Please note this is a comparison between Version 1 by Xuzhen He and Version 2 by Wendy Huang.

Tunnel Boring Machines (TBMs) typically consist of a rotating cutter head that breaks up the rock or soil and a conveyor system that removes the excavated material. TBMs are preferred over traditional drill and blast techniques due to their higher efficiency, safer working conditions, minimal environmental disturbance, and reduced project costs. TBMs have become prevalent in tunnel construction due to their high efficiency and reliability. The proliferation of data obtained from site investigations and data acquisition systems provides an opportunity for the application of machine learning (ML) techniques. ML algorithms have been successfully applied in TBM tunneling because they are particularly effective in capturing complex, non-linear relationships.

- tunnel boring machine
- machine learning
- TBM performance
- surface settlement
- time series forecasting

Summary of ML algorithms in TBM performance, surface settlement and time series forecasting.

Predicting TBM performance or surface settlement is a function of input parameters in Equation (1), while time series forecasting is expressed in Equation (2).

$$Y=\sigma \left(WX,b\left(\right)\right)$$

$$Y={X}_{n+1{}_{}=\sigma \left[W\left({X}_{1},{X}_{2},\dots ,{X}_{n}\left(\right),b\left[\right],\right)\right]}$$

Typically, penetration rate, revolutions per minute, thrust force, and cutterhead torque are considered as feature vectors in ML models ^{[1][2][3]}[13,57,58]. In addition to these four operational parameters, Lin et al. ^{[4]}[25] used PCC to identify mutually independent parameters such as face pressure, screw conveyor speed, foam volume, and grouting pressure. Zhang et al. ^{[5]}[29] applied PCA to reduce dimensionality and found the first eight principal components can capture the main information of 33 input parameters.

Extensive research has been conducted on employing ML algorithms to investigate TBM performance in **Table 1**. TBM performance refers to the effectiveness and efficiency of the machine in excavating a tunnel and involves various indicators such as penetration rate, advance rate, field penetration index, thrust force, and cutterhead torque. Understanding and optimising TBM performance is crucial for project time management, cost control, and risk mitigation.

Literature | Data Processing ^{a} |
Algorithms ^{b} |
Hyperparameter Tuning ^{c} |
Targets ^{d} |
Data Size and Data Set |
---|

Since ML models are data-driven, the quality of datasets (e.g., availability to the public, number of samples, input parameters used, etc.) is crucial. **Table 2** displays three types of models corresponding to three typical datasets and their respective limitations. It is worth noting that models are categorised according to their input parameters: Model A includes geological conditions, operational parameters, and TBM type and size, Model B only includes geological conditions, and Model C includes geological conditions and operational parameters.

^{a} MARS, multivariate adaptive regression spline; RBF, radial basis function; GRNN, general regression neural network.

Model Type | Dataset | Data Size | Parameters | Open Access | Limitations | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Grima et al. ^{[6]}[26] |
PCA | MR, ANN, ANFIS | - | Operational parameters,PR, AR | 640 tunnel project | |||||||||

Guo et al. ^{[57} | TBM type and size | No | ^{]}[20 | hard to access | ] | WT | Elman RNN | PSO | longitudinal settlement | Benardos and Kaliampakos ^{[7]}[31] |
- | ANN | - | |

Jiangji subway tunnel | Model B | Queen water tunnel | AR | 11-Athens metro | ||||||||||

151 | Geological conditions | S(X) | ||||||||||||

Zhang et al. ^{[58]}[79 | 432-Toulouse subway line B | Tiryaki ^{[8]}[28 | ||||||||||||

] | WT | ANN, SVM | - | daily settlement | 60-Wuhan metro line 2 | ] | PCA | MR, ANN | - | specific energy | 44-Three tunnel projects | |||

Pourtaghi and Lotfollahi-Yaghin ^{[46]}[33] |
- | Wavelet-ANN | - | |||||||||||

Gao et al. ^{[59]}[37] | S | _{max} |
49-Bangkok subway project | |||||||||||

- | RNN, LSTM, GRU, SVM. RF, Lasso | - | TO, TH, AR, CP | 3000-Shenzhen metro | Mikaeil et al. ^{[9]}[41] |
Dindarloo and Siami-Irdemoosa ^{[47]}- |
[76FL | ] | PCC- | Penetrability | 151-Queens water tunnel | |||

