design and analysis of time series experiments

• DOI: 10.2307/2285785
• Corpus ID: 145793465

Design and analysis of time-series experiments

• G. Glass , V. Willson , J. Gottman
• Published 1975

545 Citations

Robust testing of level changes in interrupted time-series analysis, time-series designs and analyses, persistent threats to validity in single-group interrupted time series analysis with a cross over design., challenges to validity in single-group interrupted time series analysis., time series analysis for psychological research, time series analysis for psychological research: examining and forecasting change, quasi-experiments and environmental policy, an assessment of the validity and discrimination of the intensive time‐series design by monitoring learning differences between students with different cognitive tendencies, introduction to time series analysis for organizational research, a comprehensive method of single-case data analysis: interrupted time-series simulation (itssim), related papers.

Showing 1 through 3 of 0 Related Papers

Browse Econ Literature

• Working papers
• Software components
• Book chapters
• JEL classification

More features

• Subscribe to new research

RePEc Biblio

Author registration.

• Economics Virtual Seminar Calendar NEW!

Some searches may not work properly. We apologize for the inconvenience.

Design and Analysis of Time Series Experiments

• Author & abstract
• 4 Citations
• Related works & more

Corrections

(School of Social Ecology, University of California, Irvine)

(School of Criminal Justice, University at Albany, SUNY)

Suggested Citation

Download full text from publisher.

Follow serials, authors, keywords & more

Public profiles for Economics researchers

Various research rankings in Economics

RePEc Genealogy

Who was a student of whom, using RePEc

Curated articles & papers on economics topics

Upload your paper to be listed on RePEc and IDEAS

New papers by email

Subscribe to new additions to RePEc

EconAcademics

Blog aggregator for economics research

Cases of plagiarism in Economics

About RePEc

Initiative for open bibliographies in Economics

News about RePEc

Questions about IDEAS and RePEc

RePEc volunteers

Participating archives

Publishers indexing in RePEc

Privacy statement

Found an error or omission?

Opportunities to help RePEc

Get papers listed

Have your research listed on RePEc

Open a RePEc archive

Have your institution's/publisher's output listed on RePEc

Get RePEc data

Use data assembled by RePEc

We’re fighting to restore access to 500,000+ books in court this week. Join us!

Internet Archive Audio

• This Just In
• Grateful Dead
• Old Time Radio
• 78 RPMs and Cylinder Recordings
• Audio Books & Poetry
• Computers, Technology and Science
• Music, Arts & Culture
• News & Public Affairs
• Spirituality & Religion
• Radio News Archive

• Flickr Commons
• Occupy Wall Street Flickr
• NASA Images
• Solar System Collection
• Ames Research Center

• All Software
• Old School Emulation
• MS-DOS Games
• Historical Software
• Classic PC Games
• Software Library
• Kodi Archive and Support File
• Vintage Software
• CD-ROM Software
• CD-ROM Software Library
• Software Sites
• Tucows Software Library
• Shareware CD-ROMs
• Software Capsules Compilation
• CD-ROM Images
• ZX Spectrum
• DOOM Level CD

• Smithsonian Libraries
• FEDLINK (US)
• Lincoln Collection
• American Libraries
• Canadian Libraries
• Universal Library
• Project Gutenberg
• Children's Library
• Biodiversity Heritage Library
• Books by Language
• Additional Collections

• Prelinger Archives
• Democracy Now!
• Occupy Wall Street
• TV NSA Clip Library
• Animation & Cartoons
• Arts & Music
• Computers & Technology
• Cultural & Academic Films
• Ephemeral Films
• Sports Videos
• Videogame Videos
• Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

• Wayback Machine (iOS)
• Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

• Explore the Collections
• Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

• Donate Donate icon An illustration of a heart shape

Design and Analysis of Time-Series Experiments

Bookreader item preview, share or embed this item, flag this item for.

• Graphic Violence
• Explicit Sexual Content
• Hate Speech
• Misinformation/Disinformation
• Marketing/Phishing/Advertising
• Misleading/Inaccurate/Missing Metadata

plus-circle Add Review comment Reviews

18 Previews

DOWNLOAD OPTIONS

No suitable files to display here.

EPUB and PDF access not available for this item.

IN COLLECTIONS

Uploaded by station16.cebu on May 11, 2020

SIMILAR ITEMS (based on metadata)

Student Notebook

Time-series methods in experimental research.

• Behavioral Science
• Experimental Psychology
• Methodology
• Quantitative
• Statistical Analysis

For many experimental psychologists, the go-to methodological designs are cross-sectional. Cross-sectional studies involve measuring the relationship between some variable(s) of interest at one point in time; some common examples include single-session lab studies and online surveys (e.g., via MTurk). These designs can be useful for isolating relationships between variables, establishing conditions of convergent and discriminant validity, and utilizing samples that are statistically representative of larger populations. Nevertheless, quantitative researchers have noted that attempts to measure and analyze interindividual variation are incomplete without an accompanying account of the underlying temporal dynamics that define these processes (e.g., Molenaar, 2008; Molenaar, Huizenga, & Nesselroade, 2002). This claim follows from the idea that cross-sectional designs, while potentially well-suited for large samples, are often underpowered, overgeneralized, and ill-approximated to the statistical assumptions implied by general linear methods. For these reasons, psychological scientists should consider supplementing their methodological toolkits with time-series techniques to explicitly investigate the time-dependent variation that can be observed within individual subjects.

The purpose of this article is to briefly discuss the importance of time-series methods in experimental research and to acquaint the reader with some statistical techniques that are easily accessible and can be employed when testing hypotheses with time-series data.

Measuring Behavior as a Time Series

According to Daniel T. Kaplan and Leon Glass (1995), there are two critical features of a time series that differentiate it from cross-sectional data-collection procedures:

• Repeated measurements of a given behavior are taken across time at equally spaced intervals. Taking multiple measurements is essential for understanding how any given behavior unfolds over time, and doing so at equal intervals affords a clear investigation of how the dynamics of that behavior manifest at distinct time scales.
• The temporal ordering of measurements is preserved. Doing so is the only way to fully examine the dynamics governing a particular process. If we expect that a given stimulus will influence the development of a behavior in a particular way, utilizing summary statistics will completely ignore the temporal ordering of the data and likely occlude one’s view of important behavioral dynamics.

Linear computations such as mean and variance merely describe global properties of a data set and thus may fail to capture meaningful patterns that only can be identified by looking at the sequential dependency between time points. Consequently, time-series techniques provide a valuable approach in studying psychological processes, which are, by their very nature, fundamentally embedded in time. (For a more detailed treatment of this subject, see Deboeck, Montpetit, Bergeman, & Boker, 2009.)

