Measurement plus Observation A Modern Metrological Structure

Transcription

1 e a s u r e m en etrology Measurement plus Observation A Modern Metrological Structure t S ci e n c e Karl H. Ruhm Institute of Machine Tools and Manufacturing (IWF), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland ruhm@ethz.ch a n d T ec XXI IMEKO World Congress Measurement in Research and Industry August 30 September 04, 2015, Prague, Czech Republic h n o l o g y ETH Version 00;

2 XXI IMEKO World Congress 2015, Prague Measurement in Research and Industry Measurement plus Observation!? A Modern Metrological Structure ETH 02

3 ? Measurement?? Mba KNOWLEDGE BASE ETH 03

4 Observation as part of Metrology and as a complement to Measurement. ETH 04

5 We consider Structural Aspects, no Mathematical Specialities. ETH 05

6 Measurement? Observation Diversity? Similarity? Identity? Complement? ETH 06

7 We use Measurement Instruments, do we have Observation Instruments too? Yes or No? ETH 07

8 We experience related terms Measurement Equation / Observation Equation Measurement Error / Observation Error Measurement Loading / Observation Loading Measurability / Observability ETH and so on. 08

9 We declare Measurement Uncertainties, do we have to consider Observation Uncertainties too? Yes or No? ETH 09

10 We teach Measurement Science and Technology, but where is Observation Science and Technology? ETH 10

11 Definitively, the goal of Measurement and of Observation as well, is ETH Information Acquisition! 11

12 Under which circumstances does Observation rely on natural and / or technological sensory results? ETH 12

13 Is it possible to systematically approach a consistent complement "Measurement plus Observation" ETH? 13

14 Is METROLOGY "Measurement plus Observation" ETH? 14

15 Question upon Question ETH 15

16 Maybe, a complement between Measurement and Observation becomes feasible, if we courageously avoid certain terminological obstacles. Let s Try ETH for the benefit of simplicity and clarity! 16

17 We look for consistent definitions on a mathematical basis; no everyday jargon! ETH 17

18 Anticipating Result: YES, a complement is possible. We will notice that Observation is a self-contained part of Metrology ETH 18

19 Measurement plus Observation Content 0 Introduction Questions 1 Description of Processes Properties and Behaviour 2 Measurement and Observation Structures 3 Conclusion Answers, Invitation! ETH 18

20 1 Description of Processes Properties and Behaviour ETH 20

21 We talk about Processes like economic processes production processes electronic circuit processes neurophysiological processes social processes war and peace processes and so on, including Measurement and Observation Processes ETH 21

22 Processes enable Procedures like production and assembly acquisition and collection operation and maintenance processing and calculation reconstruction and inference estimation and prediction evaluation and documentation and so on, including Measurement and Observation Procedures ETH 22

23 Goal We want to measure and observe Processes and Procedures as well. Prerequisites? We need models of the processes involved, models of quantities in and around these processes, skills concerning the tools to be used. ETH 23

24 Models We use abstract descriptions of real processes: A mathematical model of a process describes relations between designated quantities. A process may be multivariable (MIMO), linear, time invariant (LTI), dynamic. Here we only consider input signals u(t), state (inner) signals x(t), output signals y(t) with the corresponding relation y(t) = f(x(t), u(t)). ETH 24

25 Tools Signal and System Theory for the provision of consistent theoretical tools Model Theory for the description of all sorts of processes Error Theory for the improvement of process performances Uncertainty Theory for the trustability of procedure results ETH 25

26 Models On the level of Signal and System Theory we often want to arrive at specified Canonical Structures. Most useful are the structures of the State Space Description (SSD). The basic set of equations is given in vector-matrix-form by: x (t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) Signal Relation Diagram (SRD) ETH as an abstract model of the real process 26

27 State Space Description (SSD) is universally valid for many processes of interest, therefore also for the measurement process, for the observation process, and for all auxiliary processes. x (t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) Signal Relation Diagram (SRD) ETH as an abstract model of the real process 27

28 We will use the State Space Description (SSD) for the following investigations x (t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) Signal Relation Diagram (SRD) ETH as an abstract model of the real process P 28

29 The State Space Description (SSD) provides: - description - relations between quantities - structure and properties - behaviour of each process, we are talking about. x (t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) ETH 29

30 Properties of process P are given by the parameters of the matrices A, B, C, D. Behaviour of process P is given by the solutions of the differential equations for specified input quantities u(t). A(t) t A(t τ) 0 y(t) = Ce x(0) + C e Bu( τ)d τ+ Du(t) Note Mathematical models do not provide any hardware descriptions of process P whatsoever. ETH 30

31 2 Measurement and Observation Structures ETH 31

32 Measurement and Observation Procedures deliver information concerning Process P. But how? And what marks the differences? ETH 32

33 Classical Measurement Structure ETH 33

34 A multivariable, dynamic measurement process M, interconnected with the multivariable, dynamic process P, interactively acquires specified, time-dependent, measurable quantities. ETH 34

35 A dynamic measurement process M always consists of a Dynamic Sensor Process S and a Dynamic Reconstruction Process R. ETH 35

