[Bldg-sim] [Python / Custom Solvers] Analytical envelope model resolving moisture degradation and nocturnal subcooling

[GUIGOT Corentin]

This message introduces an open-source analytical solver for dynamic thermal simulation and Model Predictive Control (MPC) architectures.

Large-scale stochastic optimization and sub-hourly MPC encounter structural bottlenecks: the computational cost of spatial discretization (FDM) and the numerical instability of standard Transfer Matrix Methods (TMM) under high-frequency transient forcing. Standard state-space models also systematically assume material homogeneity, truncating hygrothermal degradation.

A frequency-domain framework based on the continuous spatial Riccati equation has been published to bypass these limits.

Applied capabilities:

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Moisture-driven degradation: The framework analytically integrates continuous spatial property gradients (λ(x)) via perturbation theory. For wetted porous media, it captures unaccounted peak heating loads (correcting a 21.9% deviation in wetted AAC envelopes) without requiring internal nodal meshing.
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Non-linear boundary conditions: It isolates Stefan-Boltzmann radiative exchanges (T⁴) as harmonic source terms to model nocturnal subcooling under clear skies, correcting the heat discharge overestimations produced by linearized LTI coefficients.
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Algorithmic stability: By algebraically bounding positive exponential wave arguments, the solver eliminates high-frequency overflow crashes. The single-step macroscopic integration executes in 0.02 ms, enabling multi-week time-domain reconstructions for parametric runs or real-time MPC dispatch.

The formal mathematical derivation, physical benchmarks, and error bounding are detailed in the published article ( https://doi.org/10.1080/19401493.2026.2657578 ) and its open-access preprint ( https://hal.science/hal-05602751 ).

The Python source code is available for direct integration on Zenodo: https://doi.org/10.5281/zenodo.19783248

Corentin Guigot
Associate Professor
CESI LINEACT
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