# Data-Driven Digital Twins for Technical Building Services Operation in Factories: A Cooling Tower Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.96) by using polynomial regression and electric power demand (R

^{2}= 0.99) by linear regression. The results are evaluated graphically and the transfer into industrial practice is discussed conclusively.

## 1. Introduction

## 2. Background

#### 2.1. Industrial Cooling Towers

#### 2.2. Data-Driven Approaches to Create Digital Twins in Factories

#### 2.3. Data-Driven Approaches for Cooling Tower Systems

## 3. A Workflow to Create Digital Twins for Technical Building Services Operation

^{2}) and mean absolute error (MAE). By means of graphical analyses, results are related to the computational time, which is an important criterion for the applicability in daily practice. Finally, the possible deployment in industrial CT management is discussed.

^{®}and Microsoft Excel©, which are, amongst others, typical tools to apply DM approaches [41,66].

#### 3.1. Business Understanding (Phase 1)

#### 3.1.1. Technical Analysis of the Cooling Tower System

#### 3.1.2. System and Business Analysis

- High electric power demand, low cooling capacity (category I): The EER during these times is low. For the presented use case, such inefficiencies occur intermittently in almost every month of the year, but particularly frequent during May, June and July.
- Low electric power demand, low cooling capacity (category II): The EER is in an acceptable range, whereas the workload of the CT system is comparatively low. On the one hand, these stages are mainly detected during winter season, when low ambient air temperatures increase the natural cooling effect (compare Equation (1)). This means, the CT system already achieves a sufficient cooling capacity with relatively low additional power demands. On the other hand, this portfolio category includes days in August and May, which are typically related with holiday season, and thus, reduced cooling demand from production system.
- High electric power demand, high cooling capacity (category III): High workload is linked to high power demands, yet acceptable EER ranges. High workload occurs particularly during the warm summer season, e.g., June and July. Furthermore, October and November show overall the highest workload of the year, which could indicate high production capacities.
- Low electric power demand, high cooling capacity (category IV): With high EER, those states are the most desirable for CT system operation. However, there are only few samples in April and May in this category.

#### 3.2. Creating a Data-Driven Digital Twin—A Data Mining Approach (Phase 2)

#### 3.2.1. Data Selection and Outlier Filtering

#### 3.2.2. Data Aggregation and Transformation

#### 3.2.3. Feature Selection

#### 3.2.4. Hyperparameter Assessment

^{2}) can be significantly improved when hyperparameters are set optimally. Figure 14a illustrates results for the SRT algorithm, where hyperparameters are the limit number of levels (i.e., the maximum depth of the decision tree) and the minimum split node size (i.e., the minimum number of records per branch in the decision tree). High R

^{2}values are reached if the limit number of levels is increased to 10 while choosing a minimum split node size of more than 31. Beyond that, no significant further improvements can be observed. The hyperparameter assessment for the MLP algorithm considers the number of hidden layers and the number of neurons per hidden layer (=hidden neurons) as hyperparameters. As Figure 14b illustrates, no clear correlations between R

^{2}and hyperparameter values could be detected. Consequently, an individual and software-supported automated hyperparameter assessment is recommendable for MLP instead of using experience values. In this case study, 3 hidden layers and 30 neurons per hidden layer are identified as optimal hyperparameter values.

#### 3.3. Evaluation and Deployment of Data Mining Results (Phase 3)

^{2}) and mean absolute error (MAE) in relation to the computational time. Detailed results, including mean absolute errors (MAE) and mean absolute percentage errors (MAPE), can be found in Appendix A.

#### 3.3.1. Prediction of Cooling Capacity

^{2}values between 0.91 (MLP

_{reg.}) and 0.96 (PR). Computational times range from 2 to 7 min, which seems to be acceptable in terms of practical application.

^{2}= 0.96), highlighting the absolute errors (red color) compared with original data. Apparently, local trends and fluctuations are predicted with high accuracy. During May until November, higher fluctuations in the cooling capacity followed by increased prediction errors are observable. This could be attributed to local weather conditions and production scheduling, as discussed before.

#### 3.3.2. Prediction of Electric Power Demand

^{2}range between 0.84 (NB) and 0.99 (LR) with related computational times between 2 and 9 min.

^{2}= 0.99). Apparently, local trends in electric power demand such as fluctuating cooling demand by weekly production schedules can be predicted. In general, as discussed in Section 3.1.2, high and low seasons are significantly visible in the electric power demand during the year. Periodical peak consumption during the week can be explained with regularly maintenance activities.

#### 3.3.3. Discussion

## 4. Conclusions and Outlook

^{2}= 0.96) for cooling capacity and linear regression (R

^{2}= 0.99) for electric power demand. The accurate prediction of cooling capacities provides valuable insights in the overall system performance and operation reliability that is crucial for the whole production system.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 1.**Components and parameters of an industrial cooling tower system based on [25].

