The remaining

question is whether the time spent on figuring out the plan

data and parametrization is worth the effort compared to the

results in terms of model fit, eventhough the aim is not to

generate a very detailed complex model. Further research will

be carried out in order to control the entire building with a

high level MPC. This means identifying MIMO models for

many mutually interconnecting zones under the remaining

requirements.

ACKNOWLEDGMENT

This work was supported by the project “SMART MSR“

(FFG, No. 832103) in cooperation with Vienna University of

Technology and evon GmbH.

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