Probability Density Analysis Research Articles

Multi-step carbon emissions forecasting using an interpretable framework of new data preprocessing techniques and improved grey multivariable convolution model

As China stands at a critical juncture in its transition towards a low-carbon future, the precise prediction and analysis of provincial carbon emissions have emerged as paramount tasks. Focusing on forecasting in this intricate and vital domain, an updated grey multivariable convolution model is designed by employing the unified new-information-oriented accumulating generation operator (UNAGO) technique to process raw sequences. Equipped with UNAGO's hyper-parameters that enable the independent scaling effects and prioritize new information, the newly-designed model offers high flexibility and adaptability for handling complex provincial carbon emissions. Subsequently, four different restricted carbon emission sequences are utilized as case studies for validation purposes, and the new model's performance is scrutinized against five contrasting methods across three prediction forecasting horizons. Comparative experimental results reveal the new model's superior level of accuracy in predicting carbon emissions across four different provinces, with MAPE values of <4 % and 10 % in the in-sample and out-of-sample periods, respectively. Furthermore, rigorous evaluations with Diebold-Mariano (DM) and Probability Density Analysis (PDA) tests confirm the model's robust and general forecasting capabilities.

Forecasting the output of high-tech industry in China: A novel nonlinear grey time-delay multivariable model with variable lag parameters

Under the rapidly developing economy in China, accurate forecasting holds vital significance for policymaking and operational planning within the high-tech industry. However, the influencing factors affecting the output, accompanied by the time-delay effect, could be nonlinear, and uncertain. Thereby, this paper proposes a new nonlinear grey multivariable model with time-varying lag parameters. To be specific, the newly designed time delay function and power exponent are introduced, which can significantly enhance the adaptability and flexibility of the proposed method. The Grey Wolf Optimization algorithm is utilized to calculate the dynamic time lag parameters and power exponent to improve the prediction reliability. Furthermore, this new approach is applied to predict the high-tech industry’s output in China, Shanghai Municipality, and the Eastern Region, with due consideration given to the time-delay effect between input factors and outputs. To assess its efficacy, some leading models are selected for comparison to the proposed model. Furthermore, the utilization of Monte-Carlo simulation, the Probability Density Analysis, and the simulations are used to demonstrate the robustness and stability of this new method. The findings show that the proposed model is a feasible and applicable approach for prediction, exhibiting outstanding accuracy.

Comparative assessment and policy analysis of forecasting quarterly renewable energy demand: Fresh evidence from an innovative seasonal approach with superior matching algorithms

In the pursuit of sustainable development, accurate renewable energy demand forecasting holds great significance for climate change mitigation and promoting sustainability. However, renewable energy forecasting has been consistently challenged by seasonality and nonlinearity. Identifying the periodic and nonlinear characteristics concealed within renewable energy sources accurately is still an unexplored problem. Consequently, an innovative nonlinear discrete seasonal grey model is proposed for renewable energy forecasting, which incorporates seasonal dummy variables and a power exponent term for handling the seasonality and nonlinear patterns in time series. Furthermore, an intelligent algorithm matching framework is proposed to augment the flexibility of the newly developed model. For practical purposes, the new methodology is contrasted against a range of benchmarks encompassing statistical, machine-learning, and traditional grey models in forecasting the quarterly total renewable energy consumption in the United States. The proposed model exhibits over 27% improvement rates over its counterparts, achieving the most superior predictive accuracies of 1.45%, 39.27, and 0.79 in MAPEP, RMSEP, and MASEP metrics, respectively. Furthermore, the probability density and sample size analyses are conducted to validate the robustness of the new model, confirming its adaptability and stability towards algorithm randomness and historical information volume. Consequently, the novel model is employed to forecast the short-to-long-terms renewable energy consumption in the U.S., showcasing an upward trend and seasonal fluctuations of the consumption for the forthcoming 24 quarters from 2023Q4 to 2029Q3. These insights can offer valuable implications to the stakeholders such as energy suppliers, utility managers, and policy advocates, highlighting actionable strategies for optimizing renewable energy consumption forecasting and aiding sustainable development initiatives.

A health monitoring technique for spherical structures based on multi-acoustic source localization

Multi-acoustic source localization (MASL) technique has important applications in the early warning and maintenance of spherical structures. Without solving complex nonlinear equations and without knowing the wave velocity distribution a priori, this work demonstrates the feasibility of MASL on the surface of spherical structures using L-shaped sensor clusters. The positions of multiple acoustic sources can be localized using only time difference of arrival values. Relative location determination and relative probability density analysis have been presented and verified to eliminate two types of pseudo-sources. Simulations are performed for isotropic and anisotropic spherical shells. The proposed technique is validated experimentally for stainless steel spherical shells. Simulation and experimental results show that the proposed technique can enable MASL in spherical structures without knowing the wave velocity in the material.

