# Latent-Space Dynamics for Prediction and Fault Detection in Geothermal Power Plant Operations

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

## 3. Prediction Results

## 4. Fault Detection in a Geothermal Power Plant

^{th}score vector. For a given significance level $\alpha $, the sample is considered normal if ${T}^{2}$is smaller than the corresponding control limit ${T}_{\alpha}^{2}$, where ${T}_{\alpha}^{2}={\chi}_{l;\alpha}^{2}$ if $L$ is large [19]. To monitor the variability in RS, the squared prediction error (SPE) index can be used [19]:

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Sensitivity analysis for the LSDNN model with respect to the dimension of the latent states and the look-back window size.

**Figure 4.**One-step-ahead prediction results of testing data. Top eight subplots: predicted measurements. Bottom four subplots: exogenous variables, including control inputs and ambient temperature.

**Figure 5.**Twelve-step-ahead prediction results of testing data. Top eight subplots: predicted measurements. Bottom four subplots: exogenous variables, including control inputs and ambient temperature.

**Figure 6.**Contributions of exogenous variables and residual dynamics to predicted latent states. The predicted latent states stay close to the encoded latent states.

**Figure 7.**Changes between the input and output of the attention mechanism for one of the latent variables. The attention weights are adjusted based on control adjustments. The latent state values after applying attention are scaled by the attention weights.

**Figure 8.**Monitoring indices of the power generation unit. All three indices rise above the control limits around 12–15, indicating the occurrence of faults.

**Figure 9.**Contribution plot of the power generation unit. “Turbo inlet superheat” and “R134A outlet temperature vaporizer B” have the largest contributions, indicating that they are the possible fault locations.

**Figure 11.**Monitoring indices of the production pump. The ${T}^{2}$ index rises above the control limit after maintenance, indicating a shift in the operation region. The SPE index exceeds the control limit after 08–06, indicating a fault that breaks the correlation structure.

Prediction Horizon | LSDNN (MAPE) | RNN Encoder–Decoder (MAPE) | LSDNN (RMSE) | RNN Encoder–Decoder (RMSE) |
---|---|---|---|---|

1 | $4.1\pm $0.2% | $4.2\pm $0.2% | $0.016\pm $0.001 | $0.017\pm $0.001 |

6 | $4.7\pm $0.2% | $4.7\pm $0.1% | $0.019\pm $0.001 | $0.02\pm $0.001 |

12 | $4.9\pm $0.2% | $4.9\pm $0.1% | $0.02\pm $0.001 | $0.02\pm $0.001 |

24 | $5.3\pm $0.3% | $5.3\pm $0.1% | $0.022\pm $0.001 | $0.022\pm $0.001 |

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**MDPI and ACS Style**

Liu, Y.; Ling, W.; Young, R.; Zia, J.; Cladouhos, T.T.; Jafarpour, B.
Latent-Space Dynamics for Prediction and Fault Detection in Geothermal Power Plant Operations. *Energies* **2022**, *15*, 2555.
https://doi.org/10.3390/en15072555

**AMA Style**

Liu Y, Ling W, Young R, Zia J, Cladouhos TT, Jafarpour B.
Latent-Space Dynamics for Prediction and Fault Detection in Geothermal Power Plant Operations. *Energies*. 2022; 15(7):2555.
https://doi.org/10.3390/en15072555

**Chicago/Turabian Style**

Liu, Yingxiang, Wei Ling, Robert Young, Jalal Zia, Trenton T. Cladouhos, and Behnam Jafarpour.
2022. "Latent-Space Dynamics for Prediction and Fault Detection in Geothermal Power Plant Operations" *Energies* 15, no. 7: 2555.
https://doi.org/10.3390/en15072555