POSSIBILITY OF USE OF NEW S3C FUZZY LOGIC FOR IMPROVEMENT
OF BAROMETER CALIBRATION PROCEDURE
Mladen B. MILINKOVIC
Federal Hydrometeorological Institute of Yugoslavia,
Belgrade, Bircaninova 6, Yugoslavia
Phone: 645779, fax: 646369, e-mail:
Dr Dragan G. RADOJEVIC,
Institute "MIHAJLO PUPIN" Automation&Control Laboratory
Belgrade, Volgina 15,Yugoslavia
Phone: 772020, fax: 774265, e-mail:
1. Introduction
National Meteorological Laboratory (NML) has been formed and equipped within the Federal Hydrometeorological Institute of Yugoslavia, 50 years ago. NML disposes with set of standards for principal meteorological parameters such as atmospheric pressure, air temperature, humidity, wind and solar radiation.
Testing equipment has been improved following the development of meteorological instruments and applied measuring techniques through automation of calibration process using PC platforms [5].
This paper deals with data sets which has been achieved through complex procedure of national standard barometer calibration and transfer (tracebility) of measured values to barometer of lower class of accuracy. In this case measured uncertainty of the individual parameters and their mutual interaction are treated in a way more general then that of classical theory of probabilities.
The paper presents possibility of use of new fuzzy logic, which is the most general implementation of Syntactic Structured and Semantic Convex (S3C) logic.
2. General
It is well known that most accurate measurement of air pressure can only be achieved by use of mercury barometers, which may be produced in such precise way to function as “absolute” instruments. Barometers of other constructions or principle, in the sense of accuracy are treated as “relative” instruments, because in use have to be calibrate against mercury barometer. Digital barometers of new generation, have a very sophisticated construction and lot of incorporated improvements, but still having the same reasons in mind, have to be treated as relative instruments. Well known fact for barometers is that if temperature influence are not compensate or removed appropriately, during the measurement some systematic error in instrument readings will certainly occur and what is most important the amount will not be constant [8].
For quite a long time measurement of air pressure with mercury barometer was complicate and time consuming process, due to need that during the calibration and/or measurement all of necessary set of correction should be included . Use of aneroid barometers, are by the sake of lower precision give some relief, but was not lower number of different factors which may induce on measurement accuracy. Real improvement has been appearance of digital barometers of new generation, which are in turn because of improved performances today are wide used in AWS, but also in precise laboratory measurements. In the first glance, number of factors which influence on measured values are reduced, but in fact is not so.
Namely, only very limited number of measuring sites have enough number (at least 3) of digital barometer of high accuracy, so that values from national standard can be conserved by their intercomparision .
Outside the National Laboratory , most common case is that there are only a few of standard of lower category , which are periodically verified with measurement of national standard barometer by use of transfer standard [2].
Consequently , all measurement are “rounded” of fact how often and successfully are measured “true value” from national standard barometer and later on, from reference barometer on meteorological station.
It is well known that measured value of air pressure must include exact measurement of height of mercury column and temperature of barometer tube.
Mutual influence of other parameter of ambient in which intercomparation and/or measurement are done also have to be known and if it is possible controlled. In that sense it would be of great importance if mutually interference parameter can be quantified, and pondered in polinom function which define measured uncertainty (error) of each measurement.
3. Realization of complex measuring chains
Laboratory has large standard mercury barometer of R.Fuess type (system Wild-Pernet-Fuess) with readings improved by means of optical device (katetometer WILD HEERBRUGS KM 169), and Digital pressure gauge MENSOR DPG II as transfer standard. These two standards are intercompared before and after each calibration process. The testing and calibration of sensors is performed in special baro-chamber by connecting them to a special input in the acquisition unit. In Laboratory there are two improved baro-chambers, as well as a special baro-chamber which is used for calibration of all station mercury barometer types over full range (800 – 1070 hPa) by means of given programmed pressure values. When stabilized measuring conditions are achieved through measuring and regulation devices controlled by PC, the acquisition of valid data starts.
4. Description of instruments and design concept
In our National Meteorological Laboratory work with national standard barometer are done under standard strict procedure which are in more details given in literature.
