Information-Theoretic Sensor and Excitation Design for Observable Multiphase Two-Fluid Networks with Entropy Constraints

• Hendra Wijaya

  Universitas Negeri Gorontalo, Faculty of Engineering, Department of Engineering, Jalan Jenderal Sudirman No. 6, Dulalowo Timur, Kota Tengah, Gorontalo, Indonesia

  Author

• Bagus Firmansyah

  Universitas Lambung Mangkurat, Jalan A. Yani KM 36, Banjarbaru, South Kalimantan, Indonesia

  Author

Multiphase thermal-hydraulic networks are monitored and controlled through sparse, heterogeneous sensors whose placement is often determined by convenience rather than identifiability. In gas--liquid systems, macroscopic predictions depend on partially observed internal states and on regime-dependent transport mechanisms that change with operating point and geometry. This paper develops a principled framework for joint sensor placement and input excitation design in networked two-fluid models, targeting state and parameter observability under thermodynamic admissibility constraints. The core idea is to quantify the value of a sensing configuration by its expected information gain about latent flow structure, computed from a constrained probabilistic dynamics model whose evolution operator is entropy stable and positivity preserving. Design variables include discrete sensor locations, sensor modalities with distinct noise and bandwidth properties, and admissible actuation trajectories that excite informative modes without violating safety limits. The resulting problem is posed as a mixed discrete--continuous optimization over mutual information and D-optimality surrogates derived from trajectory-dependent sensitivity operators. To make the design tractable at network scale, the approach introduces amortized adjoint computations for entropy-stable semidiscretizations, and it employs relaxation-based approximations for Fisher information that remain accurate in stiff, regime-transitioning conditions. Computational studies in annular and branched configurations demonstrate that optimal designs shift instrumentation toward junction-adjacent segments and prioritize differential measurements that condition latent slip and holdup modes, while carefully shaped boundary excitations can reduce posterior uncertainty without increasing risk. The framework provides a technical basis for instrumentation decisions in multiphase systems where sensing is expensive and observability is inherently limited.

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