Nonlinear Time Research Articles

Nonlinear time series analysis of state-wise COVID-19 in Malaysia using wavelet and persistent homology.

The nonlinear progression of COVID-19 positive cases, their fluctuations, the correlations in amplitudes and phases across different regions, along with seasonality or periodicity, pose challenges to thoroughly examining the data for revealing similarities or detecting anomalous trajectories. To address this, we conducted a nonlinear time series analysis combining wavelet and persistent homology to detect the qualitative properties underlying COVID-19 daily infection numbers at the state level from the pandemic's onset to June 2024 in Malaysia. The first phase involved investigating the evolution of daily confirmed cases by state in the time-frequency domain using wavelets. Subsequently, a topological feature-based time series clustering is performed by reconstructing a higher-dimensional phase space through a delay embedding method. Our findings reveal a prominent 7-day periodicity in case numbers from mid-2021 to the end of 2022. The state-wise daily cases are moderately correlated in both amplitudes and phases during the Delta and Omicron waves. Biweekly averaged data significantly enhances the detection of topological loops associated with these waves. Selangor demonstrates unique case trajectories, while Pahang shows the highest similarity with other states. This methodological framework provides a more detailed understanding of epidemiological time series data, offering valuable insights for preparing for future public health crises.

Unveiling an asymmetric relationship between global crude oil and local food prices in an oil-importing economy

AbstractRecent swift comovements of local food and global crude oil prices have attracted the attention of policymakers and researchers. To evaluate this relationship, many studies have used time series models to explore global crude oil and local food prices. However, robust research based on advanced nonlinear time series models that incorporate control variables for their formation is lacking. In this paper, nonlinear techniques are applied to assess the asymmetric nexus between Brent oil prices and local retail food prices in Slovakia. To estimate this value, we extend the single-threshold NARDL approach to the MTNARDL model. The nominal exchange rate and industrial production index are used as the control variables. Compared with conventional NARDL models, the MTNARDL model provides a more detailed representation of global oil‒local food price linkages and detects the asymmetric effect of global oil prices on food prices from both long- and short-term perspectives. Interestingly, with respect to long- and short-term food price volatility, changes in response to oil price fluctuations are greatest under a regime with rather a small number of positive and moderate changes.

An Evaluation of the Structural Behaviour of Historic Buildings Under Seismic Action: A Multidisciplinary Approach Using Two Case Studies

The evaluation of the structural behaviour of iconic historic buildings represents one of the most current structural engineering research topics. However, despite the various research works carried out during recent decades, several issues still remain open. One of the most important aspects is related to the correct reconstruction of the complex geometries that characterise this type of construction and that influence structural behaviour, especially in the presence of the horizontal loads caused by seismic action. For these reasons, different techniques have been proposed based on the use of laser scanners, Unmanned Aerial Vehicles (UAVs), and terrestrial photogrammetry. At the same time, several analysis methods have been developed that include the use of linear and non-linear approaches. In this present paper, the seismic performance of the Santa Maria Novella basilica and Santa Maria di Collemaggio basilica (before the partial collapse due to the 2009 L’Aquila earthquake) were investigated in detail by means of several numerical analyses. In particular, a series of non-linear time history analyses (NTHAs) were carried out, as reported in the Italian Building Code. To represent the non-linear behaviour of the main structural elements, smeared cracking (CSC) constitutive law was adopted. The geometry of the structures was reconstructed from a complete laser scanner survey of the churches, in order to consider all the intrinsic irregularities that characterise the heritage buildings. Finally, a comparison between the structural behaviour of the two case studies was carried out, highlighting the differences and similar aspects, focusing on possible collapse mechanisms and the identification of the most critical structural elements represented, in both cases analysed, by the main pillars of the transept.

Boosting Financial Market Prediction Accuracy With Deep Learning and Big Data

The accuracy of financial market trend prediction directly impacts investors' decisions and financial institutions' risk management, making it a focal point of research in the financial domain. While traditional statistical methods lay the foundation for market forecasting, they still face limitations in handling complex, nonlinear, and non-stationary financial time series data with accuracy and adaptability. Time series analysis plays a pivotal role in financial market prediction, revealing historical patterns and future trends within the data. Addressing the limitations of existing methods, this study proposes a deep learning-based CEEMDAN-CNN-LSTM model. Leveraging the CEEMDAN decomposition method to capture the multi-frequency components of time series, CNN extracts spatial features, and LSTM learns temporal dependencies. Experimental results demonstrate that the performance of the CEEMDAN-CNN-LSTM model surpasses traditional models on standardized evaluation metrics such as RMSE, MAE, and MAPE across four major financial datasets.