**Figure 7.**(

**a**) Boxplot of energy efficiency ratio (EER) for cooling tower (CT) system over the year (based on daily data); (

**b**) EER in relation to ambient temperature (based on hourly data, coloring indicates related operation month).

**Figure 8.**(

**a**) Portfolio analysis to characterize energy efficiency ratio (EER) of CT inspired by the energy portfolio in [16]; (

**b**) application of portfolio analysis (hourly data, coloring indicates related operation month).

**Figure 9.**Box plots of cooling capacity and electric power demand: (

**a**) before outlier filtering; (

**b**) after outlier filtering.

**Figure 10.**Correlation matrix indicates data interdependencies with positive linear correlation (

**green color**) and negative linear correlation (

**red color**).

**Figure 11.**Sankey diagram of data quantity development through data aggregation and data transformation, unit is total number of data.

**Figure 12.**Mean squared errors (MSE) from feature selection for linear regression (LR), simple regression tree (SRT) and multilayer perception (MLP) predicting the electric power demand.

**Figure 13.**Heatmap from feature selection indicating relevance of variables for selected algorithms assessed for electric power demand (dark grey color indicates high relevance).

**Figure 14.**Surface plot of hyperparameter assessment: (

**a**) R

^{2}for simple regression tree algorithm; (

**b**) R

^{2}for multilayer perception algorithm.

**Figure 16.**Time series plot of original and predicted cooling capacity and resulting error predicted with polynomial regression (PR) algorithm.

**Figure 18.**Time series plot of original and predicted electric power demand and resulting error predicted with linear regression (LR) algorithm.

Studies | Data-Driven Algorithms | Use Case | Target KPI | Brief Description | Available Data Set Details | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Artificial Neural Network | Clustering | Fuzzy Association Rules | Support Vector Machine | Linear/Polynomial Regression | Decision Trees | Random Forest | Ensemble | Time Series Analysis | Industry | Buildings | Cooling Performance | Energy Demand | Environmental Conditions | |||

Abraham et al., 2001 | ● | ● | ● | ● | ● | power demand for the Australian region | 12 months, 15 min. freq. | |||||||||

Ahmad et al., 2017 | ● | ● | ● | ● | ● | development of an expert system applied on the electric power demand of a hotel in Spain | 10,972 rows, 10 variables | |||||||||

Amasyali et al., 2016 | ● | ● | ● | ● | power demand of offices considering clouds and number of persons in the building | 60 days, 15 min. freq. | ||||||||||

Anuar et al., 2012 | ● | ● | ● | ● | ● | electric energy demand of various companies in industry and commerce | 30 min. freq. | |||||||||

Azadeh et al., 2008 | ● | ● | ● | ● | long-term development of electric energy demand in Iran | 130 rows | ||||||||||

Fan et al., 2015 | ● | ● | ● | ● | identification of recurring patterns in the power demand of a skyscraper’s TBS | 29,757 rows, 158 variables | ||||||||||

Fan et al., 2014 | ● | ● | ● | ● | ● | ● | ● | ● | prediction of maximum and total power demand of the cooling tower system for the next day | 34,616 rows, 15 min. freq. | ||||||

Gao et al., 2010 | ● | ● | ● | ● | ● | identification of operating conditions for comfort air conditioning | 68,000 rows, 7 variables | |||||||||

Hosoz et al., 2006 | ● | ● | ● | model for the construction of cooling towers to substitute experimental data | 81 rows, 5 variables | |||||||||||

Jovanovi et al., 2015 | ● | ● | ● | ● | ● | comparison of three different ANNs for a TBS at University | 3 years, 60 min. freq. | |||||||||

Qi et al., 2006 | ● | ● | ● | model for the construction of cooling towers | 8 variables | |||||||||||

Qi et al., 2016 | ● | ● | laboratory tests for mapping cooling system behavior using data mining | 400 rows, 7 variables | ||||||||||||

Tian-Hong Pan et al., 2011 | ● | ● | ● | ● | ● | description of a cooling system with data mining to reduce design effort | 8 months, 1 min. freq. | |||||||||

Wang et al., 2013 | ● | ● | ● | ● | identification of efficient operating conditions for the cooling system in a steel factory | 60,000 rows, 5 min. freq. |

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## Share and Cite

**MDPI and ACS Style**

Blume, C.; Blume, S.; Thiede, S.; Herrmann, C.
Data-Driven Digital Twins for Technical Building Services Operation in Factories: A Cooling Tower Case Study. *J. Manuf. Mater. Process.* **2020**, *4*, 97.
https://doi.org/10.3390/jmmp4040097

**AMA Style**

Blume C, Blume S, Thiede S, Herrmann C.
Data-Driven Digital Twins for Technical Building Services Operation in Factories: A Cooling Tower Case Study. *Journal of Manufacturing and Materials Processing*. 2020; 4(4):97.
https://doi.org/10.3390/jmmp4040097

**Chicago/Turabian Style**

Blume, Christine, Stefan Blume, Sebastian Thiede, and Christoph Herrmann.
2020. "Data-Driven Digital Twins for Technical Building Services Operation in Factories: A Cooling Tower Case Study" *Journal of Manufacturing and Materials Processing* 4, no. 4: 97.
https://doi.org/10.3390/jmmp4040097