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

^{1}

^{2}

^{3}

^{*}

## 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

- Zhang, L.; Zhang, F.; Qin, Z.; Han, Q.; Wang, T.; Chu, F. Piezoelectric energy harvester for rolling bearings with capability of self-powered condition monitoring. Energy
**2022**, 238, 121770. [Google Scholar] [CrossRef] - Zhang, Y.; Cao, J.; Zhu, H.; Lei, Y. Design, modeling and experimental verification of circular Halbach electromagnetic energy harvesting from bearing motion. Energy Convers. Manag.
**2019**, 180, 811–821. [Google Scholar] [CrossRef] - Zhou, Y.; Kumar, A.; Gandhi, C.P.; Vashishtha, G.; Tang, H.; Kundu, P.; Singh, M.; Xiang, J.W. Discrete entropy-based health indicator and LSTM for the forecasting of bearing health. J. Braz. Soc. Mech. Sci. Eng.
**2023**, 45, 12. [Google Scholar] [CrossRef] - Aljemely, A.H.; Xuan, J.; Al-Azzawi, O.; Jawad, F.K. Intelligent fault diagnosis of rolling bearings based on LSTM with large margin nearest neighbor algorithm. Neural Comput. Appl.
**2022**, 34, 19401–19421. [Google Scholar] [CrossRef] - Xie, W.; Li, Z.; Xu, Y.; Gardoni, P.; Li, W. Evaluation of Different Bearing Fault Classifiers in Utilizing CNN Feature Extraction Ability. Sensors
**2022**, 22, 3314. [Google Scholar] [CrossRef] - Yang, Q.; Zhang, J.; Chen, L.; Wu, D.S. Fault diagnosis of motor bearing based on improved convolution neural network based on VMD. In Proceedings of the 31st Chinese Control and Decision Conference (CCDC), Nanchang, China, 3–5 June 2019; pp. 405–409. [Google Scholar]
- Yu, J.; Wen, Y.; Yang, L.; Zhao, Z.; Guo, Y.; Guo, X. Monitoring on triboelectric nanogenerator and deep learning method. Nano Energy
**2021**, 92, 106698. [Google Scholar] [CrossRef] - Chen, L.; Choy, Y.S.; Wang, T.G.; Chiang, Y.K. Fault detection of wheel in wheel/rail system using kurtosis beamforming method. Struct. Health Monit.
**2020**, 19, 495–509. [Google Scholar] [CrossRef] - Cabada, E.C.; Leclere, Q.; Antoni, J.; Hamzaoui, N. Fault detection in rotating machines with beamforming: Spatial visualization of diagnosis features. Mech. Syst. Signal Process.
**2017**, 97, 33–43. [Google Scholar] [CrossRef] - Sun, S.L.; Wang, T.Y.; Yang, H.X.; Chu, F.L. Damage identification of wind turbine blades using an adaptive method for compressive beamforming based on the generalized minimax-concave penalty function. Renew. Energy
**2022**, 181, 59–70. [Google Scholar] [CrossRef] - He, T.; Xiao, D.H.; Pan, Q.; Liu, X.D.; Shan, Y.C. Analysis on accuracy improvement of rotor–stator rubbing localization based on acoustic emission beamforming method. Ultrasonics
**2014**, 54, 318–329. [Google Scholar] [CrossRef] - Subramanian, A.S.; Weng, C.; Watanabe, S.; Yu, M.; Yu, D. Deep learning based multi-source localization with source splitting and its effectiveness in multi-talker speech recognition. Comput. Speech Lang.
**2022**, 75, 101360. [Google Scholar] [CrossRef] - Zhang, X.L. Deep ad-hoc beamforming. Comput. Speech Lang.
**2021**, 68, 101201. [Google Scholar] [CrossRef] - Yang, Z.; Guan, S.; Zhang, X.L. Deep ad-hoc beamforming based on speaker extraction for target-dependent speech separation. Speech Communication
**2022**, 140, 87–97. [Google Scholar] [CrossRef] - Ramezanpour, P.; Mosavi, M.