We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME) regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG) method was applied to solve the objective function, which was abbreviated as IME‐NCG algorithm. The result of IME‐NCG algorithm is compared with that of ME, ME‐CG, ME‐NCG, and IME‐CG algorithm; it is found that IME‐NCG algorithm is available for identifying the random dynamic force due to smaller root mean‐square‐error (RMSE), lower restoration time, and fewer iterative steps. Example of engineering application shows that L‐curve method is introduced which is better than Generalized Cross Validation (GCV) method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill‐conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal‐seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill‐conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill‐posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

Aiming at the conventional image edge detection algorithm, the first-order differential edge detection method is easy to lose the image details and the second-order differential edge detection method is more sensitive to noise. To deal with the problem, the Tikhonov regularization method is adopted to reconstruct the input coal-rock infrared images, so as to reduce the noise interference, and then, the reconstructed image is transformed by gray level. Finally, we consider the frequency characteristics and long memory properties of fractional differential, the classical first-order Sobel and second-order Laplacian edge detection algorithms are extended to fractional order pattern, and a new pattern of fractional order differential image edge detection is constructed to realize the coal-rock fracture edge features identification. The results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller. From the point of view of location criteria and location accuracy, the fractional order differential algorithm is better than the integer order. In addition, the proposed method is compared with Canny algorithm, B-spline wavelet transform, and multidirection fuzzy morphological edge detection method, can detect more coal-rock fracture infrared image edge details, and is more robust to noise.

In order to study the dynamic force identification method of an end-plate pick of shearer, a dynamic force identification technique based on interval theory was proposed. The dynamic force interval identification model is established by describing and quantifying the identified parameters. By using the interval analysis method of the first-order Taylor expansion, the dynamic force identification is transformed into two kinds of deterministic inverse problems at the midpoint of the uncertain parameter and its gradient identification. The Tikhonov regularization method is used to solve two kinds of deterministic problems, and the upper and lower boundaries of dynamic force of the end-plate pick are determined. The results show that the deviations between the identified dynamic force and the actual dynamic force are basically within 2% and 5%, and the average uncertainties are up to 7% and 10%. Therefore, the proposed method can effectively determine the upper and lower boundaries of dynamic force of the end-plate pick, improve the solving efficiency, and provide a new research method for studying the coal rock mechanism of the pick cutting load.

A new signal processing algorithm was proposed to identify the dynamic load acting on the coal-rock structure. First, the identification model for dynamic load is established through the relationship between the uncertain load vector, and the assembly matrix of the responses was measured by the machinery dynamic system. Then, the entropy item of maximum entropy regularization (MER) is redesigned using the robust estimation method, and the elongated penalty function according to the ill-posedness characteristics of load identification, which was named as a novel improved maximum entropy regularization (IMER) technique, was proposed to process the dynamic load signals. Finally, the load identification problem is transformed into an unconstrained optimization problem and an improved Newton iteration algorithm was proposed to solve the objective function. The result of IMER technique is compared with MER technique, and it is found that IMER technique is available for analyzing the dynamic load signals due to higher signal-noise ratio, lower restoration time, and fewer iterative steps. Experiments were performed to investigate the effect on the performance of dynamic load signals identification by different regularization parameters and calculation parameters, pi, respectively. Experimental results show that the identified dynamic load signals are closed to the actual load signals using IMER technique combined with the proposed PSO-L regularization parameter selection method. Selecting optimal calculated parameters pi is helpful to overcome the ill-condition of dynamic load signals identification and to obtain the stable and approximate solutions of inverse problems in practical engineering. Meanwhile, the proposed IMER technique can also play a guiding role for the coal-rock interface identification.

In this paper, an efficient mixed spectral conjugate gradient (EMSCG, for short) method is presented for solving unconstrained optimization problems. In this work, we construct a novel formula performed by using a conjugate gradient parameter which takes into account the advantages of Fletcher–Reeves (FR), Polak–Ribiere–Polyak (PRP), and a variant Polak‐Ribiere‐Polyak (VPRP), prove its stability and convergence, and apply it to the dynamic force identification of practical engineering structure. The analysis results show that the present method has higher efficiency, stronger robust convergence quality, and fewer iterations. In addition, the proposed method can provide more efficient and numerically stable approximation of the actual force, compared with the FR method, PRP method, and VPRP method. Therefore, we can make a clear conclusion that the proposed method in this paper can provide an effective optimization solution. Meanwhile, there is reason to believe that the proposed method can offer a reference for future research.