A new approach of generalized shifted Vieta-Fibonacci polynomials to solve nonlinear variable order time fractional Burgers-Huxley equations

A new approach of generalized shifted Vieta-Fibonacci polynomials to solve nonlinear variable order time fractional Burgers-Huxley equations

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

An entropy measure-based study on flow pattern of gas–liquid two-phase flow in a U-Tube

U-tubes are widely applied in gas–liquid two-phase transportation in chemical engineering. The diverse flow patterns within these tubes significantly affect the pressure loss, heat transfer efficiency, and even the fluid-induced vibration amplitude of the tubes. This study explores the complex flow pattern features in a U-tube in a vertical plane and focuses on recognizing them. For the acquisition and classification of flow patterns, a Computational Fluid Dynamics (CFD) model for gas–liquid two-phase flow is first established, and its quantitative calculation error is ensured to be less than 5%. Then, the spatiotemporal evolution characteristics of flow patterns is analyzed. The real-time pressure drop response is chosen as the representation signal, and its nonlinear features in the time and frequency domain under different flow patterns are explored. A nonlinear time series is constructed by extracting a segment from the real-time pressure drop data, and six entropy measures are applied to analyze and identify them. Finally, the sensitivity of entropy measures to both the time series lengths and the tested sections are evaluated. Results show that there are six typical flow patterns in a U-tube. According to most entropy measures, the bubble flow has the highest complexity; however, the plug flow presents the lowest complexity. In the U-bend, pressure drop signals for the bubble and annular flows show random fluctuations within a specific range, in contrast to the marked periodicity in plug flow signals, while wavy and slug flows exhibit intermittent peak values. Including the upstream and downstream straight pipes in the analysis, rather than focusing solely on the U-bend, significantly increases the complexity of the stratified, plug, and slug flows. Fuzzy entropy is an effective tool for identifying the six flow patterns, demonstrating good resilience to variations in the length of the data series. This characteristic makes it highly useful for real-time identification of flow patterns in the U-bend sections of non-transparent U-tubes, offering considerable potential in chemical equipment.

Collapse-based seismic design method

Continuing the structural analysis until the model reaches its ultimate capacity using an incremental nonlinear time history analysis can incorporate all the behavioral complexities of the structure. This approach ensures that all factors influencing the seismic behavior of structures, which can be simulated in numerical modeling, are fully considered in the analysis. This technique addresses many shortcomings in seismic analysis and structural design, using simple criteria for the accurate design of members. With this perspective, this paper explores the collapse-based seismic design method and provides an approach to determine the ultimate tolerable seismic intensity for a structure, or an appropriate collapse seismic intensity. It also establishes design criteria based on the maximum capacity of structural members under maximum loading and utilizes the endurance time method to perform incremental nonlinear time history analysis quickly and easily. Evaluations show that models designed using this method achieve the desired performance level at different seismic hazard levels, provide sufficient seismic capacity, meet all minimum requirements of the seismic code and standards, and are optimized. Therefore, the procedure presented in this paper is introduced for the analysis, design, evaluation, and retrofitting of structures with simple, accurate, and uniform principles.

Application of one-dimensional periodic layers with elastomeric seismic isolators for three-dimensional isolation

Three-dimensional (3D) seismic isolation is an appealing idea to protect structures and their components from earthquake-induced horizontal and vertical ground motions. Past attempts to develop 3D isolation systems were ineffective due to their complexity and reliability issues. One-dimensional periodic material-based isolation systems (1D-PIS) have been extensively researched for applications as raft foundations due to their simple and construction-friendly unit cell designs. These systems aim to attenuate seismic excitations in both horizontal and vertical directions. However, the effectiveness of 1D-PIS in mitigating 3D excitations may be limited due to the potential mismatch between the frequency content of horizontal and vertical vibrations. The present study proposes to combine a conventional horizontal isolation system with a 1D-PIS in the vertical direction to achieve a simple, passive, and efficient three-dimensional isolation system for structures and components. The 1D-PIS is strengthened by incorporating steel shims within the rubber layers and implementing steel casings at its periphery, enabling its utilization as an isolated system. Small-scale experimental and numerical investigations were conducted on strengthened 1D-PIS to study its isolation characteristics in the vertical directions. The study reveals that infinite boundary conditions required for the efficacy of 1D-PIS were achieved through lateral restraint provided by steel shims and steel casings. Notably, the individual isolation characteristics of the conventional and the 1D-PIS are not compromised in the combined isolation system. Nonlinear time history analysis on a prototype combined isolation system confirms its effectiveness in attenuating the seismic response under simultaneous horizontal and vertical ground motions.