CART | - | S | _{max} |
34-Various tunnel projects | ||||||||||

Zhou et al. ^{[60]}[23] |
WT | ARIMA, LSTM, CNN-LSTM | - | HDSH, HDST, VDSH, VDST, roll, pitch |
5005-Sanyang Road Tunnel | Yagiz ^{[10]}[59] |
PCC | MR, ANN | - | Goh et al. ^{[48]}[77]PR |
-151-Queens water tunnel | |||

MARS | ||||||||||||||

Gao et al. ^{[61]}[80 | - | S | _{max} |
148-Three Singapore MRT projects | Javad and Narges | |||||||||

] | 3-sigma rule, MA, GRG | GRU | genetic algorithm | earth pressure | 1538-Luoyang metro line 2 | ^{[11]}[60] |
- | ANN | - | PR | 185-Three tunnel projects | |||

Chen et al. ^{[49]}[24] |
PCC | |||||||||||||

Erharter and Marcher ^{[} | ANN, RBF, GRNN | ^{62]}[ | - | S_{max} |
200-Changsha metro line 4 | |||||||||

81] | PCC | LSTM, RF, SVM | - | TO | 200,000-Brenner base tunnel | Mahdevari et al. ^{[12]}[43] |
- | MR, SVM | - | PR | 151-Queens water tunnel | |||

Zhang et al. ^{[20]}[47] |
PCC | |||||||||||||

Feng et al. | RF | ^{[1]} | PSO | S_{max} |
294-Changsha metro line 4 | |||||||||

[13] | 3-sigma rule, WT | DBN | - | FPI | 8915-Yingsong water diversion project | Salimi et al. ^{[} |
Zhang et al. ^{[50]}[34] |
PCC | ANN, SVM, RF, EML, GRNN | PSO | S_{max} |
294-Changsha metro line 4 | ||

Gao et al. ^{[63]}[82] |
- | ARIMA, RNN, LSTM | - | PR | Hangzhou second water source project | Zhang et al. ^{[25]}[22] |
WT, MD, GRG | LSTM, RF | PSO | S_{max} |
423-Changsha metro line 4 | |||

Li et al. ^{[64]} |
Zhang et al. ^{[51]}[78] |
PCC | XGBoost, ANN, SVM, MARS | - | S_{max} |
148-Three Singapore MRT projects | ||||||||

Kannangara et al. ^{[52]}[46] |
PCC, sequential feature selection, Boruta algorithm | RF | - | S_{max} |
264-Hangzhou metro line 2 and line 6 |

Suwansawat and Einstein ^{[44]}[32] were among the first to use ANN to predict the maximum settlement (S_{max}) for the Bangkok subway project, considering tunnel geometry, geological conditions, and operational parameters. Pourtaghi and Lotfollahi-Yaghin ^{[46]}[33] improved the ANN model by adopting wavelets as activation functions, resulting in higher accuracy than traditional ANN models. In contrast, Goh et al. ^{[48]}[77] utilised MARS and Zhang et al. ^{[51]}[78] utilised XGBoost to predict S_{max} for Singapore mass rapid transport lines with 148 samples. Interestingly, the mean standard penetration test showed opposite sensitivities in these two models. It further highlights the unreliability and unrobustness of ML models with limited samples, which may lead to overfitting or lack of generalisability. A comprehensive dataset from Changsha metro line 4, including geometry, geological conditions, and real-time operational parameters, has been used to compare the performance of various ML models such as ANN, SVM, RF, and LSTM ^{[20][25][49][50]}[22,24,34,47].
Since the observed settlement showed a Gaussian shape in the transverse profile, Boubou et al. ^{[45]}[75] incorporated the distance from the tunnel axis as an input parameter in their ANN model. They identified advance rate, hydraulic pressure, and vertical guidance parameter as the most influential factors in predicting surface settlement.
Various ML models have been employed to predict surface settlement induced by TBM tunnelling. The choice of ML algorithms and feature selection can significantly impact prediction accuracy, and researchers should carefully consider these factors when applying ML to surface settlement prediction in TBM tunnelling.
## 4. Time Series Forecasting

Time series forecasting is a real-time prediction using current and historical data to forecast future unknown values, which means input parameters are available and it does not have the practical problem of Model C. It is crucial in TBM tunnelling for predicting TBM performance, surface settlement, and moving trajectory in real time because operators can make necessary adjustments when potential issues are detected. Several studies using ML techniques for time series forecasting are shown in **Table 4**. Since the quality and quantity of data heavily influence model performance, moving average or wavelet transform are employed to eliminate noise and fine-grained variation to reveal the underlying information in time series data ^{[53][54][55][56]}[14,17,19,21].

