Non-white Noise Research Articles

A Frequency Domain Fitting Algorithm Method for Automotive Suspension Structure under Colored Noise

The suspension of a car has different structural forms but usually consists of springs, shock absorbers, guiding mechanisms, etc. As a vehicle moves, the terrain often induces a multifaceted non-white noise vibration within the vehicle. Research on this type of vibration often uses the operational modal analysis (OMA) method, due to its advantages of not requiring knowledge of excitation signals. The disadvantage is that it can only analyze systems under white noise excitation, otherwise it will bring errors. So, this paper proposes a frequency domain fitting algorithm (FDFA) based on colored noise excitation. Initially, an exposition on the foundational principles of the FDFA technique was provided, followed by a demonstration of the modal identification approach. Subsequently, a simulation scenario involving a cantilever beam, akin to a suspension system, was chosen for examination in three instances, revealing that the frequency discrepancies are under 2.94%, and for damping coefficients, they are less than 2.76%. In conclusion, the paper’s introduced FDFA technique, along with the frequency–spatial domain decomposition (FSDD) approach, were employed to determine the modal characteristics of aluminum cantilever beams subjected to four distinct colored noise stimulations. The findings indicate that when utilizing the FDFA technique, the error in modal frequency is kept below 2.5%, while the error for the damping ratio does not exceed 15%. Compared with FSDD, the accuracy was improved.

The Analytical Approach to Evaluate the Bit Error Rate Performance of PLC System in Presence of Cyclostationary Non-White Gaussian Noise

The Analytical Approach to Evaluate the Bit Error Rate Performance of PLC System in Presence of Cyclostationary Non-White Gaussian Noise

Optimal receiver ensuring maximum signal-to-noise ratio when affected by non-white non-gaussian noise

Optimal receiver ensuring maximum signal-to-noise ratio when affected by non-white non-gaussian noise

Delay Segmented Tristable Stochastic Resonance System Driven by Non-Gaussian Colored Noise and Its Application in Bearing Fault Detection

Abstract This study investigates the Delayed Segmented Tristable Stochastic Resonance (DSTSR) system under the influence of additive non-Gaussian colored noise. The research employs an improved segmented tristable potential function, wherein the equilibrium points and barrier heights can be independently controlled by parameters. Simultaneously, the segmented function on both sides reduces the restrictions of higher-order terms on the walls of the potential wells. The equivalent Langevin equation for the DSTSR system is obtained using the path integral method, the unified colored noise approximation method, and the small-delay approximation. Subsequently, the theoretical expressions for the steady-state probability density, mean first passage time (MFPT), and Signal-to-Noise Ratio (SNR) are derived from the resulting equations, and the impact of variations in system parameters on these performance metrics is discussed. Additionally, Monte Carlo simulations for MFPT are conducted to verify the accuracy of the theoretical derivations. Combining the results from the theoretical section and the impact of parameters on system performance, the article employs an adaptive genetic algorithm to optimize system parameters. This algorithm is then applied to simulation experiments and bearing fault detection. In the simulation experiments, the DSTSR system is compared with other systems. The results indicate that the DSTSR system exhibits the highest SNR improvement. Furthermore, in bearing fault detection under non-Gaussian colored noise, the DSTSR system shows higher spectral amplitude and SNR at the fault frequency compared to the tristable stochastic resonance system and the segmented tristable stochastic resonance system without time delay feedback. This suggests that stochastic resonance can effectively detect weak signals in non-Gaussian non-white noise scenarios, and the introduction of time delay contributes to the occurrence of stochastic resonance to a certain extent.