-R. Two-Stage Beamforming for Rejecting Interferences Using Deep Neural Networks. IEEE Syst. Journal
**2021**, 15, 4439–4447. [Google Scholar] [CrossRef] - Tao, T.; Zheng, H.; Yang, J.; Guo, Z.; Zhang, Y.; Ao, J.; Chen, Y.; Lin, W.; Tan, X. Sound Localization and Speech Enhancement Algorithm Based on Dual-Microphone. Sensors
**2022**, 22, 715. [Google Scholar] [CrossRef] - Ahamed, P.S.S.; Duraiswamy, P. Virtual Sensing Active Noise Control System with 2D Microphone Array for Automotive Applications. In Proceedings of the International Conference on Signal Processing and Integrated Networks, Noida, India, 7–8 March 2019; pp. 151–155. [Google Scholar]
- Wakabayashi, Y.; Yamaoka, K.; Ono, N. Rotation-Robust Beamforming Based on Sound Field Interpolation with Regularly Circular Microphone Array. In Proceedings of the ICASSP 2021–2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toronto, ON, Canada, 6–11 June 2021; pp. 771–775. [Google Scholar]
- Kidav, J.U.; Sivamangai, N.M.; Pillai, M.P.; Sreejeesh, S.G. A broadband MVDR beamforming core for ultrasound imaging. Integration
**2021**, 81, 221–233. [Google Scholar] [CrossRef] - Huang, Q.H.; Hu, R.; Fang, Y. Real-valued MVDR beamforming using spherical arrays with frequency invariant characteristic. Digit. Signal Process.
**2016**, 48, 239–245. [Google Scholar] [CrossRef] - Li, J.; White, P.R.; Bull, J.M.; Leighton, T.G.; Roche, B.; Davis, J.W. Passive acoustic localisation of undersea gas seeps using beamforming. Int. J. Greenh. Gas Control.
**2021**, 108, 103316. [Google Scholar] [CrossRef] - Ngoc, H.V.; Mayer JR, R.; Bitar-Nehme, E. Deep learning LSTM for predicting thermally induced geometric errors using rotary axes’powers as input parameters. CIRP J. Manuf. Sci. Technol.
**2022**, 37, 70–80. [Google Scholar] [CrossRef] - Nemani, V.P.; Lu, H.; Thelen, A.; Hu, C.; Zimmerman, A.T. Ensembles of probabilistic LSTM predictors and correctors for bearing prognostics using industrial standards. Neurocomputing
**2022**, 491, 575–596. [Google Scholar] [CrossRef] - Liu, J.; Pan, C.; Lei, F.; Hu, D.; Zuo, H. Fault prediction of bearings based on LSTM and statistical process analysis. Reliab. Eng. Syst. Saf.
**2021**, 214, 107646. [Google Scholar] [CrossRef] - Schmidhuber, J. Deep learning in neural networks: An overview. Neural Netw.
**2014**, 61, 85–117. [Google Scholar] [CrossRef] [PubMed] - Wang, Q.; Yu, Y.; Ahmed, H.O.A.; Darwish, M.; Nandi, A.K. Open-Circuit Fault Detection and Classification of Modular Multilevel Converters in High Voltage Direct Current Systems (MMC-HVDC) with Long Short-Term Memory (LSTM) Method. Sensors
**2021**, 21, 4159. [Google Scholar] [CrossRef] - Yin, A.; Yan, Y.; Zhang, Z.; Li, C.; Sánchez, R.-V. Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss. Sensors
**2020**, 20, 2339. [Google Scholar] [CrossRef] - Zheng, J.; Liao, J.; Chen, Z. End-to-End Continuous/Discontinuous Feature Fusion Method with Attention for Rolling Bearing Fault Diagnosis. Sensors
**2022**, 22, 6489. [Google Scholar] [CrossRef] [PubMed] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef]

**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 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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