More Web Proxy on the site http://driver.im/

research-article

Deriving Equations from Sensor Data Using Dimensional Function Synthesis

Authors:

Vasileios Tsoutsouras,

Phillip Stanley-MarbellAuthors Info & Claims

ACM Transactions on Embedded Computing Systems (TECS), Volume 18, Issue 5s

Article No.: 84, Pages 1 - 22

https://doi.org/10.1145/3358218

Published: 08 October 2019 Publication History

Abstract

We present a new method for deriving functions that model the relationship between multiple signals in a physical system. The method, which we call dimensional function synthesis, applies to data streams where the dimensions of the signals are known. The method comprises two phases: a compile-time synthesis phase and a subsequent calibration using sensor data.

We implement dimensional function synthesis and use the implementation to demonstrate efficiently summarizing multi-modal sensor data for two physical systems using 90 laboratory experiments and 10 000 synthetic idealized measurements. We evaluate the performance of the compile-time phase of dimensional function synthesis as well as the calibration phase overhead, inference latency, and accuracy of the models our method generates.

The results show that our technique can generate models in less than 300 ms on average across all the physical systems we evaluated. When calibrated with sensor data, our models outperform traditional regression and neural network models in inference accuracy in all the cases we evaluated. In addition, our models perform better in training latency (over 8660× improvement) and required arithmetic operations in inference (over 34× improvement). These significant gains are largely the result of exploiting information on the physics of signals that has hitherto been ignored.

References

[1]

Eric Allen, David Chase, Victor Luchangco, Jan-Willem Maessen, and Guy L. Steele, Jr. 2004. Object-oriented units of measurement. In Proceedings of the 19th Annual ACM SIGPLAN Conference on Object-oriented Programming, Systems, Languages, and Applications (OOPSLA’04). ACM, New York, NY, USA, 384--403.

[2]

Tudor Antoniu, Paul A. Steckler, Shriram Krishnamurthi, Erich Neuwirth, and Matthias Felleisen. 2004. Validating the unit correctness of spreadsheet programs. In Proceedings of the 26th International Conference on Software Engineering (ICSE’04). IEEE Computer Society, Washington, DC, USA, 439--448.

Digital Library

[3]

Michel Babout, Hafid Sidhoum, and Louis Frecon. 1990. AMPERE: A programming language for physics. European Journal of Physics 11, 3 (1990), 163.

[4]

David Barber. 2012. Bayesian Reasoning and Machine Learning. Cambridge University Press.

Digital Library

[5]

Geoffrey Biggs and Bruce A. Macdonald. 2008. A pragmatic approach to dimensional analysis for mobile robotic programming. Auton. Robots 25, 4 (Nov. 2008), 405--419.

Digital Library

[6]

Edgar Buckingham. 1914. On physically similar systems; Illustrations of the use of dimensional equations. Physical Review 4, 4 (1914), 345--376.

[7]

Donald E. Carlson. 1979. A mathematical theory of physical units, dimensions, and measures. Archive for Rational Mechanics and Analysis 70, 4 (1979), 289--305.

[8]

Feng Chen, Grigore Roşu, and Ram Prasad Venkatesan. 2003. Rule-based analysis of dimensional safety. In Proceedings of the 14th International Conference on Rewriting Techniques and Applications (RTA’03). Springer-Verlag, Berlin, Heidelberg, 197--207.

Digital Library

[9]

Robert F. Cmelik and Narain H. Gehani. 1988. Dimensional analysis with C++. IEEE Softw. 5, 3 (May 1988), 21--27.

Digital Library

[10]

Donald E. Carlson. 1978. On some new results in dimensional analysis. (1978).

[11]

Harald Hanche-Olsen. 2004. Buckingham’s pi-theorem. NTNU: http://www.math.ntnu.no/&tilde;hanche/notes/buckingham/buckingham-a4.pdf (2004).

[12]

Paul N. Hilfinger. 1988. An ada package for dimensional analysis. ACM Trans. Program. Lang. Syst. 10, 2 (April 1988), 189--203.

Digital Library

[13]

Daniel J. A. Hills, Adrian M. Grütter, and Jonathan J. Hudson. 2015. An algorithm for discovering Lagrangians automatically from data. PeerJ Computer Science 1 (nov 2015), e31.

[14]

Mark Hills, Feng Chen, and Grigore Roşu. 2012. A rewriting logic approach to static checking of units of measurement in C. Electron. Notes Theor. Comput. Sci. 290 (Dec. 2012), 51--67.