Existence and stability of a weakly damped laminated beam with a nonlinear delay

AbstractA weakly damped laminated beam system with nonlinear time delay is studied. The existence and uniqueness are proved by Faedo–Galerkin approach. We prove that the system is stable under some specific conditions on the weight of the delay and the equal wave speeds of propagation. The general energy decay rate is established by using multiplier method and some properties of convex functions. This decay result is obtained without imposing any restrictive growth assumption on the damping term at the origin. In addition, our result improves and develops some existing results in the literature.

Self-centering rocking steel frame with column mid-height uplift: Experimental and numerical investigation

This paper proposes a self-centering rocking steel frame with column mid-height uplift (SCRSF-CMU) that exhibits high post-yield stiffness and energy dissipation capacity. The hysteretic performance of the SCRSF-CMU was investigated through cyclic loading tests. A numerical model of the SCRSF-CMU was established and validated against experimental results. Subsequently, the seismic performance of the SCRSF-CMU was compared with that of the self-centering rocking steel frame with column base uplift (SCRSF-CBU) using nonlinear time history analysis. Finally, the seismic responses of the SCRSF-CMU and SCRSF-CBU under varying earthquake intensities were analyzed using the endurance time analysis. The results indicate that the designed SCRSF-CMU demonstrates excellent lateral force resistance, energy dissipation, and self-centering capabilities. The rocking effect and the restoring force of the post-tensioned steel strands effectively controlled the residual lateral displacement of the specimens. The multi-scale numerical model of the SCRSF-CMU accurately captured its hysteretic behavior and deformation patterns. Compared to the SCRSF-CBU, the SCRSF-CMU exhibited superior rocking deformation capacity, post-yield stiffness, and hysteretic energy dissipation. Under MCE excitation, both SCRSF-CMU and SCRSF-CBU showed uniform inter-story drift distribution with minimal residual deformation, creating a satisfactory condition for the post-earthquake repair work if necessary. The high post-yield stiffness of the SCRSF-CMU was more effective in reducing both maximum and residual displacements. Endurance time analysis revealed that SCRSF-CMU and SCRSF-CBU exhibited relatively uniform inter-story drift distribution under SLE, DBE, and MCE earthquakes. Under FE excitation, the inter-story drift ratio of both structures were nearly identical; however, under DBE and MCE excitations, the maximum roof drift ratio and inter-story drift ratio of the SCRSF-CBU were larger, indicating that the SCRSF-CBU had higher deformation demands than the SCRSF-CMU.

Nonlinear second order plus time delay model identification and nonlinear PID controller tuning based on extended linearization method

PID control systems based on the first order plus time delay model (FOPTD), which approximate the full system dynamics, are well-accepted for a wide range of linear processes. While such controllers can be applied to overdamped nonlinear processes, they often experience excessive overshoots and oscillations for general nonlinear processes. To overcome this limitation, we propose a novel method to design a nonlinear PID controller based on the second order plus time delay (SOPTD) model. The system nonlinearity requires parameter adjustments of the linearized model across operational ranges. Hence, in this work, it is handled by the extended linearization method (ELM), ensuring local stability under the assumptions of slow and small changes in operating points. Importantly, the model achieves global input-to-output stability even without the above constraints, provided there are no structural and parametric errors. The resulting nonlinear SOPTD model can describe changes in process gain and two time constants as the operation point varies. We demonstrate the applicability of our approach with a polymerization reactor simulation and liquid-level control experiments.

Seismic mitigation of porcelain cylindrical electrical equipment using synergistic concept with base isolation and tuned mass damper

Porcelain cylindrical electrical equipment (PCEEs), such as potential and current transformers, are critical components of electrical substations and essential to power supply networks. Nevertheless, previous strong earthquakes have rendered high vulnerability and poor performance of PCEE during seismic occurrences. To improve seismic performance of PCEE and alleviate adverse seismic impacts, an innovative synergistic mitigation method based on base isolation (BI) and tuned mass damper (TMD) was proposed and subsequently employed to PCEE. Combining BI with TMD allows for a greater utilization of each technology’s capabilities while also circumventing some of the limits of each. While TMD effectiveness is sensitive to input ground motion frequencies, BI could act as a filter to tune input frequency and help TMD fulfill better damping effectiveness. TMD could in return help BI achieve better stability under long-period dominant or pulse-like ground motions. The BI-TMD effectiveness and robustness were investigated using finite element modeling and nonlinear time history analysis. A comprehensive parametric study that considers variable PCEE frequencies, BI periods, TMD mass ratios, and TMD control frequencies was conducted. Results show that the proposed BI-TMD method can significantly enhance the effectiveness and robustness beyond BI single control in mitigating seismic responses of PCEE.

