Modeling the behavior of nonlinear systems in a distributed fashion is of paramount in many industrial applications. Distributed means no sensor node in the wireless network has complete information about the data. Also, there is no centralized unit, and the communication can take place only with the single-hop neighborhood. The prodigious amount of data exchange between nodes limits the life of any distributed network that results in an inefficient ad-hoc network deployment. The current article develops a compressed-sensing (CS) based distributed Volterra–Laguerre modeling approach. It can remarkably decrease the communication load among the nodes that benchmarks the performance of full information exchange configuration. Further reduction in communication is achieved by capitalizing the spatial sparsity of the localized phenomena. The latter approach utilizes the inactive node strategy along with CS where a fraction of nodes are turned off. It conserves more energy than CS-based approach. ADMM-based sparse signal recovery method is then proposed to encompass the NP-hard limitation of \(l_0\)-norm minimization. The proposed recovery method is employed at each node to recover the uncompressed estimates of the neighboring nodes compressed data. Simulation results on a 2nd-order nonlinear system are obtained, expressing the potential performance of the proposed approaches.

以分布式方式对非线性系统的行为进行建模在许多工业应用中至关重要。分布式意味着无线网络中的传感器节点没有关于数据的完整信息。此外，没有集中单元，只能与单跳邻域进行通信。节点之间的大量数据交换限制了任何分布式网络的寿命，从而导致自组织网络部署效率低下。当前文章开发了一种基于压缩感知 (CS) 的分布式 Volterra-Laguerre 建模方法。它可以显着降低节点之间的通信负载，作为全信息交换配置的性能基准。通过利用局部现象的空间稀疏性，可以进一步减少交流。后一种方法利用非活动节点策略以及 CS，其中一小部分节点被关闭。它比基于 CS 的方法节省更多的能量。然后提出了基于 ADMM 的稀疏信号恢复方法来包含\(l_0\) -范数最小化。在每个节点采用所提出的恢复方法来恢复相邻节点压缩数据的未压缩估计。获得了二阶非线性系统的仿真结果，表达了所提出方法的潜在性能。