[15]

R. T. House. 1983. A proposal for an extended form of type checking of expressions. Comput. J. 26, 4 (Nov. 1983), 366--374.

Digital Library

[16]

Dan Jonsson. 2014. Dimensional analysis: A centenary update. 1 (2014), 1--16.

[17]

Andrew Kennedy. 1994. Dimension types. In Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems (ESOP’94). Springer-Verlag, London, UK, UK, 348--362.

Digital Library

[18]

Andrew J. Kennedy. 1997. Relational parametricity and units of measure. In Proceedings of the 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’97). ACM, New York, NY, USA, 442--455.

Digital Library

[19]

Patrick W. Langley. 1977. BACON: A production system that discovers empirical laws. In Proceedings of the 5th International Joint Conference on Artificial Intelligence - Volume 1 (IJCAI’77). San Francisco, CA, USA, 344.

[20]

Jonathan Lim and Phillip Stanley-Marbell. 2018. Newton: A language for describing physics. CoRR abs/1811.04626 (2018).

[21]

Lord Rayleigh. 1915. The principle of similitude. Nature 95 (dec 1915), 66--68.

[22]

William H. Press, Saul a. Teukolsky, William T. Vetterling, and Brian P. Flannery. 1996. Numerical Recipes in Fortran 77: The Art of Scientific Computing. Second Edition. Vol. 1.

[23]

Mikael Rittri. 1995. Dimension inference under polymorphic recursion. In Proceedings of the Seventh International Conference on Functional Programming Languages and Computer Architecture (FPCA’95). ACM, New York, NY, USA, 147--159.

Digital Library

[24]

Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. 2017. Data-driven discovery of partial differential equations. Science Advances 3, 4 (2017), e1602614.

[25]

Michael Schmidt and Hod Lipson. 2009. Distilling free-form natural laws from experimental data. Science 324, 5923 (2009), 81--85.

[26]

Volker Simon, Bernhard Weigand, and Hassan Gomaa. 2017. Dimensional Analysis for Engineers. Springer.

[27]

Ain A. Sonin. 2004. A generalization of the Π-theorem and dimensional analysis. Proceedings of the National Academy of Sciences 101, 23 (2004), 8525--8526.

[28]

Gilbert Strang. 2016. Introduction to Linear Algebra (fifth ed.). Wellesley-Cambridge Press, Wellesley, MA.

[29]

G. Taylor. 1950. The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 201, 1065 (1950), 175--186.

[30]

Zerksis D. Umrigar. 1994. Fully static dimensional analysis with C++. SIGPLAN Not. 29, 9 (Sept. 1994), 135--139.

Digital Library

[31]

Yihua Wu. 1989. Discovering natural laws by reduction. Journal of Computer Science and Technology 4, 1 (1989), 35--51.

Cited By

Mu PMavrogeorgis NVasiladiotis CTsoutsouras VKaparounakis OStanley-Marbell PBarbalace ARodríguez GSadayappan PSukumaran-Rajam A(2024)CoSense: Compiler Optimizations using Sensor Technical SpecificationsProceedings of the 33rd ACM SIGPLAN International Conference on Compiler Construction10.1145/3640537.3641576(73-85)Online publication date: 17-Feb-2024
https://dl.acm.org/doi/10.1145/3640537.3641576
Dmytriv VSahan OGorodnyak R(2023)Application of the theory of dimensions in research of floor materials dispensers in multifactor experimentAvtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì10.23939/istcipa2023.57.01357(13-20)Online publication date: 2023
https://doi.org/10.23939/istcipa2023.57.013
Shin YShin DBae D(2023)Virtual Environment Model Generation for CPS Goal Verification using Imitation LearningACM Transactions on Embedded Computing Systems10.1145/363380423:1(1-29)Online publication date: 27-Nov-2023
https://dl.acm.org/doi/10.1145/3633804
Show More Cited By

Index Terms

Deriving Equations from Sensor Data Using Dimensional Function Synthesis

Recommendations

Deriving equations from sensor data using dimensional function synthesis

We present a new method for deriving functions that model the relationship between multiple signals in a physical system. The method, which we call dimensional function synthesis, applies to data streams where the dimensions of the signals (e.g., length, ...
Low-Dimensional Data Representation in Data Analysis
Proceedings of the 6th IAPR TC 3 International Workshop on Artificial Neural Networks in Pattern Recognition - Volume 8774