Analyzing Time-Series Data

Once you’ve collected a series of behavioral measurements on your variable(s) of interest, there are a variety of ways to explore and quantify the observed dynamics. Here are a few techniques that can be used to investigate patterns within time-series data:

Autocorrelation/Cross-correlation. An autocorrelation reflects the magnitude of time dependency between observations within a time series. An autocorrelation plot depicts correlations between measurements X t and X t+n , such that each value represents the extent to which any given behavior is related to previous behaviors within the series. A cross-correlation involves relating two time series that are shifted in time at lag n (i.e., X t and Y t+n ), and can reveal, for example, whether one process tends to “lead” the other’s behavior or whether they oscillate together.

Recurrence quantification analysis (RQA). RQA begins by simply plotting a time series against itself (i.e., X t against X t ) and then quantifies whether certain states of the behavior remain stable or recur in time, as well as what percentage of the series is constituted by deterministic patterns. Cross-RQA also can be used to analyze the degree of recurrence and deterministic patterning between two processes, and it has been applied to the study of interpersonal coordination and postural control (e.g., Shockley, Santana, & Fowler, 2003) as well as to the quantification of emotional synchrony in dyadic conflict discussions (Main, Paxton, & Dale, 2016).

Phase space reconstruction (PSR). When obtaining a behavioral time-series, one of your goals could be to determine what variables are involved in producing particular patterns of behavior and what the possible structure of the underlying dynamics may be. One way to accomplish this is to reconstruct the phase space, which is a multidimensional plot that represents all possible states within the process and can be used to approximate the number of variables involved in producing the observed behavioral changes. For example, we may interpret high trait self-esteem as representing a strong tendency for an individual to adopt and maintain positive self-evaluations. Collecting repeated measurements of state self-esteem and then performing a PSR could help describe the strength of that individual’s tendency to retain a positive image of herself as well as reveal the compensatory dynamics that follow from a negative self-evaluative state.

Spectral analysis. Mathematically, any time series can be transformed into a linear composition of sine and cosine waves with varying frequencies. One goal in analyzing time-series data is often to find out what deterministic cycles (i.e., which of the component waves) account for the most variance within the series. Performing a spectral decomposition transforms a time series into a set of constituent sine and cosine waves that then are used to calculate the series’ power spectral density function (PSD). Plotting the series’ PSD reveals the squared correlations between each component frequency and the series as a whole, yielding a similarly intuitive interpretation to R 2 in multiple regression. In this vein, Gottschalk, Bauer, and Whybrow (1995) applied spectral analysis toward studying the changes in self-reported mood among bipolar patients and control subjects, finding that bipolar individuals tended to exhibit cyclical patterns of mood change that were significantly more chaotic and deterministic than the comparatively random fluctuations observed in control subjects.

Differential equation modeling. Essentially, differential equations allow one to study how different variables change with one another as well as how the state of one variable can be influenced by how it is changing (Deboeck & Bergeman, 2013). Derivative estimates of a single time series can be calculated by a number of different techniques from which differential equations then are constructed and tested based on the researcher’s predictions about how those variables are related. An intuitive example of this might be in considering a committed romantic relationship, in which changes in one person’s level of emotional satisfaction conceivably lead to changes in their partner’s level of satisfaction and vice versa. Each partner’s feelings might be coupled with the other’s in a complex manner, such that differential equations could be used to model their emotional relationship and show how changes in one person’s mood are inextricably linked with changes in the other’s mood.

Applying These Techniques to Your Research

Though these methods may appear foreign and somewhat challenging at first, they quickly become more intuitive once seen in an applied context. The above list represents only some of the more common techniques used in time-series analysis, especially those that have been applied successfully within the psychological sciences. œ

References and Further Reading

Deboeck, P. R., & Bergeman, C. S. (2013). The reservoir model: A differential equation model of psychological regulation. Psychological Methods, 18 , 237–256.

Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009). Using derivative estimates to describe intraindividual variability at multiple time scales. Psychological Methods, 14 , 367–386.

Gottschalk, A., Bauer, M. S., & Whybrow, P. C. (1995). Evidence of chaotic mood variation in bipolar disorder. Archives of General Psychiatry, 52 , 947–959.

Holden, J. G., Riley, M. A., Gao, J., & Torre, K. (2013). Fractal analyses: Statistical and methodological innovations and best practices. Retrieved September 13, 2016, from http://www.frontiersin.org/books/Fractal_Analyses_Statistical_And_Methodological_Innovations_And_Best_Practices/179

Kaplan, D., & Glass, L. (1995). Understanding nonlinear dynamics . New York, NY: Springer.

Main, A., Paxton, A., & Dale, R. (2016). An exploratory analysis of emotion dynamics between mothers and adolescents during conflict discussions. Emotion . Advance online publication. doi:10.1037/emo0000180

Molenaar, P. C. M. (2008). Consequences of the ergodic theorems for classical test theory, factor analysis, and the analysis of developmental processes. In S. M. Hofer & D. F. Alwin (Eds.), Handbook of cognitive aging: Interdisciplinary perspectives (pp. 90–104). Thousand Oaks, CA: SAGE Publications.

Molenaar, P. C. M., Huizenga, H. M., & Nesselroade, J. R. (2003). The relationship between the structure of interindividual and intraindividual variability: A theoretical and empirical vindication of Developmental Systems Theory. In U. M. Staudinger & U. Lindenberger (Eds.), Understanding human development (pp. 339–360). Dordrecht, the Netherlands: Kluwer.

Riley, M. A., & Van Orden, G. C. (2005). Tutorials in contemporary nonlinear methods for the behavioral sciences . Retrieved March 1, 2005, from http://www.nsf.gov/sbe/bcs/pac/nmbs/nmbs.jsp

Shockley, K., Santana, M. V., & Fowler, C. A. (2003). Mutual interpersonal postural constraints are involved in cooperative conversation. Journal of Experimental Psychology: Human Perception and Performance, 29 , 326–332.

About the Author

Trevor Swanson is a third-year PhD student studying experimental psychology at the University of Kansas. His research focuses on the temporal dynamics of self-evaluation, and his broader interests include the application of dynamical systems theory in studying psychopathology. He can be contacted at [email protected] .

Research Briefs

Recent highlights from APS journals articles on learning about working memory, psychological measurement, patterns of implicit and explicit attitudes, and much more.

Careers Up Close: Jolynn Pek on Quantifying Uncertainty

Pek analyzes sources of uncertainty in statistical results and develops new approaches to practicing replicable psychological science.

Speaking Evidence to Policy

The Commission on Evidence-Based Policymaking has issued a report that points to significant new opportunities in research and leadership for psychological scientists with expertise in areas including judgment and decision making, analysis and research design, data privacy and ethics issues, and more.

Buy for others

Buying and sending ebooks to others.

• Select quantity
• Buy and send eBooks
• Recipients can read on any device

These ebooks can only be redeemed by recipients in the US. Redemption links and eBooks cannot be resold.

Sorry, there was a problem.

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required .

