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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".