An interpretable online prediction method for remaining useful life of lithium-ion batteries

Accurate prediction of the remaining useful life (RUL) of lithium-ion batteries is advantageous for maintaining the stability of electrical systems. In this paper, an interpretable online method which can reflect capacity regeneration is proposed to accurately estimate the RUL. Firstly, four health indicators (HIs) are extracted from the charging and discharging process for online prediction. Then, the HIs model is trained using support vector regression to obtain future features. And the capacity model of Gaussian process regression (GPR) is trained and analyzed by Shapley additive explanation (SHAP). Meanwhile, the state space for capacity prediction is constructed with the addition of Gaussian non-white noise to simulate the capacity regeneration. And the modified predicted HIs and noise are obtained by unscented Kalman filter. Finally, according to SHAP explainer, the predicted HIs acting as the baseline and the modified HIs containing information on capacity regeneration are chosen to predict RUL. In addition, the bounds of confidence intervals (CIs) are calculated separately to reflect the regenerated capacity. The experimental results demonstrate that the proposed online method can achieve high accuracy and effectively capture the capacity regeneration. The absolute error of failure RUL is below 5 and the minimum confidence interval is only 2.

The Simons Observatory: Pipeline comparison and validation for large-scale B-modes

Context. The upcoming Simons Observatory Small Aperture Telescopes aim at achieving a constraint on the primordial tensor-to-scalar ratio r at the level of σ(r = 0)≲0.003, observing the polarized CMB in the presence of partial sky coverage, cosmic variance, inhomogeneous non-white noise, and Galactic foregrounds. Aims. We present three different analysis pipelines able to constrain r given the latest available instrument performance, and compare their predictions on a set of sky simulations that allow us to explore a number of Galactic foreground models and elements of instrumental noise, relevant for the Simons Observatory. Methods. The three pipelines employ different combinations of parametric and non-parametric component separation at the map and power spectrum levels, and use B-mode purification to estimate the CMB B-mode power spectrum. We applied them to a common set of simulated realistic frequency maps, and compared and validated them with focus on their ability to extract robust constraints on the tensor-to-scalar ratio r. We evaluated their performance in terms of bias and statistical uncertainty on this parameter. Results. In most of the scenarios the three methodologies achieve similar performance. Nevertheless, several simulations with complex foreground signals lead to a > 2σ bias on r if analyzed with the default versions of these pipelines, highlighting the need for more sophisticated pipeline components that marginalize over foreground residuals. We show two such extensions, using power-spectrum-based and map-based methods, that are able to fully reduce the bias on r below the statistical uncertainties in all foreground models explored, at a moderate cost in terms of σ(r).

Singular Stochastic Differential Equations for Time Evolution of Stocks Within Non-white Noise Approach

Singular Stochastic Differential Equations for Time Evolution of Stocks Within Non-white Noise Approach

Spectroscopic effects of distributed-line phenomena in integrated feedback resistors for charge-sensitive pre-amplifiers

The distributed capacitive coupling of high-valued resistors with ground planes modifies their effective impedance and power spectral density of noise, especially at high frequency. This effect is clearly visible in poly-silicon resistors inside integrated circuits. When such resistors are used in the feedback network of Charge Sensitive Pre-amplifiers an excess noise arises with a non-white noise spectral density. The effect is a worsening of the spectroscopic resolution. The relevance of such effect with respect to the conventional noise sources is discussed in different practical cases.

Performance Analysis of a WPCN-Based Underwater Acoustic Communication System

Underwater acoustic communication (UWAC) has a wide range of applications, including marine environment monitoring, disaster warning, seabed terrain exploration, and oil extraction. It plays an indispensable and increasingly important role in marine resource exploration and marine economic development. In current UWAC systems, the terminal nodes are usually powered by energy-limited batteries. Due to the harshness of the underwater environment, especially in the ocean environment, it is very costly and difficult, even impossible, to replace the batteries for the terminal nodes in UWACs, which results in the short lifetime and unreliability of the terminal nodes and the systems. In this paper, we present the application of a wireless powered communication network (WPCN) to the UWAC systems to provide an auxiliary and convenient energy supplement for solving the energy-limited problem of the terminal nodes, where the hybrid access point (H-AP) transfers energy to the terminal nodes in the downlink. In contrast, the terminal nodes use the harvested energy to transmit the information to the H-AP in the uplink. To evaluate the proposed WPCN-based UWAC systems, we investigate the performance of the average bit error rate (BER), outage probability, and achievable information rate for the systems in a frequency-selective sparse channel and non-white noise environment. We derive the closed-form expression for the probability density function (PDF) of the received signal-to-noise ratio (SNR). Based on this, we further derive novel closed-form expressions for the average BER and the outage probability of the systems. Numerical results confirm the validity of the proposed analytical results. It is shown that there exists an optimal signal frequency and time allocation factor for the systems to achieve optimal performance, and a larger optimal time allocation factor is preferred for a smaller hybrid access point (H-AP) transmit power or a larger transmission distance, while a smaller optimal signal frequency is required for a larger transmission distance.

