Single Pick Cutting Rock Load Identification Based on Improved Regularization Method

To explore the relationship between the cutting vibration and the cutting load of a single pick, this paper studied a new method for a single pick cutting rock load identification. This paper improved the low accuracy problem of the regularization method in the inverse process of frequency response function in the traditional load identification method by introducing a filter operator. By combining the inverse pseudo excitation method and the improved regularization method, the identification of the load dependent on the vibration signal was realized. A single pick cutting rock test equipment was built, which could simulate the actual working conditions of pick cutting rock in underground or tunnel. By changing cutting speed, cutting angle, cutting line spacing and cutting depth of the single pick, the change trends of real cutting load and identification load were obtained. The load identification method proposed in this paper was consistent with the change trend of the real load under the single pick cutting state. Therefore, the method had good recognition accuracy and the maximum load recognition error was 17.35%. Compared with the traditional load identification method, the identification error was reduced by a maximum of 1.98%. This method can identify the cutting load of single pick and modify the morbidity problem of frequency response function matrix. The method has a better recognition effect on the cutting load of the pick than the traditional recognition method. The research could benefit for the design of the cutting system and the arrangement of the pick on the coal mine or tunneling machinery.


Introduction
The cutting system is the most important mechanical system in coal mining or tunneling machinery. It is the key to determine the cutting performance and cutting efficiency. The pick is the part of the cutting system that is in direct contact with the cutting object, which bears the Acquiring the cutting load generally adopts the method of directly measuring the cutting electricity. However, the cutting electricity is often mixed with auxiliary electricity such as walking electricity, hydraulic electricity and dust removal electricity, which are not easy to distinguish. The cutting electricity also contains comprehensive cutting information such as the feed force and the rotation force, which make it difficult to obtain the information of the pick breaking load (Wang et al. 2013). Therefore, it is necessary to build a single pick rock breaking test system and to establish a method to study the influence of a single pick cutting parameters on the cutting load. Dogruoz et al (2014)  Load identification is the inverse problem of structural dynamics. It is a process of identifying excitations according to characteristic parameters and responses of the structure itself. Load identification technology has been widely used in various fields such as structural health monitoring in civil engineering (He et al. 2011) and durability testing in the automotive field (Raath and Waveren 1998). Load identification methods can be roughly divided into three categories: time domain method (Liu et al. 2016), frequency domain method (Wu et al. 2018) and modern intelligent method (Lee and Liu 2014). Time domain method includes series expansion method (Li and Deng 2016), Kalman filter method (Zhi et al. 2018) and inverse system method (Wang et al. 2016). The application in complex mechanical systems has great limitations, because the input and output of the time domain system are relatively complicated convolution relationship and the amount of calculation after discretization is too large. Modern intelligence method includes neural network method (Zhou et al. 2019), wavelet transform method (Hassan et al. 2015;Patel et al. 2018) and genetic algorithm method (Wei and Zhang 2018;Treetrong et al. 2014). It is rarely used in practical engineering applications, because the modern intelligence algorithm requires a large number of training samples and the establishment of the topology structure is difficult (Ren et al. 2018). Although the frequency domain method also has many shortcomings such as morbidity of frequency response function and modal truncation, it is widely used in actual engineering situations because it requires fewer training samples and the calculation amount is small.
The frequency response matrix in the load inversion problem is often morbid. The proper handling of the morbidity problem is the key to the success of load identification. Choi et al. (2006;2007)  For the inverse problem of multipoint (l>m) arbitrary excitation, the known response spectrum matrix is decomposed into: Where r is the rank of [SYY], and m≤r; { } is the j-th order feature pair of the Hermite matrix. To construct a pseudo response: To get inversion corresponding pseudo excitation: Therefore, the excitation spectrum matrix can be obtained as: The frequency response function of the system can be obtained by the finite element method. The test device is a single pick and single swing device, hence can be simplified to a cantilever beam. The free mode and working mode of the cantilever beam could be obtained in (Song et al. 2018;Song et al. 2019). Therefore, the solution of the natural frequency response function of the test device simplified as a cantilever beam will not be explained too much in this paper.

