# A Hybrid Bimodal LSTM Architecture for Cascading Thermal Energy Storage Modelling

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Problem Description

^{3}stratified water tank that contains water, has three different inputs/outputs (on three levels, bottom, middle and top), and receives its energy from two sources. The first source is an array of solar panels (840 m

^{2}of solar collectors, 370 kW) that provides energy in the form of hot water to the system. The second source is a cluster of biomass boilers (with a total heating power capacity of 4.8 MW) that operate on wood chips and oil, as well as a combined heat and power (CHP) plant that operates on wood chips. These separate boilers are considered as a unified, single source in our analysis.

#### 2.2. Data Acquisition and Characteristics

#### 2.3. Preprocessing Phase

_{A}, D

_{B}, and D

_{C}) each one containing only the relevant features that serve as inputs/output for each component (as shown in Table 1). This way, each model was built by the right features that have actual importance and physical meaning for each particular model.

#### 2.4. Proposed LSTM Architecture

#### 2.5. Benchmarking Machine Learning Algorithms

#### 2.6. Modelling Approaches: Component-Specific and Cascading

_{A}, D

_{B}, and D

_{C}) each one containing only the relevant features that serve as inputs/output for each component (as shown in Table 1). This way, each model was built by the right features that have actual importance and physical meaning for each component. For the validation and evaluation of the models, each subgroup was split into two portions. The training portion, denoted as tr, which is a random 80% of the initial subgroup, is the amount of data upon which the algorithms are fitted, and the models are built. The testing portion, denoted as te, which is the remaining random 20%, is the amount of data that is kept hidden during the training process and is used for the validation of the models’ performance. The following six datasets were generated as the output of this step: D

_{A_tr}, D

_{A_te}, D

_{B_tr}, D

_{B_te}, D

_{C_tr}and D

_{C_te}. The evaluation of each model’s performance for the present study was based on three common performance metrics, the mean absolute error (MAE), mean squared error (MSE) and root mean squared error (RMSE), that are explained below.

## 3. Results

#### 3.1. Experimental Design

_{i_tr}, i = A, B, C. The resulted trained ML models were tested on the subsets D

_{i_te}, i = A, B, C. The validation of each ML model was conducted with the application of three performance metrics, MSE, MAE and RMSE and a comparative analysis was performed.

#### 3.2. Performance of The Individual Modelling Approaches for Each Component

#### 3.3. Performance of the Cascading Architecture

^{−4}for the MSE and MAE that were therefore considered as insignificant. This small observed deviation demonstrates that the proposed cascading model works with almost the same accuracy as with the model that was individually trained with the real input-output tank data.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Detailed representation of the interconnection of the different components of the system, along with the respective inputs and outputs.

**Figure 2.**Schematic of the physical connection between the solar panels (SP), heat exchanger (HE), biomass boiler (BB) and the heat storage tank (HS).

**Figure 13.**Real (

**a**) vs. predicted (

**b**) output of the individual heat storage model for the 6 January 2015, along with their absolute difference (

**c**) (AD).

**Figure 16.**Real (

**a**) vs. predicted (

**b**) output of the heat storage model within the cascading architecture for the 6 January 2015, along with their absolute difference (

**c**) (AD).

Feature Name | Solar Panels | Heat Exchanger | Heat Storage Tank |
---|---|---|---|

T1 Solar collector field 1 (°C) | Input | - | - |

T2 Solar collector field 2 (°C) | Input | - | - |

T3 Solar collector field 3 (°C) | Input | - | - |

T4 Solar collector field 4 (°C) | Input | - | - |

T5 Solar collector field 5 (°C) | Input | - | - |

T6 Solar collector field 6 (°C) | Input | - | - |

T7 Solar collector field 7 (°C) | Input | - | - |

T8 feed-in Solar prim. (°C) | Output | Input | - |

T9 return Solar prim. (°C) | Return Input | Input | - |

T10 feed-in Solar sec. (°C) | - | Output | Input |

T11 return Solar sec. (°C) | - | Return Input | - |

T12 Temp. 1 heat storage (up) (°C) | - | - | Input |

T13 Temp. 2 heat storage (°C) | - | - | Input |

T14 Temp. 3 heat storage (°C) | - | - | Input |

T15 Temp. 4 heat storage (°C) | - | - | Input |

T16 Temp. 5 heat storage (°C) | - | - | Input |

T17 feed-in biomass boiler (°C) | - | - | Input |

T18 return biomass boiler (°C) | - | - | Input |

T19 feed-in before mixing valve (°C) | - | - | Output |

T20 return before mixing valve (°C) | - | - | Return Input |

T21 outside temp. (°C) | Universal Input | ||

Total number of training samples multiplied by the features of each component | 3,511,480 | 1,755,740 | 3,862,628 |