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

Image Unavailable

• To view this video download Flash Player

Design and Analysis of Time Series Experiments 1st Edition, Kindle Edition

• ISBN-13 978-0190661557
• Edition 1st
• Sticky notes On Kindle Scribe
• Publisher Oxford University Press
• Publication date May 11, 2017
• Language English
• File size 17801 KB
• See all details

Kindle E-Readers

• Kindle Paperwhite
• Kindle Paperwhite (5th Generation)
• Kindle Touch
• Kindle Voyage
• Kindle Oasis
• All new Kindle paperwhite
• All New Kindle E-reader
• Kindle Oasis (9th Generation)
• Kindle Paperwhite (10th Generation)
• Kindle Paperwhite (11th Generation)
• All New Kindle E-reader (11th Generation)
• Kindle Scribe (1st Generation)
• Kindle (10th Generation)
• Kindle Oasis (10th Generation)

Fire Tablets

• Fire HD 8 (8th Generation)
• Fire 7 (9th Generation)
• Fire HD 10 (9th Generation)
• Fire HD 8 (10th Generation)
• Fire HD 10 (11th Generation)
• Fire HD 10 Plus
• Fire 7 (12th Generation)
• Fire HD 8 (12th Generation)
• Fire HD 8 Plus

Free Kindle Reading Apps

• Kindle for Android Phones
• Kindle for Android Tablets
• Kindle for iPhone
• Kindle for iPad
• Kindle for Mac
• Kindle for PC
• Kindle for Web

Customers who bought this item also bought

Editorial Reviews

About the author, product details.

• ASIN ‏ : ‎ B072Q5B197
• Publisher ‏ : ‎ Oxford University Press; 1st edition (May 11, 2017)
• Publication date ‏ : ‎ May 11, 2017
• Language ‏ : ‎ English
• File size ‏ : ‎ 17801 KB
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Enabled
• Sticky notes ‏ : ‎ On Kindle Scribe
• Print length ‏ : ‎ 386 pages
• #1,697 in Social Science Research
• #1,859 in Public Health (Kindle Store)
• #2,477 in Sociology of Social Theory

Customer reviews

• 5 star 4 star 3 star 2 star 1 star 5 star 76% 24% 0% 0% 0% 76%
• 5 star 4 star 3 star 2 star 1 star 4 star 76% 24% 0% 0% 0% 24%
• 5 star 4 star 3 star 2 star 1 star 3 star 76% 24% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 2 star 76% 24% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 1 star 76% 24% 0% 0% 0% 0%

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

• Sort reviews by Top reviews Most recent Top reviews

Top reviews from the United States

There was a problem filtering reviews right now. please try again later..

Report an issue

• About Amazon
• Investor Relations
• Amazon Devices
• Amazon Science
• Sell products on Amazon
• Sell on Amazon Business
• Sell apps on Amazon
• Become an Affiliate
• Advertise Your Products
• Self-Publish with Us
• Host an Amazon Hub
• › See More Make Money with Us
• Amazon Business Card
• Shop with Points
• Reload Your Balance
• Amazon Currency Converter
• Amazon and COVID-19
• Your Account
• Your Orders
• Shipping Rates & Policies
• Returns & Replacements
• Manage Your Content and Devices

• Conditions of Use
• Privacy Notice
• Consumer Health Data Privacy Disclosure
• Your Ads Privacy Choices

Coupling nonlinear dynamics and multi-objective optimization for periodic response and reduced power loss in turbochargers with floating ring bearings

• Published: 28 August 2024

Cite this article

• Ioannis Polyzos 1 ,
• Emmanouil Dimou 1 &
• Athanasios Chasalevris 1  

The paper utilizes a novel approach for the dynamic design of automotive turbocharger rotors by employing nonlinear dynamics of time periodic systems, emphasizing the influence of bearing design variables to prevent sub-synchronous components in system’s response. The investigation focuses on the response of an unbalanced turbocharger rotor on floating ring bearings using a collocation-type method which has been developed for the needs of the work, being then integrated with pseudo arc length continuation for the calculation of unstable solution branches of the system, in several design sets, and with poor initial values. The analytical model includes a rigid rotor model and short bearing approximations for the two floating ring bearings, which introduce strong nonlinear forces in series (inner film and outer film at each bearing). Floquet theory is employed to analyse the non-autonomous dynamic system, and stability characteristics of the response limit cycles are assessed through Floquet multipliers, whose magnitude serves as a stability index in the algorithm. A genetic algorithm based multi-objective optimization is combined to the robust collocation-type method to achieve reduced values for Floquet multipliers, ensuring that response limit cycles maintain stability and periodicity, thereby preventing the occurrence of bifurcations which normally lead to sub-synchronous response components. Twelve design variables are computed to satisfy low rotor eccentricity and power loss. Acceptable design sets are verified for efficacy by assessing system response through time integration, akin to a virtual experiment. This approach significantly reduces computational time and resource requirements compared to traditional Design of Experiment (DoE) procedures and is not constrained by complex models of the rotor, bearings, or other components. A feature of the method is that it offers an insight on the stability and its quality, rather than simply assessing a threshold speed of instability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Dynamic Analysis of a High-Speed Rotor Supported by Optimized Bearings at Steady and Transient Operating Conditions

Application of Optimization Methods in Rotor Dynamics

An optimization-based identification study of cylindrical floating ring journal bearing system in automotive turbochargers

Explore related subjects.

• Automotive Engineering

Data availability

All data generated during the study are available from the corresponding author by request.

Code availability

Custom code was used for the composition of the dynamic system, the collocation method, and the pseudo arc length continuation of limit cycles and of fixed points. Time integration when needed was performed by [64]. Optimization was performed by [67].

Abbreviations

Angular acceleration

Inner, outer relative eccentricity

Inner, outer dynamic viscosity of the lubricant

Inner, outer attitude angle of the shaft, ring

Rotating angle of the ring

Inner, outer relative clearance

Rotating speed of shaft, ring

Inner, outer radial clearance

Inner, outer eccentricity

Gravitational acceleration

Polar mass moment of inertia of the ring

Polar, diametrical mass moment of inertia of rotor

Inner, outer bearing length/diameter ratio

Bearing span (shaft length)

Inner, outer bearing length

Pressure distribution in the inner, outer film

Radius of shaft, ring (outer)

Stability index

Frictional torque in the inner, outer film

Unbalance, G-6.3 per ISO at speed \(150\,{\text{kRPM}}\)

Ring thickness

Absolute horizontal displacement of journal, ring

Absolute vertical displacement of journal, ring

Andronov-Hopf bifurcation

Centre of mass

Compressor side bearing

Compressor wheel

Degree of freedom

Design of experiment

Floquet multiplier

Genetic algorithm

Limit point of cycles

Neimark-Sacker bifurcation

Ordinary differential equation

Period doubling bifurcation

Turbocharger

Turbine side bearing

Turbine wheel

San Andrés, L., Rivadeneira, J.C., Gjika, K., Groves, C.J., LaRue, G.: Rotordynamics of small turbochargers supported on floating ring bearings—highlights in bearing analysis and experimental validation. J. Tribol. 129 (2), 391–397 (2006). https://doi.org/10.1115/1.2464134

