# Measurement of Flow Fluctuation in the Flow Standard Facility Based on Singular Value Decomposition

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Flow Stability of the Flow Standard Facility

## 3. Principle of Proposed Measuring Method Based on SVD

## 4. Simulation Experiment

#### 4.1. Generation and Pre-Processing of Simulated Flow Fluctuation Signal

^{3}/h. According to Equations (1) and (2), flow fluctuations 1% and 0.5% correspond to the amplitudes of the sinusoidal fluctuation 0.707 m

^{3}/h and 0.354 m

^{3}/h, respectively. For the simulation and experiment, the sampling frequencies were set as 20 Hz and 160 Hz for sinusoidal fluctuation signals of 1 Hz and 8 Hz, respectively, and the sampling frequency was set as 160 Hz when the two signals were superposed. A quantity of 1000 data points were collected continuously as the result data for different fluctuation signals in the simulation experiment.

#### 4.2. Parameters Setting of Measuring Method Based on SVD

^{3}/h and 0.354 m

^{3}/h, respectively.

#### 4.3. Simulation Results

## 5. Experiment and Result

#### 5.1. Experiment Setup

#### 5.2. Experiment Result

^{3}/h, and the water temperature was 17.2 °C. Due to the limitation of experimental conditions (currently, there is only one flow fluctuation generator), the external flow fluctuation generated by the flow fluctuation generator, the flow fluctuation of the flow standard facility itself in the pipeline, and flowmeter noise were superimposed together and used as the superimposed signal of multi-frequency flow fluctuation signals and noise.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Simulated result for 1 Hz signal: (

**a**) noise variance, 0.01; (

**b**) noise variance, 0.1; (

**c**) noise variance, 1.

**Figure 4.**Simulated result for 8 Hz signal: (

**a**) noise variance, 0.01; (

**b**) noise variance, 0.1; (

**c**) noise variance, 1.

**Figure 5.**Simulated result for superposition signal: (

**a**) noise variance, 0.01; (

**b**) noise variance, 0.1; (

**c**) noise variance, 1.

**Figure 6.**Simulated result for extracted signals: (

**a**) noise variance, 0.01; (

**b**) noise variance, 0.1; (

**c**) noise variance, 1.

**Figure 9.**The main pipeline and photo of experimental setup: (

**a**) the main pipeline of the flow standard facility; (

**b**) photo of experimental setup in the flow standard facility.

**Figure 15.**Experimental result for extracted signals in experiment No. 2: (

**a**) the flow fluctuation signal; (

**b**) frequency spectrums.

**Figure 16.**Experimental result for extracted signals in experiment No. 3: (

**a**) the flow fluctuation signal; (

**b**) frequency spectrums.

Noise | Variance | 0.01 | 0.1 | 1 |

SNR | 32.19 dB | 9.16 dB | −13.86 dB | |

SVD Method | Attenuation | 5.40 × 10^{−3} m^{3}/h | 2.52 × 10^{−2} m^{3}/h | 2.50 × 10^{−2} m^{3}/h |

SNR | 100.53 dB | 77.26 dB | 66.90 dB | |

Median Filter | Attenuation | 5.61 × 10^{−2} m^{3}/h | 1.50 × 10^{−1} m^{3}/h | 4.99 × 10^{−1} m^{3}/h |

SNR | 47.62 dB | 23.15 dB | −20.14 dB |

Noise | Variance | 0.01 | 0.1 | 1 |

SNR | 18.32 dB | −4.70 dB | −27.73 dB | |

SVD Method | Attenuation | 5.41 × 10^{−3} m^{3}/h | 2.54 × 10^{−2} m^{3}/h | 2.87 × 10^{−2} m^{3}/h |

SNR | 86.42 dB | 62.40 dB | 48.49 dB | |

Median Filter | Attenuation | 1.15 × 10^{−2} m^{3}/h | 2.49 × 10^{−2} m^{3}/h | 3.64 × 10^{−2} m^{3}/h |

SNR | 25.37 dB | 3.52 dB | −21.06 dB |

Noise | Variance | 0.01 | 0.1 | 1 |

SNR | 34.42 dB | 11.39 dB | −11.63 dB | |

SVD Method | Attenuation | 5.22 × 10^{−3} m^{3}/h | −6.41 × 10^{−3} m^{3}/h | 7.66 × 10^{−2} m^{3}/h |

SNR | 119.18 dB | 103.64 dB | 46.56 dB | |

Median Filter | Attenuation | 5.71 × 10^{−2} m^{3}/h | 1.58 × 10^{−1} m^{3}/h | 4.78 × 10^{−1} m^{3}/h |

SNR | 49.91 dB | 26.79 dB | −9.51 dB |

Noise | Variance | 0.01 | 0.1 | 1 |

SNR | 34.42 dB | 11.39 dB | −11.63 dB | |

1 Hz Signal | Attenuation | −1.49 × 10^{−3} m^{3}/h | 1.85 × 10^{−2} m^{3}/h | 5.97 × 10^{−2} m^{3}/h |

SNR | 102.44 dB | 69.03 dB | 52.72 dB | |

8 Hz Signal | Attenuation | 1.10 × 10^{−3} m^{3}/h | 3.15 × 10^{−3} m^{3}/h | −1.45 × 10^{−2} m^{3}/h |

SNR | 96.16 dB | 82.17 dB | 36.27 dB |

Signal | Noise Variance | 0 | 0.01 | 0.1 | 1 |

1 HZSignal | Simulated fluctuation | 1.00% | 1.03% | 1.22% | 2.23% |

Median filter | 1.00% | 1.09% | 1.64% | ||

SVD method | 1.01% | 1.03% | 1.01% | ||

8 HZSignal | Simulated fluctuation | 0.50% | 0.54% | 0.83% | 2.04% |

Median filter | 0.51% | 0.67% | 1.40% | ||

SVD method | 0.51% | 0.53% | 0.51% |

Noise Variance | 0 | 0.01 | 0.1 | 1 |

Simulated Fluctuation | 1.12% | 1.14% | 1.27% | 2.28% |

Median Filter | 1.12% | 1.17% | 1.69% | |

SVD Method | 1.12% | 1.09% | 1.06% | |

1 Hz Signal | 1.00% | 1.00% | 0.97% | 0.94% |

8 Hz Signal | 0.50% | 0.50% | 0.50% | 0.49% |

Experiment No. | 1 | 2 | 3 |
---|---|---|---|

Direct calculation | 0.25% | 1.01% | 0.57% |

Median filter | 0.22% | 0.95% | 0.47% |

SVD method | 0.22% | 0.99% | 0.53% |

Sinusoidal fluctuation | / | 0.97% | 0.48% |

Facility fluctuation signal | / | 0.22% | 0.22% |

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**MDPI and ACS Style**

Meng, T.; Wei, H.; Gao, F.; Shi, H.
Measurement of Flow Fluctuation in the Flow Standard Facility Based on Singular Value Decomposition. *Sensors* **2021**, *21*, 6850.
https://doi.org/10.3390/s21206850

**AMA Style**

Meng T, Wei H, Gao F, Shi H.
Measurement of Flow Fluctuation in the Flow Standard Facility Based on Singular Value Decomposition. *Sensors*. 2021; 21(20):6850.
https://doi.org/10.3390/s21206850

**Chicago/Turabian Style**

Meng, Tao, Huanchang Wei, Feng Gao, and Huichao Shi.
2021. "Measurement of Flow Fluctuation in the Flow Standard Facility Based on Singular Value Decomposition" *Sensors* 21, no. 20: 6850.
https://doi.org/10.3390/s21206850