Multi-Depot Electric Vehicle–Drone Collaborative-Delivery Routing Optimization with Time-Varying Vehicle Travel Time

This paper presents an electric vehicle-drone (EV–drone) collaborative-delivery routing optimization model that leverages the time-varying characteristics of electric vehicles and drones across multiple distribution centers (i.e., central depots) to address the logistics industry’s low-carbon transformation in the last-mile delivery. The model aims to minimize total delivery costs by formulating a mixed-integer programming (MIP) model that accounts for essential constraints such as nonlinear charging time, time-varying EV travel time, delivery time window, payload capacity, and maximum range. An improved adaptive large-neighborhood search (ALNS) algorithm is developed to solve the model. Experimental results validate the effectiveness of the proposed algorithm and highlight the impact of EV and drone technology parameters, along with the time-varying EV travel times, on the economic efficiency of delivery distribution and route planning.

Harnessing Available Evidence in Single-Case Experimental Studies: The Use of Multilevel Meta-Analysis.

The use of multilevel models to combine and compare the results of multiple single-case experimental design (SCED) studies has been proposed about two decades ago. Since then, the number of multilevel meta-analyses of SCED studies steadily increased, together with the complexity of multilevel models used. At the same time, many studies were done to empirically evaluate the approach in a variety of situations, and to study how the flexibility of multilevel models can be employed to account for many complexities that often are encountered in SCED research, such as autocorrelation, linear and nonlinear time trends, specific designs, external event effects, multiple outcomes, and heterogeneity. In this paper, we give a state-of-the-art of the multilevel approach, by making an overview of basic and more extended models, summarizing simulation results, and discussing some remaining issues.

Impact of Various High Intensity Earthquake Characteristics on the Inelastic Seismic Response of Irregular Medium-Rise Buildings

In the twenty-first century, the seismic design of buildings seems to have become a fully recognized topic. There are guidelines and standards which should be taken into account by designers in seismic areas. Designers using modern international guidelines have ascertained that the behavior of structures is not as expected. New challenges in the construction industry result in the construction of structures with new, unusual shapes. These are structures that do not meet the assumptions of safe construction in seismic areas. Contemporary buildings are also characterized by their irregular distribution of structural elements. Such solutions are not beneficial from the point of view of seismic engineering and can lead to reduced dynamic resistance and damage in such structures. In this paper, a five-storey, irregular-shaped reinforced concrete (RC) building model was subjected to different earthquakes with varying magnitudes, PGA (peak ground acceleration) and PGV (peak ground velocity) values, and durations of the intense shock phase. Once the model was verified using previous in situ measurements, the building model was subjected to five earthquakes. A numerical nonlinear analysis of the building was performed using a verified FEA (finite element analysis) model in the time domain through non-linear time history analysis with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The building’s dynamic properties were measured using various methods of excitation. The model was influenced, among others, by two far-field representative events caused by the last earthquake in Turkey, which resulted in strong ground motion. The analysis results identified the locations of structural damage and allowed for the assessment of the structure’s dynamic resistance. The results of the calculations prove that the duration of the intensive phase of extortion is one of the reasons for building damage in earthquake-prone areas. Building damage occurs with earthquakes that are characterized by an intensive phase of excitation with a long duration and high values of velocity in the earthquake components. The article highlights the inadequate dynamic resistance of the building, leading to excessive displacements and unfavorable structural solutions. Damage to buildings at this earthquake intensity caused damage to the load-bearing structure, which was not designed for such intensities. This paper is a research report with a specific case study of medium-rise irregular RC buildings.