Article   Google Scholar  

Schweizer, B.: Total instability of turbocharger rotors—physical explanation of the dynamic failure of rotors with full-floating ring bearings. J. Sound Vib. 328 (1–2), 156–190 (2009). https://doi.org/10.1016/j.jsv.2009.03.028

Schweizer, B.: Dynamics and stability of turbocharger rotors. Arch. Appl. Mech. 80 (9), 1017–1043 (2009). https://doi.org/10.1007/s00419-009-0331-0

Koutsovasilis, P., Driot, N., Lu, D., Schweizer, B.: Quantification of sub-synchronous vibrations for turbocharger rotors with full-floating ring bearings. Arch. Appl. Mech. 85 (4), 481–502 (2014). https://doi.org/10.1007/s00419-014-0924-0

Chatzisavvas, I., Nowald, G., Schweizer, B., and Koutsovasilis, P., 2017, “Experimental and Numerical Investigations of Turbocharger Rotors on Full-Floating Ring Bearings with Circumferential Oil-Groove,” Volume 8: Microturbines, Turbochargers and Small Turbomachines; Steam Turbines, V008T26A025. https://doi.org/10.1115/gt2017-64628 .

Lück, S., Schödel, M., Menze, M., Göing, J., Seume, J. R., and Friedrichs, J., 2022, “Impact of Compressor and Turbine Operating Range Extension on the Performance of an Electric Turbocharger for Fuel Cell Applications,” ASME Turbo Expo 2022, ASME. https://doi.org/10.1115/gt2022-82974 .

Zheng, X., and Zhang, Y., 2008, “Research and Design of a Centrifugal Compressor for Fuel Cell Turbocharger,” SAE Technical Paper Series, (2008–01–1692). https://doi.org/10.4271/2008-01-1692 .

Boyaci, A., Seemann, W., and Schweizer, B., 2012, “Stability and Bifurcation Behavior of Turbocharger Rotors - Comparison of Full-Floating and Semi-Floating Ring Bearings,” 14th Int. Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-14.

Schweizer, B., Sievert, M.: Nonlinear oscillations of automotive turbocharger turbines. J. Sound Vib. 321 (3–5), 955–975 (2009). https://doi.org/10.1016/j.jsv.2008.10.013

Chasalevris, A.: An investigation on the dynamics of high-speed systems using nonlinear analytical floating ring bearing models. Int. J. of Rot. Mach. 2016 , 1–22 (2016). https://doi.org/10.1155/2016/7817134

Peixoto, T.F., Nordmann, R., Cavalca, K.L.: Dynamic analysis of turbochargers with thermo-hydrodynamic lubrication bearings. J. Sound Vib. (2021). https://doi.org/10.1016/j.jsv.2021.116140

Peixoto, T.F., Cavalca, K.L.: A review on the rotor dynamics of automotive turbochargers. Mech. Mach. Sci. 114 , 97–126 (2022)

San Andrés, L., and Kerth, J., 2004, “Thermal Effects on the Performance of Floating Ring Bearings for Turbochargers,” Proceedings of the Institution of Mechanical Engineers, Part J: J. of Eng. Tribology, 218(5): 437–450. https://doi.org/10.1243/1350650042128067 .

Koutsovasilis, P., Schweizer, B.: Parameter variation and data mining of oil-film bearings: a stochastic study on the reynolds’s equation of lubrication. Arch. Appl. Mech. 84 (5), 671–692 (2014). https://doi.org/10.1007/s00419-014-0824-3

Ashtekar, A., Sadeghi, F.: “Experimental and Analytical Investigation of High-Speed Turbocharger Ball Bearings. J. Eng. Gas Turbines and Power (2011). https://doi.org/10.1115/1.4004004

Ruo, H., Xin-bin, G.E., Chao-chen, M.A.: Research on the critical speed of a mixed-flow turbocharger with hybrid ceramic ball bearing. J. Beijing Inst. Technol. 18 (3), 298–303 (2009)

Google Scholar  

Conley, B., Sadeghi, F.: Impact of whirl and axial motion on ball bearing turbocharger dynamics. Tribol. Trans. 66 (2), 338–349 (2023). https://doi.org/10.1080/10402004.2022.2153774

San Andrés, L., Ryu, K., Diemer, P.: Prediction of gas thrust foil bearing performance for oil-free automotive turbochargers. J. Eng. Gas Turb. Power (2014). https://doi.org/10.1115/1.4028389

Agrawal, G., 1997, “Foil Air/Gas Bearing Technology — an Overview,” Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery. https://doi.org/10.1115/97-gt-347 .

Chatzistavris, A., Chasalevris, A.: A design method to eliminate sub synchronous response in automotive turbochargers utilizing nonlinear dynamics of time periodic systems. J. S. Vib. 573 , 118192 (2024). https://doi.org/10.1016/j.jsv.2023.118192

Shampine, L.F., Reichelt, M.W.: The MATLAB ODE Suite. SIAM J. Sci. Comput. 18 (1), 1–22 (1997). https://doi.org/10.1137/s1064827594276424

Article   MathSciNet   Google Scholar  

Gavalas, I., Chasalevris, A.: Nonlinear dynamics of turbine generator shaft trains: evaluation of bifurcation sets applying numerical continuation. J. Eng. Gas Turb. Power (2022). https://doi.org/10.1115/1.4055533

Dimou, E., Gavalas, I., Dohnal, F., Chasalevris, A.: Locating period doubling and neimark-sacker bifurcations in parametrically excited rotors on active gas foil bearings. Mech. Mach. Sci. 140 , 324–341 (2023)

Doedel, E. J., Lecture Notes on Numerical Analysis of Nonlinear Equations, Department of Computer Science, Concordia University, Montreal, Canada.

Allgower, E.L., Georg, K.: Numerical Continuation Methods. Springer (2012)

Meijer, H. G. E., Dercole, F., and Oldeman, B., 2009, “Numerical Bifurcation Analysis,” research.utwente.nl.

Ocvirk, F. W., 1952, “Short-Bearing Approximation for Full Journal Bearings,” NACA Technical Note, (2808).

Hori, Y.: Hydrodynamic Lubrication. Springer (2016)

Gavalas, I., Chasalevris, A., Mehralian, F., Firouz-Abadi, R.D.: On the quality of stability and bifurcation sets in rotors with permanent shaft bow on nonlinear supports. Int. J. Non-Linear Mech. 158 , 104563 (2024). https://doi.org/10.1016/j.ijnonlinmec.2023.104563

Papafragkos, P., Gavalas, I., Raptopoulos, I., Chasalevris, A.: Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems. Nonlin. Dyn. 111 (1), 67–95 (2022). https://doi.org/10.1007/s11071-022-07837-1

The Mathworks. Matlab Optimization Toolbox. Release 2023b.