Resource allocation optimization in multiuser OFDM relay-assisted underwater acoustic sensor networks

Resource allocation optimization (RAO) is a crucial design issue for providing green communications in the sixth generation (6G) of underwater acoustic (UWA) sensor networks (SNs). To have a suitable convergence speed in the machine learning (ML)-based algorithms used for finding the solution of the online RAO problems, the optimal or suboptimal solution of the offline form of the online problem should be utilized as the initial setting. Moreover, knowing the closed-form of the best initial setting in terms of the channel parameters leads to more efficiency in the ML-based algorithms from the robustness standpoint. In this paper, we formulate and solve two new offline RAO problems for joint relay selection and power allocation in the orthogonal frequency division multiplexing UWA cooperative communication systems. We first obtain a new formula for the signal to noise ratio (SNR) per-subcarrier in the cooperative UWA communication system with amplify and forward relaying including multiple users and multiple relays. In our analyses, unlike terrestrial channel and by considering the physical facts seen in the practical UWA channel, we assume non-white Gaussian noise along with the frequency-dependent pathloss for obtaining the SNR per-subcarrier function. Then, we use it in the definition of our RAO problems. Our proposed problems are non-convex and we present a promising method for converting them to the convex problems. In our problems, the objective function is the total power transmitted over the network. In addition, the sum-rate and probability of error are constrained to control the quality of service. Also, we derive some new closed-form formulas for reliable cooperation, relay selection, and power loading. Extensive simulation studies are carried out to assess the convergence, effectiveness, and robustness of our proposed algorithms to the channel impairments for different conditions.

Batch Optimal FIR Smoothing: Increasing State Informativity in Nonwhite Measurement Noise Environments

Strictly nonwhite measurement noise (NMN) is observed in many industrial processes. Therefore, effective smoothing is often required to extract useful information about the process state with maximum accuracy. This paper proposes a batch <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>-lag optimal finite impulse response (OFIR) smoother, operating under NMN with full block covariance matrices. It is shown that the OFIR smoother significantly outperforms the Rauch-Tung-Striebel (RTS) smoother and the unbiased FIR (UFIR) smoother. Testing is provided based on object tracking. The results are validated by a practical example of a three degree-of-freedom helicopter system, which confirms that OFIR smoothing provides better noise reduction than UFIR smoothing, RTS smoothing, and modified RTS smoothing using state augmentation and measurement differencing.

Deep Learning Algorithms for BCH Decoding in Satellite Communication

Deep learning is widely used in various fields due to the advancement of algorithms, the enrichment of high-efficiency databases, and the increase in computing power. Especially in the satellite communication, the learning and parallel computing capabilities of neural networks make them ideal for decoding. Many researchers have recently applied deep learning neural networks to decode high-density parity check (HDPC) codes (such as BCH and RS code), improving the decoder’s performance. This review aims to provide general insights on applying neural network decoders to satellite communications. Due to the neural network’s learning ability, the neural network-based decoder can be trained to change the weights, thereby reducing the influence of non-white noise in satellite communications, such as the influence between the satellite and the terrestrial network and the mutual interference within the satellites. To compensate for non-white noise, shortest circles in Tanner graph and unreliable information, a decoder system model for satellite communication constructed by three neural networks is presented.