Reliability analysis and inverse optimization method for floating wind turbines driven by dual meta-models combining transient-steady responses

This study introduces an innovative framework aimed at enhancing the reliability, lifespan, and cost-effectiveness of floating wind turbines. By seamlessly integrating transient and steady-state response surface methods, this approach reduces the dimensionality of high-cost, high-fidelity simulation data for floating wind turbines. It effectively utilizes time-domain stochastic response history samples, addressing two critical aspects in reliability analysis, including statistical properties related to maximum loads relevant for static strength design and the distribution characteristics of vibration amplitudes pertinent to fatigue damage design. The processed data is used to construct a forward 1st metamodel, which is integrated into a multi-objective optimization algorithm. This algorithm determines optimal hyperparameters based on stochastic environmental conditions. Subsequently, an inverse 2nd metamodel is established, working in conjunction with the 1st metamodel, forming a dual structure for reliability analysis. Extensive Monte Carlo simulations and probability density analyses demonstrate the effectiveness of the adaptive flexible controller frequency strategy, obtained using the proposed framework, in reducing vibration-induced blade-tip-tower collision risks and long-term vibration damage, particularly at low to medium wind speeds. This significantly improves turbine stability and safety, enhancing overall performance. The proposed methodology provides valuable insights into the design, manufacturing, and operation of floating wind turbines.

Identifying a real space measure of charge-shift bonding with probability density analysis.

Charge-shift bonds have been hypothesized as a third type of chemical bonds in addition to covalent and ionic bonds. They have first been described with valence bond theory where they are identified by the resonance energy resulting from ionic contributions. While other indicators have been described, a clear real space fingerprint for charge-shift bonding is still lacking. Probability density analysis has been developed as a real space method, allowing chemical bonding to be identified from the many-electron probability density |Ψ|2 where the wave function Ψ can be obtained from any quantum chemical method. Recently, barriers of a probability potential, which depends on this density, have proven to be good measures for delocalization and covalent bonding. In this work, we employ many examples to demonstrate that a well-suited measure for charge-shift bonding can be defined within the framework of probability density analysis. This measure correlates well with the charge-shift resonance energy from valence bond theory and thus strongly supports the charge-shift bonding concept. It is, unlike the charge-shift resonance energy, not dependent on a reference state. Moreover, it is independent of the polarity of the bond, suggesting to characterize bonds in molecules by both their polarity and their charge-shift character.

Research on the Evaluation and Enhancement Strategies of College Students’ Health Human Capital in “Healthy Hunan” under the Background of Big Data

Abstract This paper precisely explores the structure and characteristics of college students’ healthy human capital and its influencing factors. It aims to enhance students’ positive and healthy mindset and promote optimism in life and learning. A solid analytical framework is constructed by sorting out the ordered multicategorical logistic regression model and parameter estimation methods and the application steps of the propensity score matching model. College students from ten colleges and universities in Hunan Province were selected as research subjects, and a questionnaire was designed to assess their healthy human capital. The specific factors affecting college students’ healthy human capital accumulation were analyzed in depth through the probability density analysis of propensity score matching, standard support hypothesis testing, and the parallel line test and regression results of the ordered multicategorical regression model. The findings show that the curves of the experimental and control groups after propensity score matching almost overlap in the [0.2,0.4] interval, indicating the method’s validity. A more important finding is that the number of college students with poor self-assessed physical health is 8.063 times higher than that of college students with self-assessed mental health as good, which emphasizes the significant impact of mental health on healthy human capital. Therefore, to effectively improve the health human capital of college students, students, families and universities must form a linkage mechanism and work together to cultivate college students’ health awareness.

Probability Density Analysis of Nonlinear Random Ship Rolling

Probability Density Analysis of Nonlinear Random Ship Rolling

A novel structure adaptive fractional derivative grey model and its application in energy consumption prediction

The importance of energy in modern life is self-evident. Forecasting future energy consumption can help governments and businesses formulate reasonable energy supply and demand policies to ensure energy security and economic development. To this end, a novel adaptive fractional grey model with fractional derivative was established. Firstly, a novel fractional cumulative operator is proposed that operates in a fractional-order domain and has the potential to alternate between giving priority to new or old information. This method facilitates the effective utilization of data when working with a limited number of samples. Secondly, the model's adaptability and flexibility were improved through the introduction of a nonlinear term in the whitening equation; and the fractional derivative was introduced into the whitening equation to solve the problem of poor adaptability of existing integer-order derivative to nonlinearity and volatility. To enhance the model’s performance, the study utilized the Grey Wolf Optimization (GWO) algorithm to optimize the model parameters. Furthermore, the robustness of the proposed model was verified using Monte Carlo simulations and probability density analysis; and the experimental results indicated that the proposed model exhibits better robustness. Finally, three actual cases of China’s total energy consumption, total crude oil consumption and domestic heat consumption are predicted.

