Precision forecasting of spray-dry desulfurization using Gaussian noise data augmentation and k-fold cross-validation optimized neural computing

Perceptron models have become integral tools for pattern recognition and classification problems in engineering fields. This study envisioned implementing artificial neural networks to forecast the performance of a mini-spray dryer for desulfurization activities. This work adopted k-fold cross-validation, a rigorous technique that evaluates model performance across multiple data segments. Several ANN models (21) were trained on data obtained from sulfation conditions, including sulfation temperature (120 °C-200 °C), slurry pH (4-12), stoichiometric ratio (0.5-2.5), slurry solid concentration (6%-14%) as the feed input and sulfur capture as the response. Three hundred synthetic datasets generated using the Gaussian noise data augmentation underwent a 10-fold cross-validation process before simulation on neural networks triggered by the logsig and tansig activation functions. The computation accuracy was further evaluated by altering the number of hidden cells from 2 to 10. The ANN architectures were assessed using statistical metrics such as mean square error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and the coefficient of determination (R2) techniques. Overall, error estimation suggests cross-validation and data augmentation are critical in efficient neural network generalization. The logsig function trained with 10 hidden cells presented closer data articulation when mapped onto actual values.

Hopf Bifurcations of Moore-Greitzer PDE Model with Additive Noise

The Moore-Greitzer partial differential equation (PDE) is a commonly used mathematical model for capturing flow and pressure changes in axial-flow jet engine compressors. Determined by compressor geometry, the deterministic model is characterized by three types of Hopf bifurcations as the throttle coefficient decreases, namely surge (mean flow oscillations), stall (inlet flow disturbances) or a combination of both. Instabilities place fundamental limits on jet-engine operating range and thus limit the design space. In contrast to the deterministic PDEs, the Hopf bifurcation in stochastic PDEs is not well understood. The goal of this particular work is to rigorously develop low-dimensional approximations using a multiscale analysis approach near the deterministic stall bifurcation points in the presence of additive noise acting on the fast modes. We also show that the reduced-dimensional approximations (SDEs) contain multiplicative noise. Instability margins in the presence of uncertainties can be thus approximated, which will eventually lead to lighter and more efficient jet engine design.

Estimations and Control of Julia Sets of the SIS Model Perturbed by Noise

The estimations and control of Julia sets of the SIS(susceptible-infectious-susceptible) model under noise perturbation are studied. At first, a discrete SIS model is introduced, and the effects of additive and multiplicative noises on the fractal characteristics of the SIS model are discussed. Then, estimations of the Julia sets of the SIS model under additive and multiplicative noise perturbations are given, respectively. At last, the feedback control method is used to set appropriate controllers to realize control of the Julia set, and the influence of noise on the Julia set of the SIS model is reduced. The reason why this method is effective is also explained.

A robust quantized consensus protocol for discrete-time multi-agent systems with additive noise

This paper investigates the consensus problem of multiple discrete-time integrator agents with communication constraints and additive process noise. It proposes a protocol to achieve the approximate consensus of agents over inter-agent communication networks with finite bit rates. Under that protocol, dynamic encoding and decoding algorithms are implemented for each pair of neighboring agents to transmit quantized states at a finite bit rate. With received quantized states of neighboring agents, the control input of each agent is locally computed. Particularly input saturation is introduced into the local controllers of agents and places both lower and upper bounds on the local control inputs of agents. These control input bounds can be known in advance and greatly enhance the robustness of the consensus protocol. Under the proposed protocol, the approximate consensus can be guaranteed at any finite bit rate to encode the states of agents. It is shown that even a single bit per time step is enough for the desired approximate consensus. The additive process noise does not increase the bit rate required for that approximate consensus. Moreover, the proposed consensus protocol can be designed with only an upper bound on the number of agents and is more robust than some previous consensus protocols which may require the global information of the inter-agent network topology, such as the second largest eigenvalue of the Laplacian matrix. Even when some communication links are broken due to communication failure or some nodes leave, the same set of consensus parameters can still robustly guarantee the expected approximate consensus. Simulations are conducted to illustrate the effectiveness of the proposed quantized consensus protocol.

