Kalman Filtering Experiments for Multi-Floor Shear Models

This repository collects Jupyter notebooks that compare multiple Kalman filtering strategies on Gaussian shear-frame building models. The notebooks sweep through single- and multi-floor observation scenarios, linear and nonlinear measurement models, and small (3 floor) versus larger (10 floor) structures. Each experiment saves the generated ensembles, probability density functions (PDFs), and plots so you can reproduce or extend the studies.

Repository Layout

Path	Description
KF/	Classic Kalman Filter notebooks (kalman_singlefloor.ipynb, Kalman_update_2floor.ipynb) plus stored priors/updates (pdf_prior_2data.npz, pdf_update_*.npz) and the reference plot KF_floor3_1observed.pdf.
EnkF/	Ensemble Kalman Filter studies (EnKF_singlefloor.ipynb, EnkF_multiplefloors.ipynb, EnkF_multiplefloors_nonlinear.ipynb, check.ipynb), supporting ensembles (enkf_prior_*, enkf_update_*.npz), and comparison figures in matched/.
PCKF/	Polynomial Chaos Kalman Filter notebooks for linear and nonlinear observation models plus extensive PDF exports (e.g., PCKF_floor*_2data_nonlinear_{10k,100k,1mill,10mill}.pdf). The matched/ folder contains overlays used to verify agreement with EnKF/KF.
example_10dof/	Ten-degree-of-freedom examples for both EnKF and PCKF (standard and averaged-measurement variants) along with linear/nonlinear comparison data in matched/linear and matched/nonlinear.

Supporting artifacts such as sample.txt, data_sample.txt, and pckf_prior_alpha.npz capture the raw ensembles and chaos coefficients that feed the update steps.

Requirements

• Python 3.9+
• JupyterLab or Jupyter Notebook
• NumPy
• SciPy (for scipy.stats, scipy.special)
• Matplotlib

Install dependencies into a virtual environment to keep the workspace isolated:

python3 -m venv .venv
source .venv/bin/activate
pip install --upgrade pip
pip install jupyterlab numpy scipy matplotlib

Getting Started

1. Activate the virtual environment and launch Jupyter:

   source .venv/bin/activate
   jupyter lab

2. Open any notebook in the folder of interest (KF/, EnkF/, PCKF/, or example_10dof/).
3. Run the cells from top to bottom. Most notebooks expose key scenario parameters near the top:
   • floors selects the structural dimension (3 or 10).
   • observed chooses how many floors are instrumented (e.g., 1, 2, 3, or 5 averaged floors for 10-DOF studies).
   • nsamp (or npc) controls ensemble size/Polynomial Chaos order.
   • Gamma, noisevar, and epsilon specify measurement noise assumptions.

Running the Experiments

KF (KF/)

• kalman_singlefloor.ipynb reconstructs a single observed floor in the 3-floor model and analytically derives covariance matrices for validation.
• Kalman_update_2floor.ipynb expands to multiple observed floors and writes PDFs to pdf_update_single.npz, pdf_update_2data.npz, and pdf_update_multiple.npz for downstream comparison.
• Use the exported KF_floor3_1observed.pdf plot or regenerate it by re-running the notebook; PDFs are stored with a consistent naming scheme so EnKF/PCKF notebooks can load them.

Ensemble Kalman Filter (EnkF/)

• EnKF_singlefloor.ipynb and EnkF_multiplefloors.ipynb follow the same structural model but rely on Monte Carlo ensembles; they output the priors/updates as enkf_prior_*.npz and enkf_update_*.npz.
• EnkF_multiplefloors_nonlinear.ipynb replaces the observation model with a nonlinear mapping and employs kernel density estimates via scipy.stats.gaussian_kde.
• check.ipynb provides quick sanity plots or scalar checks.
• The matched/ subdirectory holds side-by-side PDFs (EnKF vs. PCKF) for each floor to verify the agreement of the ensemble approximation.

Polynomial Chaos Kalman Filter (PCKF/)

• PCKF_linear.ipynb and PCKF_nonlinear.ipynb load the saved EnKF ensembles (see the np.load('./../EnKF/enkf_*.npz') calls) to match the stochastic inputs and then propagate Polynomial Chaos coefficients (pckf_prior_alpha.npz, pckf_update_alpha.npz).
• Each notebook exports KDE plots for individual floors with varying sample budgets (10k, 100k, 1mill, 10mill), letting you study convergence as ensemble size grows.
• The matched/nonlinear folder mirrors the EnKF comparisons and helps confirm that the chaos expansion reproduces the target PDFs floor-by-floor.

10-DOF Examples (example_10dof/)

• EnkF_10floors.ipynb and PCKF_10floors.ipynb scale the approach to ten floors with direct measurements, while the _averaged variants (EnkF_10floors_averaged.ipynb, PCKF_10floors_averaged.ipynb) use averaged measurement matrices (see the custom Hk definitions).
• matched/linear and matched/nonlinear contain nested folders (1data, 2data, 3data, 10data) with the saved priors/posteriors (pckf_prior_pdfs.npz, pckf_update_pdfs.npz) and Polynomial Chaos coefficients, allowing you to reproduce the figures or feed the data into other notebooks.
• Each notebook saves an accompanying pckf_prior_pdfs.npz, pckf_update_pdfs.npz, and (when relevant) pckf_prior_alpha.npz / pckf_update_alpha.npz, enabling deterministic reruns without regenerating the ensembles.

Data and Outputs

• .npz archives capture ensembles, priors, and posteriors for KF, EnKF, and PCKF runs. They are ready to be reloaded with numpy.load for downstream analyses.
• .pdf files (for example PCKF_floor3_2data_nonlinear_1mill.pdf or EnKF_floor1_2data.pdf) summarize the PDFs for each floor, observation count, and noise setting. Many are duplicated under matched/ folders to simplify cross-filter comparisons.
• Plain-text helpers such as EnkF/sample.txt and example_10dof/data_sample.txt store the actual observation draws that seeded a notebook run.

Extending the Studies

• Adjust observed, floors, or Hk inside the notebooks to test different sensor layouts or averaged measurements.
• Increase nsamp/npc to study convergence (the existing 10k to 10mill PDFs provide a reference for how the density evolves).
• Swap the nonlinear observation sections in EnkF_multiplefloors_nonlinear.ipynb and PCKF_nonlinear.ipynb with your own measurement equations, keeping the saved .npz files in sync if you want to compare filters.
• Use the matched/ artifacts as regression baselines; rerun a notebook, regenerate the PDFs, and compare them to the saved plots to confirm nothing drifted.

Questions ?

Contact : Sudhi Sharma P V Email: sudhisharmapadillath@gmail.com