82]. However, it is less meaningful to predict TBM performance just a few seconds or millimetres in advance, as shown in **Table 5**. Therefore, multi-step forecasts were explored, and it was found that errors increase significantly with an increasing forecast horizon ^{[62][66][69]}[39,81,84].

^{a} WT, wavelet transform; MD, Mahalanobis distance; GRG, grey rational grade. ^{b} MR, multiple regression (linear/non-linear); GP, genetic programming; GBoost, gradient boosting; GEP, gene expression programming; EML, extreme machine learning; PNN, polynomial neural network; DNN, deep neural network.

The penetration rate (PR) measures the speed of boring distance divided by the working time, typically quantified in m/h or mm/min. PR plays a crucial role in tunnelling operations as it directly affects overall productivity. A higher penetration rate results in faster tunnel excavation, ultimately reducing project time and costs. For predicting PR, ANIFS, ANN, and SVM models have shown promising results in various studies. For instance, the ANIFS model ^{[6]}[26] demonstrated better performance than multiple regression and empirical methods based on a database of 640 TBM projects in rock. The ANIFS model (Model A) is adaptable as it takes into account geological conditions, operational parameters, and even TBM type and size, but most TBM datasets are not available for public access.
The ANN and SVM models ^{[10][12]}[43,59] outperformed linear and non-linear regression when applied to the publicly available Queen water tunnel dataset with 151 samples. In the sensitivity analysis, interestingly, the brittleness index was found to be the least effective parameter in the SVM model ^{[12]}[43] but the most sensitive parameter in the RF model ^{[38]}[70]. These contrasting results can be attributed to a limited number of samples for training, which leads to overfitting or lack of generalisability of Model B.
In the project of Pahang–Selangor raw water transfer with 1286 samples, ML models for predicting PR were robust and reliable because of more data and adding operational parameters ^{[14][21][34]}[30,50,63]. However, TBM performance is a real-time operational parameter that cannot be obtained before the start of a project, making it infeasible to apply Model C in practice. For example, although the average thrust force is an effective parameter for predicting PR ^{[21]}[63], it is an operational input in Model C and is unavailable as it is collected in real-time as well as PR itself.
Given the expression for predicting PR using statistical analysis, optimisation techniques can be applied to optimise the correlations of weighting in multiple regression ^{[39]}[52]. On the other hand, optimisation techniques can be used to fine-tune the hyperparameters of ML models, such as the XGBoost model by Zhou et al. ^{[34]}[50]. **Figure 2** compares the model performance using different optimisation techniques, with **Figure 2**a showing the MR model and **Figure 2**b showing the XGBoost model. The accuracy improves by utilising optimisation techniques, but the difference between different optimisation techniques is small.
**Figure 2.** Comparison optimisation techniques (**a**) MR model based on dataset from Queen water tunnel; (**b**) XGBoost model based on dataset from Pahang–Selangor raw water transfer.
Advance rate (AR) is a crucial indicator in tunnelling operations, calculated as the boring distance divided by the working time and stoppages. Compared with PR, AR additionally considers stoppages due to TBM maintenance, cutters change, breakdowns, or tunnel collapses. Comparing AR prediction models, the ANN model by Benardos and Kaliampakos ^{[7]}[31] was limited by the small size of the Athens metro dataset. In contrast, the Pahang–Selangor raw water transfer dataset allowed for the development of more robust and reliable ML models for AR prediction ^{[17][26][32][33]}[35,54,55,65].
Field penetration index (FPI) evaluates TBM efficiency in the field calculated as the average cutter force divided by penetration per revolution. For predicting FPI, ANIFS and RF models performed well when applied to the Queen water tunnel dataset ^{[31][37]}[3,42]. Furthermore, Salimi et al. ^{[13][19][36]}[27,48,69] successfully developed ML models to predict FPI in different rock types and conducted a sensitivity analysis to better understand the relationship between FPI and input parameters.
Thrust force (TH) refers to the force that TBM exerts on the excavation face, whereas cutterhead torque (TO) refers to the twisting force applied to the cutterhead. The amount of TH or TO depends on the hardness and strength of the material being excavated and the size and type of TBM being used. Regarding the prediction of TH and TO, Sun et al. ^{[16]}[18] built RF models for heterogeneous strata, while Lin et al. ^{[4][35]}[25,68] utilised PSO-LSTM and PSO-GRU models based on the dataset from Shenzhen intercity railway. Bai et al. ^{[27]}[45] utilised an SVM classifier to identify the location of interbedded clay or stratum interface and subsequently developed ML models to predict TH, TO, and FP.
Although these ML models offer high accuracy in predicting TBM performance, their applicability is limited due to their project-specific nature (Model B and Model C) and lack of generalisability across different TBM types and geological conditions ^{[40]}[71]. Despite these limitations, ML models remain highly flexible in adding or filtering related parameters and implicitly capturing the impact of uncertain parameters, providing valuable insights into TBM performance optimisation.
## 3. Surface Settlement

