工程结构经常受到多维随机载荷的作用，多维随机载荷时间历程的精确模拟对于结构的可靠性设计具有重要意义。本研究在对多维随机载荷谱表示法进行严格的理论公式推导基础上，详细分析了合成时域载荷功率谱矩阵与目标功率谱矩阵存在较大偏差的原因，为多维随机载荷时域模拟修正提供了理论依据。提出了基于谱修正法的多维随机载荷时域模拟算法，通过计算合成时域载荷功率谱矩阵与目标功率谱矩阵的偏差，引入误差反馈项，并采用迭代技术修正合成时域载荷的功率谱矩阵，进而使合成时域载荷的功率谱矩阵能够趋近于目标功率谱矩阵。最后对一个三维随机载荷模型进行数值分析。结果表明，基于谱修正法合成的多维随机载荷时间历程的功率谱矩阵能精确匹配目标功率谱矩阵。

Engineering structures are often subjected to multi-dimensional random loads, and the accurate simulation of multi-dimensional random load time history is of great significance to the reliability design of structures. Based on the rigorous theoretical formula derivation of spectrum representation method about the multi-dimensional random load, the cause for the large deviation between the spectrum density matrix of the synthetic load and that of target load was analyzed in detail, providing a theory support for the multi-dimensional random load time domain simulation correction. A multi-dimensional random load time domain simulation algorithm based on the spectrum correction method was proposed. By calculating the deviation between the spectrum density matrix of the synthetic time domain load and that of the target load, the iterative technique was developed to modify the spectrum density matrix of the synthetic time domain load through feedback of errors. Furthermore, the spectrum density matrix of the synthetic time domain load was made to approach to that of the target load. Finally, a numerical analysis about three dimensional random load model was carried out. The results show that the spectrum density matrix of the synthetic multi-dimensional random load time history based on the spectrum correction method can accurately match the spectrum density matrix of the target load.