Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUnivariate ReLU neural network and its application in nonlinear system identification
64
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights about the system. Specifically, the neural network consists of neurons with linear and UReLU activation functions, and the UReLU functions are defined as the ReLU functions respect to each dimension. The UReLU neural network is a single hidden layer neural network, and the structure is relatively simple. The initialization of the neural network employs the decoupling method, which provides a good initialization and some insight into the nonlinear system. Compared with normal ReLU neural network, the number of parameters of UReLU network is less, but it still provide a good approximation of the nonlinear dynamic system. The performance of the UReLU neural network is shown through a Hysteretic benchmark system: the Bouc-Wen system. Simulation results verify the effectiveness of the proposed method.
rate research
Read More
In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed based on the model of hinging hyperplanes (HH). The EHH neural network is a distributed representation, the training of which involves solving several convex optimization problems and is fast. It is proved that for every EHH neural network, there is an equivalent adaptive hinging hyperplanes (AHH) tree, which was also proposed based on the model of HH and find good applications in system identification. The construction of the EHH neural network includes 2 stages. First the initial structure of the EHH neural network is randomly determined and the Lasso regression is used to choose the appropriate network. To alleviate the impact of randomness, secondly, the stacking strategy is employed to formulate a more general network structure. Different from other neural networks, the EHH neural network has interpretability ability, which can be easily obtained through its ANOVA decomposition (or interaction matrix). The interpretability can then be used as a suggestion for input variable selection. The EHH neural network is applied in nonlinear system identification, the simulation results show that the regression vector selected is reasonable and the identification speed is fast, while at the same time, the simulation accuracy is satisfactory.
Networked dynamic systems are often abstracted as directed graphs, where the observed system processes form the vertex set and directed edges are used to represent non-zero transfer functions. Recovering the exact underlying graph structure of such a networked dynamic system, given only observational data, is a challenging task. Under relatively mild well-posedness assumptions on the network dynamics, there are state-of-the-art methods which can guarantee the absence of false positives. However, in this article we prove that under the same well-posedness assumptions, there are instances of networks for which any method is susceptible to inferring false negative edges or false positive edges. Borrowing a terminology from the theory of graphical models, we say those systems are unfaithful to their networks. We formalize a variant of faithfulness for dynamic systems, called Granger-faithfulness, and for a large class of dynamic networks, we show that Granger-unfaithful systems constitute a Lebesgue zero-measure set. For the same class of networks, under the Granger-faithfulness assumption, we provide an algorithm that reconstructs the network topology with guarantees for no false positive and no false negative edges in its output. We augment the topology reconstruction algorithm with orientation rules for some of the inferred edges, and we prove the rules are consistent under the Granger-faithfulness assumption.
Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially in cases under resonance condition with natural system modes, where the magnitudes of the oscillations could be greater in places far from the source. Therefore, it is of interest to construct a global time-frequency (TF) representation (TFR) of the system, which can capture the oscillatory components present in the system. In this paper we develop a systematic methodology for frequency identification and component filtering of non-stationary power system forced oscillations (FO) based on multi-channel TFR. The frequencies of the oscillatory components are identified on the TF plane by applying a modified ridge estimation algorithm. Then, filtering of the components is carried out on the TF plane applying the anti-transform functions over the individual TFRs around the identified ridges. This step constitutes an initial stage for the application of the Dissipating Energy Flow (DEF) method used to locate FO sources. Besides, we compare three TF approaches: short-time Fourier transform (STFT), STFT-based synchrosqueezing transform (FSST) and second order FSST (FSST2). Simulated signals and signals from real operation are used to show that the proposed method provides a systematic framework for identification and filtering of power systems non-stationary forced oscillations.
We consider a cooperative system identification scenario in which an expert agent (teacher) knows a correct, or at least a good, model of the system and aims to assist a learner-agent (student), but cannot directly transfer its knowledge to the student. For example, the teachers knowledge of the system might be abstract or the teacher and student might be employing different model classes, which renders the teachers parameters uninformative to the student. In this paper, we propose correctional learning as an approach to the above problem: Suppose that in order to assist the student, the teacher can intercept the observations collected from the system and modify them to maximize the amount of information the student receives about the system. We formulate a general solution as an optimization problem, which for a multinomial system instantiates itself as an integer program. Furthermore, we obtain finite-sample results on the improvement that the assistance from the teacher results in (as measured by the reduction in the variance of the estimator) for a binomial system.
The state estimation problem can be solved through different methods. In terms of robustness, an effective approach is represented by the Least Absolute Value (LAV) estimator, though vulnerable to leverage points. Based on a previously proposed theorem, in this paper we enunciate, and rigorously demonstrate, a new lemma that proves the identifiability of leverage points in LAV-based state estimation. On the basis of these theoretical foundations, we propose an algorithm for leverage point identification whose performance is validated by means of extensive numerical simulations and compared against more traditional approaches, like Projection Statistics (PS). The obtained results confirm that the proposed method outperforms PS and represents a significant enhancement for LAV-based state estimators as it correctly identifies all the leverage points, independently of the accuracy or the presence of measurement gross errors. A dedicated application example with respect to power system state estimation is finally included and discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
