## 2 Impact Energy Recognition Algorithm Based on Fiber Bragg Grating Strain Sensing Technology
### Low Velocity Impact Feature Extraction Algorithm  
Signal amplitude, spectral amplitude, wavelet transform, the EMD algorithm, and other methods can be used for feature extraction of the low velocity impact signal detected by grating sensor. Due to the characteristics of the composite material with variable thickness, each order component of the classical EMD algorithm is approximately orthogonal, but the frequency aliasing is serious [21]. Therefore, an improved whitening EMD algorithm is proposed here to directly decompose several independent Intrinsic Mode Function(IMF) components from high frequency to low frequency from complex time series, and then spectrum analysis is carried out to obtain the impact eigenvalue. The main function of the standard EMD algorithm is to remove the signal superimposed wave and make the data waveform more symmetrical [22]. Whitening the EMD algorithm can whiten the component matrix to reduce the aliasing and eliminate the need for multiple sampling,avoiding the serious problem of modal aliasing of the original modal signal, and increase the accuracy of energy recognition.  
In the first step, using the EMD algorithm, any original signal \(M(t)\) can be decomposed into Formula (3). \(S_{i}^{\prime}(t)\) is the decomposition volume, \(r_{n}(t)\) is the signal residual. The first-order component \(S_{1}^{\prime}(t)\) contains the highest frequency component of \(M(t)\), and \(r_{n}\) indicates the trend of the signal. Using the standard deviation of the continuous treatment results as the basis of the judgment of whether the decomposition process can be terminated or not, the standard deviation is taken as 0.3, one of the following conditions is satisfied, and the screening process can be terminated: \(S_{n}^{\prime}(t)\) or \(r_{n}(t)\) is less than the predetermined error; \(r_{n}(t)\) is a monotonous function.  
\[\sum_{i=1}^{n}S_{i}^{\prime}(t)+r_{n}(t) \tag{3}\]  
In the second step, correlation matrix values of whitening are obtained in Formula (4). \(x\) is a random signal, R is the cumulative matrix, \(\Sigma^{-1}R^{T}\) is the whitening matrix. Whitening EMD algorithm also need to meet the following conditions: The similarity between each component is less than the predetermined threshold; The \(Z\) matrix of \(S_{i}^{\prime}(t)\) is whitened to reduce aliasing. From this, each order component \(S_{i}(t)\) is obtained.  
\[W_{x}=R\Sigma^{2}R^{T} \tag{4}\]  
In the third step, we discuss the orthogonality of the component \(S_{i}(t)\), which is obtained from the decomposition formula and the whitening correlation matrix is obtained from Formula (5). Where \(S_{n+1}(t)=r_{n}(t)\). If the component \(S_{i}(t)\) is orthogonal, then the second term to the right of Formula (5) should be 0, global orthogonal exponent is obtained in Formula (6). Then the orthogonal exponent of any two components \(S_{k}\), \(S_{j}\) can be obtained from Formula (7). The components of each order are orthogonal, and because each component is decomposed from the original data, the whitening EMD algorithm has better self-adaptability.  
\[M^{2}(t)=\sum_{i=0}^{n+1}s_{i}^{2}(t)+2\sum_{i=1}^{n+1}\sum_{i}s_{i}(t)s_{k}(t) \tag{5}\]  
\[\sum_{i=0}^{T}(\sum_{j=1}^{n+1}\sum_{k=1}^{n+1}s_{j}(t)s_{k}(t)/M^{2}(t)) \tag{6}\]  
\[\sum_{i=0}^{T}\frac{s_{k}s_{j}}{s_{k}+s_{j}} \tag{7}\]  
The above derivation process shows that the proposed whitening EMD algorithm avoids the serious problem of modal aliasing of the original modal signal, effectively improves the signal processing rate, improves the validity of the impact feature and increases the accuracy of energy recognition. Unlike standard algorithms, this improved algorithm eliminates the need for multiple samplings and has practical effects on engineering specimens that are susceptible to impact.