# A Non-Destructive System Based on Electrical Tomography and Machine Learning to Analyze the Moisture of Buildings

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Selected Hardware Issues, Sample Models, and Reconstructions

#### 2.2. Wall Moisture Tests with the Use of the Gauss-Newton (GNM) Method

#### 2.3. Masonry Humidity Testing by the Least Angle Regression (LARS) Method

- The predictors should be standardized. The intercept ${\beta}_{0}$ in expression (1) is equal a mean of the response variable and we put ${\beta}_{1}={\beta}_{2}=\dots ={\beta}_{k}=0$. Active set A (set of predictors) is empty.
- Calculate the residuals $r=Y-{\beta}_{0}-{X}_{\left(A\right)}{\beta}_{\left(A\right)}$ for the linear model with all predictors from active set A. Determine the predictor X
_{j}(which is not in active set) most correlated with residuals r and attach to the active set A. - Move coefficient ${\beta}_{j}$ from 0 towards its least-squares coefficient $\langle {X}_{j},r\rangle $ until some other competitor ${X}_{k}$ has a much correlation with the current residuals as does ${X}_{k}$.
- Move ${\beta}_{j}$ and ${\beta}_{s}$ in the direction defined by their joint least square coefficient of the current residual on $\langle {X}_{j},{X}_{s}\rangle $ until some other competitor ${X}_{l}$ has a much correlation with the current residual.

#### 2.4. Masonry Humidity Testing by the ElasticNet Method

#### 2.5. Masonry Humidity Testing by the Gauss-Newton Method

**y**(observation of the dependent variable) vector ${e}^{\left(l\right)}$. It is a vector of differences between the empirical values of the dependent variable and the lth of its approximations $f\left({x}_{t},{\beta}^{\left(l\right)}\right)$.

- ${y}_{t}$—observations of the explanatory variable,
- ${x}_{t}=\left[{x}_{t}\right]$—P vector of observations for explanatory variables,
- ${\beta}_{t}=\left[{\beta}_{j}\right]$—K vector of structural parameters,
- ${\epsilon}_{t}$—implementations of random elements (we assume that random components are uncorrelated, have an average of zero and equal, positive and finite variance).

#### 2.6. Masonry Humidity Testing by the Neural Imaging

## 3. Results

#### 3.1. Results of Wall Moisture Tests Obtained Using the Least Angle Regression (LARS) Method

#### 3.2. Results of Wall Moisture Tests Obtained Using the ElasticNet Method

#### 3.3. Results of Wall Moisture Tests Obtained Using the Neural Imaging

#### 3.4. Moisture Test of Real Object

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The rising moisture resulting from the direct connection of soil with masonry [14].

**Figure 2.**Relationship between saturation and resistivity of concrete [15].

**Figure 3.**An image of building walls’ dampness developed on the basis of the results of an electrical test. Higher moisture concentrations are depicted by a color of higher intensity [17].

**Figure 6.**A tomographic laboratory to study the moisture inside the cellular lightweight concrete block.

**Figure 7.**The concept of the electrodes: (

**a**) way of fixing rubber electrodes to the building wall, (

**b**) set of rubber electrodes, (

**c**) structure of a single rubber electrode.

**Figure 8.**The geometrical model of the tested wet wall with 32 electrodes: (

**a**) the pattern image, (

**b**) the image reconstructed by Gauss-Newton method.

**Figure 9.**The geometrical model 3D with 4 × 8 electrodes—the image reconstruction: (

**a**) pattern model, (

**b**) Gauss-Newton method with Laplace regularization.

**Figure 10.**The geometrical model 3D with 2 × 16 electrodes—the image reconstruction: (

**a**) pattern model, (

**b**) reconstruction created with the use of Gauss-Newton method with Laplace regularization.

**Figure 11.**The geometrical model 3D with 2 × 8 electrodes—the image reconstruction: (

**a**) pattern model, (

**b**) reconstruction created with the use of Gauss-Newton method with Laplace regularization.

**Figure 13.**The way of converting a real number vector into the lightweight concrete block’s spatial image.

**Figure 15.**The result of Least Angle Regression (LARS) moisture testing of the lightweight concrete block for the case of 2 × 8 electrodes.

**Figure 16.**The result of Least Angle Regression (LARS) moisture testing of the lightweight concrete block for the case of 2 × 16 electrodes.

**Figure 17.**The result of ElasticNet moisture testing of the lightweight concrete block for the case of 2 × 8 electrodes.

**Figure 18.**The result of ElasticNet moisture testing of the lightweight concrete block for the case of 2 × 16 electrodes.

**Figure 19.**The result of Artificial Neural Network system (ANN) moisture testing of the lightweight concrete block for the case of 2 × 8 electrodes.

**Figure 20.**The result of Artificial Neural Network system (ANN) moisture testing of the lightweight concrete block for the case of 2 × 16 electrodes.

**Figure 21.**The result of the real object Artificial Neural Networks (ANN) moisture testing of the lightweight concrete block for the case of 2 × 8 electrodes.

Samples | MSE | R | |
---|---|---|---|

Training set | 4298 | 5.31979 × 10^{−6} | 9.99983 × 10^{−1} |

Validation set | 921 | 1.68249 × 10^{−5} | 9.99947 × 10^{−1} |

Testing set | 921 | 2.03645 × 10^{−5} | 9.99934 × 10^{−1} |

Method | RMSE | |
---|---|---|

2D Samples | 3D Samples | |

ANN | 0.106301 | 0.010819 |

LARS | 0.122599 | 0.029800 |

ElasticNET | 0.282520 | 0.036500 |

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**MDPI and ACS Style**

Rymarczyk, T.; Kłosowski, G.; Kozłowski, E. A Non-Destructive System Based on Electrical Tomography and Machine Learning to Analyze the Moisture of Buildings. *Sensors* **2018**, *18*, 2285.
https://doi.org/10.3390/s18072285

**AMA Style**

Rymarczyk T, Kłosowski G, Kozłowski E. A Non-Destructive System Based on Electrical Tomography and Machine Learning to Analyze the Moisture of Buildings. *Sensors*. 2018; 18(7):2285.
https://doi.org/10.3390/s18072285

**Chicago/Turabian Style**

Rymarczyk, Tomasz, Grzegorz Kłosowski, and Edward Kozłowski. 2018. "A Non-Destructive System Based on Electrical Tomography and Machine Learning to Analyze the Moisture of Buildings" *Sensors* 18, no. 7: 2285.
https://doi.org/10.3390/s18072285