Casestudie Breakdown prediction Contell PILOT - Transumo

More documents

Recommendations

Info

1. y ˆ = ax + b (Linear function) 2. 3. 4. b y ˆ = ax (Exponential function) bx y ˆ = ae (Euler function) a yˆ = (Hyperbola) x + b 5. y ˆ = aln( x) + b (Logarithmic function) The assumption of a linear trend leads to the usage of y ˆ = ax + b as regression function. An appliance to the method of least squares leads to Formula 5-5: Min n ∑ i= 1 ( y − b − i ax i ) 2 Formula 5-5: Method of Least Squares for an Assumed Linear Trend To determine the parameters a and b it is necessary to partially differentiate Formula 5-5 to these parameters. Afterwards, these equations have to be solved to a and b. Performing these two steps leads to the following optimal linear regression Formula 5-6: ([Bourier03], p, 169-171) yˆ = ax + b with a = ∑ ∑ b = y − ax x y − nxy i i 2 xi − nx Formula 5-6: Regression Function for Describing Linear Trend 2 Other types of functions, like the mentioned one above, can also be used for regression purposes. The general idea stays the same, only the calculation steps vary with different functions. As other types of regression are not of interest within this diploma thesis, 48 they will not be regarded here. 49 48 See section 5.10.2 for details 49 More details can be found (e.g. [Eckey02], p. 171-184; [Bourier03], p. 172-179) 62
5.4.2 The Major Problems of Regression Up to now, this section just introduced the approach of regression. The last part of this section will now review its two major problems: ([Eckey02], p. 179) • An incorrect chosen type of function leads to unacceptable results • Significant outliers influence the determination of a regression function The first problem can be solved partly by trying several types of functions. Afterwards, the best result can be selected. This is especially useful in cases of automated regression, where the general type of function may change. Problematic is the appliance of regression to purely random data, because a selection of a certain type of function might be impossible. The second problem could even be worse, because a correct type of function might lead to significant incorrect results, due to an influence of outliers. The two following figures exemplify this. Both, Figure 5-2 and Figure 5-3 contain a linear trend. But the obtained regression function for the first dataset is significantly wrong due to a single outlier. Figure 5-2: Incorrect Regression Function due to an Outlier ([Eckey02], p. 180) (adapted) Figure 5-3: Correct Regression Function ([Eckey02], p.180) (adapted) 63
Page 1 and 2:
Technische Universität Braunschwei
Page 3 and 4:
4.4 Review of Current State of Rese
Page 5 and 6:
Index of Tables Table 2-1: Error of
Page 7 and 8:
1 Introduction 1.1 Initial Position
Page 9 and 10:
2 Sensor Based Temperature Monitori
Page 11 and 12:
compressor. They are served by a ce
Page 13 and 14:
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
Page 65 and 66: The mode is the most frequent value
Page 67: Figure 5-1: Two Samples of Regressi
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,
Page 117 and 118: Appendix 1 - Implementation of Inte
Page 119 and 120:
%Name and location of the source fi
Page 121 and 122:
Appendix 2 - Implementation of Stat
Page 123 and 124:
dailydate = [dailydate; floor(date(
Page 125 and 126:
%Count Dooropenings per Day dailydo
Page 127 and 128:
xlswrite(strcat(path, 'Excel\', fil
Page 129 and 130:
print('-dtiff', strcat(path, 'Graph
Page 131 and 132:
ar([dailydate(1):dailydate(length(s
Page 133 and 134:
Appendix 3 - Implementation of Data
Page 135 and 136:
Duration = 0; maxtemp = 0; elseif (
Page 137 and 138:
%Contains [Duration, Number of Occu
Page 139 and 140:
disp(strcat('Dooropening
show all

Casestudie Breakdown prediction Contell PILOT - Transumo

Create successful ePaper yourself

Delete template?

Save as template?