Linear Estimation Strategies Applied to a Spring-Mass-Damper System
Bibliographic record
Abstract
Spring-mass-damper (SMD) systems are considered a benchmark setup in vibration-based systems. The system is considered linear for certain ranges during an excitation. For a simple system, the model is considered a second order system with one of the following behaviours for an impulse/unit input: exponential, sinusoidal, polynomial, or combined from the previous performances. The performance depends highly on the values of the parameters including the values of the mass, spring constant, and viscous damper coefficient. In this brief paper, one of the new promising filtering techniques, referred to as the sliding innovation filter (SIF), is used to estimate the system trajectories including the position and velocity. The filter is known for being robust and stable when system parameters change, which makes it a suitable candidate when the SMD system crosses the ranges of its linearized model or one of the parameters changes significantly. To complicate the case, only one state is assumed to be measured, which is the position. In this paper, a revised formulation of the SIF with the Luenberger method is introduced for cases with fewer measurements than states. The results are compared with the well-known Kalman Filter (KF). The results demonstrate that the proposed filter works well with the presence of uncertainties.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".