Cross-State Condition Indicator Construction Using Monotonicity-Constrained Symbolic Regression: A Motor-Operated Valve Case Study

Condition indicators derived from multivariate monitoring signals are widely used to characterize ordered changes in machine operating states. However, an indicator constructed in one operating state may fluctuate or even reverse its direction when the same representation is applied to another state. A monotonicity-constrained symbolic regression method is developed to construct an explicit condition indicator that preserves its direction across predefined operating states. Candidate expressions are generated by deterministic exhaustive enumeration in a designated root state and screened in one or more branch states without coefficient refitting. Global Spearman monotonicity describes the overall relation with observation order, and a segment match ratio identifies local directional reversals. The method is evaluated on a motor-operated valve tested under combined thermal, pressure, and vibration stresses, with closing specified as the root state and opening as the branch state, the two states being named by the actuation that is performed and separated in the recorded drive current. The selected indicator is dominated by a decreasing trend in both states and achieves monotonicity magnitudes of 0.872 and 0.887 and segment match ratios of 0.667 and 0.833 for closing and opening, respectively; its opening-state monotonicity exceeds those of the single-feature, PCA, autoencoder, and error-driven symbolic-regression baselines. Applied to screened data from one prototype valve without refitting, the fixed expression retains its overall direction. These results demonstrate that the proposed method constructs an explicit and interpretable condition indicator while preserving its direction across predefined operating states. The constructed quantity is an indicator of ordered operational change, not a wear measurement. Broader applicability to other electromechanical machines and state sets remains to be established.