Casestudie Breakdown prediction Contell PILOT - Transumo

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Another group of mean values are the weighted and moving ones. A weighted arithmetic mean, for instance, can be used to calculate a correct mean temperature, if the underlying dataset contains different time ranges. It is also possible to assign a higher importance to newer values (e.g. current outliers). The moving arithmetic mean always calculates a mean value by using the same number of values. Typically, the newest values are taken. As long as monitoring data is saved within constant time ranges, this method allows a calculation of mean values for a defined time span, e.g. the last three hours. Furthermore, it is also possible to add weighting to this kind of mean. Up to now, the presented statistical values just analyzed an average behavior. It was not possible to get further information of outliers. Therefore, the standard deviation is needed. It describes the mean variation of data values and is calculated by using the Formula 5-3. ([Eckey02], p. 71) σ = ∑ ( X i n − X ) 2 Formula 5-3: The Standard Deviation Formula This measure offers quite a lot of information in combination with the arithmetic mean. A low standard deviation indicates only slight changes around the mean value. By contrast, a high standard deviation indicates greater changes. Section 5.10.1 describes a promising approach, how these just presented basic statistical measures can be used to improve the current situation of insufficient information. 5.4 Regression The general idea of regression is to describe a dataset of value pairs (x, y) by a functional model, as described in section 5.1 ([Gentle02], p. 301). Looking at time series data, regression tries to determine a functional model that describes the change of a value y over time x. Figure 5-1 pictures two examples of regression. 60
Figure 5-1: Two Samples of Regression ([Bourier03], p. 167) (adapted) 5.4.1 The Determination of Regression Functions A common approach to determine such a regression function is the method of least squares. This method is divided into three steps: ([Bourier03], p, 167) 1. The determination of general trend from a graphical visualization or knowledge 2. The assignment of this general trend to a mathematical type of function 3. The numerical determination of the function’s parameters The first two steps are normally trivial and have to be done as initialization part. The third step has to determine the function’s parameters the way, the function describes the developing of values best. To do that, the distance between determined regression function and all available values has to be minimal, which leads to the method of least squares in Formula 5-4. The square is necessary to avoid illegal results. 47 Min n ∑ i= 1 ( y − yˆ ) i i 2 with y = Occured value at time t = i i yˆ = Value of regression function at time t = i i Formula 5-4: Method of Least Squares Based on this method, a regression function can be determined for a given type of function. Often applied types are: ([Daßler95], p. 43) 47 See ([Bourier03], p. 168-169) for details 61
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Technische Universität Braunschwei
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4.4 Review of Current State of Rese
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Index of Tables Table 2-1: Error of
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1 Introduction 1.1 Initial Position
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2 Sensor Based Temperature Monitori
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compressor. They are served by a ce
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the specified value, it works very
Page 15 and 16: of this, over a hundred irregular p
Page 17 and 18: a centralized one. An isolated appl
Page 19 and 20: Figure 2-8: Lack of Information Pro
Page 21 and 22: Moreover, the fridge’s filling le
Page 23 and 24: store this kind of data but only of
Page 25 and 26: 3 Current Monitoring Systems The la
Page 27 and 28: device’s condition. Especially th
Page 29 and 30: a converter that is also available
Page 31 and 32: To indicate important events within
Page 33 and 34: 1. Display stored data in table for
Page 35 and 36: This way of visualizing data is the
Page 37 and 38: free text. Moreover it is possible
Page 39 and 40: dependent limit and delay settings,
Page 41 and 42: Aside from these functions, the kin
Page 43 and 44: 1. Temperature verification in retr
Page 45 and 46: alarms by the use of additionally a
Page 47 and 48: The third mentioned Centron Environ
Page 49 and 50: 4 Current State of Research As alre
Page 51 and 52: even this improvement is still face
Page 53 and 54: Another current approach is regress
Page 55 and 56: S o n 2 = ∑ Yi −Yi n −1 i= 2
Page 57 and 58: This algorithm returns an upper and
Page 59 and 60: • Critical values • Pre-warning
Page 61 and 62: 5 Possible and Promising Ways of Da
Page 63 and 64: could be: “The mean increase of a
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Page 69 and 70: 5.4.2 The Major Problems of Regress
Page 71 and 72: The next section will introduce tim
Page 73 and 74: explained in section 5.4. If such a
Page 75 and 76: pictured in Formula 5-12. Beside a
Page 77 and 78: P ( m) = P ( r ) ⋅ P ( m−r ) wi
Page 79 and 80: But the greatest problem is again t
Page 81 and 82: clustering as well as an analysis o
Page 83 and 84: The general idea of supervised lear
Page 85 and 86: sometimes data of a door opening se
Page 87 and 88: Beside the introduced notification
Page 89 and 90: A classification could be achieved
Page 91 and 92: Table 5-1: Estimated Improvements A
Page 93 and 94: As all these software products fail
Page 95 and 96: 6.2 Case Study The UMC St. Radboud
Page 97 and 98: Figure 6-3: Maximum Values at Dayti
Page 99 and 100: Figure 6-5: Minimum Values at Dayti
Page 101 and 102: Figure 6-9: Standard Deviation at D
Page 103 and 104: Table 6-3: Reported Notifications (
Page 105 and 106: Important for the determination of
Page 107 and 108: Remarkable is a comparison to the a
Page 109 and 110: Interviews with several employees f
Page 111 and 112: 7 Summary Cooling devices within me
Page 113 and 114: Bibliography Books and Articles: [B
Page 115 and 116: [Wittenberg98] Reinhard Wittenberg,
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Appendix 1 - Implementation of Inte
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%Name and location of the source fi
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Appendix 2 - Implementation of Stat
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dailydate = [dailydate; floor(date(
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%Count Dooropenings per Day dailydo
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xlswrite(strcat(path, 'Excel\', fil
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print('-dtiff', strcat(path, 'Graph
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ar([dailydate(1):dailydate(length(s
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Appendix 3 - Implementation of Data
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Duration = 0; maxtemp = 0; elseif (
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%Contains [Duration, Number of Occu
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disp(strcat('Dooropening
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