The surface settlement, the subsidence of the ground surface above a tunnel due to excavation, poses risks to surrounding structures and utilities. Accurate prediction of surface settlement is essential for mitigating potential damages during tunnel construction. Engineers can minimise ground movement and reduce the risk of damage by adjusting excavation parameters and support structures. **Table 3** reviews papers on settlement induced by TBM tunnelling and excludes construction methods such as drilling, blasting, and the new Austrian Tunnelling Method ^{[41][42][43]}[72,73,74].

^{a} MA, moving average. ^{b} DBN, deep belief network; KNN, k-nearest neighbours. ^{c} HDSH, horizontal deviation of shield head; HDST, horizontal deviation of shield tail; VDSH, vertical deviation of shield head; VDST, vertical deviation of shield tail.

Literature | Data Processing ^{a} |
Algorithms ^{b} |
Hyperparameter Tuning | Targets ^{c} |
Data Size and Data Set |
---|---|---|---|---|---|

[ | |||||

2 | |||||

] | |||||

PCC | |||||

LSTM | |||||

- | TO, TH | 4650-Yingsong water diversion project | |||

Qin et al. ^{[65]}[36] |
cosine similarity | CNN-LSTM, XGBoost, RF, SVM, LSTM, RNN, CNN | - |

Literature | Category | Historical Data | Forecast Horizon | |||||
---|---|---|---|---|---|---|---|---|

Step behind | Distance behind | Step ahead | Distance ahead | |||||

Gao et al. ^{[59]}[37] |
high-frequency | 5 steps | 1.25 mm ^{a} |
1 step | 0.25 mm ^{a} |
|||

Qin et al. ^{[65]}[36] |
10 steps | - | 1 step | - | ||||

Huang et al. ^{[68]}[53] |
6 steps | 22.4 mm ^{a} |
1 step | 3.73 mm ^{a} |
||||

Erharter and Marcher ^{[62]}[81] |
50 steps | 2.75 m | 1 or 100 steps | 0.055 or 5.5 m | ||||

Shi et al. ^{[66]}[39] |
10 steps | - | 1–5 steps | - | ||||

Gao et al. ^{[61]}[80] |
low-frequency | 5 steps | 7.5 m | 1 step | 1.5 m | |||

Feng et al. ^{[1]}[13] |
7 steps | 7 m | ||||||

TO | ||||||||

150,000-Singapore metro T225 project | ||||||||

1 step | 1 m | ^{13]}[27] |
PCA | MR, SVM, ANFIS | - | FPI | 75-Zagros lot 1B and 2 | |

Armaghani et al. ^{[14]}[30] |
- | ANN | PSO, ICA | PR | 1286-Pahang-Selangor raw water transfer | |||

Yes | overfitting or lack of generalisability | Armaghani et al. ^{[15]}[61] |
- | MR, GEP | - | PR | 1286-Pahang-Selangor raw water transfer | |

Sun et al. ^{[16]}[18] |
Kriging interpolation, rate of change | RF | - | TH, TO, PR | 88-Shenzhen metro | |||

Armaghani et al. ^{[17]}[55] |
- | ANN | PSO, ICA | AR | 1286-Pahang-Selangor raw water transfer | |||