Assessing the performance of Granger-Geweke causality: Benchmark dataset and simulation framework

Nonparametric methods based on spectral factorization offer well validated tools for estimating spectral measures of causality, called Granger–Geweke Causality (GGC). In Pagnotta et al. (2018) [1] we benchmarked nonparametric GGC methods using EEG data recorded during unilateral whisker stimulations in ten rats; here, we include detailed information about the benchmark dataset. In addition, we provide codes for estimating nonparametric GGC and a simulation framework to evaluate the effects on GGC analyses of potential problems, such as the common reference problem, signal-to-noise ratio (SNR) differences between channels, and the presence of additive noise. We focus on nonparametric methods here, but these issues also affect parametric methods, which can be tested in our framework as well. Our examples allow showing that time reversal testing for GGC (tr-GGC) mitigates the detrimental effects due to SNR imbalance and presence of mixed additive noise, and illustrate that, when using a common reference, tr-GGC unambiguously detects the causal influence׳s dominant spectral component, irrespective of the characteristics of the common reference signal. Finally, one of our simulations provides an example that nonparametric methods can overcome a pitfall associated with the implementation of conditional GGC in traditional parametric methods.

How Stochasticity Influences Leading Indicators of Critical Transitions

Many complex systems exhibit critical transitions. Of considerable interest are bifurcations, small smooth changes in underlying drivers that produce abrupt shifts in system state. Before reaching the bifurcation point, the system gradually loses stability ('critical slowing down'). Signals of critical slowing down may be detected through measurement of summary statistics, but how extrinsic and intrinsic noises influence statistical patterns prior to a transition is unclear. Here, we consider a range of stochastic models that exhibit transcritical, saddle-node and pitchfork bifurcations. Noise was assumed to be either intrinsic or extrinsic. We derived expressions for the stationary variance, autocorrelation and power spectrum for all cases. Trends in summary statistics signaling the approach of each bifurcation depend on the form of noise. For example, models with intrinsic stochasticity may predict an increase in or a decline in variance as the bifurcation parameter changes, whereas models with extrinsic noise applied additively predict an increase in variance. The ability to classify trends of summary statistics for a broad class of models enhances our understanding of how critical slowing down manifests in complex systems approaching a transition.

Acoustic environment identification by Kullback-Leibler divergence

This paper presents a forensic methodology that determines, from among a set of recording places, the probable place where allegedly a disputed digital audio recording was made. The methodology considers that digital audio recordings are noisy signals that have two involved noise components. One component is the multiplicative noise, which is an internal feature on the audio recording that is related to the recording device. The other component is the additive noise, which is an external feature on the audio recording that can be related to the recording place. Therefore, the proposed methodology estimates a likelihood rate that helps to decide which recording place is more plausible to be associated with a disputed audio recording. This likelihood rate is defined as the probability of a finding, supposing that a specific proposition is true, divided by the probability of a finding if an alternative proposition is true. Such probabilities are calculated by performing a statistical comparison through the Kullback-Leibler divergence [1], between the probability distribution function of the additive noise associated to the disputed recording and the probability distribution function of the additive noises associated to a set of audio recordings made on the possible recording places. Then, in order to determine the recording place, the analyst requires a list of possible places where the recording could have been carried out; in these places some reference recordings will be made. In this work, the additive noise is estimated by the Geometric Approach to Spectral Subtraction (GA-SS) filter [2], applied to the noisy audio recording.

Fixed versus variable internal noise in contrast transduction: The significance of Whittle's data

A longstanding issue in vision research concerns whether the internal noise involved in contrast transduction is fixed or variable in relation to contrast magnitude. Previous attempts to resolve the issue have focused on the analysis of contrast discrimination data, despite the fact that the effects of internal noise on thresholds are necessarily compounded by the shape of the underlying transducer function. An alternative approach is to compare data obtained from a particular class of scaling experiment - one based on a comparison of perceived contrast differences - with data from discrimination experiments gathered across the full range of contrast. Data from two studies by the late Paul Whittle provide the basis for such an analysis, pointing to the conclusion that contrast internal noise is fixed not variable.