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This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

The real-time identification of time-varying cable force is critical for accurately evaluating the fatigue damage of cables and assessing the safety condition of bridges. In the context of unknown wind excitations and only one available accelerometer, this paper proposes a novel cable force identification method based on an improved adaptive extended Kalman filter (IAEKF). Firstly, the governing equation of the stay cable motion, which includes the cable force variation coefficient, is expressed in the modal domain. It is transformed into a state equation by defining an augmented Kalman state vector with the cable force variation coefficient concerned. The cable force variation coefficient is then recursively estimated and closely tracked in real time by the proposed IAEKF. The contribution of this paper is that an updated fading-factor matrix is considered in the IAEKF, and the adaptive noise error covariance matrices are determined via an optimization procedure rather than by experience. The effectiveness of the proposed method is demonstrated by the numerical model of a real-world cable-supported bridge and an experimental scaled steel stay cable. Results indicate that the proposed method can identify the time-varying cable force in real time when the cable acceleration of only one measurement point is available.

Extended Kalman filtering with unknown input (EKF-UI) is often used to estimate the structural system state, parameters and unknown input in structural health monitoring. However, the real-time performance of EKF-UI is bound to whether the measurement equation has a direct feedthrough of unknown input, which great limits its application scope. Based on the zero-order-hold assumption and random walk assumption of unknown input, a novel adaptive discrete state equation is derived in this paper. The new equation establishes a connection between the current state and the current input and allows the adjustment of the sensitivity matrix of the unknown input. Then, based on the adaptive discrete state equation and minimum variance unbiased estimation principle, an adaptive generalized extended Kalman filter with unknown input is derived. The proposed algorithm eliminates the limitation that the real-time performance is restricted by whether the measurement equation has a direct feedthrough of the input and realizes the optimization of the state and input estimates in the sense of minimum variance. To demonstrate the feasibility of the proposed method, numerical example of a shear frame structure with Bouc–Wen hysteresis nonlinearity and experimental test of a five-story shear frame are conducted. The comparison with existing methods shows the advantages of the proposed method.

Simulation of multivariate cross-correlated random field samples (RFSs) is often required in reliability analysis of engineering structures. Conventional parametric methods for cross-correlated RFSs simulation generally require extensive measurements to obtain reliable random field parameters (e.g., type of auto-correlation function, correlation length, and cross-correlation matrix), for characterizing both the auto-correlation and cross-correlation structures among various cross-correlated engineering quantities. However, measurement data available in practice is often limited due to time, budget, technical and/or access constraints. Therefore, it is difficult to provide an accurate estimation of random field parameters (e.g., auto-correlation and cross-correlation matrix), rendering a challenging question of how to properly simulate multivariate cross-correlated RFSs from sparse measurements, especially when the number of engineering quantities of interest is large. This study aims to address this difficulty by developing a novel cross-correlated random field generator based on Bayesian compressive sensing (BCS) and Markov chain Monte Carlo (MCMC) simulation. The proposed method is data-driven and non-parametric, and it directly uses sparse measurements as input and provides cross-correlated RFSs as output. More importantly, the proposed method is able to deal with a large number of cross-correlated quantities for big data analytics in a high-dimension domain.

Precise measurement of the sound source directivity not only requires special equipment, but also is time-consuming. Alternatively, one can reduce the number of measurement points and apply spatial interpolation to retrieve a high-resolution approximation of directivity function. This paper discusses the interpolation error for different algorithms with emphasis on the one based on spherical harmonics. The analysis is performed on raw directivity data for two loudspeaker systems. The directivity was measured using sampling schemes of different densities and point distributions (equiangular and equiareal). Then, the results were interpolated and compared with these obtained on the standard 5° regular grid. The application of the spherical harmonic approximation to sparse measurement data yields a mean error of less than 1 dB with the number of measurement points being reduced by 89%. The impact of the sparse grid type on the retrieval error is also discussed. The presented results facilitate optimal sampling grid choice for low-resolution directivity measurements.

