Sensor is the core module in signal perception and measurement applications. Due to the harsh external environment, aging, and so forth, sensor easily causes failure and unreliability. In this paper, three kinds of common faults of single sensor, bias, drift, and stuck-at, are investigated. And a fault diagnosis method based on wavelet permutation entropy is proposed. It takes advantage of the multiresolution ability of wavelet and the internal structure complexity measure of permutation entropy to extract fault feature. Multicluster feature selection (MCFS) is used to reduce the dimension of feature vector, and a three-layer back-propagation neural network classifier is designed for fault recognition. The experimental results show that the proposed method can effectively identify the different sensor faults and has good classification and recognition performance.

At present, the sensor is widely used in various processes to obtain a variety of physical quantity of data. In practical applications, due to the harsh external environments, battery depletion, aging, and other reasons, the sensor is prone to failure or even damage [

Wavelet transform is a widely used time-frequency analysis technology. Using wavelet transform, signals are decomposed into multilevel time-frequency components. Suitable wavelet basis for wavelet decomposition is important for fault information representation [

After wavelet decomposition, the main problem is how to extract fault information from the coefficients in decomposed subbands. The traditional Shannon entropy only considers the probability distribution of the signal value and does not consider the order structure of the signal value. Paper [

On the other hand, the disadvantage of PE is the lack of amplitude information about the signal except sequential pattern [

From the viewpoint of structure feature presentation, PE can extract the local microstructure feature and wavelet transform can extract the global macrostructure feature. So the combination of wavelet transform with MWPE can comprehensively represent the feature of the sensor fault. A wavelet based multiscale weighted permutation entropy (WMWPE) is proposed in this paper. WMWPEs of different subbands are used to extract signal features. Because the dimensions of WMWPE features are relatively high, it may cause low identification accuracy and time consuming. So the selection of the most important features in WMWPEs is needed [

Naturally, after feature selecting using MCFS, the multifault classifier is needed to conduct the fault diagnosis. A three-layer BP neural network is adopted as classifier to identify fault. The

The remainder of this paper is organized as follows. Section

The permutation entropy (PE) is defined as follows [

The definition of PE with

The maximum value of

For any time series,

Weighted permutation entropy (WPE) incorporates significant amplitude information from the time series when retrieving the sequential patterns. The main motivation aims at saving useful amplitude information carried by the signal. WPE is defined as follows [

Given a time series

Thus, each pair of weight value

Multiscale analysis [

The MWPE procedure is summarized in the following steps. Firstly, the original time series

Coarse-grained procedure.

MWPE is a function of scale factor

Before computing multiscale weighted permutation entropy, four important parameters including the length

The value of PE mainly depends on the embedding dimension

The time delay

The length of time series

To illustrate the rationality of parameters selection, some experiments are conducted. The experiment data used in this paper is 1-minute gas sensor data. Sampling rate is 100 Hz and the data has 6000 sampling points. Given that the scale factor

The relationship of

In Figure

The relationship of

In this paper, the scale factor

Although the MWPE takes advantage of the local microstructure information and amplitude information of signal, the macrostructure information is not explored. Wavelet transform is a powerful method to explore it and can be used to extract the global macrostructure information of the signal. So the combination of wavelet transform with MWPE can comprehensively describe the multiple features of the signal.

Given the analyzed signal

The WMWPE based fault identification method takes advantage of wavelet transform, WMWPE, MCFS, and BP-NN. It provides a full working flow of feature selection and fault identification as shown in Figure

Flowchart of sensor fault feature extraction and recognition method.

Use maximum energy-to-Shannon entropy ratio criterion to choose a proper wavelet base.

The sensor signals are decomposed by the selected wavelet base. A series of wavelet subband signals are obtained, and the appropriate subband signal is selected to extract feature.

Calculate multiscale weighted permutation entropy of the selected wavelet subbands, and WMWPEs are got.