Modified Regularization Method
The inverse pseudo excitation method needs to invert the frequency response function to solve the pseudo excitation or test excitation.
The regularization method to solve the inverse matrix of the frequency response function is a method that is easy to understand and has a short calculation time. However, this method often results in a lower load identification accuracy because of morbidity matrix or improper selection of parameter values. Therefore, this paper established a new selection criterion for the key parameters in the regularization method to improve the accuracy of the traditional load identification method.
(1) Singular Value Decomposition The singular value decomposition method is often used to calculate the generalized inverse of the matrix. Singular value decomposition of H as follows: Where H + is Moore-Penrose generalized inverse; represents the left singular value vector; represents the right singular value vector; represents the singular value.
Where λ is the regularization parameter. The operator gλ(s) is a modified operator includin g the traditional Tikhonov regularization operator.
Therefore, equation (9) can be written as: With the increase of σ, the convergence order of the relative error of the regularization solution increases with it. From equation (9), it is found that the regularization parameter λ plays an important role in the final solution. When the selected regularization parameter is larger, the load cannot be well identified; when the selected regularization parameter is smaller, the regularization solution of load identification will be unstable and cannot reasonably approximate the load identified. Therefore, a reasonable selection of regularization parameter is the key to the success of regularization solution. At present, the most used method for selecting regularization parameter is the L-curve criterion (Hansen 1999).
However, the L-curve is sometimes too smooth to find the λ value corresponding to the maximum point of the bending derivative on the curve. Therefore, this paper used the GCV criterion to select the optimal regularization parameter. The GCV function is expressed as (Mao et al. 2010 The relative movement of the pick and the rock completes the cutting process.
To explore the applicability of the above-

Test object
The test object uses an alloy steel pick, whose material is 35CrMnSiA high-strength steel,

Results and discussion
To validate the applicability of the load identification method, the data in this paper is not subject to data processing. Taking   The influence of the cutting depth on the cutting system is greater than the other three factors.
Therefore, when the cutting object is hard rock, the cutting depth should be as small as possible while considering the cutting efficiency.   To compare with the load identification method before improvement, that is, compared with the regularization method which does not introduce a filter operator gλ(s), the error quantization index is defined: Where 1 represents the root mean square of the amplitude of the identified load power spectrum; 2 represents the root mean square of the real load power spectrum amplitude.
The identification error is shown in Table 3: The improved regularization method in all three measurement points can reduce the load identification error and the modified reduction error is up to 1.98%. It can also be seen from Table 3 that the farther the sensor is from the cutting surface, the greater the load identification error. The reason is that the components other than the cutting energy contained in the vibration signal have a greater impact on the load.
Therefore, the problem of load identification can be meaningful if it is discussed within a certain range. Even though, the improved load identification method in this paper can modify the inverse distortion problem of the frequency response function around the natural frequency to a certain extent.

Conclusions
(1) A single pick cutting rock load identification method is presented. This method can identify the cutting load of a single pick according to the actual measured vibration and can use the inverse pseudo excitation method, singular value decomposition method and modified regularization method to modify the morbidity problem of frequency response function matrix. The test results show that the method has a better recognition effect on the cutting load of the pick and the recognition error is smaller than the traditional recognition method.
(2) With the increase of cutting depth, cutting line speed, cutting angle and cutting line spacing, the load of single pick cutting rock increases nonlinearly, slightly decreases, first increases and then decreases and changes irregular. It reflects the force trends of single pick cutting rock, which provide a certain research basis for the design of pick and cutting systems.
(3) The phenomenon of energy concentration in the frequency spectrum of the pick cutting vibration signal with the increase of the speed should be further studied and analyzed, which provides another research topic for improving the accuracy of load identification.