# Acceleration Harmonics Identification for an Electro-Hydraulic Servo Shaking Table Based on a Nonlinear Adaptive Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Description

^{2}, its corresponding sinusoidal acceleration response is shown in Figure 2. In time domain, it is clear that the acceleration response is not a standard sine wave but a distorted one. There are other seven harmonics (from the second to the eighth) except the fundamental frequency signal in the sinusoidal acceleration response shown in Figure 2 and Figure 3. Besides, in order to demonstrate the impact of the nonlinear hydraulic system, the total harmonic distortion (THD) is introduced. The value of THD can be calculated by using Equation (1), and its analysis result is shown in Table 2. From Table 2, it can be seen that the amplitude of the fundamental response is less than the excitation signal. Besides, the third harmonic is the largest harmonic among other seven harmonics, i.e., it plays a most prominent part in THD. The amplitude of the sixth harmonic is the same as that of the Seventh, at 0.006, but both are less than the eighth harmonic. The fifth harmonic is in the least domination, at 0.016. The value of the THD is 7.06%.

## 3. Harmonic Identification Scheme Based on Adaline-LMM Algorithm

_{1}, t

_{2}and t

_{3}are thresholds which are used to control the impulse-suppressing degree and can be determined by estimating the variance of the impulse free signal. These threshold parameters can be estimated as [17]:

## 4. Simulation Results

## 5. Experiment Results

_{2}which is set as 1.071. The estimation error is displayed in Figure 14 which is used to demonstrate the estimation accuracy. It is noted that the estimation error fluctuates largely at the beginning of the identification but it is rapidly converged to a relative small range (within 0.08) after 2 s. There are two different lines, the dashed one and the red line contained in Figure 15. The dashed line is the actual system response and the red line presents the identified signal. Initially, the red line has a wide fluctuation, however, after the Adaline-LMM algorithm has been trained, the identified signal is ultimately well converged to the actual signal within 2 s. That is, the identified signal matches the actual signal very well and the harmonic identification precision of the proposed algorithm is rather successful.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Category | Parameter Value |
---|---|

Axes | 6 |

Size | 3 × 3 m |

Frequency range | 0–100 Hz |

Vertical actuators | 4 at 70 kN |

Vertical acceleration (no payload) | 5.6 g |

Longitudinal and lateral actuators | 4 at 70 kN |

Horizontal acceleration (no payload) | 3.7 g |

THD | Harmonic Amplitude (m/s^{2}) | |||||||
---|---|---|---|---|---|---|---|---|

7.06% | Fundamental | Second | Third | Fourth | Fifth | Sixth | Seventh | eighth |

0.859 | 0.005 | 0.057 | 0.004 | 0.016 | 0.006 | 0.006 | 0.008 |

Harmonic Order | Set Values | Estimated Values (LMM) | ||
---|---|---|---|---|

Amplitude (m/s^{2}) | Phase (rad) | Amplitude (m/s^{2}) | Phase (rad) | |

Fundamental response | 3 | 1.2 | 2.999999 | 1.199999 |

Second harmonic | 0.6 | 0.9 | 0.599999 | 0.899999 |

Third harmonic | 0.5 | 0.7 | 0.500000 | 0.700000 |

Fourth harmonic | 0.4 | 0.5 | 0.399999 | 0.500000 |

Fifth harmonic | 0.3 | 0.4 | 0.300000 | 0.400000 |

Sixth harmonic | 0.2 | 0.3 | 0.199999 | 0.299999 |

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**MDPI and ACS Style**

Yao, J.; Xiao, C.; Wan, Z.; Zhang, S.; Zhang, X.
Acceleration Harmonics Identification for an Electro-Hydraulic Servo Shaking Table Based on a Nonlinear Adaptive Algorithm. *Appl. Sci.* **2018**, *8*, 1332.
https://doi.org/10.3390/app8081332

**AMA Style**

Yao J, Xiao C, Wan Z, Zhang S, Zhang X.
Acceleration Harmonics Identification for an Electro-Hydraulic Servo Shaking Table Based on a Nonlinear Adaptive Algorithm. *Applied Sciences*. 2018; 8(8):1332.
https://doi.org/10.3390/app8081332

**Chicago/Turabian Style**

Yao, Jianjun, Chenguang Xiao, Zhenshuai Wan, Shiqi Zhang, and Xiaodong Zhang.
2018. "Acceleration Harmonics Identification for an Electro-Hydraulic Servo Shaking Table Based on a Nonlinear Adaptive Algorithm" *Applied Sciences* 8, no. 8: 1332.
https://doi.org/10.3390/app8081332