Mean Integrated Absolute Error
Contents |
not to be an easy question to answer! There are, in fact, many different measures which can be used to compare the quality of controlled responses. Academic measures mean absolute error formula The term 'academic' is not intended to be pejorative (especially since I am mean absolute error excel one!). The control measures describe in this section are very precise and give exact comparisons between different control schemes,
Mean Absolute Error Vs Mean Squared Error
or different sets of tuning parameters, and are widely used in academic journal papers and simulation studies. They are also completely useless for measuring the performance of real control systems. The
Mean Absolute Error Example
three commonly used measures are Integral Squared Error (ISE), Integral Absolute Error (IAE) and Integral Time-weighted Absolute Error (ITAE), and are defined as: All the measures require a fixed experiment to be performed on the system (i.e. a fixed setpoint or disturbance change) and the integrals are evaluated over a fixed time period (in theory to infinity, but usually until a time long mean absolute error interpretation enough for the responses to settle). ISE integrates the square of the error over time. ISE will penalise large errors more than smaller ones (since the square of a large error will be much bigger). Control systems specified to minimise ISE will tend to eliminate large errors quickly, but will tolerate small errors persisting for a long period of time. Often this leads to fast responses, but with considerable, low amplitude, oscillation. IAE integrates the absolute error over time. It doesn't add weight to any of the errors in a systems response. It tends to produce slower response than ISE optimal systems, but usually with less sustained oscillation. ITAE integrates the absolute error multiplied by the time over time. What this does is to weight errors which exist after a long time much more heavily than those at the start of the response. ITAE tuning produces systems which settle much more quickly than the other two tuning methods. The downside of this is that ITAE tuning also produces systems with sluggish initial response (necessary to avoid sustained oscillation). A VisSim model with a PI controlled tuned to optimise
from GoogleSign inHidden fieldsBooksbooks.google.com - The existence of high speed, inexpensive computing has made it easy to look at data in ways that were once impossible. Where
Mean Relative Error
once a data analyst was forced to make restrictive mean absolute error range assumptions before beginning, the power of the computer now allows great freedom in deciding mean absolute error weka where an analysis should go. One...https://books.google.com/books/about/Smoothing_Methods_in_Statistics.html?id=wFTgNXL4feIC&utm_source=gb-gplus-shareSmoothing Methods in StatisticsMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableSpringer ShopAmazon.comBarnes&Noble.com - $141.33 and upBooks-A-MillionIndieBoundFind in a http://www.online-courses.vissim.us/Strathclyde/measures_of_controlled_system_pe.htm libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Smoothing Methods in StatisticsJeffrey S. SimonoffSpringer Science & Business Media, Jun 6, 1996 - Mathematics - 338 pages 1 Reviewhttps://books.google.com/books/about/Smoothing_Methods_in_Statistics.html?id=wFTgNXL4feICThe https://books.google.com/books?id=wFTgNXL4feIC&pg=PA35&lpg=PA35&dq=mean+integrated+absolute+error&source=bl&ots=1uZnFZjlgY&sig=ePGFaRDZn-0s7hFZyClmjj3w0II&hl=en&sa=X&ved=0ahUKEwiZ7I6B5uHPAhVKyoMKHUwBC4YQ6AEIMjAD existence of high speed, inexpensive computing has made it easy to look at data in ways that were once impossible. Where once a data analyst was forced to make restrictive assumptions before beginning, the power of the computer now allows great freedom in deciding where an analysis should go. One area that has benefited greatly from this new freedom is that of non parametric density, distribution, and regression function estimation, or what are generally called smoothing methods. Most people are familiar with some smoothing methods (such as the histogram) but are unlikely to know about more recent developments that could be useful to them. If a group of experts on statistical smoothing methods are put in a room, two things are likely to happen. First, they will agree that data analysts seriously underappreciate smoothing methods. Smoothing meth ods