A rapid localization technique for detecting multiple damages in plate-like structures with unknown material properties

When using Lamb wave for damage detection in plate-like structures, factors such as unknown material properties, anisotropy and iterative operation for solving nonlinear equations make it difficult to accurately localize damages. This problem becomes even more difficult when multiple damages exist in the plate. To overcome these difficulties, a rapid technique for localizing multiple damages in plate-like structures without any prior knowledge of direction-dependent velocity profile is proposed in this paper. The time difference of arrival is obtained by performing cross-correlation processing on the damage features extracted from the received signal. Damage artifacts are removed using relative location determination and relative probability density analysis. Multi-damage localization at different locations were simulated. The proposed technique is validated experimentally for steel plates. Simulation and experimental results show that the proposed technique can realize multiple damage localization in plate-like structures with unknown material properties. With the help of L-shaped sensor clusters, damage locations for isotropic and anisotropic materials can be quickly predicted without solving nonlinear equations and without taking into account the dispersion effects. The results suggest that a suitable threshold range is set to 0.5–0.7 to remove damage artifacts.

Forecasting China's electricity generation using a novel structural adaptive discrete grey Bernoulli model

The generation forecast helps to develop the scheduling plan of power sources, build a power balance system and ensure the adequacy of power supply to the power system at the macro level. Therefore, a novel structurally adaptive discrete grey Bernoulli model, called DHGBM(1,1), is proposed in this paper for the prediction of power generation. Firstly, the Hausdorff fractional order cumulative generation operation makes it possible to achieve new information prioritisation. As for the structure of the model, we have extended the nonlinear grey Bernoulli model with the introduction of a nonlinear dynamic structure term, which allows the model to simulate variable generation data and improves the adaptability of the model. In a comparative test of the algorithms, the well-performing differential evolution algorithm was used for hyperparameter optimisation of the model to obtain better predictive performance. Monte Carlo simulations and probability density analysis verified the excellent robustness of the model. In addition, through the simulation tests, we obtained a reasonable range of parameters for the structural terms, thus limiting the complexity of the model, and the phenomenon of model overfitting was effectively prevented. Finally, five actual cases of China's hydro, China's thermal, China's nuclear, China's wind power generation and China's electricity exports are predicted.

Spatial association-considered real-time risk rate assessment of high arch dams using observed displacement and combination prediction model

Structural health monitoring is an important approach to diagnose dam safety. The main purpose of this paper is to improve the accuracy of displacement prediction and real-time risk rate assessment of high arch dams by utilizing the deformation spatial association of multiple displacement monitoring points. Two strategies are integrated for the former. First, in addition to the traditional objective of minimizing the fitting error, deformation spatial association is also determined as an optimization objective for machine learning models. Second, five frequently used models are adopted as sub-models, and the overfitting degree is then used as an evaluation index to select optimal sub-models that included in the combination prediction model. On this basis, probability density analysis is conducted for displacement residuals, and a quantification function is defined to assess the real-time risk rate of a single monitoring point. The real-time risk rate of a high arch dam is then calculated according to the risk rates of multiple monitoring points, during which the spatial association are taken into account by the Copula function. Research results of the Jinping-I arch dam indicate that the deformation spatial association is very beneficial for improving the accuracy of dam safety diagnosis, where the prediction mean square error of four machine learning models decreases with an average rate of 66.92%, 45.37%, 35.45% and 73.12%, respectively, and the combination prediction method can further improve the displacement prediction accuracy by 23.79%. The observation data-based high-risk period of arch dams mainly occurs in operation scenarios that the rising or dropping rate of reservoir water level changes sharply. The joint risk rate can effectively avoid the accidental influence of a single monitoring point, and it exhibits an exponential decrease with the increasing number of used monitoring points. For the Jinping-I arch dam, a minimum number of 10 monitoring points is required.