Within the period of our regular periodical supervision (long-term tracebility) we also performed detailed measurement of indoor microclimate, by borrowed Indoor Climate Analyzer (ICA) Type 1213, manufactured by Bruel&Kjaer (Denmark). This is a precision instrument for measuring the individual physical parameters which influence the indoor climate. It measures air and surface temperatures, humidity, air velocity and radiant temperature asymmetry. Up to 60 measurement of each parameter can be store in a nonvolatile memory.
This measurement was of special interest for us because we were able to examine individual and mutual influence of mentioned parameter on measurement accuracy. Previously defined condition of “ideal measurement” was; air temperature 20oC, RH 30-40%, radiant temperature asymmetry not exceed 5oC, no vibration, outside wind from 0-1 m/sec, pressure tendency < 1 hPa/h.
Periodical verification of standard barometer by chance, have coincided with request to NML for calibration of new mercury station barometers (Theodor Friedric, type 5119 /3 psc/, tracebility to PTB) and digital barometers; (Digital Pressure Transducer SETRA 270 /2 psc/, and SETRA 470 /3 psc/ and Digital Pressure Gage SETRA 370 /9 psc/, tracebility to NIST) . We have used that favorable occasion to perform complex measurement session.
Schematic presentation of measuring chain for analysis of influence of measuring condition on barometer calibration are given on Fig. 1.
Combination of work on standard and barometers with simultaneous work on digital barometers, for two week, result in set of 840 measured values on which are adequate statistic for evaluation are applied [4] . Results was “calibration curves”.
For analysis of overall measured uncertainty (error), following parameters are concerned:
- rate of influence of air temperature on mercury column temperature;
- influence of air temperature on katetometar body temperature , (coefficient of scale distortion
are 0,0000085 mm/oC) ;
- precise measure of capillary depression and state of vacuum [3];
- possibilities of incorporation uncertainty of measurement of local g.
Note: All barometers are placed at same height with deviation <0.03m.
During the measurement following rules are applied:
- measurement was done by same person;
- measurement was done using the same procedure;
- monitoring of process and evaluation of data from standard and controlled instruments was done by use of our software.
Measurement was done by use of specially constructed baro chamber for station barometers (all type), which enable precise variation of air pressure in range of ± 100 hPa.
Digital barometer was calibrated in baro chamber and controlled with digital transfer barometer MENSOR DPG II (USA) in the range from 800 to 1100 hPa, with 10 hPa steps.
5. Data evaluation and error analysis
Classical approach are based on linearity and additivity of individual influence on measurement uncertainty.
However, in general case, relation between uncertainty and its influence are not linear, so new approach which has been applied aimed to analyze different influences and their interactions.
Some correlation has been established, i.e. under the consideration was influence of individual factor (which has been pondered as a result of long term investigation) and afterwards spectral probabilities was done which define ± 2s, in which have to be a “true value”.
Since, the probabilities are based on quite unprecise inclusion/elimination of possible events, those were used to introduce a conception of new fuzzy logic as a broader frame.
6. Summary
As a difference to classical statistic, logical statistic (based on new fuzzy logic) make possible testing of nonaditive causal-consequence relations. Nonaditivity, in this sense means that effect of more influences on uncertainty are not simple sum of individual ones. Therefore, uncertainty are treated as a function of cause interaction, and new approach identify the logic of cause influence to uncertainty.
The prototype of those software’s are developed in Institute "MIHAJLO PUPIN" Automation&Control Laboratory, and are based on MATLAB 6.1.
Application of fuzzy logic on results obtained by measurement, have sense in such circumstances, when measurement results are under influence of more parameter of physics, physique-chemical process, or combination of physical and electrical quantities etc.
By our opinion , those highly difficult problem in near future can be successfully solved by use of new fuzzy logic. When soon we would be able to followed with more confidence and automatically, all element which influence on air density during the operation in Wind tunnel, we expect that valuable results, with use of this fuzzy logic, will be obtained in border range of generated air speeds. Intensive work on that field are in progress.
We expect that application of new S3C fuzzy logic on data sets which has been achieved in calibration of other meteorological parameter would improved evaluation of calibration results in National Meteorological Laboratory of FHMI.