Koopialipoor et al. ^{[18]}[62] |
- | ANN, DNN | - | PR | 1286-Pahang-Selangor raw water transfer | |||

Salimi et al. ^{[19]}[48] |
PCA | MR, CART, GP | - | FPI | 580-Seven tunnel projects | |||

Zhang et al. ^{[20]}[47] |
PCC | RF | PSO | TO, TH, PR, FP | 294-Changsha metro line 4 | |||

Koopialipoor et al. ^{[21]}[63] |
- | ANN | firefly algorithm | PR | 1200-Pahang-Selangor raw water transfer | |||

Mokhtari and Mooney ^{[22]}[44] |
PCC, Relief | SVM | BO | PR | Northgate Link tunnel | |||

Wang et al. ^{[23]}[64] |
- | ANN, LSTM, RF, SVM | - | AR | 806-Nanning metro line 1 | |||

Zhang et al. ^{[24]}[49] |
- | SVM, CART, RF, bagging, Ada boosting | BO | PR | 151-Queens water tunnel | |||

] | WT, MD, GRG | LSTM, RF | PSO | TH, TO, PR, RPM, CP | ||||

Model C | Pahang-Selangor raw water transfer | 1286 | Geological conditions, Operational parameters |
3549-Changsha metro line 4 and Zhengzhou metro line 2 | ||||

Zhang et al. ^{[} |
Zhou et al. ^{[26]}[65] |
- | ANN, GP | - | AR | 1286-Pahang-Selangor raw water transfer | ||

Bai et al. ^{[27]}[45] |
PCC, Seasonal-trend decomposition | MR, SVM, DT, GBoost | - | TO, TH, FP | 450-Xi’an metro | |||

Bardhan et al. ^{[28]}[66] |
- | hybrid ensemble model | - | PR | 185-Three tunnel project | |||

Harandizadeh et al. ^{[29]}[56] |
- | ANFIS-PNN | ICA | PR | 209-Pahang-Selangor raw water transfer | |||

Lin et al. ^{[30]}[67] |
- | MR, ANN, SVM, LSTM, GRU, EML | PR | 1000-Shenzhen railway | ||||

Parsajoo et al. ^{[31]}[42] |
- | ANFIS | artificial bee colony | FPI | 150-Queens water tunnel | |||

Zeng et al. ^{[32]}[35] |
- | EML | PSO | AR | 1286-Pahang-Selangor raw water transfer | |||

Zhou et al. ^{[33]}[54] |
- | XGBoost | BO | AR | 1286-Pahang-Selangor raw water transfer | |||

Zhou et al. ^{[34]}[50] |
- | ANN, RF, XGBoost, SVM | GWO, PSO, SCA, SSO, MVO, MFO | PR | 1286-Pahang-Selangor raw water transfer | |||

Lin et al. ^{[4]}[25] |
- | LSTM | PSO | TH | 1500-Shenzhen railway | |||

Lin et al. ^{[35]}[68] |
- | GRU | PSO] | - | MR, CART | - | FPI | 666-Eight tunnel projects |

Model A | 640 tunnel projects | - | Geological conditions, | |||||

TO | ||||||||

1500-Shenzhen railway | ||||||||

Yes | hard to apply in practice | |||||||

^{25} | ||||||||

^{]} | ||||||||

[ | ||||||||

22 | ||||||||

Salimi et al. | ||||||||

^{[} | ||||||||

^{36} | ||||||||

^{]} | ||||||||

[ | ||||||||

69 | ||||||||

Yang et al. | ||||||||

^{[} | ||||||||

^{37} | ||||||||

^{]} | ||||||||

[ | ||||||||

3 | ||||||||

] | ||||||||

- | ||||||||

SVM | ||||||||

GWO, biogeography-based optimisation | ||||||||

PR | 503-Shenzhen metro line |

Literature | Data Processing | Algorithms ^{a} |
Hyperparameter Tuning | Targets | Data Size and Data Set | |||||
---|---|---|---|---|---|---|---|---|---|---|

Suwansawat and Einstein ^{[44]}[32] |
- | ANN | - | S_{max} |
49-Bangkok subway project | |||||