K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, Ltd, Chichester, England, 2001.

Goldberg, D.E.: Genetic Algorithms in Search Optimization & Machine Learning. Addison-Wesley (1989)

D. Broomhead, D. Lowe, Radial basis functions, multi-variable functional interpolation and adaptive networks, Royal Signals and Radar Establishment Malvern, United Kingdom, RSRE-MEMO-4148, 1988.

Abramson, M.A., Audet, J.E.C., Dennis, J.E., Jr., Sebastien, L.D.: OrthoMADS: a deterministic MADS instance with orthogonal directions. SIAM J. Optimiz. 20 (2), 948–966 (2009). https://doi.org/10.1137/080716980

Audet, S., Dennis, J.E., Jr.: Analysis of generalized pattern searches. SIAM J. Optimiz. 13 (3), 889–903 (2003). https://doi.org/10.1137/S1052623400378742

Download references

Acknowledgements

The work in this paper did not receive any fund.

Author information

Authors and affiliations.

School of Mechanical Engineering, National Technical University of Athens, Zografos Campus, Heroon Polytechniou 9 Str, 15780, Athens, Greece

Ioannis Polyzos, Emmanouil Dimou & Athanasios Chasalevris

You can also search for this author in PubMed   Google Scholar

Contributions

Ioannis Polyzos programmed part of the numerical solvers, produced part of the results/figures, and executed part of the literature review. Emmanouil Dimou programmed the core of the collocation method and part of the numerical continuation method, and produced part of the results. Athanasios Chasalevris supervised the work, performed part of the literature review, produced part of the results, provided the relative guidance in the programming of the numerical solvers, and prepared the most part of the manuscript. All authors reviewed the paper.

Corresponding author

Correspondence to Athanasios Chasalevris .

Ethics declarations

Conflict of interest.

The authors declare that they have no conflict of interest or competing interest with regard to the publication of this manuscript.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Single objective optimization “ga”

The MATLAB global optimization solver “ga” [ 31 ] implements a genetic algorithm [ 33 ] for constrained, single-objective optimization problems. The algorithm is initialized by creating a random initial design set, within specified bounds, and performs an iterative process for creating a sequence of new design sets (generations). At every iteration, the algorithm selects from the previous generation a selected number of points to parent the next generation based on the value of the objective function the elements of the point are termed genes. Then three types of “children” are created for the next generation:

“Elite “children”, where single “parents” (those with the lowest objective function value) pass their genes to the next generation without any changes.

“Crossover children”, where the genes of two “parents” are combined to create a single “child”.

“Mutation children”, where the genes of a single “parent” are randomly mutated by adding a random vector from a Gaussian distribution to the original.

The fraction of elite and crossover “children” in the next generation is specified and the number of mutated “children” is selected in order to keep the population size constant. The amount of mutation is typically proportional to the standard deviation of the population which decreases with every new generation.

The algorithm terminates when the number of generations has reached a specified maximum or when the objective function is satisfied within a specified tolerance or when the objective function value has remained constant within a specified tolerance for a specified number of generations, termed stalled generations.

Appendix B: Single objective optimization “surrogateopt”

The MATLAB global optimization solver “surrogateopt” [ 31 ] uses an algorithm designed for solving computationally expensive, black-box single-objective optimization problems with bounded constraints. The algorithm is initialized by choosing a selected number of quasi-random design input sets within the bounds using a sampling method e.g. Latin Hypercube Sampling. Then the objective function is evaluated at these points and a surrogate function is created by interpolating a radial basis function [ 34 ] through these points. The initial point with the smallest value of the objective function is termed the incumbent and the algorithm, starting from the incumbent point, searches for a minimum of a merit function \(f(x)\) that is the weighted sum of the scaled surrogate value \(S(x)\) and the scaled distance \(D(x)\) , see Eq. ( 16 ).

where \(s_{{{\text{min}}}}\) , \(s_{{{\text{max}}}}\) are the minimum and maximum surrogate values among the sample points, \(s(x)\) is the surrogate value at the point \(x\) , \(d_{{{\text{min}}}}\) , \(d_{{{\text{max}}}}\) are the minimum and maximum distances of the evaluated points from the final evaluated point and \(d(x)\) is the minimum distance of the point \(x\) to an evaluated point. The scaled surrogate value is nonnegative and zero at the at the points which have minimal surrogate value among the sample points and the scaled distance term is nonnegative and zero and zero at the points which are maximally far from the evaluated points. A large value in the weighting parameter \(w\) favors minimizing the surrogate value and a small value favors points which are far from evaluated points, which leads the search to new regions.

Depending on the value of the weighting parameter and the problem type (linear, binary, integer constraints), surrogateopt will use a different type of sampling to perform the local search for the minimization of the merit function, e.g. random, OrthoMADS [ 35 ], Generalized Pattern Search [ 36 ] or crossover from the ga algorithm.

The objective function is evaluated at the point with the minimum merit function value and the interpolated function is updated, the sampling region is rescaled and the sampling is repeated. Once all sampling points are within a specified tolerance from the incumbent, then the surrogate function is created anew (surrogate reset) and the previous steps are repeated until a set number of objective function evaluations is reached or the objective function value is within a specified tolerance.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Polyzos, I., Dimou, E. & Chasalevris, A. Coupling nonlinear dynamics and multi-objective optimization for periodic response and reduced power loss in turbochargers with floating ring bearings. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-10148-2

Download citation

Received : 23 April 2024

Accepted : 09 August 2024

Published : 28 August 2024

DOI : https://doi.org/10.1007/s11071-024-10148-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Turbocharger rotordynamics
• Nonlinear dynamics
• Bifurcation elimination
• Design optimization
• Numerical continuation
• Find a journal
• Publish with us
• Track your research

