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A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

The specific objective of the study is to investigate the presence of natural rate of crime rates in selected emerging economies by using panel unit roots. The majority of the literature examines the issue using conventional unit root tests in a country-specific context. Meanwhile, there is no panel unit root investigation has been undertaken considering both cross-sectional dependence (CD) and structural changes.

As a result, this study is to fill the aforementioned gap and validate the natural rate of crime rates for 10 countries by using a Fourier panel unit root test. The advantage of the test is that structural shifts are modelled as gradual or smooth changes with a Fourier approximation, and it also accounts cross-sectional dependency. Thus, the Fourier panel unit root test may have better performance in capturing potential changes in the nature of data.

The result of the conventional unit roots test shows evidence of the hysteresis effect in crime, as it stands does not adequately account for smooth transitions or breaks. On contrary, the Fourier panel unit root test confirms the natural rate hypothesis in crime rates. The present results highlight the detrimental effects of crime cannot be abated by short-run deterrence policies.

Contrary to previous studies, the theoretical implications of the study imply that the empirical models consider the dynamic nature of crime rates should account for natural rate properties instead of the hysteresis assumption.

This investigation aims to determine the effect of trade uncertainty on domestic investment (DI) and foreign direct investment (FDI) for the Turkish economy from the first quarter of 2005 to the first quarter of 2020.

The authors adopt the vector autoregression (VAR) model augmented with Fourier terms. Using this methodology, the authors obtain the empirical results of the impulse-response functions and the variance decomposition analysis.

The empirical results demonstrate that a shock to trade uncertainty has a slight negative impact on DI for up to approximately 1.5 years, whereas its impact on FDI is negative but long-lasting. Moreover, the contribution of trade uncertainty to FDI is relatively higher than to DI in the error variance decomposition for the investigated period. These empirical results can be beneficial for shaping the Turkish authorities' trade policies in the following periods.

These findings have implications within the macroeconomic setting. Government authorities can provide tax exemptions for specified sectors and debureaucratize investment processes for both domestic and foreign entrepreneurs. Additionally, institutional quality and property rights should be protected strictly and developed gradually.

This study is the first to examine the impact of world trade uncertainty on Türkiye’s DI and FDI. Because trade uncertainty might act as fixed costs, this creates the option value of waiting and seeing the market, and firms hesitate to incur investment.

In order to achieve sustainable development objectives, safeguard the ecosystem, combat global warming and preserve biodiversity for a more sustainable and secure future, the ecological footprint (EF) must be reduced. Therefore, embracing holistic methods, emphasizing renewable energy (RN) and environmental taxes (ET) is crucial. Therefore, the present study aims to capture the effect of ET and RN on EF in Germany.

To achieve this aim, the novel Fourier-based Autoregressive Distributive Lag (ADL) cointegration and the time and frequency-based connections among the variables are investigated in this work throughout the 1994–2021 time span using the wavelet analytic methods, including wavelet power spectrum (WPS) and wavelet coherence (WC) methods, respectively.

The study’s results express that (1) RN, ET and EF are cointegrated in the long run; (2) EF and RN have volatility; (3) RN use in Germany prevents environmental deterioration and (4) ET decreases EF.

The research findings imply that Germany needs rigorous environmental restrictions and enforcement of alternate energy sources for energy use plans and sustainable production objectives.

To the best of our knowledge, the effect of RN and ET on EF in Germany has not been comprehensively explored by using newly developed econometrics techniques and a single dataset. Therefore, the study provides important policy implementations for the German government and is also likely to open debate on the concept.

The purpose of this study is to determine whether the Ottoman Empire’s net interest payments and foreign debt were sustainable or not in terms of their burden on budget revenues, using the method of historical econometric analysis.

In this study, the period between 1847 and 1882 of the Ottoman Empire is analyzed for sustainability analysis. Within the framework of the study, unit root tests and econometric analysis methods frequently used in the literature were used to analyze the sustainability of public debt. In the econometric analysis, in addition to various unit root tests, current econometric analysis methods, in particular Fourier expansion, were also used.

