| F s | sampling rate for acquiring a signal |
| F B | highest frequency component contained in a signal |
| M | number of precision items |
| N | data length of discrete signals |
| s[i] | ith data point of a discrete signal |
| p | pth precision item | | raw sensor data of pth precision item | | cleaned sensor data of pth precision item |
| g[k] | DWT low‐pass filters |
| h[k] | DWT high‐pass filters |
| L | number of decomposition levels; |
| j | scale parameters |
| n | translation parameter |
| cj[n] | nth discrete wavelet coefficient of at level j | | nth approximation coefficient at level j | | nth detail coefficient at level j | | nth modified wavelet coefficients at level j | | nth modified approximation coefficient at level j | | nth modified detail coefficient at level j |
| λ | threshold of cj[n] |
| MAD(cL − 1[n]) | mean absolute deviation of cL − 1[n] | | modified approximation coefficients |
| avg | arithmetic mean or average of |
| std | standard derivation of |
| max | maximal magnitude of |
| min | minimal magnitude of |
| ptp | peak‐to‐peak amplitude of |
| kurt | kurtosis for measuring the peakedness of |
| skew | skewness for measuring the asymmetry of |
| RMS | root mean square value of |
| CF | crest factor of |
| T | duration of a continuous‐time signal |
| t | specific time t of a continuous‐time signals |
| cr xy | correlation coefficient value of two signals: x(t) and y(t) |
| CR xy | cross‐correlation value of two signals: x(t) and y(t) |
| γ xy | covariance value of two signals: x(t) and y(t) |
| m | displacement unit of a signal |
| * | complex conjugate of a signal |
| SF CR(xy) | a feature set of CRxy |
| FFT[n] | frequency amplitude at the nth Hz by FFT |
| SF FFT(q) | qth certain frequency band delimited by a lower frequency and an upper frequency |
| Q | number of frequency band |
| uf q | qth upper frequency of the critical characteristics; and |
| lf q | qth lower frequency of the critical characteristics. |
| SF FFT(q) | qth FFT‐based SF |
| u | uth wavelet packet at level L, u= 1, 2, …, L; |
| v | subband length for each wavelet packet at level L, v = N/2L |
| SF WPT(u) | uth WPT‐based SF |
| h | compressed code of the middle layer in AEN; | | output reconstructed from c in the middle layer of AEN; |
| f EN | encoder layer of AEN; |
| f DE | decoder layer of AEN; |
| f a | activation function of AEN; |
| W EN | network weight for node in the encoder; |
| W DE | network weight for node decoder; |
| b EN | bias for node in the encoder layer; |
| b DE | bias for node in the decoder layer |
| SF AEN | SFs extracted from AEN |
