*2.1. Concept of Damage Identification*

Figure 1 presents the sequential process flow of the proposed damage identification method. The proposed method estimates the damage distribution that reproduces a moving diagram of ultrasonic wave propagation through the following steps. (1) Ultrasonic imaging inspection is conducted, and an ultrasonic feature in the moving diagram is adopted as target data. A potential damaged site is extracted from an extensive inspection area as the design domain. (2) An analysis model of the extracted domain is discretized into finite elements, and the initial damage parameter is assigned to each element. (3) Finite element analysis of ultrasonic propagation is performed, and the ultrasonic feature is evaluated at the present damage distribution. (4) The error between the estimated ultrasonic feature and the target data is calculated. Then, (5) the correct number of damage parameters is explored by mathematical programming. (6) The damage parameters are updated, and the process is repeated from step (3) until convergence. As a result, the position, size, and shape of damage are obtained on a per-element basis.

**Figure 1.** The conceptual flowchart of damage identification based on topology optimization.
