# MVDR-LSTM Distance Estimation Model Based on Diagonal Double Rectangular Array

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## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Microphone Array

#### 2.2. MVDR

_{0}according to the frequency band division method of 1/3 octave bandwidth, the upper frequency of the 1/3 octave band ${f}_{h}={f}_{0}\times \sqrt[3]{2}$, and the lower limit frequency ${f}_{h}={f}_{0}\xf7\sqrt[3]{2}$. According to the specified center frequency and frequency band index, a synthetic beam is synthesized from the processed microphone channel data to form a sound signal, the feature matrix of the target sound signal is obtained, and the feature matrix is processed as the input layer of the LSTM model.

#### 2.3. LSTM

_{t}. The efficiency of the storage unit is determined by three gates: the input gate i

_{t}, output gate o

_{t}, and forgetting gate f

_{t}. The upgraded equation can be expressed as:

_{t}and early hidden state h

_{t−1}, one can obtain the forgetting gate f

_{t}, whose values range from 0 to 1. When the value of f

_{t}reaches 1, the last memory cell c

_{t−1}of incoming data is strongly preserved. On the other hand, when the value of f

_{t}reaches 0, the incoming data are distributed and cannot be retained. (2) Input gates can be removed from the new input functions x

_{t}and early hidden state h

_{t}and added to the memory cell, specifying c

_{t}. (3) Therefore, the output gate must select an item from the memory cell that can be processed to form a new hidden state h

_{t}[26,27,28,29].

## 3. Simulation

#### 3.1. MVDR Algorithm Simulation

#### 3.2. Microphone Array Formation Selection

## 4. Experiments

#### 4.1. LSTM Model Parameter Settings

#### 4.2. Experimental Setup

#### 4.3. Experimental Process

- Step 1—The microphone array was used to collect the idler fault audio signal.
- Step 2—MVDR processing was performed on the collected signal to generate idler fault distance data.
- Step 3—We processed the data again to build the dataset.
- Step 4—We divided the data into the training set (90%) and testing set (10%).
- Step 5—We trained and tested the model to draw conclusions.

#### 4.4. Background Noise Interference Experiment

#### 4.5. Impact Noise Interference Experiment

#### 4.6. Evaluation Criteria and Comparison of Models

#### 4.6.1. Data Comparison for Diagonal Double Rectangular Microphone Array

#### 4.6.2. Data Comparison for Circular Microphone Array

## 5. Conclusions

- Due to the special structure of an idler, the human diagnosis steps are cumbersome and time is wasted. Based on deep learning, our model removed the tedious step of manually extracting idler fault features, which could greatly shorten the time required and improve the efficiency of idler fault diagnosis.
- Through simulation experiments, we found that the diagonal dual rectangular microphone array had higher resolution and noise resistance compared to the other microphone arrays and could be beneficial to the estimation of roller fault distance.
- After adjusting the model structure and parameters, we trained the generated idler fault distance samples. The accuracy of the proposed model was 100%, with better performance than the other models and results closer to the true values.
- Five fault locations during idler operation were analyzed, and the experimental results showed that the proposed model had the ability to estimate the fault distance and provide better robustness. It could be used as a standard for judging the fault distance of idlers and provide ideas for combining beamforming algorithms and deep learning with idler fault diagnosis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Simulation results of each array: (

**a**–

**c**) schematic diagram of diagonal double rectangular array and two- and three-dimensional positioning diagrams, (

**d**–

**f**) linear array diagram and two-and three-dimensional positioning diagrams, (

**g**–

**i**) circular array schematic diagram and two- and three-dimensional positioning diagrams, (

**j**–

**l**) cross array schematic diagram and two- and three-dimensional positioning diagrams, (

**m**–

**o**) rectangular array schematic diagram and two- and three-dimensional positioning diagrams.

**Figure 5.**Model accuracy under different numbers of hidden layers: (

**a**) Accuracy when the number of hidden layers is 1, (

**b**) Accuracy when the number of hidden layers is 2, (

**c**) Accuracy when the number of hidden layers is 3.

**Figure 6.**Schematic diagram of the experimental layout: (

**a**) experimental schematic diagram, (

**b**) field experiment diagram.

**Figure 9.**LSTM model performance under background noise interference: (

**a**,

**b**) accuracy and loss rate of training and test sets, respectively.

**Figure 11.**LSTM model performance under impact noise interference: (

**a**,

**b**) accuracy and loss rate of training and test sets, respectively.

**Figure 12.**Line chart illustrating the accuracy of the three models for the diagonal double rectangular array.

**Figure 13.**Diagonal double rectangular array per-model confusion matrix results: (

**a**–

**c**) MVDR-LSTM, CBF-MVDR, and FBF-LSTM confusion matrixes, respectively.

**Figure 14.**KPCA dimensionality reduction diagram for each model with the diagonal double rectangular array: (

**a**–

**c**) MVDR-LSTM, CBF-MVDR, and FBF-LSTM KPCA dimensionality reduction analyses, respectively.

**Figure 16.**Circular array per-model confusion matrix results: (

**a**–

**c**) MVDR-LSTM, CBF-MVDR, and FBF-LSTM confusion matrixes, respectively.

**Figure 17.**KPCA dimensionality reduction diagram for each model with the circular array: (

**a**–

**c**) MVDR–LSTM, CBFMVDR, and FBF-LSTM KPCA dimensionality reduction analyses, respectively.

Parameter Name | Parameter Value |
---|---|

Number of arrays | 18 |

Desired signal angle | 10 |

Interference signal angle | −30, 30 |

SNR | 10 |

INR | 10 |

Number of stories | 100 |

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**MDPI and ACS Style**

Zhang, X.; Wu, W.; Li, J.; Dong, F.; Wan, S.
MVDR-LSTM Distance Estimation Model Based on Diagonal Double Rectangular Array. *Sensors* **2023**, *23*, 5094.
https://doi.org/10.3390/s23115094

**AMA Style**

Zhang X, Wu W, Li J, Dong F, Wan S.
MVDR-LSTM Distance Estimation Model Based on Diagonal Double Rectangular Array. *Sensors*. 2023; 23(11):5094.
https://doi.org/10.3390/s23115094

**Chicago/Turabian Style**

Zhang, Xiong, Wenbo Wu, Jialu Li, Fan Dong, and Shuting Wan.
2023. "MVDR-LSTM Distance Estimation Model Based on Diagonal Double Rectangular Array" *Sensors* 23, no. 11: 5094.
https://doi.org/10.3390/s23115094