The results of econometric analyses showed that the burden of interest payments and foreign debt on the budget of the Ottoman state was unsustainable. This situation clearly shows the reason for the official bankruptcy of the Ottoman Empire, which was declared in 1875.

Although this study reveals the bankruptcy process of an important structure such as the Ottoman Empire in the historical process through econometric analyses, it also gives a very important message to today’s states. Accordingly, today’s state policies and decision-making mechanisms should take these results into account and strive to make the burden of public interest payments sustainable. It is believed that the study will shed light on the public finance policies of today’s states by drawing lessons from the collapse process of the Ottoman state.

Unlike the historical assessments in the literature on the decline of the Ottoman Empire, this study presents a cliometric approach by applying current econometric analysis techniques to past historical data. The study explains the unsustainability of the Ottoman Empire’s interest payments and external debt burden in the period under consideration in a way that, to the best of the authors’ knowledge, has not been done before.

The purpose of this paper is to propose a new method that allows to compare the magnetic pressures of different pulse width modulation (PWM) strategies in a fast and efficient way.

The voltage harmonics are determined using the double Fourier integral. As for current harmonics and waveforms, a new generic model based on the Park transformation and a dq model of the machine was established taking saturation into consideration. The obtained analytical waveforms are then injected into a finite element software to compute magnetic pressures using nodal forces.

The overall proposed method allows to accelerate the calculations and the comparison of different PWM strategies and operating points as an analytical model is used to generate current waveforms.

While the analytical expressions of voltage harmonics are already provided in the literature for the space vector pulse width modulation, they had to be calculated for the discontinuous pulse width modulation. In this paper, the obtained expressions are provided. For current harmonics, different models based on a linear and a nonlinear model of the machine are presented in the referenced papers; however, these models are not generic and are limited to the second range of harmonics (two times the switching frequency). A new generic model is then established and used in this paper after being validated experimentally. And finally, the direct injection of analytical current waveforms in a finite element software to perform any magnetic computation is very efficient.

The color painting of ancient buildings has high historical and artistic value but is prone to aging due to long-term outdoor exposure. The purpose of this study is to develop a new type of sealing coating to mitigate the impact of ultraviolet (UV) light on color painting.

The new coating was subjected to a 500-h UV-aging test. Compared with the existing acrylic resin Primal AC33, the UV aging behavior of the new coating, such as color difference and gloss, was studied with aging time. The Fourier infrared spectra of the coatings were analyzed after the UV-aging test.

Compared with AC33, the antiaging performance of SF8 was substantially improved. SF8 has a lower color difference value and better light retention and hydrophobicity. The Fourier transform infrared spectroscopy results showed that the C-F bond and Si-O bonds in the resin of the optimized sealing coating protected the main chain C-C structure from degradation during the aging process; thus, the resin maintained good stability. The hindered amine light stabilizer TN292 added to the coating inhibited the antiaging process by trapping active free radicals.

To address the problem of UV aging of oil-decorated colored paintings, a new type of sealing coating with excellent antiaging properties was developed, laying the foundation for its demonstration application on the surface of ancient buildings.

This study aims to investigate the behavior of the green biomass-derived copper (lignin/silica/fatty acids) complex, copper lignin/silica/fatty acids (Cu-LSF) complex, when incorporated into the nonpolar ethylene propylene diene (EPDFM) rubber matrix, focusing on its reinforcing and antioxidant effect on the resulting EPDM composites.

The structure of the prepared EPDM composites was confirmed by Fourier-transform infrared spectroscopy, and the dispersion of the additive fillers and antioxidants in the EPDM matrix was investigated using scanning electron microscopy. Also, the rheometric characteristics, mechanical properties, swelling behavior and thermal gravimetric analysis of all the prepared EPDM composites were explored as well.

