This article is concerned with the outlier-resistant state estimation problem for industrial pipe networks (PNs). PN signals, e.g., pressure and temperature, are modeled as low-pass time-varying graph signals, and an outlier-resistant graph-frequency domain (GFD) filter is proposed. This article extends the innovation saturation (IS) mechanism from the node domain to the GFD. A GFD IS function is developed with a more compact structure, which reduces outlier effects by restricting PN signals' smoothness. Since the PN signal is time-varying, the saturation function is embedded in the Kalman filter as an inequality constraint. The close-form solution to the filter is derived by replacing the nonlinear inequality constraints with high-pass graph Fourier transforms, and the cutoff frequency is found by analyzing the graph-frequency component of prior and posterior. A steel industrial PN is used to evaluate the proposal. Results indicate that the proposed filter exhibits superior performance in PN systems, particularly internal nodes.

Industrial gas-electricity networks typically operate in several modes due to large demand variations. In this study, the nonlinear spatio-temporal transient phenomenon of gas networks (GN) is analyzed by a novel modeling approach, named Takagi-Sugeno fuzzy linear graph (TSFLG), and then a parameter space decomposition (PSD)-based adaptive parameter estimation algorithm is developed for greater efficiency. By merging TS fuzzy theory, the nonlinear terms are replaced by a set of linear elements interpolated by membership functions, which are then connected in series to construct the TSFLG structure. The GN is partitioned into several subnetworks for parallel estimation, and the coupling parameters are determined by the covariance intersection fusion rule. Within each subnetwork, efficiency is further improved by estimating alternately linear and nonlinear parameters. The proposal is assessed in an industrial GN with 12 nodes. Test results indicate that the proposed improves efficiency by 38.64$\%$ while maintaining accuracy.

This article addresses the distributed consensus filtering problem of heterogeneous multienergy networks, where subnetworks exhibit different dynamics and are coupled by output constraints. The global consensus is reached by propagating constraints between subnetworks in the form of interval vectors. Guaranteed intervals satisfying given constraints are returned, which are then used to correct the local states through the probability density function truncation. Given the dependence and wrapping effects during constraint propagation, a hybrid Newton forward–backward propagation (FBP) contractor is proposed for avoiding overly pessimistic estimates. It extends the FBP contractor by replacing the natural inclusion function with centered forms. In addition, an event-triggered mechanism is designed to enhance the efficiency of constraint propagation, which allows the threshold values to be adaptively adjusted according to interval widths. Finally, the proposal is assessed in a steel industrial gas–electricity network with 25 nodes, and the results verify the performance in estimation accuracy, especially for coupling nodes.