Boubou et al. ^{[45]}[75] |
- | ANN | - | |||||||

Shi et al. | ||||||||||

^{[} | ||||||||||

^{66} | ||||||||||

^{]} | ||||||||||

[ | ||||||||||

39 | ||||||||||

] | ||||||||||

WT, variational mode decomposition | LSTM, CNN, RNN, SVM, RF | - | TO | 60,000-Singapore metro T225 project | ||||||

Wang et al. ^{[56]}[21] |
WT, light gradient boosting machine | LSTM | - | PR, TO | 25,543-Sutong gas transmission line | |||||

Xu et al. ^{[53]}[14] |
3-sigma rule, MA, PCC | SVM, RF, CNN, LSTM, GBoost, KNN, Bayesian ridge regression | - | PR, TO, TH, RPM | 7000-Yingsong water diversion project | |||||

463-Changsha metro line 4 and Zhengzhou metro line 2 | ||||||||||

Shen et al. ^{[54} | ||||||||||

Shan et al. ^{[55]}[19] |
5 steps | 7.5 m | 1–5 steps | Zhang et al. ^{[67]}[83] |
- | RF | - | S_{max} |
386-Changsha Metro Line 4 | |

Huang et al. ^{[68]}[53] |
SelectKBest | LSTM | BO | TO | Yingsong water diversion project | |||||

1.5–7.5 m | Shan et al. ^{[55]}[19] |
MA | RNN, LSTM | - | PR^{]}[17] |
WT, Kriging interpolation | LSTM, SVM, RNN | - | HDSH, HDST, VDSH, VDST, roll, pitch | 1200-Shenzhen intercity railway |

Zhang et al. ^{[5]}[29] |
PCA, PCC | GRU, RNN, SVM | - | HDSH, HDST, VDSH, VDST, | 22,010-Guang-Fo intercity railway |

High-frequency data is collected directly from the data acquisition system every few seconds or minutes. High-frequency prediction of next-step TBM performance can be achieved with high accuracy using RNN, LSTM, and GRU. These ML algorithms have been found to outperform others by incorporating both current and historical parameters ^{[56][59][63][65][68]}[21,36,37,53,

^{a} The distance is estimated based on the time step, sampling period, and average penetration rate.

High-frequency data can be preprocessed into low-frequency data, where each data point represents a fixed segment or working cycle spanning 1–2 m. Low-frequency data, such as that from the Yingsong water diversion project, have been used to forecast average operational parameters ^{[53][64]}[2,14] and predict next-step TBM performance in different geological conditions ^{[1]}[13]. In contrast, Shan et al. ^{[55]}[19] employed RNN and LSTM to predict near-future TBM performance (1.5–7.5 m ahead), focusing on the difference in geological conditions between training data and test data. While one-step forecasts are highly accurate, predictions decrease in accuracy as the forecast horizon increases.
Regarding the number of steps back required to predict future TBM performance, **Table 5** demonstrates that the number of steps used for training ranges from 5 to 10, except for those who used data from the last 50 steps. High-frequency prediction normally uses data just a few millimetres beforehand for training, while low-frequency prediction uses data up to seven metres beforehand. Nevertheless, these data are collected a few millimetres to a few meters away from the current cutterhead location and essentially reflect the current operation of the TBM ^{[70]}[85].
To account for the surface settlement developing over time in a single point, Guo et al. ^{[57]}[20] used an Elman RNN to predict the longitudinal settlement profile, while Zhang et al. ^{[58]}[79] integrated wavelet transform and SVM to forecast daily surface settlement. Zhang et al. ^{[67]}[83] used historical geometric and geological parameters to build an RF model to predict operational parameters in the next step. They then combined predicted operational parameters with geometric and geological parameters to estimate S_{max} in the next step based on another RF model.
To improve moving trajectory, current, and historical parameters have been used to predict real-time TBM movements such as horizontal deviation of shield head, horizontal deviation of shield tail, vertical deviation of shield head, vertical deviation of shield tail, roll, and pitch ^{[5][54][60]}[17,23,29]. When deviations reach the alarm value, the TBM route can be regulated by fine-tuning the thrust force and strokes in the corresponding positions.
Time series forecasting techniques vary in effectiveness depending on the frequency of data collection, the forecast horizon, and the specific application in TBM tunnelling. Understanding these differences and selecting the appropriate ML algorithm is essential for optimising tunnelling operations.