Recognition of DC01 Mild Steel Laser Welding Penetration Status Based on Photoelectric Signal and Neural Network

Achieving online inspection and recognition of laser welding quality is essential for intelligent industrial manufacturing. The weld penetration status is an important indicator for assessing the welding quality, and the optical signal is the most common changing feature in the laser welding process. This paper proposes a new method based on a photoelectric signal and neural network for laser welding penetration status identification. A laser welding experimental system platform based on a photoelectric sensor is built, the laser welding experimental material is DC01 mild steel, and the photoelectric signal in the laser welding process is collected. The collected signal is then processed, and features are extracted using wavelet packet transform and probability density analyses. The mapping relationship between the signal features and weld penetration status is investigated. A deep learning convolutional neural network (CNN)-based weld penetration status recognition model is constructed, with multiple eigenvalue vectors as input, and the model training and recognition results are analyzed and compared. The experimental results show that the photoelectric signal features are highly correlated with the weld penetration status, and the constructed CNN weld penetration status recognition model has an accuracy of up to 98.5% on the test set, demonstrating excellent performance in identifying the quality of the laser welding. This study provides the basis for the online inspection and intelligent identification of laser welding quality.

Forecasting Chinese provincial CO2 emissions: A universal and robust new-information-based grey model

Under China's new development philosophy, CO2 emissions forecasting is becoming more and more crucial for attaining carbon peaking and carbon neutrality targets. In light of this, this research suggests a new-information-based grey model built on cutting-edge methodologies that integrates the inventive damping accumulative generating operator, the data smoothing index, and particle swarm optimization. These three updates allow readers to anticipate the Chinese 30 provincial carbon emissions, which are characterized by insufficient information, regional heterogeneity, and complex patterns. For verification purposes, we investigate the robustness test referring to Monte-Carlo simulation and probability density analysis except as the multi-step-ahead forecasting. Extensive provincial experiments demonstrate that this proposed model considerably outperforms various prevailing competitors with remarkable universality, including grey models, artificial intelligence methods, and statistical models. Moreover, our critical empirical discovery is that this new model's performance fluctuates minimally across 30 provinces, with the average MAPE values less than 5% and 10% in the in-sample and out-of-sample periods, respectively, whereas the other benchmarks display unsteady simulation and prediction results. Furthermore, we employ the elite model to estimate Chinese 30 provincial CO2 emissions for the following three years, whose projections are endorsed by other studies and international organizations. Most importantly, our results provide insights for practitioners in formulating and implementing decarbonization policies and plans for specific provinces.

Canards Oscillations, Noise-Induced Splitting of Cycles and Transition to Chaos in Thermochemical Kinetics

We study how noise generates complex oscillatory regimes in the nonlinear thermochemical kinetics. In this study, the basic mathematical Zeldovich–Semenov model is used as a deterministic skeleton. We investigate the stochastic version of this model that takes into account multiplicative random fluctuations of temperature. In our study, we use direct numerical simulation of stochastic solutions with the subsequent statistical analysis of probability densities and Lyapunov exponents. In the parametric zone of Canard cycles, qualitative effects caused by random noise are identified and investigated. Stochastic P-bifurcations corresponding to noise-induced splitting of Canard oscillations are parametrically described. It is shown that such P-bifurcations are associated with splitting of both amplitudes and frequencies. Studying stochastic D-bifurcations, we localized the rather narrow parameter zone where transitions from order to chaos occur.

Automatic characterization of stroke patients’ posturography based on probability density analysis

ObjectiveThe probability density analysis was applied to automatically characterize the center of pressure (COP) data for evaluation of the stroke patients’ balance ability.MethodsThe real-time COP coordinates of 38 stroke patients with eyes open and closed during quiet standing were obtained, respectively, from a precision force platform. The COP data were analyzed and characterized by the commonly used parameters: total sway length (SL), sway radius (SR), envelope sway area (EA), and the probability density analysis based parameters: projection area (PA), skewness (SK) and kurtosis (KT), and their statistical correlations were analyzed. The differences of both conventional parameters and probability density parameters under the conditions of eyes open (EO) and eyes closed (EC) were compared.ResultsThe PA from probability density analysis is strongly correlated with SL and SR. Both the traditional parameters and probability density parameters in the EC state are significantly different from those in the EO state. The obtained various statokinesigrams were calculated and categorized into typical sway types through probability density function for clinical evaluation of the balance ability of stroke patients.ConclusionsThe probability density analysis of COP data can be used to characterize the posturography for evaluation of the balance ability of stroke patients.

