The paper introduces the multivariate Higuchi fractal dimension (MvHFD) and its advanced version, multivariate multiscale Higuchi fractal dimension (MvmHFD), to address the limitations of traditional fractal dimension metrics in analyzing multichannel time series data. Traditional fractal dimensions can only analyze single-channel time series at a specific scale, while MvHFD and MvmHFD incorporate multichannel information processing and multiscale processing technology, respectively, to characterize the complexity of multichannel time series at multiple scales. The effectiveness of MvHFD and MvmHFD is validated through simulated and real signal experiments. In the simulated experiments, MvHFD demonstrates superior stability and computational efficiency compared to other metrics like multivariate dispersion entropy (MvDE), multivariate fuzzy entropy (MvFE), and multivariate sample entropy (MvSE). MvmHFD further enhances the signal discrimination capability, outperforming other metrics in distinguishing different mechanical signals. In the real signal experiments, MvmHFD is applied to eight-channel mechanical signals, including bearing and gear signals. The results show that MvmHFD has a higher recognition rate than other metrics, achieving 100% recognition for three features, which is at least 17.2% higher than other metrics. The study concludes that MvmHFD is a robust and effective tool for analyzing the complexity of multichannel time series data, particularly in the context of mechanical signal analysis.The paper introduces the multivariate Higuchi fractal dimension (MvHFD) and its advanced version, multivariate multiscale Higuchi fractal dimension (MvmHFD), to address the limitations of traditional fractal dimension metrics in analyzing multichannel time series data. Traditional fractal dimensions can only analyze single-channel time series at a specific scale, while MvHFD and MvmHFD incorporate multichannel information processing and multiscale processing technology, respectively, to characterize the complexity of multichannel time series at multiple scales. The effectiveness of MvHFD and MvmHFD is validated through simulated and real signal experiments. In the simulated experiments, MvHFD demonstrates superior stability and computational efficiency compared to other metrics like multivariate dispersion entropy (MvDE), multivariate fuzzy entropy (MvFE), and multivariate sample entropy (MvSE). MvmHFD further enhances the signal discrimination capability, outperforming other metrics in distinguishing different mechanical signals. In the real signal experiments, MvmHFD is applied to eight-channel mechanical signals, including bearing and gear signals. The results show that MvmHFD has a higher recognition rate than other metrics, achieving 100% recognition for three features, which is at least 17.2% higher than other metrics. The study concludes that MvmHFD is a robust and effective tool for analyzing the complexity of multichannel time series data, particularly in the context of mechanical signal analysis.