̄ m ( u ) = φ ̃ m ( u ) /λ m , m = 0 , 1 , . . . , 6. The range of values of ( c, δ ) is rectan- gular [0 . 8 , 2 . http://www.researchgate.net/figure/242928388_fig2_Figure-2-The-mean-integrated-absolute-error-versus--0-and--6--n--40. 2] × [1 / 30 , 1 / 3]. Figure 1 plots the error I n,m versus https://books.google.com/books?id=_LvgBwAAQBAJ&pg=PA418&lpg=PA418&dq=mean+integrated+absolute+error&source=bl&ots=LArwDiXTvk&sig=nMtFSrwsUI4565Sx7EufpTwMeOs&hl=en&sa=X&ved=0ahUKEwiZ7I6B5uHPAhVKyoMKHUwBC4YQ6AEIVDAJ n for m = 0 , 2 , 6. Apparently, the best rate is observed for m = 2, i.e., for λ 2 = 1. The latter agrees with conclusions obtained in § 6. Moreover, let us observe that the measured rate for m = 2 is better than n − 2 / 5 . In order to gain further insight into the dependence between the estimate performance absolute error and the dynamical-subsystem order, the second experiment was made. Here the number of input-output data was fixed at n = 40. Figure 2 displays the error versus the number a . That number equals λ 6 for m = 6 and λ 0 for m = 0. The values of a were chosen from ( − 2 , 0 . 1) ∪ (0 . 1 , 2). The result shows the strong dependence of the estimate quality on the impulse response of the dynamical subsystem. mean absolute error Moreover, it is seen that I n, 0 > I n, 6 , i.e., the higher order impulse response values should be preferable. The third class of experiments was concerned with the problem of selection of the bandwidth (see § 7). Let the Hammerstein model be of the formGo to publicationJoin ResearchGate to access over 30 millionfigures and 100+ million publications – all in one place.Join for freeGo to publicationDownloadCopy referenceCopy captionEmbed figurePublished in Cascade non-linear system identification by a non-parametric method Full-text Article · Jan 1994 · International Journal of Systems Science WLODZIMIERZ GREBLICKI MIROSLAW PAWLAK Citations "...ndependent of for any time instants and such that , it holds that . Using the results presented in [9] , concerning dependence between input-output cross-correlation in Hammerstein system and the terms ..."Since is zero-mean and is independent of for any time instants and such that , it holds that . Using the results presented in [9] , concerning dependence between input-output cross-correlation in Hammerstein system and the terms of impulse response we have , where , and hence where , , and . . . . . . Expand Text Nonlinearity Recovering in Hammerstein System from Short Measurement Sequence [Show abstract] [Hide abstract] ABSTRACT: The problem of data pre-filtering for nonparametric identification of Hammerstein system from short (finite) data set is considered. The two-stage method is proposed. First, the linear dynamic block is identified using instrumental variables technique, and the inverse of the obtained model is used for output filtering. Next, the standard
from GoogleSign inHidden fieldsBooksbooks.google.com - In recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally...https://books.google.com/books/about/Elements_of_Computational_Statistics.html?id=_LvgBwAAQBAJ&utm_source=gb-gplus-shareElements of Computational StatisticsMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableSpringer ShopAmazon.comBarnes&Noble.comBooks-A-MillionIndieBoundFind in a libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Elements of Computational StatisticsJames E. GentleSpringer Science & Business Media, Apr 18, 2006 - Computers - 420 pages 0 Reviewshttps://books.google.com/books/about/Elements_of_Computational_Statistics.html?id=_LvgBwAAQBAJIn recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally intensive, eitherbecausetheyrequireverylargenumbersofnumericalcompu- tions or because they depend on visualization of many projections of the data. The class of statistical methods characterized by computational intensity and the supporting theory for such methods constitute a discipline called “com- tational statistics”. (Here, I am following Wegman, 1988, and distinguishing “computationalstatistics”from“statisticalcomputing”, whichwetaketomean “computational methods, including numerical analysis, for statisticians”.) The computationally-intensive methods of modern statistics rely