• Search Menu

Sign in through your institution

• Browse content in Arts and Humanities
• Browse content in Archaeology
• Anglo-Saxon and Medieval Archaeology
• Archaeological Methodology and Techniques
• Archaeology by Region
• Archaeology of Religion
• Archaeology of Trade and Exchange
• Biblical Archaeology
• Contemporary and Public Archaeology
• Environmental Archaeology
• Historical Archaeology
• History and Theory of Archaeology
• Industrial Archaeology
• Landscape Archaeology
• Mortuary Archaeology
• Prehistoric Archaeology
• Underwater Archaeology
• Zooarchaeology
• Browse content in Architecture
• Architectural Structure and Design
• History of Architecture
• Residential and Domestic Buildings
• Theory of Architecture
• Browse content in Art
• Art Subjects and Themes
• History of Art
• Industrial and Commercial Art
• Theory of Art
• Biographical Studies
• Byzantine Studies
• Browse content in Classical Studies
• Classical History
• Classical Philosophy
• Classical Mythology
• Classical Numismatics
• Classical Literature
• Classical Reception
• Classical Art and Architecture
• Classical Oratory and Rhetoric
• Greek and Roman Epigraphy
• Greek and Roman Law
• Greek and Roman Papyrology
• Greek and Roman Archaeology
• Late Antiquity
• Religion in the Ancient World
• Social History
• Digital Humanities
• Browse content in History
• Colonialism and Imperialism
• Diplomatic History
• Environmental History
• Genealogy, Heraldry, Names, and Honours
• Genocide and Ethnic Cleansing
• Historical Geography
• History by Period
• History of Emotions
• History of Agriculture
• History of Education
• History of Gender and Sexuality
• Industrial History
• Intellectual History
• International History
• Labour History
• Legal and Constitutional History
• Local and Family History
• Maritime History
• Military History
• National Liberation and Post-Colonialism
• Oral History
• Political History
• Public History
• Regional and National History
• Revolutions and Rebellions
• Slavery and Abolition of Slavery
• Social and Cultural History
• Theory, Methods, and Historiography
• Urban History
• World History
• Browse content in Language Teaching and Learning
• Language Learning (Specific Skills)
• Language Teaching Theory and Methods
• Browse content in Linguistics
• Applied Linguistics
• Cognitive Linguistics
• Computational Linguistics
• Forensic Linguistics
• Grammar, Syntax and Morphology
• Historical and Diachronic Linguistics
• History of English
• Language Acquisition
• Language Evolution
• Language Reference
• Language Variation
• Language Families
• Lexicography
• Linguistic Anthropology
• Linguistic Theories
• Linguistic Typology
• Phonetics and Phonology
• Psycholinguistics
• Sociolinguistics
• Translation and Interpretation
• Writing Systems
• Browse content in Literature
• Bibliography
• Children's Literature Studies
• Literary Studies (Asian)
• Literary Studies (European)
• Literary Studies (Eco-criticism)
• Literary Studies (Romanticism)
• Literary Studies (American)
• Literary Studies (Modernism)
• Literary Studies - World
• Literary Studies (1500 to 1800)
• Literary Studies (19th Century)
• Literary Studies (20th Century onwards)
• Literary Studies (African American Literature)
• Literary Studies (British and Irish)
• Literary Studies (Early and Medieval)
• Literary Studies (Fiction, Novelists, and Prose Writers)
• Literary Studies (Gender Studies)
• Literary Studies (Graphic Novels)
• Literary Studies (History of the Book)
• Literary Studies (Plays and Playwrights)
• Literary Studies (Poetry and Poets)
• Literary Studies (Postcolonial Literature)
• Literary Studies (Queer Studies)
• Literary Studies (Science Fiction)
• Literary Studies (Travel Literature)
• Literary Studies (War Literature)
• Literary Studies (Women's Writing)
• Literary Theory and Cultural Studies
• Mythology and Folklore
• Shakespeare Studies and Criticism
• Browse content in Media Studies
• Browse content in Music
• Applied Music
• Dance and Music
• Ethics in Music
• Ethnomusicology
• Gender and Sexuality in Music
• Medicine and Music
• Music Cultures
• Music and Religion
• Music and Media
• Music and Culture
• Music Education and Pedagogy
• Music Theory and Analysis
• Musical Scores, Lyrics, and Libretti
• Musical Structures, Styles, and Techniques
• Musicology and Music History
• Performance Practice and Studies
• Race and Ethnicity in Music
• Sound Studies
• Browse content in Performing Arts
• Browse content in Philosophy
• Aesthetics and Philosophy of Art
• Epistemology
• Feminist Philosophy
• History of Western Philosophy
• Metaphysics
• Moral Philosophy
• Non-Western Philosophy
• Philosophy of Science
• Philosophy of Language
• Philosophy of Mind
• Philosophy of Perception
• Philosophy of Action
• Philosophy of Law
• Philosophy of Religion
• Philosophy of Mathematics and Logic
• Practical Ethics
• Social and Political Philosophy
• Browse content in Religion
• Biblical Studies
• Christianity
• East Asian Religions
• History of Religion
• Judaism and Jewish Studies
• Qumran Studies
• Religion and Education
• Religion and Health
• Religion and Politics
• Religion and Science
• Religion and Law
• Religion and Art, Literature, and Music
• Religious Studies
• Browse content in Society and Culture
• Cookery, Food, and Drink
• Cultural Studies
• Customs and Traditions
• Ethical Issues and Debates
• Hobbies, Games, Arts and Crafts
• Natural world, Country Life, and Pets
• Popular Beliefs and Controversial Knowledge
• Sports and Outdoor Recreation
• Technology and Society
• Travel and Holiday
• Visual Culture
• Browse content in Law
• Arbitration
• Browse content in Company and Commercial Law
• Commercial Law
• Company Law
• Browse content in Comparative Law
• Systems of Law
• Competition Law
• Browse content in Constitutional and Administrative Law
• Government Powers
• Judicial Review
• Local Government Law
• Military and Defence Law
• Parliamentary and Legislative Practice
• Construction Law
• Contract Law
• Browse content in Criminal Law
• Criminal Procedure
• Criminal Evidence Law
• Sentencing and Punishment
• Employment and Labour Law
• Environment and Energy Law
• Browse content in Financial Law
• Banking Law
• Insolvency Law
• History of Law
• Human Rights and Immigration
• Intellectual Property Law
• Browse content in International Law
• Private International Law and Conflict of Laws
• Public International Law
• IT and Communications Law
• Jurisprudence and Philosophy of Law
• Law and Politics
• Law and Society
• Browse content in Legal System and Practice
• Courts and Procedure
• Legal Skills and Practice
• Legal System - Costs and Funding
• Primary Sources of Law
• Regulation of Legal Profession
• Medical and Healthcare Law
• Browse content in Policing
• Criminal Investigation and Detection
• Police and Security Services
• Police Procedure and Law
• Police Regional Planning
• Browse content in Property Law
• Personal Property Law
• Restitution
• Study and Revision
• Terrorism and National Security Law
• Browse content in Trusts Law
• Wills and Probate or Succession
• Browse content in Medicine and Health
• Browse content in Allied Health Professions
• Arts Therapies
• Clinical Science
• Dietetics and Nutrition
• Occupational Therapy
• Operating Department Practice
• Physiotherapy
• Radiography
• Speech and Language Therapy
• Browse content in Anaesthetics
• General Anaesthesia
• Browse content in Clinical Medicine
• Acute Medicine
• Cardiovascular Medicine
• Clinical Genetics
• Clinical Pharmacology and Therapeutics
• Dermatology
• Endocrinology and Diabetes
• Gastroenterology
• Genito-urinary Medicine
• Geriatric Medicine
• Infectious Diseases
• Medical Toxicology
• Medical Oncology
• Pain Medicine
• Palliative Medicine
• Rehabilitation Medicine
• Respiratory Medicine and Pulmonology
• Rheumatology
• Sleep Medicine
• Sports and Exercise Medicine
• Clinical Neuroscience
• Community Medical Services
• Critical Care
• Emergency Medicine
• Forensic Medicine
• Haematology
• History of Medicine
• Browse content in Medical Dentistry
• Oral and Maxillofacial Surgery
• Paediatric Dentistry
• Restorative Dentistry and Orthodontics
• Surgical Dentistry
• Browse content in Medical Skills
• Clinical Skills
• Communication Skills
• Nursing Skills
• Surgical Skills
• Medical Ethics
• Medical Statistics and Methodology
• Browse content in Neurology
• Clinical Neurophysiology
• Neuropathology
• Nursing Studies
• Browse content in Obstetrics and Gynaecology
• Gynaecology
• Occupational Medicine
• Ophthalmology
• Otolaryngology (ENT)
• Browse content in Paediatrics
• Neonatology
• Browse content in Pathology
• Chemical Pathology
• Clinical Cytogenetics and Molecular Genetics
• Histopathology
• Medical Microbiology and Virology
• Patient Education and Information
• Browse content in Pharmacology
• Psychopharmacology
• Browse content in Popular Health
• Caring for Others
• Complementary and Alternative Medicine
• Self-help and Personal Development
• Browse content in Preclinical Medicine
• Cell Biology
• Molecular Biology and Genetics
• Reproduction, Growth and Development
• Primary Care
• Professional Development in Medicine
• Browse content in Psychiatry
• Addiction Medicine
• Child and Adolescent Psychiatry
• Forensic Psychiatry
• Learning Disabilities
• Old Age Psychiatry
• Psychotherapy
• Browse content in Public Health and Epidemiology
• Epidemiology
• Public Health
• Browse content in Radiology
• Clinical Radiology
• Interventional Radiology
• Nuclear Medicine
• Radiation Oncology
• Reproductive Medicine
• Browse content in Surgery
• Cardiothoracic Surgery
• Gastro-intestinal and Colorectal Surgery
• General Surgery
• Neurosurgery
• Paediatric Surgery
• Peri-operative Care
• Plastic and Reconstructive Surgery
• Surgical Oncology
• Transplant Surgery
• Trauma and Orthopaedic Surgery
• Vascular Surgery
• Browse content in Science and Mathematics
• Browse content in Biological Sciences
• Aquatic Biology
• Biochemistry
