Background technology
In the coal-fired station of China, ball mill pulverizing system is used very extensive, as the coal pulverizer of key equipment wherein, the overwhelming majority still runs on artificial judgement and manual reset condition, coal pulverizer chute blockage, overtemperature, race powder, leaks out, owes phenomenons such as coal and happen occasionally in running, sometimes even cause the device damage accident, cause unit outage, bring very big economic loss to power plant.The more important thing is that coal pulverizer is the power consumption rich and influential family of power plant, its power consumption accounts for about 20% of station service, because coal pulverizer still adopts manually operated means at present, coal pulverizer can't operate under the optimum condition always, and it is big with electric consumption to make power plant, deficiency in economic performance.
The power consumption of pulverized coal preparation system is mainly from coal pulverizer and mill exhauster, and that an important feature of coal pulverizer is its operation power consumption and the relation of its load (coal pulverizer in coal load quantity) is little, the difference of general no-load power and peak power can not surpass 15% of rated power, the meeting that has is lower, and this is to rotate simplified and the lifting steel ball because coal pulverizer power mainly is consumed in.The electrical energy consumption of ventilation that is used for powder process is also little with the relation of exerting oneself, and maximum effect can not surpass 8%.Therefore, to the optimization of pulverized coal preparation system, be exactly under the situation of certain power consumption, improve the power efficiency of coal pulverizer as far as possible.
The automaticity of external thermal power plant pulverized coal preparation system is higher, Computer Control Technology has also obtained general use, but the many employings of external power plant is the medium-speed pulverizer unit pulverized-coal system, different with the ball mill pulverizing system structure of domestic extensive employing, can't indiscriminately imitate.
The automaton of coal pulverizer has been adopted in domestic also some thermal power plant, except that the hardware selection is upward uneven, also is not quite similar on control strategy and control algolithm.Domestic present automatic control major part for pulverized coal preparation system serves as that the control target is regulated coal-supplying amount with coal load quantity in the coal pulverizer only, we know, the size of the powder process amount (promptly exerting oneself) of pulverized coal preparation system is ground exerts oneself, drying is exerted oneself and is ventilated three's the restriction of exerting oneself, implemented control if only the automatic adjusting of coal-supplying amount is just exerted oneself to its coal-grinding, and other two exert oneself still manually to operate, though on control algolithm, domestic some advanced control algolithms that also adopted, but because it is that manual engagement is regulated automatically, make and on structure, just be in a kind of automanual state, and three are not exerted oneself and optimize simultaneously, finally cause on the result of use also unsatisfactory.
The problem that exists at single loop, the research to the multiloop control of pulverized coal preparation system has at present also had significant progress, and so-called multiloop promptly is to be the control target to improve that coal-grinding is exerted oneself, drying is exerted oneself and ventilation is exerted oneself, the aperture of regulating coal-supplying amount and air door.Relevant control input quantity is interior coal load quantity, outlet temperature and entrance negative pressure, and the control output quantity then is coal-supplying amount, hot blast door aperture and recirculation air door aperture (or cold-air flap aperture).Aspect multiloop control, the employing that has be classical pid algorithm, this algorithm is to control coal-supplying amount, control the hot blast door and control according to entrance negative pressure according to outlet temperature according to interior coal load quantity, see it is that three loops are independently controlled from structure, this pattern makes the controller simplicity of design, is easy to realize.But the parameter in later stage is regulated, and needs are set 3 cover pid parameters but also will be worked in coordination, and this has just become a difficult point.In addition, because a main feature of pulverized coal preparation system is exactly its close coupling, control is independently implemented in three loops, this method not only lacks reliable theoretical foundation but also also can't fundamentally solve coupled problem in practice.Employing PREDICTIVE CONTROL that has or decoupling zero control algolithm, but this class control need be known the control mathematics model, and pulverized coal preparation system is nonlinear complication system, its precise math model is difficult to obtain, and therefore makes this class algorithm be not suitable for applying.Neutral net not too relies on the control mathematics model, but, because the algorithm of neutral net class all needs a training set and its training process more loaded down with trivial details, and pulverized coal preparation system has certain requirement on the real-time of control, makes neutral net be subjected to many restrictions in actual promotion and application.Fuzzy control does not need to control the model of object yet, and its control law is to be based upon on specialty and operator's the knowledge and experience, no matter make its simple possible all in design or the enforcement.But also can't directly use for the FUZZY ALGORITHMS FOR CONTROL that this mimo system is common, and the combination of a plurality of fuzzy controllers then can cause control algolithm too complicated.Therefore simultaneously, this class algorithm all is to belong to definite value to control this class, promptly allows to guarantee the stable operation of coal pulverizer, but can't make coal pulverizer operate in EIAJ point near, thereby do not reach energy-conservation effect.