Predict Gold Price Trend Based on ARIMA Model

As a financial product, gold is one of the more important spot and futures trading products in the commodity market. Based on the time series model, the gold price can be fitted and predicted, in order to explore the law of gold price changes. It has positive implications for investors and government managers. This article selects the Prime Day price in 2018 as the research object. Combined with domestic and foreign research content on financial time series. First, through the time series diagram test and the unit root test, it is obtained that the gold daily price series is a cycle-free and non-stationary series. Therefore, the time series needs to be differentiated. Second, a new stationary sequence is obtained by making second-order differences. Third, after the time sequence diagram test, ADF test, and white noise test, the sequence is a non-white noise sequence. Comparing the AIC values of multiple time series models, the most ideal model for the series should be the ARIMA (2,2,2) model. The significance test of the model shows that the fitted model is significantly effective. And the significance test of the model parameters is also passed. Then make predictions with this model. Comparing the predicted value with the future real gold price, it is found that the predicted value is close to the real value. This is a good reference for the country to formulate relevant economic policies.

Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features.

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.

Investigation of the trade-off between the complexity of the accelerometer bias model and the state estimation accuracy in INS/GNSS integration

Abstract The integration of Inertial Navigation Systems and Global Navigation Satellite Systems (GNSS) represents the core navigation unit for mobile platforms in open sky environments. A realistic assessment of the accuracy of the navigation solution depends on the accurate modelling of inertial sensor errors. Sensor noise and biases contribute most to short-term navigation errors. For the latter, different models can be used, varying in complexity. This paper investigates how the use of two different models for the accelerometer bias affects the accuracy of the state estimate in an extended Kalman filter. For this purpose, the Allan variance technique is applied to a data sequence from a specific inertial sensor to identify and quantify the underlying noise processes. The estimated noise parameters are used to characterise a bias model for the accelerometers that in addition to the static bias model takes non-white noise processes of the inertial sensor under investigation into account. This detailed accelerometer bias model is compared to a classical modelling approach that only considers static biases. Both approaches are evaluated based on simulation studies for continuous and intermittent GNSS coverages. The results show no significant difference between the two modelling approaches in terms of horizontal position and attitude precision. Furthermore, the correctness of the accelerometer bias estimates is not significantly affected by the modelling approach. All in all, it can be concluded that a detailed bias model of the accelerometers does not outperform the classical modelling approach.

Analysis and Research on Chaotic Dynamics of Evaporation Duct Height Time Series with Multiple Time Scales

The evaporation duct is a particular type of atmospheric structure that always appears on the open ocean. Predicting the evaporation duct height (EDH) accurately and in a timely manner is of great significance for the practical application of marine wireless communication equipment. Understanding the characteristics of EDH time series is an essential prerequisite for establishing an appropriate prediction model. Moreover, the sampling timescales of EDH data may influence the dynamic characteristics of the EDH time series as well. In this study, EDH time series datasets at three timescales, hourly, daily, and monthly, were constructed as the case study. Statistical methods, namely the augmented Dickey–Fuller test and Ljung–Box test, were adopted to verify the stationary and white noise characteristics of the EDH time series. Then, rescaled range analysis was applied to calculate the Hurst exponent to study the fractal characteristics of the EDH time series. An extensive analysis and discussion of the chaotic dynamics of the EDH time series are provided. From the perspective of nonlinear dynamics, the phase space was constructed from the time delay τ and embedding dimension m, which were calculated from the mutual information method and the Grassberger–Procaccia algorithm, respectively. The maximum Lyapunov exponent was also calculated by the small data volume method to explore the existence of chaos in the EDH time series. According to our analysis, the EDH time series are stationary and have a non-white noise characteristic. The Hurst exponents for all three timescales were greater than 0.5, indicating the predictability of the EDH time series. The phase space diagrams exhibited strange attractors in a well-defined region for all the timescales, suggesting that the evolution of the EDH time series can possibly be explained by deterministic chaos. All of the maximum Lyapunov exponents were positive, confirming the chaos in the EDH time series. Further, stronger chaotic characteristics were found for the finer-resolution time series than the coarser-resolution time series. This study provides a new perspective for scholars to understand the fluctuation principles of the evaporation duct at different timescales. The findings from this study also lay a theoretical and scientific foundation for the future application of chaotic prediction methods in the research on the evaporation duct.

