Surrogate-Assisted Inverse Design of the Power-Law Index in Axially Functionally Graded Fluid-Conveying Pipes for Target Modal and Deflection Performance

A surrogate-assisted inverse design framework is presented for selecting the power-law index of clamped–clamped axially functionally graded (AFG) Timoshenko pipes conveying fluid. The GITT model, 336-sample database, and trained MLP forward surrogate were developed in our previous study; the present contribution begins with the formulation and solution of the inverse problem. Millisecond-speed MLP inference is embedded in grid, particle swarm optimization (PSO), and genetic algorithm (GA) searches for prescribed modal-frequency and deflection targets. Single-variable, two-variable, weighted-sum, constrained, and Pareto formulations are examined. Continuous candidates from the single-variable cases are subjected to GITT-database interpolation verification, which is explicitly distinguished from a new independent GITT calculation. The feasible single- and dual-modal examples produce small database-interpolated target residuals, whereas an intentionally unattainable triplet case retains an approximately 16% fundamental-frequency residual and demonstrates the need for feasibility screening. The two-variable maps reveal non-unique parameter couplings and are treated as exploratory surrogate results unless the complete candidate coincides with, or is independently assessed against, the available database. A five-network ensemble assesses repeatability with respect to training-data partitioning only, while a sensitivity analysis connects the selected indices to the high-sensitivity gradation range. In the synchronized Case A benchmark, the online MLP grid and PSO searches require approximately 0.044 and 0.210 s, respectively, excluding the inherited offline GITT-database construction cost.