36 This concept is (in principle) true also for natural sensory processes (receptors), including the multitude of methods of perception in brain and brain-like processes. ETH 36

37 Unfortunately, not all specified quantities in and around process P are measurable by measurement process M. A model-based dynamic Observation Process O must step into the breach. ETH 37

38 A Dynamic Observation Process O depends on a Model of Process P and on a certain amount of Sensory Data (natural, technological) concerning process P. Observation uses them by producing model-based additional Information about the Process. ETH 38

39 There are Four Types of Observation Processes O - Simulating Observation Process SO - Open-Loop Observation Process OLO - Reconstructing Observation Process RO - Closed-Loop Observation Process CLO ETH 39

40 Assumption 1 No sensory data about process P is available! Oh! Without information no observation procedure? Trick We feed anticipated input data u(t) of process P to the observation process O, which is the model of the process. This results in the extremely important offline Simulating Observation Process SO ETH 40

41 No sensory data about process P is available! Given: Anticipated information about input quantities u(t) of process P Requested: Information about state quantities x(t) and / or output quantities y(t) Simulating Observer Process SO ETH 41

42 Simulation Observation Process Example Simulation of the Temperature Distribution on a Brake Disk. ETH 42

43 Assumption 2: Given: Information about input quantities u(t) of process P, available by measurement. Requested: Information about state quantities x(t) and / or output quantities y(t) Open-Loop Observer Process OLO ETH 43

44 Example Open-Loop Observer OLO for the Determination of the Heat Consumption within a Process P Open-Loop Observer Process OLO ETH 44

45 Assumption 3: Given: Information about output quantities y(t) of process P, available by measurement. Requested: Information about state quantities x(t) Reconstructing Observer Process RO ETH 45

46 Example Reconstructing Observer Process RO for the Determination of the input quantities u S (t) of a Sensor Process S A reconstruction process R is a reconstructing observation process RO ETH 46

47 Assumption 4: Given: Information about input quantities u(t) and output quantities y(t) of process P, available by measurement. Requested: Information about state quantities x(t) Closed Loop Observer Process CLO ETH 47

48 Closed Loop Observer Process CLO ETH 48

49 Recapitulation Four Types of Observation Processes O - Simulating Observation Process SO no sensory data available - Open-Loop Observation Process OLO only input sensory data available - Reconstructing Observation Process RO only output sensory data available - Closed-Loop Observation Process CLO input and output sensory data available Rather Simple! ETH 49

50 Observation Process What else do we have concerning Terminology? ETH 50

51 "Observation Canonical Structure" Given: Arbitrary process model. Requested: Observation canonical structure of the process model. The observation canonical structure of a process model is useful for an easier design of an observation process. From any arbitrary process model we get an observation canonical structure via a Similarity Transform Procedure. ETH 51

52 "Observability" Given: - Process model and - Output quantities y(t), specified and available by sensory procedures. Question: - Which state (inner) quantities x(t) can be observed (inferred, reconstructed) model-based by given output quantities y(t)? ETH 52

53 Testing the Process Property Observability delivers a structural and parametric property of the model of a dynamic process of interest, indicating, whether the state (inner) quantities x(t) of this process can be observed (not measured! ). ETH 53

54 Question: When is a process model observable? There is an observability criterion in form of an Observability Matrix Q obs, which considers structure and parameters of System Matrices A and C. rank{ Q } = (N) obs 0 CA 1 CA n 1 Qobs = CA N 2 CA N 1 ETH CA 54 with!

55 Observability If a system is not observable, this property can be changed by an appropriate choice of measurement quantities and / or of additional sensors. Sometimes the selection of alternative sensor locations may help. ETH 55

56 3 Conclusion Answers, Invitation! ETH 56

57 Observation is model-based detection, determination, estimation, calculation, assessment, evaluation, identification, quantification of specified, real and abstract quantities, however based on external natural and technological sensory data. ETH 57

58 Future Fascination: Measurement plus Observation This point of view is quite new. Mba KNOWLEDGE BASE 57

59 We have Measurement Devices (sensors, sensory receptors, and so on) and we have Observation Devices (computers, processors, calculators, and so on) ETH 59

60 The presented Observation Structures are designed for multivariate (MIMO), linear, time invariant (LTI) dynamic systems. The fundament is Signal and System Theory. ETH 60

61 We consider Measurement Errors and Uncertainties, and, in addition, we have to consider Observation Errors and Uncertainties. ETH 61

62 We experience related terms Measurement Equation / Observation Equation Measurement Error / Observation Error Measurement Loading / Observation Loading Measurability / Observability ETH This is correct indeed! 62

63 We have Measurement Science and Technology, and we have Observation Science and Technology! ETH 63

64 Observation Processes depend on external natural and / or technological sensory data, they are mere signal processing processes ETH 64

65 We claim that Observation and Measurement, are self-contained and equivalent parts of Metrology ETH 65

66 In practice, many metrological structures unintentionally contain Observation Processes. ETH 66

67 The presented definitions and terms concerning observation base all on mathematical analysis; no everyday jargon! ETH 67

68 Dear Friends of Measurement join the ETH Friends of Observation within Metrology! 68