A novel structure adaptive new information priority discrete grey prediction model and its application in renewable energy generation forecasting

• A novel accumulation generation operator is developed by weighting coefficient. • A novel structure adaptive new information priority grey model is proposed. • The robustness analysis of the new model is established. • Comparative study shows that new model is superior to other various grey models. Renewable energy has made a significant contribution to global power generation. Therefore, accurate mid-to-long term renewable energy generation forecasting is becoming more and more important for integrating renewable energy systems with smart grid and energy strategic planning. For this purpose, a novel structure adaptive new information priority discrete grey prediction model is established, and the disturbance analysis shows that it is suitable for small sample modeling. Firstly, the fractional dynamic weighted coefficient is introduced to define the accumulative generating operator satisfying the new information priority principle, which can realize the effective utilization of system information with insufficient information and accurately extract the development mode of system sequence from sparse samples. In terms of model structure, the nonlinear term and periodic fluctuation term are introduced to simulate the nonlinear and periodic fluctuation trend of renewable energy generation data, which improves the adaptability of the grey prediction model to the nonlinear and fluctuating time series. By designing the comparative experiment of optimization algorithm, Grey Wolf Optimizer (GWO) is selected to optimize the structural parameters of the model, giving the proposed model higher flexibility and stronger adaptability. In order to illustrate the performance of the model, the new model is compared with statistical econometrics technology, artificial neural network (ANN) and various existing grey models in three cases: World biofuel power generation, China's renewable energy power generation and small-scale solar photovoltaic power generation in the United States. The experimental results show that the proposed model is superior to other competitive models in terms of fitting accuracy and prediction accuracy. In addition, Monte-Carlo Simulation and probability density analysis further show that the proposed model can provide the best prediction effect and has high robustness.

Distortion Analysis of RF Power Amplifier Using Probability Density of Input Signal and AM-AM Characteristics

When confirming the ACLR (adjacent channel leakage power ratio), which are representative indicators of distortion in the design of PA (power amplifier), it is well known how to calculate the AM-AM/PM characteristics of PA, input time series data of modulated signals, and analyze the output by Fourier analysis. In 5G (5th generation) mobile phones, not only QPSK (quadrature phase shift keying) modulation but also 16QAM (quadrature modulation), 64QAM, and 256QAM are becoming more multivalued as modulation signals. In addition, the modulation band may exceed 100MHz, and the amount of time series data increases, and the increase in calculation time becomes a problem. In order to shorten the calculation time, calculating the total amount of distortion generated by PA from the probability density of the modulation signal and the AM (amplitude modulation)-AM/PM (phase modulation) characteristics of PA is considered. For the AM-AM characteristics of PA, in this paper, IMD3 (inter modulation distortion 3) obtained from probability density and IMD3 by Fourier analysis, which are often used so long, are compared. As a result, it was confirmed that the result of probability density analysis is similar to that of Fourier analysis, when the nonlinearity is somewhat small. In addition, the agreement between the proposed method and the conventional method was confirmed with an error of about 2.0dB of ACLR using the modulation waves with a bandwidth of 5MHz, RB (resource block) being 25, and QPSK modulation.

A novel discrete multivariable grey model with spatial proximity effects for economic output forecast

The temporal and spatial characteristics of the collected data typically play an essential role in time series forecasting. However, traditional grey models pay more attention to temporal information, meanwhile disregarding the presence of spatial features critical to producing accurate forecasts. Moreover, the grey theory has few attempts to overcome this problem. Given this situation, this paper proposes a novel multivariable grey prediction model considering the spatial proximity effect for time series forecasting. More specifically, the complete spatial distance index is defined initially based on the geographical and economic distance to quantify the intensity of the spatial proximity impact. On this basis, the spatial proximity effect term is constructed and incorporated into the conventional discrete multivariable grey model, establishing the novel model. Subsequently, the particle swarm optimization algorithm determines the optimal weight coefficient in the developed index. For illustration and verification purposes, the proposed model performs experiments predicting Jiangsu's economic outputs compared to five prevalent benchmarks. Furthermore, three statistical metrics, the Diebold-Mariano test, the Monte Carlo experiments, and the probability density analysis are employed to validate the model's efficacy and robustness. Empirical results demonstrate that the proposed method outperforms all five competitors with strong robustness and broad generalization. Therefore, this new model is used for forecasting Jiangsu's future economic outputs from 2021 to 2025.

Mitigating the cross talk of orbital angular momentum modes in free-space optical communication by using an annular vortex beam and a focusing mirror

The probability density analysis formula of the single orbital angular momentum (OAM) mode of an annular vortex beam with a focusing mirror in a turbulent atmosphere is derived theoretically, and the effects of different parameters on the OAM spectrum are investigated numerically, and the results show that the OAM diffusion of the annular vortex beam is weaker than the Gaussian vortex beam in a turbulent atmosphere under the same conditions, and the annular vortex beam with a focusing mirror can more effectively reduce the crosstalk of OAM modes. Our findings will be useful for improving FSO system performance.