• Bioinformatics and Computational Biology
• Developmental Biology
• Ecology and Conservation
• Evolutionary Biology
• Genetics and Genomics
• Microbiology
• Molecular and Cell Biology
• Natural History
• Plant Sciences and Forestry
• Research Methods in Life Sciences
• Structural Biology
• Systems Biology
• Zoology and Animal Sciences
• Browse content in Chemistry
• Analytical Chemistry
• Computational Chemistry
• Crystallography
• Environmental Chemistry
• Industrial Chemistry
• Inorganic Chemistry
• Materials Chemistry
• Medicinal Chemistry
• Mineralogy and Gems
• Organic Chemistry
• Physical Chemistry
• Polymer Chemistry
• Study and Communication Skills in Chemistry
• Theoretical Chemistry
• Browse content in Computer Science
• Artificial Intelligence
• Computer Architecture and Logic Design
• Game Studies
• Human-Computer Interaction
• Mathematical Theory of Computation
• Programming Languages
• Software Engineering
• Systems Analysis and Design
• Virtual Reality
• Browse content in Computing
• Business Applications
• Computer Security
• Computer Games
• Computer Networking and Communications
• Digital Lifestyle
• Graphical and Digital Media Applications
• Operating Systems
• Browse content in Earth Sciences and Geography
• Atmospheric Sciences
• Environmental Geography
• Geology and the Lithosphere
• Maps and Map-making
• Meteorology and Climatology
• Oceanography and Hydrology
• Palaeontology
• Physical Geography and Topography
• Regional Geography
• Soil Science
• Urban Geography
• Browse content in Engineering and Technology
• Agriculture and Farming
• Biological Engineering
• Civil Engineering, Surveying, and Building
• Electronics and Communications Engineering
• Energy Technology
• Engineering (General)
• Environmental Science, Engineering, and Technology
• History of Engineering and Technology
• Mechanical Engineering and Materials
• Technology of Industrial Chemistry
• Transport Technology and Trades
• Browse content in Environmental Science
• Applied Ecology (Environmental Science)
• Conservation of the Environment (Environmental Science)
• Environmental Sustainability
• Environmentalist Thought and Ideology (Environmental Science)
• Management of Land and Natural Resources (Environmental Science)
• Natural Disasters (Environmental Science)
• Nuclear Issues (Environmental Science)
• Pollution and Threats to the Environment (Environmental Science)
• Social Impact of Environmental Issues (Environmental Science)
• History of Science and Technology
• Browse content in Materials Science
• Ceramics and Glasses
• Composite Materials
• Metals, Alloying, and Corrosion
• Nanotechnology
• Browse content in Mathematics
• Applied Mathematics
• Biomathematics and Statistics
• History of Mathematics
• Mathematical Education
• Mathematical Finance
• Mathematical Analysis
• Numerical and Computational Mathematics
• Probability and Statistics
• Pure Mathematics
• Browse content in Neuroscience
• Cognition and Behavioural Neuroscience
• Development of the Nervous System
• Disorders of the Nervous System
• History of Neuroscience
• Invertebrate Neurobiology
• Molecular and Cellular Systems
• Neuroendocrinology and Autonomic Nervous System
• Neuroscientific Techniques
• Sensory and Motor Systems
• Browse content in Physics
• Astronomy and Astrophysics
• Atomic, Molecular, and Optical Physics
• Biological and Medical Physics
• Classical Mechanics
• Computational Physics
• Condensed Matter Physics
• Electromagnetism, Optics, and Acoustics
• History of Physics
• Mathematical and Statistical Physics
• Measurement Science
• Nuclear Physics
• Particles and Fields
• Plasma Physics
• Quantum Physics
• Relativity and Gravitation
• Semiconductor and Mesoscopic Physics
• Browse content in Psychology
• Affective Sciences
• Clinical Psychology
• Cognitive Psychology
• Cognitive Neuroscience
• Criminal and Forensic Psychology
• Developmental Psychology
• Educational Psychology
• Evolutionary Psychology
• Health Psychology
• History and Systems in Psychology
• Music Psychology
• Neuropsychology
• Organizational Psychology
• Psychological Assessment and Testing
• Psychology of Human-Technology Interaction
• Psychology Professional Development and Training
• Research Methods in Psychology
• Social Psychology
• Browse content in Social Sciences
• Browse content in Anthropology
• Anthropology of Religion
• Human Evolution
• Medical Anthropology
• Physical Anthropology
• Regional Anthropology
• Social and Cultural Anthropology
• Theory and Practice of Anthropology
• Browse content in Business and Management
• Business Strategy
• Business Ethics
• Business History
• Business and Government
• Business and Technology
• Business and the Environment
• Comparative Management
• Corporate Governance
• Corporate Social Responsibility
• Entrepreneurship
• Health Management
• Human Resource Management
• Industrial and Employment Relations
• Industry Studies
• Information and Communication Technologies
• International Business
• Knowledge Management
• Management and Management Techniques
• Operations Management
• Organizational Theory and Behaviour
• Pensions and Pension Management
• Public and Nonprofit Management
• Social Issues in Business and Management
• Strategic Management
• Supply Chain Management
• Browse content in Criminology and Criminal Justice
• Criminal Justice
• Criminology
• Forms of Crime
• International and Comparative Criminology
• Youth Violence and Juvenile Justice
• Development Studies
• Browse content in Economics
• Agricultural, Environmental, and Natural Resource Economics
• Asian Economics
• Behavioural Finance
• Behavioural Economics and Neuroeconomics
• Econometrics and Mathematical Economics
• Economic Systems
• Economic History
• Economic Methodology
• Economic Development and Growth
• Financial Markets
• Financial Institutions and Services
• General Economics and Teaching
• Health, Education, and Welfare
• History of Economic Thought
• International Economics
• Labour and Demographic Economics
• Law and Economics
• Macroeconomics and Monetary Economics
• Microeconomics
• Public Economics
• Urban, Rural, and Regional Economics
• Welfare Economics
• Browse content in Education
• Adult Education and Continuous Learning
• Care and Counselling of Students
• Early Childhood and Elementary Education
• Educational Equipment and Technology
• Educational Strategies and Policy
• Higher and Further Education
• Organization and Management of Education
• Philosophy and Theory of Education
• Schools Studies
• Secondary Education
• Teaching of a Specific Subject
• Teaching of Specific Groups and Special Educational Needs
• Teaching Skills and Techniques
• Browse content in Environment
• Applied Ecology (Social Science)
• Climate Change
• Conservation of the Environment (Social Science)
• Environmentalist Thought and Ideology (Social Science)
• Management of Land and Natural Resources (Social Science)
• Natural Disasters (Environment)
• Pollution and Threats to the Environment (Social Science)
• Social Impact of Environmental Issues (Social Science)
• Sustainability
• Browse content in Human Geography
• Cultural Geography
• Economic Geography
• Political Geography
• Browse content in Interdisciplinary Studies
• Communication Studies
• Museums, Libraries, and Information Sciences
• Browse content in Politics
• African Politics
• Asian Politics
• Chinese Politics
• Comparative Politics
• Conflict Politics
• Elections and Electoral Studies
• Environmental Politics
• Ethnic Politics
• European Union
• Foreign Policy
• Gender and Politics
• Human Rights and Politics
• Indian Politics
• International Relations
• International Organization (Politics)
• Irish Politics
• Latin American Politics
• Middle Eastern Politics
• Political Methodology
• Political Communication
• Political Philosophy
• Political Sociology
• Political Behaviour
• Political Economy
• Political Institutions
• Political Theory
• Politics and Law
• Politics of Development
• Public Administration
• Public Policy
• Qualitative Political Methodology
• Quantitative Political Methodology
• Regional Political Studies
• Russian Politics
• Security Studies
• State and Local Government
• UK Politics
• US Politics
• Browse content in Regional and Area Studies
• African Studies
• Asian Studies
• East Asian Studies
• Japanese Studies
• Latin American Studies
• Middle Eastern Studies
• Native American Studies
• Scottish Studies
• Browse content in Research and Information
• Research Methods
• Browse content in Social Work
• Addictions and Substance Misuse
• Adoption and Fostering
• Care of the Elderly
• Child and Adolescent Social Work
• Couple and Family Social Work
• Direct Practice and Clinical Social Work
• Emergency Services
• Human Behaviour and the Social Environment
• International and Global Issues in Social Work
• Mental and Behavioural Health
• Social Justice and Human Rights
• Social Policy and Advocacy
• Social Work and Crime and Justice
• Social Work Macro Practice
• Social Work Practice Settings
• Social Work Research and Evidence-based Practice
• Welfare and Benefit Systems
• Browse content in Sociology
• Childhood Studies
• Community Development
• Comparative and Historical Sociology
• Disability Studies
• Economic Sociology
• Gender and Sexuality
• Gerontology and Ageing
• Health, Illness, and Medicine
• Marriage and the Family
• Migration Studies
• Occupations, Professions, and Work
• Organizations
• Population and Demography
• Race and Ethnicity
• Social Theory
• Social Movements and Social Change
• Social Research and Statistics
• Social Stratification, Inequality, and Mobility
• Sociology of Religion
• Sociology of Education
• Sport and Leisure
• Urban and Rural Studies
• Browse content in Warfare and Defence
• Defence Strategy, Planning, and Research
• Land Forces and Warfare
• Military Administration
• Military Life and Institutions
• Naval Forces and Warfare
• Other Warfare and Defence Issues
• Peace Studies and Conflict Resolution
• Weapons and Equipment

