# Innovative Actuator Fault Identification Based on Back Electromotive Force Reconstruction

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Scope of The Work

#### 2.2. Model Overview

#### 2.3. Trapezoidal EMA

#### 2.4. F16 Longitudinal Dynamics Model

#### 2.5. Faults Generation

#### 2.6. Back-EMF Reconstruction

#### 2.7. Curves Sampling

#### 2.8. Neural Networks Description

## 3. Results

#### 3.1. Sampling Mode 1

#### 3.2. Sampling Mode 2

#### 3.3. Sampling Mode 3, Single Hidden Layer

#### 3.4. Sampling Mode 3, Double Hidden Layer

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Model overview [33].

**Figure 3.**Trapezoidal EMA subsystem [33].

**Figure 4.**F16 longitudinal dynamics model [34].

**Figure 5.**Normalized reconstructed back electromotive force (back-EMF) coefficient in nominal and faulty condition.

**Figure 6.**Variation of m for two different intra-commutations periods considering 5 randomly seeded back-EMF coefficient curves.

**Figure 10.**Single hidden layer networks performance as function of neurons and training function, sampling mode 1.

**Figure 11.**Single hidden layer networks performance as function of neurons and training function, sampling mode 2.

**Figure 12.**Single hidden layer networks performance as function of neurons and training function, sampling mode 3.

**Figure 13.**Correlation between targets (i.e., expected outputs) and actual outputs of the network for sampling mode 3, 18 neurons and trainlm algorithm, for training and validation datasets.

**Figure 14.**Distribution of the mean absolute error (MAE) on the identification of the considered fault modes, for increasing number of neurons in the layer. Errors were determined for a custom identification set, randomly sampled in the acceptable range defined by Equations (2) and (3). (

**a**) Short circuits. (

**b**) Eccentricity. (

**c**) Phase.

**Figure 15.**Double hidden layer networks performance as function of neurons and training function, sampling mode 3.

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## Share and Cite

**MDPI and ACS Style**

Quattrocchi, G.; Berri, P.C.; Dalla Vedova, M.D.L.; Maggiore, P.
Innovative Actuator Fault Identification Based on Back Electromotive Force Reconstruction. *Actuators* **2020**, *9*, 50.
https://doi.org/10.3390/act9030050

**AMA Style**

Quattrocchi G, Berri PC, Dalla Vedova MDL, Maggiore P.
Innovative Actuator Fault Identification Based on Back Electromotive Force Reconstruction. *Actuators*. 2020; 9(3):50.
https://doi.org/10.3390/act9030050

**Chicago/Turabian Style**

Quattrocchi, Gaetano, Pier C. Berri, Matteo D. L. Dalla Vedova, and Paolo Maggiore.
2020. "Innovative Actuator Fault Identification Based on Back Electromotive Force Reconstruction" *Actuators* 9, no. 3: 50.
https://doi.org/10.3390/act9030050