After feature extraction, calculate MCFS score of the WMWPE features. According to the MCFS score ranked from high to low, select the features corresponding to the top

The selected

In this paper, the experimental data set is the measurement recordings collected from an array of 72 metal-oxide gas sensor array-based chemical detection platform [

Normal sensor data and fault sensor data. (a) Normal data, (b) bias, (c) stuck-at, and (d) drift.

The average WMWPE of 120 sensor signals after wavelet decomposition. (a) Low frequency-level 3. (b) High frequency-level 1. (c) High frequency-level 2. (d) High frequency-level 3.

A three-layer BP-NN neural network is used as classifier in the experiments. The hidden layer of the network has 10 neural nodes for learning. The network is trained by scaled conjugate gradient back-propagation method. Mean squared error is used as performance function. To obtain the generalized identification performance, 10-fold cross-validation [

To illustrate the identification performance of WMWPE on different subbands

Average identification accuracy and standard deviation of 20 WMWPEs of different subband.

Subband | Average identification accuracy ± standard deviation |
---|---|

LF_{3} | |

HF_{1} | |

HF_{2} | |

HF_{3} | |

Table

Identification results of WMWPE feature of LF_{3} subband.

Actual type | Identification results | |||
---|---|---|---|---|

Normal | Bias | Stuck-at | Drift | |

Normal | | 0% | 0% | |

Bias | 0% | 100% | 0% | 0% |

Stuck-at | 0% | 0% | 100% | 0% |

Drift | | | 0% | |

After calculating MCFS of 20 WMWPE features, the top

Average identification accuracy of the selected feature vectors.

Feature dimension | The scale index of selected features | Average identification accuracy ± standard deviation |
---|---|---|

1 | | |

2 | | |

3 | | |

4 | | |

5 | | |

6 | | |

7 | | |

8 | | |

9 | | |

10 | | |

All 20 features | | |

Table

Average identification accuracy of using different features.

Features | Average identification accuracy ± standard deviation |
---|---|

WMWPE | |

MWPE | |

WWPE | |

WPE | |

MPE | |

PE | |

Identification results of different features.

Actual type | Identification results | |||
---|---|---|---|---|

Normal | Bias | Stuck-at | Drift | |

MWPE | ||||

Normal | | 0% | 0% | |

Bias | 0% | | | 0% |

Stuck-at | 0% | | | 0% |

Drift | | | 0% | |

| ||||

WWPE | ||||

Normal | | 0% | 0% | |

Bias | 0% | | | 0% |

Stuck-at | 0% | | | 0% |

Drift | | 0% | | |

| ||||

WPE | ||||

Normal | | | | |

Bias | | | | |

Stuck-at | | | | |

Drift | | | | |

| ||||

MPE | ||||

Normal | | | | 0% |

Bias | | | | 0% |

Stuck-at | | | | 0% |

Drift | | 0% | 0% | |

As shown in Tables

Comparing the results of WMWPE to WWPE, MWPE to WPE, and MPE to PE, the multiscales analysis can improve the identification precision over 16%. The main reason is that the multiscale feature can explore more local structure information of the signals than the single scale feature.

Comparing the results of MWPE to MPE and WPE to PE, the amplitude information can bring about 25% and 9% increase of average identification accuracy, respectively.

So the macro- and microstructure information and amplitude information are all explored by WMWPE. The experiment results validate that the proposed method based on WMWPE can achieve high identification accuracy for sensor fault.

How to find an effective feature extraction method for sensor fault analysis and identification is always an important issue. Taking full advantage of macrostructure information, microstructure information, and amplitude information of the typical sensor faults, this paper proposed a new sensor fault feature extraction and identification method based on wavelet transform and multiscale weighted permutation entropy. The appropriate based wavelet selection, feature extraction, multicluster feature selection, and BP classifier are investigated. Actual chemical gas concentration data is used to evaluate the performance of the proposed method. Experiment results show that the proposed WMWPE extracts more comprehensive feature information and can achieve higher fault recognition accuracy than other kinds of features.

The authors declare no competing interests.