Landmark-Based Registration of Curves via the Continuous Wavelet Transform

Gait phase normalization resolves the problem of different phases being compared in gait cycle normalization

For time-continuous analysis of gait, the problem of variations in cycle durations is resolved by normalizing to the gait cycle, but results depend on the definition of the cycle start. Gait cycle normalization ignores variations in gait phase durations, which results in averaging and comparing data across different phases. We propose gait phase normalization as part of a comprehensive method for independently analyzing magnitude and timing differences. First, gait phases are identified and differences in absolute and/or relative timing of phase durations or any point of interest between conditions or groups are analyzed using standard statistics. Next, time-continuous gait data is normalized to gait phases, and statistical parametric mapping (SPM) is used to assess magnitude differences in gait data. This approach is demonstrated on data recorded from ten young healthy adults walking on a treadmill at five different speeds. Sagittal knee angle was normalized to gait cycle or gait phase using five different gait cycle start events. Walking at different speeds resulted in significant changes in gait phase durations, highlighting a problem ignored by gait cycle normalization. SPM results for knee angle normalized to gait cycle varied from normalization to gait phases. Gait phase normalized SPM results were robust to the definition of the cycle start, in contrast to gait cycle normalized data. The approach of analyzing phase durations and normalizing data to gait phases overcomes previous limitations and enables a comprehensive analysis of magnitude and timing differences in time-continuous gait data and could be readily adapted to other tasks.

Challenges in the Development of Soft Sensors for Bioprocesses: A Critical Review

Among the greatest challenges in soft sensor development for bioprocesses are variable process lengths, multiple process phases, and erroneous model inputs due to sensor faults. This review article describes these three challenges and critically discusses the corresponding solution approaches from a data scientist’s perspective. This main part of the article is preceded by an overview of the status quo in the development and application of soft sensors. The scope of this article is mainly the upstream part of bioprocesses, although the solution approaches are in most cases also applicable to the downstream part. Variable process lengths are accounted for by data synchronization techniques such as indicator variables, curve registration, and dynamic time warping. Multiple process phases are partitioned by trajectory or correlation-based phase detection, enabling phase-adaptive modeling. Sensor faults are detected by symptom signals, pattern recognition, or by changing contributions of the corresponding sensor to a process model. According to the current state of the literature, tolerance to sensor faults remains the greatest challenge in soft sensor development, especially in the presence of variable process lengths and multiple process phases.