#
Reducing Simulation Performance Gap in Hemp-Lime Buildings Using Fourier Filtering †^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}K); external walls 0.19 W/(m

^{2}K); roof 0.13 W/(m

^{2}K); windows 1.2 W/(m

^{2}K). The total design heat loss coefficient derived from these figures was 44.51 W/K. The design air permeability was 2.1 m

^{3}/h/m

^{2}. These design figures were considerably different from those obtained from co-heating tests and air tightness tests: 69.28 W/K for heat loss coefficient, and 3.61 m

^{3}/h/m

^{2}for measured air permeability. Details of the measurements and the reasons for discrepancies between design and measured values are discussed in Reference [11].

- (1)
- create a dynamic simulation model of an existing building built from hemp-lime material, which is also being monitored;
- (2)
- represent the time series of the monitored and simulated parameters, such as temperature or relative humidity, as separate Fourier transforms;
- (3)
- assume that the monitored time series is the result of a certain response function acting on the simulated time series (in other words that the monitored time series is the result of convolution between the simulated time series and the response function) and obtain the response function through de-convolution of the two corresponding Fourier transforms; this response function is named a “Fourier filter”;
- (4)
- create a dynamic simulation model of a future building built from hemp-lime material and obtain time series of its performance parameters, such as temperature or relative humidity;
- (5)
- represent the time series obtained through dynamic simulation as Fourier transforms;
- (6)
- create a convolution between the Fourier transforms from the previous step and the Fourier filter;
- (7)
- the result is a representation of a time series of a monitored parameter for the future building built from hemp-lime material (a building that is at the design stage and therefore non-existing).

_{i,f}, 1 ≤ i ≤ K

_{i,e}and S

_{i,e}:

_{j}= M

_{i,e}/S

_{i,e}

_{i,f}is obtained as S

_{i,f}. Subsequently, multiplication of the two Fourier transforms S

_{i,f}and R

_{j}gives:

_{i,f}R

_{j}= M

_{i,f}

_{i,f}⇒ m

_{i,f}, 1 ≤ i ≤ K

#### 2.1. Practical Application of the Method

#### 2.1.1. Creating the Filter

^{m}, where m = 1, 2, 3, …, etc. Therefore the length of the time series used for creating the filter, restricted by the number of available points, was chosen to be 2

^{7}= 128 (Figure 1).

#### 2.1.2. Applying the Filter

^{13}= 8192, and 2

^{14}= 16,384. The former number of points does not cover the full annual number of hours, and the latter exceeds them. We, therefore, need to use the latter number to cover the entire annual simulation of a building with an hourly time step. The remaining data points between 8761 and 16,384 need to be filled with values that do not distort the result. In order to identify the extent of potential result distortion, experiments with different data padding approaches were carried out (Figure 2).

## 3. Results

## 4. Discussion

#### 4.1. Design Implications

#### 4.2. Results Overview

_{h}= 0.83 ± 0.12, therefore between 71% and 95%. For cooling set temperature of 24 °C, the saving of cooling energy calculated on the basis of Equation (8) is S

_{c}= 1, therefore 100%.

#### 4.3. Application and Constraints

#### 4.4. Notes on Signal and Filter Padding

#### 4.5. Notes on the Length of the Time Series Used for Creating the Filter

#### 4.6. The Motivation for and the History of the Development of this Method

^{m}points, and as 2

^{11}= 2048 was a too short time series, 2

^{12}= 4096 had to be used. The full simulation year of 8760 points had to be therefore split into three parts of 4096 points. Additionally, as the full length of 3 × 4096 = 12,288 was considerably longer than the full simulation year, there had to be an overlap between the three parts. This itself required manual handling of data in order to split the full simulation year and position the overleaping points. The additional complication was the long execution time, so that the entire process of preparation of data, the running of the FFT algorithm, and the aggregation of the results from the three parts into a single data set of 8760 points, altogether took 3–4 h for each simulation case.

