Non-Parametric Nonlinear Parameter-Varying Parallel-Cascade Identification of Dynamic Joint Stiffness
Bibliographic record
Abstract
OBJECTIVE: The paper presents a method to identify ankle joint dynamic stiffness during functional tasks where intrinsic and reflex stiffness change with a time-varying scheduling variable (SV), such as joint position or torque. METHODS: The method models joint stiffness with two pathways: (1) A parameter-varying (PV) impulse response function (IRF) describing intrinsic stiffness; and (2) a reflex stiffness model comprising a PV static nonlinearity followed by a PV linear element. RESULTS: Monte-Carlo simulations demonstrated that the method accurately estimated all elements of the intrinsic and reflex pathways as they changed with a SV. Experimental results with a healthy individual subjected to large, imposed ankle movements demonstrated that: (a) Intrinsic stiffness changed substantially as a function of ankle position; elasticity was lowest near the mid-position and increased with either dorsiflexion or plantarflexion. (b) Reflex gain increased and the velocity threshold for reflex excitation decreased monotonically with ankle dorsiflexion. (c) Reflex dynamics resembled a second-order, low-pass system that was invariant with ankle position. (d) The identified PV Parallel-Cascade (PC) model accurately predicted the torque response to novel trajectories of ankle movement. CONCLUSION: The PV-PC method can accurately and reliably estimate how intrinsic and reflex stiffness change with a time-varying SV. SIGNIFICANCE: The method is novel with multiple advantages: (a) It provides a unified algorithm that characterizes the changes in the parameters of all joint stiffness elements needed to understand their role in postural/movement control; (b) It is efficient requiring only two trials; (c) The models identified can predict the joint stiffness response to novel movements informing orthoses and prostheses design.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".