Relation of resonant frequency and appropriate linear predictive order for evaluating concrete strength by quality factor

Concrete is a popular construction material used broadly in many kinds of structures. The compressive strength is the most important performance of the concrete responsible to the safety of such structures. Although method of sampling a specimen is commonly employed, it makes damage to the structures. While Schmidt Hammer measures the hardness of the surface, but it relates to the compressive strength with poor accuracy owing to the influence of the conditions of the surface. Considering that the ultrasound propagating inside the concrete with higher strength will decrease less, the quality factor of the ultrasound signals should be higher, we have proposed a new method that evaluates the concrete strength non-destructively using the quality factor of resonant peak of multi-reflected ultrasound propagated inside the concrete. The quality factor is calculated by a linear predictive coefficient (LPC) processing on the ultrasonic signals, where the order of the LPC is an important parameter, by which the number of the poles of the LPC model is determined. Neither too many poles, which include too much details of the original signal with noise, nor too few poles, which lack of the proprieties at the resonant peaks, may express the propriety of ultrasonic propagation clearly. In this paper, as one of the approach of optimizing the parameters employed in measurement and signal processing, the relation between the resonant frequency and the appropriate order of LPC is discussed by numerical simulation and experiment. In the experiment, three types of concrete specimen with identical dimensions but different strengths (48.4 N/mm², 37.1 N/mm² and 27.9 N/mm² respectively) and four kinds of sound sources and receivers with different resonant frequency (28 kHz, 46 kHz, 68 kHz and 105 kHz, respectively) are employed. In the numerical simulation, a low-pass IIR filter is introduced to simulate the absorption of ultrasonic propagation in the concr- te. Though the absorption is very complicated and hard to be reconstructed by numerical simulation, the absorption differences corresponding to different strengths are simulated by changing the coefficients of the IIR filter as a simplified model to study the relation between resonant frequencies and appropriate orders of LPC for strength evaluation. The results of both the experiment and the numerical simulation show a similar tendency that with a higher resonant frequency, the appropriate order of LPC turns higher and its range turns narrower. Therefore, in the view of stability of the quality factor employed to evaluate the concrete strength, measurement with lower resonant frequency is expected.