AQI Prediction Based on CEEMDAN-ARMA-LSTM

In the context of carbon neutrality and air pollution prevention, it is of great research significance to achieve high-accuracy prediction of the air quality index. In this paper, Beijing is used as the study area; data from January 2014 to December 2019 are used as the training set, and data from January 2020 to December 2021 are used as the test set. The CEEMDAN-ARMA-LSTM model constructed in this paper is used for prediction and analysis. The CEEMDAN model is used to decompose the data to improve the data information utilization. The smooth non-white noise components are fed into the ARMA model, and the remaining components and residuals are fed into the LSTM model. The results show that the MAE, MAPE, MSE, and RMSE of this model are the smallest. Compared with the CEEMDAN-LSTM, LSTM, and ARMA-GARCH models, MAE improved by 22.5%, 53.4%, and 21.5%, MAPE improved by 21.4%, 55.3%, and 26.1%, MSE improved by 39.9%, 76.9%, and 28.5%, and RMSE improved by 22.5%, 52.0%, and 15.4%. The accuracy improvement is significant and has good application prospects.

An Adaptive Operational Modal Analysis under Non-White Noise Excitation Using Hybrid Neural Networks

To adaptively identify the modal parameters for time-invariant structures excited by non-white noise, this paper proposes a new operational modal analysis (OMA) method using hybrid neural networks. In this work, taking the acceleration response directly as the input data of the networks not only simplifies the data processing, but also retains all the characteristics of the data. The data processed by the output function is the output data of the network, and its peak corresponds to the modal frequency. The proposed output function greatly reduces the computational cost. In addition, a small sample dataset ensures that the hybrid neural networks identify the modal parameters with the highest accuracy in the shortest possible time. Interestingly, the hybrid neural networks combine the advantages of the convolutional neural network (CNN) and gate recurrent unit (GRU). To illustrate the advantages of the proposed method, the cantilever beam and the rudder surface excited by white and non-white noise are taken as examples for experimental verification. The results reveal that the proposed method has a strong anti-noise ability and high recognition accuracy, and is not limited by ambient excitation type.

An Iterative Filter for FLL-Assisted-PLL Carrier Tracking At Low $C/N_0$ and High Dynamic Conditions

This article presents an iterative frequency lock loop (FLL)-assisted-phase lock loop (PLL) (FPLL) design in state space according to the minimum mean square error criterion. This is achieved by constructing a high fidelity carrier signal model with the consideration of the non-Gaussian nonwhite measurement noise characteristics. Two popular arctangent discriminators, e.g., two-quadrant (Atan) and four-quadrant (Atan2) are used to produce the PLL and FLL measurements for FPLL, respectively. The filter gain is selected to minimize the trace of the error covariance matrix and an iteration approach to quickly compute the steady-state filter gain is introduced. The nonlinearity in the discriminator and filter behaviors in FPLL at low $C/N_0$ and high dynamic conditions are investigated. The closed-form expressions of the closed-loop transfer function as well as error transfer function are clarified. The thermal noise induced tracking jitters on each carrier state, e.g., phase, doppler, and doppler rate, are derived, analyzed, and verified via Monte Carlo simulation, accordingly. The theoretical properties show that the iterative FPLL achieves the following. 1) The comparable tracking performance to the well-designed PLL-only. 2) The enhanced tracking accuracy over the well-designed FLL-only. 3) The improved tracking sensitivity over the conventional Kalman filter-based FPLL (KF-FPLL), at low $C/N_0$ condition and high dynamic conditions.

Approximate Message Passing algorithms for rotationally invariant matrices

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational invariance in law, where W may have a spectral distribution that is different from the semicircle and Marcenko–Pastur laws characteristic of white noise. The Onsager corrections and state evolutions in these algorithms are defined by the free cumulants or rectangular free cumulants of the spectral distribution of W. Their forms were derived previously by Opper, Çakmak and Winther using nonrigorous dynamic functional theory techniques, and we provide rigorous proofs. Our motivating application is a Bayes-AMP algorithm for Principal Components Analysis, when there is prior structure for the principal components (PCs) and possibly nonwhite noise. For sufficiently large signal strengths and any non-Gaussian prior distributions for the PCs, we show that this algorithm provably achieves higher estimation accuracy than the sample PCs.