Seismic evaluation of plan irregular reinforced concrete building equipped with comb teeth metallic passive damper

Active and passive damping devices exhibit significant energy dissipating behavior under seismic loads and are being used to control vibration in buildings worldwide. Comb Teeth Damper (CTD) is one of the most promising recent types of passive dampers which consist of steel plates with multiple teeth designed to dissipate seismic energy by in-plane flexural yielding. In this study, the CTD was modeled and analyzed under lateral cyclic load using the finite element analysis software, ABAQUS. The first phase of this investigation was a comprehensive parametric study on CTD with two different numbers of teeth, namely 4 teeth (4 CTD) and 5 teeth (5 CTD); each model with six different thicknesses, namely 5, 10, 15, 20, 25, and 30 mm. The parametric study showed that by increasing the number of teeth, the load-carrying capacity, initial stiffness, and energy dissipation capacity have increased considerably. A similar trend was observed when the thickness of the damper was increased. From the results of the parametric study, 5CTD with 15 mm thickness damper model was identified as a suitable model for utilizing in Reinforced Concrete (RC) buildings using optimization algorithm. In the second phase, a G + 14 storey plan irregular RC building was modeled in the structural engineering software ETABS and subjected to six different strong earthquake ground motions. The non-linear time history analysis was performed on the building with and without identified CTD and found that the building equipped with dampers reduced 56% top displacement, 60% inter-storey drift, and 33% energy dissipation.

Seismic behavior of base isolated precast frame

The performance of the base-isolated precast frame is examined for both near-field and far-field earthquakes. For comparison, the corresponding base isolated monolithic frame is analyzed. The frames are isolated using a friction pendulum system (FPS), which is appropriately designed to take up the vertical load coming on the frames. The same isolators are provided for the monolithic and precast frames. Two types of precast frames are considered, namely frames with emulated and non-emulated connections. An ensemble of 7 different earthquakes is used for each type of earthquake to obtain the average responses, which include maximum base shear, maximum acceleration, maximum top story displacement, and maximum inter-story drift ratio (MIDR). SAP2000 is used for the non-linear time history analysis of the frames for different earthquakes. The studies are made for three levels of PGA, namely 0.4 g, 0.6 g, and 0.8 g. The study shows that a significant reduction in base shear, top story displacement and MIDR is achieved by base isolating the precast frames. However, the corresponding base isolated monolithic frame offers more reductions in response especially for MIDR. Of the two types of precast frames, the one with emulated connection shows marginally higher reductions of response as compared to the non-emulated connection. Further, the percentage reductions in responses in main shock and after shock remain almost the same for all cases.

Harmonics: Frequencies of Inheritance from Scotland to Aotearoa, New Zealand

I am a first-generation immigrant from Scotland who moved to Aotearoa, New Zealand as a young child. Using the metaphor of ‘harmonics’, which comes from playing the cello, I consider the ‘frequencies’ I have inherited through two women in my ancestral lineage. This work is grounded by theories of non-linear time, such as ‘quantum entanglements’ and ‘hauntings’, primarily through the work of Karen Barad. My writing theorises an approach to tracing family histories using these ideas from quantum physics alongside ‘harmonics’ as an analytical tool. This method explores how frequencies of inheritance can be tracked through generations and what this might mean for immigrants who do not live in their ancestral lands. In my writing, I recall stories and memories, pad them with historical literature about what was occurring societally at the time, and analyse them through embodied and place-based theories. Towards the end, I finish by elucidating how the ‘harmonics’ of these stories ‘sound’ through me, in poetry. Our ‘I’ is a story of entanglements; our ancestors are the metaphysical and genealogical dust in which we are coated.

Seismic response control of shear frame structure using a novel tuned-mass type composite column

Concrete filled steel tube (CFST) column is widely applied in shear frame structure in seismic-prone area owing to its superior earthquake resistant performance. However, CFST column might still suffer damage under a severe earthquake. This paper proposes a novel tuned-mass type column-in-column (CIC) system to improve the seismic behavior of the CFST column and hence protect the structure. The CIC system is formed by splitting the CFST column into a primary column and a secondary column, while the overall cross section area and hence the load-bearing capacity is not changed. By optimally selecting the springs and dashpots to interconnect the two columns, the CIC can act as a non-conventional tuned mass damper (TMD) to reduce seismic vibrations of structures. To demonstrate the proposed CIC concept, a single-story and a five-story frame structure with and without control are designed. Nonlinear time history analyses are performed to study the seismic responses of these structures considering different seismic design levels, earthquake ground motions and CIC control schemes. Numerical results show that the CIC system can effectively reduce the seismic induced story acceleration, displacement and drift ratio of frame structures with the reduction ratios approximately between 21 % and 30 %, and the ratios on reducing the base shear force and bending moment are between 27 % and 31 %, and between 34 % and 49 %, respectively. The proposed CIC control concept is a new solution for mitigations of seismic responses of CFST frame structures.