^{14}= 16,384 points were used for the FFT, and the positions from 8761 onwards in the time series were padded as explained in Section 2.1.2. Secondly, the speed of FFT execution in the Java code was 545 milliseconds on a 2.6 GHz Intel Core i7 laptop, therefore less than one second, which represented a considerable time saving in comparison with several hours of the semi-manual work. This improved approach enabled the application of the method to a number of building design projects, as explained in the next section.

#### 4.7. Types and Sizes of Buildings Designed Using this Method

## 5. Conclusions

^{2}. Some of these buildings have been built; some are still in the design stage; and some were not built from hemp-lime material as originally intended. In the buildings that have already been built, the capital savings on the M&E services have been two thirds in comparison with similar buildings built from conventional materials.

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{0,1,…,k} | weighting factors |

BEMS | building energy management system |

DFT | discrete Fourier transform |

EPW | Energy Plus Weather file extension |

f(x) | periodic function of x |

FFT | fast Fourier transform |

max | maximum of the temperature difference |

m_{i,e} | discrete values of the monitored time series of the existing building for 1 ≤ i ≤ K |

M_{i,e} | discrete Fourier transform (DFT) of the monitored time series m_{i,e} |

M_{i,f} | DFT of the representation of monitored time series m_{i,f} of the future building |

m_{i,f} | representation of the monitored time series of the non-existing building for 1 ≤ i ≤ K |

min | minimum of the temperature difference |

n | harmonics index |

K | total number of harmonics |

N | number of data points/hours in the year |

POE | post occupancy evaluation |

R_{j} | the response function = the Fourier filter |

r_{j} | discrete values of the response function for 1 ≤ j ≤ K |

RH | relative humidity |

RMSE | root mean squared error |

S_{h} | saving of heating energy |

S_{c} | saving of cooling energy |

S_{i,e} | DFT of the simulated time series of the existing building s_{i,e} |

s_{i,e} | discrete values of the simulated time series of the existing building for 1 ≤ i ≤ K |

S_{i,f} | DFT of the simulated time series of the future building s_{i,f} |

s_{i,f} | discrete values of the simulated time series of the future building/the building being designed, 1 ≤ i ≤ K |

T_{i,f} | Fourier filtered fluctuating temperature for i-th hour of the year |

T_{i,s} | simulated fluctuating temperature for i-th hour of the year |

T_{set,h} | heating set temperature |

T_{set,c} | cooling set temperature |

ε | symbol expression for RMSE |

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**Figure 1.**A comparison between measured and simulated internal conditions in an experimental building built from lime-bonded hemp (monitored values courtesy of the University of Bath).

**Figure 5.**Air tightness test in the monitored building. (

**a**) External thermal images after the co-heating test—a photo montage representing the thermal image of the house using the ground and floor and first floor thermal images; (

**b**) loft hatch leakage during air tightness test.

**Figure 6.**IES model of the monitored house (monitored house shown in blue, adjacent houses shown in magenta). (

**a**) front view; (

**b**) rear view.

**Figure 7.**Comparison between IES temperature, Fourier filtered temperature, and monitored air temperature of the living room.

**Figure 8.**Comparison between IES relative humidity, Fourier filtered relative humidity, and monitored relative humidity of the living room.

Building Type | Floor Area (m^{2}) |
---|---|

Winery | 770 |

Museum store for artefacts | 870 |

School building | 180 |

Pharmaceutical sample storage and archive | 1190 |

Detached house | 330 |

Detached house | 413 |

Warehouse | 7960 |

Crematorium | 800 |

Supermarket | 3320 |

Total | 15,833 |

© 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Jankovic, L.
Reducing Simulation Performance Gap in Hemp-Lime Buildings Using Fourier Filtering †. *Sustainability* **2016**, *8*, 864.
https://doi.org/10.3390/su8090864

**AMA Style**

Jankovic L.
Reducing Simulation Performance Gap in Hemp-Lime Buildings Using Fourier Filtering †. *Sustainability*. 2016; 8(9):864.
https://doi.org/10.3390/su8090864

**Chicago/Turabian Style**

Jankovic, Ljubomir.
2016. "Reducing Simulation Performance Gap in Hemp-Lime Buildings Using Fourier Filtering †" *Sustainability* 8, no. 9: 864.
https://doi.org/10.3390/su8090864