7. References
1. Barometers; OIML R 97; OIML International Recommendation, 1990
Organization Internationale de Metrologie Legale, France.
2. Guide to Meteorological Instruments and Methods of Observation; WMO-No.8 Sixth edition, WMO, Geneva , CH, 1996
3. Dr. K. Godecke; Die Kapillardepresion bei Hg-Barometern und Manometern. FREINWERKTECHNIK, 65, HAMBURG, 1961
4. Dr. J.P. van der Meulen; The WMO Automatic Digital Barometer Intercomparison, WMO/TD- No.474. Geneva, CH., 1992
5. Mladen B. MILINKOVIC; Dr.Dragan G. RADOJEVIC; New approach to the development of calibration procedures and decision support system realized in Yugoslavia – TECO-2000, Beijing, CHINA, 2000
6. Dr. Dragan. G. RADOJEVIC; [0,1]-valued logic: A natural generalization of Boolean logic, YUJOR- Yugoslav Journal of Operations Research, Belgrade, Yugoslavia, (2000), Vol. 10. No.2
7. Dr. Dragan G. RADOJEVIC; Syntactic Structured and Semantic Convex (S3C) logic&fuzzy sets;(to be published)
8. Strain SOKIC; Meteoroloski instrumenti, I deo. Savezni hidrometeoroloski zavod, Beograd, 1957
Acknowledgement
Author has a great privilege to have support in evaluation of methods in barometry from Mr. Strajin Sokic, our best expert in that field, WMO expert for instruments and founder of National Meteorological Laboratory. Unfortunately, he is not with us any more (he passed away in march this year, in age of 76). This is a irrecoverable loss for our service.
8. Appendix
Summary of main characteristic of Syntactic Structured and Semantic Convex (S3C) logic
This summary presents possibility of use of new fuzzy logic, which is the most general implementation of Syntactic Structured and Semantic Convex (S3C) logic. S3C logic consists of:
(a) Structured syntactic level, and
(b) Linear convex interpolation on semantic level.
In S3C logic on syntactic level, well-formulated logical formulae are structured (characterized) by logical ({0,1}-valued) set functions. Boolean algebra is defined on the set of all structures of nary well-formulated logic formulae with two binary and one unary logical operations for which all logical properties - tautologies of classical logic are satisfied (Idempotence, Commutativity, Associativity, Absorption, Distributivity, Universal bounds, Complementarity, Involution, Dualization). As a consequence the new structural functionality principle, are defined on syntactic level. The structural functionality principle says that the structure of a compound logical formula can be directly calculated on the basis of structures of component formulae. The structural functionality principle is fundamental logical principle and it is irrelevant of its semantic implementations: {0,1}-valued (classical) logic, multi-valued and/or [0,1]-valued logic - S3C fuzzy logic. Only in the case of classical logic the truth functionality principle is a direct consequence of the structural functionality principle and this is the reason why this principle is natural only for classical logic. Application of this principle should not take place in a general case; it is the main cause of problems in other many valued and/or fuzzy logic’s.
In S3C fuzzy logic, logical formula function is a linear convex interpolation of logical formula structure elements. Interpolation coefficients are basic logic functions, which depend on the truth-values of elementary logical formulae (atoms) - as variables; and on the chosen t-norm from the set of the feasible t-norms - as a parameter.
Contrary to others fuzzy logic’s, S3C fuzzy logic has all main properties of classical logic:
(a) All tautologies (and/or contradiction) of classical logic are tautologies (and/or contradiction) of S3C fuzzy logic (for example the basic logical laws apply: excluded middle and contradictions).
(b) Semantic equivalent logical expressions in the classical logic are equivalent in S3C fuzzy logic too.
(c) The choice of the basic logical operators (the basic set of logical operators by means of which all other operators are constructed) is irrelevant in S3C fuzzy logic as in the classical logic.
(d) The number of semantically different logical formulae in S3C fuzzy logic depends only on the number of logical variables (i. e., the number of possible truth values is irrelevant for the number of possible semantic different formulae).
(e) Classical deduction and completeness theorems apply.