Many Data Analysis tasks deal with data which are presented in high-dimensional spaces, and the 'curse of dimensionality' phenomena is often an obstacle to the use of many methods, including Neural Network methods, for solving these tasks. To avoid ...
Sensor data fusion in the context of electric vehicles charging stations using a Network-on-Chip

This paper presents a platform for evaluating sensor data fusion algorithms based on a Network-on-Chip (NoC). Initially the NoC is simulated by MPSoCSim, which contains an ARM and several MicroBlaze processors. The approach is furthermore evaluated on a ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Embedded Computing Systems

ACM Transactions on Embedded Computing Systems Volume 18, Issue 5s

Special Issue ESWEEK 2019, CASES 2019, CODES+ISSS 2019 and EMSOFT 2019

October 2019

1423 pages

ISSN:1539-9087

EISSN:1558-3465

DOI:10.1145/3365919

Editor:
Sandeep K. Shukla
Indian Institute of Technology, India

Issue’s Table of Contents

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 08 October 2019

Accepted: 01 July 2019

Revised: 01 June 2019

Received: 01 April 2019

Published in TECS Volume 18, Issue 5s

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

22
Total Citations
View Citations
382
Total Downloads

Downloads (Last 12 months)19
Downloads (Last 6 weeks)1

Reflects downloads up to 08 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Mu PMavrogeorgis NVasiladiotis CTsoutsouras VKaparounakis OStanley-Marbell PBarbalace ARodríguez GSadayappan PSukumaran-Rajam A(2024)CoSense: Compiler Optimizations using Sensor Technical SpecificationsProceedings of the 33rd ACM SIGPLAN International Conference on Compiler Construction10.1145/3640537.3641576(73-85)Online publication date: 17-Feb-2024
https://dl.acm.org/doi/10.1145/3640537.3641576
Dmytriv VSahan OGorodnyak R(2023)Application of the theory of dimensions in research of floor materials dispensers in multifactor experimentAvtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì10.23939/istcipa2023.57.01357(13-20)Online publication date: 2023
https://doi.org/10.23939/istcipa2023.57.013
Shin YShin DBae D(2023)Virtual Environment Model Generation for CPS Goal Verification using Imitation LearningACM Transactions on Embedded Computing Systems10.1145/363380423:1(1-29)Online publication date: 27-Nov-2023
https://dl.acm.org/doi/10.1145/3633804
Lindemann LJiang LMatni NPappas G(2023)Risk of Stochastic Systems for Temporal Logic SpecificationsACM Transactions on Embedded Computing Systems10.1145/358049022:3(1-31)Online publication date: 19-Apr-2023
https://dl.acm.org/doi/10.1145/3580490
Lindemann LQin XDeshmukh JPappas GMitra SVenkatasubramanian NDubey AFeng LGhasemi MSprinkle J(2023)Conformal Prediction for STL Runtime VerificationProceedings of the ACM/IEEE 14th International Conference on Cyber-Physical Systems (with CPS-IoT Week 2023)10.1145/3576841.3585927(142-153)Online publication date: 9-May-2023
https://dl.acm.org/doi/10.1145/3576841.3585927
Chen YChang YKuo T(2023)DTC: A Drift-Tolerant Coding to Improve the Performance and Energy Efficiency of -Level-Cell Phase-Change MemoryIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2023.324156342:10(3185-3195)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1109/TCAD.2023.3241563
Chen YWu CChang YKuo T(2023)Energy Efficiency Enhancement of SCM-Based Systems: Write-Friendly CodingIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2022.320423142:5(1425-1437)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1109/TCAD.2022.3204231
Siddhu LNassar HBauer LHakert CHölscher NChen JHenkel J(2023)Swift-CNN: Leveraging PCM Memory’s Fast Write Mode to Accelerate CNNsIEEE Embedded Systems Letters10.1109/LES.2023.329874215:4(234-237)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1109/LES.2023.3298742
Chari PBa YZhou STalegaonkar CAthreya SKadambi A(2023)On Learning Mechanical Laws of Motion From Video Using Neural NetworksIEEE Access10.1109/ACCESS.2023.326040511(30129-30145)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3260405
Chen YChang YKuo T(2022)Drift-tolerant Coding to Enhance the Energy Efficiency of Multi-Level-Cell Phase-Change MemoryProceedings of the ACM/IEEE International Symposium on Low Power Electronics and Design10.1145/3531437.3539701(1-6)Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1145/3531437.3539701
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Figures

Tables

Media

View Issue’s Table of Contents