• < Previous chapter
• Next chapter >

3 Noise Modeling

• Published: May 2017
• Cite Icon Cite
• Permissions Icon Permissions

Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average ( ARIMA ) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov ( KS ) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function ( ACF ). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function ( PACF ). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.

Personal account

• Sign in with email/username & password
• Get email alerts
• Save searches
• Purchase content
• Activate your purchase/trial code
• Add your ORCID iD

Institutional access

Sign in with a library card.

• Sign in with username/password
• Recommend to your librarian
• Institutional account management
• Get help with access

Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:

IP based access

Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.

Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.

• Click Sign in through your institution.
• Select your institution from the list provided, which will take you to your institution's website to sign in.
• When on the institution site, please use the credentials provided by your institution. Do not use an Oxford Academic personal account.
• Following successful sign in, you will be returned to Oxford Academic.

If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.

Enter your library card number to sign in. If you cannot sign in, please contact your librarian.

Society Members

Society member access to a journal is achieved in one of the following ways:

Sign in through society site

Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:

• Click Sign in through society site.
• When on the society site, please use the credentials provided by that society. Do not use an Oxford Academic personal account.

If you do not have a society account or have forgotten your username or password, please contact your society.

Sign in using a personal account

Some societies use Oxford Academic personal accounts to provide access to their members. See below.

A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.

Some societies use Oxford Academic personal accounts to provide access to their members.

Viewing your signed in accounts

Click the account icon in the top right to:

• View your signed in personal account and access account management features.
• View the institutional accounts that are providing access.

Signed in but can't access content

Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.

For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.

Our books are available by subscription or purchase to libraries and institutions.

• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Rights and permissions
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.