In today’s world, smart electric vehicles are deeply integrated with smart energy, smart transportation and smart cities. In electric vehicles (EVs), owing to the harsh working conditions, mechanical parts are prone to fatigue damages, which endanger the driving safety of EVs. The practice has proved that the identification of periodic impact characteristics (PICs) can effectively indicate mechanical faults. This paper proposes a novel model-based approach for intelligent fault diagnosis of mechanical transmission train in EVs. The essential idea of this approach lies in the fusion of statistical information and model information from a dynamic process. In the algorithm, a novel fractal wavelet decomposition (FWD) is used to investigate the time-frequency representation of the input signal. Based on the sparsity of the PIC model in the Hilbert envelope spectrum, a method for evaluating PIC energy ratio (PICER) is defined based on an over-complete Fourier dictionary. A compound indicator considering kurtosis and PICER of dynamic signal is designed. Using this index, evaluations of the impulsiveness of the cycle-stationary process can be enabled, thus avoiding serious interference from the sporadic impact during measurements. The robustness of the proposed approach to noise is demonstrated via numerical simulations, and an engineering application is employed to validate its effectiveness.

In recent years, the rapid development of artificial intelligence and advanced signal processing technologies have attracted substantial attention in smart cities, which facilitate related fields from traditional ways to intelligent applications. Electrical vehicles (EVs) are of great importance to global environmental protection because of their zero exhaust emissions [

Vibration monitoring is an important mean to prevent mechanical downtime [

At present, scholars are working in two directions. One is the new signal decomposition method, the other is the intelligent identification method of fault characteristics. In terms of signal decomposition, wavelet transform [

In this paper, a novel model-based approach, enhanced by sparse representation, is proposed for mechanical fault diagnosis in EV. In the signal decomposition, the fractal wavelet representation is used, which is an efficient signal decomposition tool with centralized multi-resolution ability. In feature recognition and selection, the complex harmonic characteristics of PICs in the wavelet envelope domain are used, and a sparse representation enhancement method based on an over-complete Fourier dictionary (OFD) is proposed. The method realizes the quantitative evaluation of the proportion of PICs in the signal. Through the above measures, the robustness of the proposed method to multi-component coupling signal and noise is greatly enhanced. The superiority and effectiveness of the proposed method are verified by numerical simulation and engineering experiments.

Wavelet transform is an effective tool for the multi-scale decomposition of signals. However, the center frequency of each subspace of the classical wavelet transform is different. In this section, a novel fractal wavelet decomposition (FWD), based on a dual tree wavelet basis [

Translation sensitivity is a significant defect of classical discrete wavelet decomposition, which often results in false features in the decomposition results. Maximal overlap decomposition strategy can avoid this defect, but the computational efficiency is significantly reduced. Dual tree wavelet transform (DTWT), proposed by Kingsbury, achieves a good trade off between accuracy and efficiency and the merit of translation invariance (TI) is realized. The wavelet of DTWT is a complex-valued function, as follows.

Although DTWT can alleviate the distortion of TV to the extracted features, it cannot solve the problem of transition band feature extraction in dyadic wavelet subspace. To address this problem, centralized multiresolution (CMR) is proposed by Chen [

IWPs can be generated using

A

Subspace | Center frequency | Band width |
---|---|---|

DWP | ||

IWP |

As shown in

Compared with the classical basis expansion method, the sparse representation (SR) allows the addition of other optimization constraints, which can better suppress the monitoring noise. For a discrete signal

Let

where

In fast Fourier transform (FFT), an orthonormal basis is used for decomposing the input signal. The spectral interval for adjacent sinusoidal atoms is

The column vector

On the basis of augmented Lagrangian theory, the above problem has an equivalent matrix form, given as:

Let

1: |

2: |

3: |

4: |

5: |

6: |

7: |

When localized damage occurs in mechanical parts, periodic impacts are often generated in the monitoring signal, which causes multiple harmonics in the envelope spectrum. In order to evaluate the amount of PIC in the signal, it is necessary to calculate the sum of the energy of each harmonic.

A sinusoidal signal

Applying the SFD algorithm on the synthesized signal by setting

In contrast to the FFT spectrum where the energy of the harmonic components leaks in the entire frequency domain, the energy of the signal in the SFD spectrum is compressed in a narrow band with a bandwidth of only 0.2 Hz. An approximation signal

In order to demonstrate the performance of SFD, the spectrum is compared with the FFT spectrum and the FFT spectrum with Hanning window. As shown in

To analyze the impact of the redundancy of

In order to test the ability of SFD spectra to characterize noisy harmonic components, white noise is added to the simulation signal in the formula. The time domain waveform of a noisy signal

The SFD spectrum, generated by the proposed method, is shown in

In this subsection, the performance of SFD on PICs is validated. In the time domain, a typical PIC can be modeled as

where

In the condition monitoring of EV, the PIC caused by the local damage of mechanical parts can be regarded as a multi-harmonic signal with noise in the envelope demodulation spectrum. Combined with FWD and SFD introduced in this paper, an intelligent fault diagnosis method is proposed. Taking the mechanical transmission chain and fault frequency and speed as prior knowledge, the procedure of the algorithm is as below. For a wavelet packet

To verify the effectiveness of the proposed approach, a case study using actual signals from engineering experiments, is investigated. The tested mechanical part is a roller element bearing with slight peeling on the outer race. Specifications of the test bearing are shown in

Item | Value |
---|---|

Contacting angle [ |
0 |

Pitch diameter D [mm] | 225 |

Roller diameter d [mm] | 34 |

Roller number | 17 |

The time domain waveform and the FFT spectrum of a record of vibration signals are shown in

If the indicator of PER is not calculated in the algorithm, the processing results are shown in

From the materials given above, it is known that the SFD spectrum has an extremely high resolution. This is quite different from the classical windowed spectral analysis. According to the Heisenberg uncertainty principle, the main lobe resolution and the side lobe attenuation rate cannot be improved simultaneously. The SFD spectrum proposed in this paper is based on the principle of sparse representation and does not depend on the window function, which can ensure a very high resolution of the main lobe while accelerating the rate of side lobe attenuation. Nevertheless, it is also found that such improvements are limited and still cannot completely break through the constraints of the Heisenberg uncertainty principle.

In this paper, the problem of PICs extraction is studied, which is the core problem in the mechanical fault diagnosis of electric vehicles. In order to improve the accuracy and robustness of fault feature identification, statistical information and model information in the monitoring signal were combined comprehensively. A sparse Fourier decomposition method based on OFD is proposed, which realizes the quantitative evaluation of the energy proportion of fault feature components on the envelope spectrum in signal time-frequency representation. This model information plays an important role in eliminating the interference of measurement noise in the analysis signal. The effectiveness of the proposed sparsity-enhanced model-based fault diagnosis method is demonstrated by numerical simulations and case studies.

This research is supported financially by the National Natural Science Foundation of China (Grant No. 51805398), the Natural Science Basic Research Program of Shaanxi (Grant No. 2023-JC-YB-289), the Project of Youth Talent Lift Program of Shaanxi University Association for Science and Technology (Grant No. 20200408), the Fundamental Research Funds for the Central Universities (Grant No. JB211303).

The authors declare that they have no conflicts of interest to report regarding the present study.