Nonlinear guided wave has been recognized as a potential means to characterize the state of material microstructures in solids. However, nonlinear guided wave approaches based on second harmonic generation or combined harmonic generation induced by counter-directional wave mixing, are applicable only under the condition that transmitters and receivers are placed at two different ends of the tested structures. These approaches are not effective for characterization of the structures with only one accessible end. In this paper, modeling of the backward combined harmonic at difference frequency induced by one-way mixing of two primary co-directional guided waves is investigated in a circular pipe, where the transmitters and receivers are placed at the same end of the pipe. The backward combined harmonic, generated at difference frequency and propagating in the direction opposite to that of two primary co-directional guided waves, is successfully observed numerically. A strong frequency mixing response characterized by a cumulative growth effect of the generated backward combined harmonic is demonstrated. The use of the generated backward combined harmonic for localized material degradation characterization and location is numerically examined in the given pipe. The obtained results indicate that the use of the backward combined harmonic can locate and characterize the localized material degradations in the given pipe by controlling the mixing zone of two primary co-directional guided waves. This study provides a promising means for characterization of localized degradations in pipes.

非线性导波已被认为是表征固体中材料微观结构状态的一种潜在手段。但是，基于二次谐波生成或由反向波混合引起的组合谐波生成的非线性导波方法仅在将发射器和接收器置于被测结构的两个不同端的情况下适用。这些方法对于仅具有一个可接近端的结构表征是无效的。在本文中，研究了在圆形管道中将两个主要同向导波的单向混合引起的差频后向组合谐波建模，其中发射器和接收器位于管道的同一端。向后组合谐波，在数值上成功地观察到了以不同频率产生并沿与两个主同向导波相反的方向传播的电磁波。演示了一个强大的混频响应，其特征在于所产生的反向组合谐波的累积增长效应。在给定的管道中，将对使用生成的向后组合谐波进行局部材料退化表征和定位进行数值检查。获得的结果表明，通过控制两个主要的同向导波的混合区域，使用反向组合谐波可以定位并表征给定管道中的局部材料退化。这项研究为表征管道中的局部降解提供了一种有前途的方法。