(untitled) (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
Computing the lower and upper boundaries of a response interval process is essential for interval uncertainty propagation over a continuous evolution variable, but conventional discretization-optimization schemes require repeated inner extremum searches at many state points and are costly for complex models. This paper develops a dual-layer Bi-Extremum Alternating Surrogate (BEAS) framework. In the inner layer, the expected-improvement criteria for minimization and maximization are coupled within a shared Kriging-based Efficient Global Optimization framework, so the minimum and maximum responses at a fixed state point are found using one surrogate model and one training set. In the outer layer, an alternating strategy updates the two boundary surrogates in half-steps: the by-product extremum of every inner call is delivered to the opposite boundary and, subject to a distance-based screening rule, injected into its training set, with a buffer as a zero-cost fallback, so both extrema of each expensive call are exploited. On two analytical examples, BEAS reproduces the boundaries of conventional double-loop calculations while markedly reducing inner-layer calls and performance-function evaluations.