Method | MAE | MSE | RMSE |
---|---|---|---|

Decision Tree | 0.073 | 0.029 | 0.172 |

Random Forest | 0.067 | 0.015 | 0.124 |

AdaBoost | 0.353 | 0.195 | 0.441 |

Bagged Trees | 0.067 | 0.015 | 0.124 |

Boosted Trees | 0.168 | 0.063 | 0.252 |

Linear Regression | 0.259 | 0.125 | 0.354 |

Bayesian Ridge | 0.259 | 0.125 | 0.354 |

Stochastic Gradient | 0.259 | 0.125 | 0.354 |

Lasso Regression | 0.820 | 0.997 | 0.999 |

Elastic Net | 0.623 | 0.558 | 0.747 |

Least Angle | 0.259 | 0.125 | 0.354 |

SVR linear | 0.257 | 0.128 | 0.358 |

SVR poly | 0.419 | 0.305 | 0.552 |

SVR rbf | 0.154 | 0.058 | 0.242 |

ANN MLP | 0.096 | 0.024 | 0.154 |

H2M-LSTM | 0.059 | 0.012 | 0.110 |

Method | MAE | MSE | RMSE |
---|---|---|---|

Decision Tree | 0.026 | 0.005 | 0.069 |

Random Forest | 0.023 | 0.003 | 0.055 |

AdaBoost | 0.172 | 0.048 | 0.219 |

Bagged Trees | 0.023 | 0.003 | 0.055 |

Boosted Trees | 0.057 | 0.010 | 0.099 |

Linear Regression | 0.081 | 0.019 | 0.136 |

Bayesian Ridge | 0.081 | 0.019 | 0.136 |

Stochastic Gradient | 0.081 | 0.019 | 0.136 |

Lasso Regression | 0.830 | 0.998 | 0.999 |

Elastic Net | 0.525 | 0.396 | 0.629 |

Least Angle | 0.081 | 0.019 | 0.136 |

SVR linear | 0.082 | 0.019 | 0.139 |

SVR poly | 0.361 | 0.718 | 0.847 |

SVR rbf | 0.059 | 0.008 | 0.091 |

ANN MLP | 0.033 | 0.004 | 0.060 |

H2M-LSTM | 0.020 | 0.002 | 0.045 |

Method | MAE | MSE | RMSE |
---|---|---|---|

Decision Tree | 0.042 | 0.009 | 0.094 |

Random Forest | 0.033 | 0.005 | 0.071 |

AdaBoost | 0.192 | 0.060 | 0.244 |

Bagged Trees | 0.033 | 0.005 | 0.072 |

Boosted Trees | 0.074 | 0.014 | 0.120 |

Linear Regression | 0.145 | 0.052 | 0.229 |

Bayesian Ridge | 0.145 | 0.052 | 0.229 |

Stochastic Gradient | 0.144 | 0.052 | 0.229 |

Lasso Regression | 0.818 | 1.001 | 1.000 |

Elastic Net | 0.584 | 0.513 | 0.716 |

Least Angle | 0.145 | 0.052 | 0.229 |

SVR linear | 0.129 | 0.057 | 0.238 |

SVR poly | 0.252 | 0.154 | 0.392 |

SVR rbf | 0.055 | 0.008 | 0.089 |

ANN MLP | 0.039 | 0.005 | 0.071 |

H2M-LSTM | 0.028 | 0.003 | 0.055 |

**Table 5.**Performance metrics for the machine learning algorithms used within the cascading architecture.

Method | MAE | MSE | RMSE |
---|---|---|---|

Decision Tree | 0.044 | 0.010 | 0.099 |

Random Forest | 0.034 | 0.005 | 0.073 |

AdaBoost | 0.180 | 0.053 | 0.231 |

Bagged Trees | 0.034 | 0.006 | 0.074 |

Boosted Trees | 0.075 | 0.015 | 0.121 |

Linear Regression | 0.145 | 0.052 | 0.229 |

Bayesian Ridge | 0.145 | 0.052 | 0.229 |

Stochastic Gradient | 0.145 | 0.053 | 0.229 |

Lasso Regression | 0.818 | 1.001 | 1.000 |

Elastic Net | 0.584 | 0.513 | 0.716 |

Least Angle | 0.145 | 0.052 | 0.229 |

SVR linear | 0.129 | 0.057 | 0.239 |

SVR poly | 0.269 | 0.209 | 0.457 |

SVR rbf | 0.055 | 0.008 | 0.089 |

ANN MLP | 0.037 | 0.005 | 0.073 |

H2M-LSTM | 0.029 | 0.003 | 0.055 |

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## Share and Cite

**MDPI and ACS Style**

Anagnostis, A.; Moustakidis, S.; Papageorgiou, E.; Bochtis, D. A Hybrid Bimodal LSTM Architecture for Cascading Thermal Energy Storage Modelling. *Energies* **2022**, *15*, 1959.
https://doi.org/10.3390/en15061959

**AMA Style**

Anagnostis A, Moustakidis S, Papageorgiou E, Bochtis D. A Hybrid Bimodal LSTM Architecture for Cascading Thermal Energy Storage Modelling. *Energies*. 2022; 15(6):1959.
https://doi.org/10.3390/en15061959

**Chicago/Turabian Style**

Anagnostis, Athanasios, Serafeim Moustakidis, Elpiniki Papageorgiou, and Dionysis Bochtis. 2022. "A Hybrid Bimodal LSTM Architecture for Cascading Thermal Energy Storage Modelling" *Energies* 15, no. 6: 1959.
https://doi.org/10.3390/en15061959