In addition, the novelty of our study lies in devising the concept of time offset for TOA error correction due to signal noise and applying it to the objective function. However, those papers required using a group of sensors arranged in an L-shape, while our study did not require any specific sensor alignments. Other studies also used minimization of an objective function to locate the source coordinates without any knowledge of the elastic properties of the material. ∂ f ∂ x = 4 ∑ i ≠ j t − ( t j − s j ) 2 ( x − x i ) 2 + ( y − y i ) 2 α 2 − t − ( t i − s i ) 2 ( x − x j ) 2 + ( y − y j ) 2 α 2 × t − ( t j − s j ) 2 ( x − x i ) − t − ( t i − s i ) 2 ( x − x j ) ∂ f ∂ y = 4 ∑ i ≠ j t − ( t j − s j ) 2 ( x − x i ) 2 + ( y − y i ) 2 α 2 − t − ( t i − s i ) 2 ( x − x j ) 2 + ( y − y j ) 2 α 2 × t − ( t j − s j ) 2 ( y − y i ) α 2 − t − ( t i − s i ) 2 ( y − y j ) α 2 ∂ f ∂ t = 4 ∑ i ≠ j t − ( t j − s j ) 2 ( x − x i ) 2 + ( y − y i ) 2 α 2 − t − ( t i − s i ) 2 ( x − x j ) 2 + ( y − y j ) 2 α 2 × t − ( t j − s j ) ( x − x i ) 2 + ( y − y i ) 2 α 2 − t − ( t i − s i ) ( x − x j ) 2 + ( y − y j ) 2 α 2 ∂ f ∂ α = 4 ∑ i ≠ j t − ( t j − s j ) 2 ( x − x i ) 2 + ( y − y i ) 2 α 2 − t − ( t i − s i ) 2 ( x − x j ) 2 + ( y − y j ) 2 α 2 × t − ( t j − s j ) 2 ( y − y i ) 2 α − t − ( t i − s i ) 2 ( y − y j ) 2 α ∂ f ∂ s k = 4 ∑ k ≠ i ( ( x − x i ) 2 + ( y − y i ) 2 α 2 ) ( t − s k ) × ( ( x − x i ) 2 + ( y − y i ) 2 α 2 ) ( t − s k ) 2 − ( ( x − x k ) 2 + ( y − y k ) 2 α 2 ) ( t − s i ) 2 + 2 λ s k As a result of the experiment, it has been confirmed that it has an accuracy within 5% and works stably against noise. Many experiments were conducted to evaluate the accuracy and robustness of the crack location by the SDMM. The result of applying the SDMM is the estimated crack position of the material, the crack start time, and the wave propagation velocity, of which the estimated crack position is used as the final result. We call the proposed ASL method the speed deviation minimization method (SDMM), because it is designed to minimize the difference in speed measured by each sensor. In addition, we add the TOA error correction constant to the objective function and apply a well-known Tikhonov regularization method for stable solving of the optimization problem. The objective function of the least squares is generated by assuming that the propagation velocity of an elastic wave in an anisotropic material is constant and based on the ellipse equation, which is modified so that the unknown velocity term is erased. The proposed ASL method has an iterative scheme to minimize the nonlinear least squares. This method allows for arbitrary placement of the sensor and includes the TOA errors. In this paper, we propose an ASL method using only the TOA in anisotropic plates.
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