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

Quantum state tomography (QST) is a central technique to fully characterize an unknown quantum state. However, standard QST requires an exponentially growing number of quantum measurements against the system size, which limits its application to smaller systems. Here, we explore the sparsity of underlying quantum state and propose a QST scheme that combines the matrix product states’ representation of the quantum state with a supervised machine learning algorithm. Our method could reconstruct the unknown sparse quantum states with very high precision using only a portion of the measurement data in a randomly selected basis set. In particular, we demonstrate that the Wolfgang states could be faithfully reconstructed using around 25% of the whole basis, and that the randomly generated quantum states, which could be efficiently represented as matrix product states, could be faithfully reconstructed using a number of bases that scales sub-exponentially against the system size.

Due to the technological advancements and smart deployment, wireless sensor networks (WSNs) receive much attention in numerous real-time application fields. The stringent limitations of the battery of sensor devices and dubious wireless medium incur enormous challenges in the secure data collection and routing. Integration of compressive sensing and cryptography mechanism provide an efficient paradigm for reliable and energy efficient data collection over WSNs. With the aim of reducing communication cost and resilience against different WSN security attacks, this paper proposes a paillier cryptosystem and compressive sensing based routing (PC 2 SR) protocol. To achieve its objective, the proposed PC 2 SR designs three mechanisms that are paillier cryptosystem based key distribution and management, intra-cluster data gathering, and secure data transmission. Initially, the PC 2 SR provides paillier security keys to each device for data authentication. Instead of providing a long term security keys among two entities, the lightweight key refreshing mechanism of paillier cryptosystem in PC 2 SR updates the keys over a specific time interval. Secondly, the design of the Spatio-temporal measurement matrix within the intra-cluster reduces the computation and communication costs considerably. The integration of zero noise factors with all transmitted data assists the BS in detecting and isolating malicious behaviors in the network. Thus, the PC 2 SR efficiently offers high security in terms of integrity and confidentiality over WSN. We compare PC 2 SR to existing schemes, CSDA developed in 2017 and CSHEAD in early 2021 which outperform CSDA. The new scheme PC 2 SR offer better performance for all KPIs and thus is the best model combining data confidentiality and attack detection in WSN

This paper proposes a dual adaptive Kalman filter to identify parameters of a dynamic system that may experience sudden damage by a dynamic excitation such as earthquake ground motion. While various filter techniques have been utilized to estimate system’s states, parameters, input (force), or their combinations, the filter proposed in this paper focuses on tracking parameters that may change suddenly using sparse measurements. First, an advanced state-space model of parameter estimation employing a regularization technique is developed to overcome the lack of information in sparse measurements. To avoid inaccurate or biased estimation by conventional filters that use covariance matrices representing time-invariant artificial noises, this paper proposes a dual adaptive filtering, whose slave filter corrects the covariance of the artificial measurement noises in the master filter at every time-step. Since it is generally impossible to tune the proposed dual filter due to sensitivity with respect to parameters selected to describe artificial noises, particle swarm optimization (PSO) is adopted to facilitate optimal performance. Numerical investigations confirm the validity of the proposed method through comparison with other filters and emphasize the need for a thorough tuning process.

The increasing use of distributed generation and electric vehicle charging stations provokes violations of the operational limits in low voltage grids. The mitigation of voltage limit violations is addressed by Volt/var control strategies, while thermal overload is avoided by using congestion management. Congestions in low voltage grids can be managed by coordinating the active power contributions of the connected elements. As a prerequisite, the system state must be carefully observed. This study presents and investigates a method for the sparse measurement-based detection of feeder congestions that bypasses the major hurdles of distribution system state estimation. Furthermore, the developed method is used to enable congestion management by the centralized coordination of the distributed electric vehicle charging stations. Different algorithms are presented and tested by conducting load flow simulations on a real urban low voltage grid for several scenarios. Results show that the proposed method reliably detects all congestions, but in some cases, overloads are detected when none are present. A minimal detection accuracy of 73.07% is found across all simulations. The coordination algorithms react to detected congestions by reducing the power consumption of the corresponding charging stations. When properly designed, this strategy avoids congestions reliably but conservatively. Unnecessary reduction of the charging power may occur. In total, the presented solution offers an acceptable performance while requiring low implementation effort; no complex adaptations are required after grid reinforcement and expansion.