The impact-echo (IE) acoustic inspection method is a non-destructive evaluation technique, which has been widely applied to detect the defects, structural deterioration level, and thickness of plate-like concrete structures. This paper presents a novel climbing robot, namely Rise-Rover, to perform automated IE signal collection from concrete structures with IE signal analyzing based on machine learning techniques. Rise-Rover is our new generation robot, and it has a novel and enhanced absorption system to support heavy load, and crawler-like suction cups to maintain high mobility performance while crossing small grooves. Moreover, the design enables a seamless transition between ground and wall. This paper applies the fast Fourier transform and wavelet transform for feature detection from collected IE signals. A distance metric learning based support vector machine approach is newly proposed to automatically classify the IE signals. With the visual-inertial odometry of the robot, the detected flaws of inspection area on the concrete plates are visualized in 2D/3D. Field tests on a concrete bridge deck demonstrate the efficiency of the proposed robot system in automatic health condition assessment for concrete structures.