Results revealed that the Cu-LSF complex dispersed well in the nonpolar EPDM rubber matrix, in thepresence of coupling system, with enhanced Cu-LSF-rubber interactions and increased cross-linking density, which reflected on the improved rheological and mechanical properties of the resulting EPDM composites. From the various investigations performed in the current study, the authors can suggest 7–11 phr is the optimal effective concentration of Cu-LSF complex loading. Interestingly, EPDM composites containing Cu-LSF complex showed better antiaging performance, thermal stability and fluid resistance, when compared with those containing the commercial antioxidants (2,2,4-trimethyl-1,2-dihydroquinoline and N-isopropyl-N’-phenyl-p-phenylenediamine). These findings are in good agreement with our previous study on polar nitrile butadiene rubber.

The current study suggests the green biomass-derived Cu-LSF complex to be a promising low-cost and environmentally safe alternative filler and antioxidant to the hazardous commercial ones.

The purpose of this study is to investigate the effects of nanoadditive lubricants on the vibration and noise characteristics of helical gears compared with conventional lubricants. The experiment aims to analyze whether nanoadditive lubricants can effectively reduce gear vibration and noise under different speeds and loads. It also analyzes the sensitivity of the vibration reduction to load and speed changes. In addition, it compares the axial and radial vibration reduction effects. The goal is to explore the application of nanolubricants for vibration damping and noise reduction in gear transmissions. The results provide a basis for further research on nanolubricant effects under high-speed conditions.

Helical gears of 20CrMnTi were lubricated with conventional oil and nanoadditive oils. An open helical gearbox with spray lubrication was tested under different speeds (200–500 rpm) and loads (20–100 N·m). Gear noise was measured by a sound level meter. Axial and radial vibrations were detected using an M+P VibRunner system and fast Fourier transform analysis. Vibration spectrums under conventional and nanolubrication were compared. Gear tooth surfaces were observed after testing. The experiment aimed to analyze the noise and vibration reduction effects of nanoadditive lubricants on helical gears and the sensitivity to load and speed.

The key findings are that nanoadditive lubricants significantly reduce the axial and radial vibrations of helical gears under low-speed conditions compared with conventional lubricants, with a more pronounced effect on axial vibrations. The vibration reduction is more sensitive to rotational speed than load. At the same load and speed, nanolubrication reduces noise by 2%–5% versus conventional lubrication. Nanoparticles change the friction from sliding to rolling and compensate for meshing errors, leading to smoother vibrations. The nanolubricants alter the gear tooth surfaces and optimize the microtopography. The results provide a basis for exploring nanolubricant effects under high speeds.

The originality and value of this work is the experimental analysis of the effects of nanoadditive lubricants on the vibration and noise characteristics of hard tooth surface helical gears, which has rarely been studied before. The comparative results under different speeds and loads provide new insights into the vibration damping capabilities of nanolubricants in gear transmissions. The findings reveal the higher sensitivity to rotational speed versus load and the differences in axial and radial vibration reduction. The exploration of nanolubricant effects on gear tribological performance and surface interactions provides a valuable reference for further research, especially under higher speed conditions closer to real applications.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0220/

Robotic arms’ interactions with the external environment are growing more intricate, demanding higher control precision. This study aims to enhance control precision by establishing a dynamic model through the identification of the dynamic parameters of a self-designed robotic arm.

This study proposes an improved particle swarm optimization (IPSO) method for parameter identification, which comprehensively improves particle initialization diversity, dynamic adjustment of inertia weight, dynamic adjustment of local and global learning factors and global search capabilities. To reduce the number of particles and improve identification accuracy, a step-by-step dynamic parameter identification method was also proposed. Simultaneously, to fully unleash the dynamic characteristics of a robotic arm, and satisfy boundary conditions, a combination of high-order differentiable natural exponential functions and traditional Fourier series is used to develop an excitation trajectory. Finally, an arbitrary verification trajectory was planned using the IPSO to verify the accuracy of the dynamical parameter identification.

Experiments conducted on a self-designed robotic arm validate the proposed parameter identification method. By comparing it with IPSO1, IPSO2, IPSOd and least-square algorithms using the criteria of torque error and root mean square for each joint, the superiority of the IPSO algorithm in parameter identification becomes evident. In this case, the dynamic parameter results of each link are significantly improved.

A new parameter identification model was proposed and validated. Based on the experimental results, the stability of the identification results was improved, providing more accurate parameter identification for further applications.