The specific embodiment
Referring to Fig. 1, the moving law of coal pulverizer can reflect intuitively by its characteristic working curve.From figure curve 2 as can be seen an a matter of great account be in fact, not dull increase of exerting oneself of coal pulverizer along with the increase of coal load quantity in it, the power of coal pulverizer neither dullness increase along with the increase of coal load quantity in it, therefore coal pulverizer is in running, exert oneself and coal load quantity between exist extremum characteristic really.
Heat-engine plant steel ball coal-grinding coal-grinding machine powder-making system automatic control method, employing be a kind of double-layer control structure, what the upper strata was that adaptive searching optimal algorithm and lower floor adopt is the multidimensional FUZZY ALGORITHMS FOR CONTROL, specifically controls block diagram and sees accompanying drawing 2.The upper strata adaptive searching optimal algorithm changes the setting value of coal load quantity, coal pulverizer outlet temperature value and coal pulverizer entrance negative pressure in the coal pulverizer simultaneously, lower floor controls according to these three setting values, after treating that three amounts reach setting value, get the measurement period of a period of time, calculate present pulverizer capacity composite evaluation function as adaptive searching optimal algorithm.The variation of the composite evaluation function of relatively exerting oneself, determine whether more excellent, and the decision change of three setting values next time, concrete control algolithm flow process is seen accompanying drawing 3.Lower floor uses the multidimensional FUZZY ALGORITHMS FOR CONTROL, with the deviation of the deviation of the deviation of coal load quantity in the coal pulverizer, coal pulverizer outlet temperature and coal pulverizer entrance negative pressure as input quantity and output variable is coal-supplying amount, hot blast door aperture and recirculation air door aperture (or cold-air flap aperture).The domain of the linguistic variable of each variable correspondence is all selected [2 ,-1,0,1,2 ,], and the language value is all selected [NB, NS, ZO, PS, PB], and representative is negative big, negative little, zero, just little, honest respectively.Fuzzy rule is set up according to expert's knowledge and technology personnel's experience, so this multidimensional FUZZY ALGORITHMS FOR CONTROL, and it is also very strong not only can to solve coupling serious problem but also its robustness.
Because collective and distributive type control system (being DCS) is the control scheme of the present main separation of thermal power plant, so adopt DCS to realize control method of the present invention, various automation functions such as signals collecting and preliminary treatment, multidimensional FUZZY ALGORITHMS FOR CONTROL and adaptive searching optimal algorithm can be become a unified system.In addition, the pulverized coal preparation system of domestic most of power plant is the pulverized coal carried by hot air system, so instantiation is an object with the pulverized coal carried by hot air system just, and for the system of transporting pulverized coal with exhaust gas, only needs to replace the recirculation air door get final product as the control output quantity with cold-air flap.
The independently developed digital multifunctional mill load of applicant monitor is adopted in the detection of material stock amount in the ball mill.The structure of this digital multifunctional mill load monitor as shown in Figure 4, its circuit part comprises: being used to provides ± 15V, ± 5V ,+voltage reference circuit 15 of the power module 8 of 3.3V output, be used to provide+2.5V reference voltage, also include current signal 1, sound transducer 2, Signal Matching device 3, traffic filter 4, RMS-DC converter 5, AD converter 6, microcontroller 7, LCD display circuit 9, communicating circuit 10, parameter storage 11, DA converter 12, voltage and current converter 13 and system monitoring circuit 14;
The output of the two-way noise signal that sound transducer 2 is gathered links to each other with the input of Signal Matching circuit 3, the output of Signal Matching device 3 links to each other with the input of traffic filter 4, the output of traffic filter 4 links to each other with the input of RMS-DC converter 5, the output of RMS-DC converter 5 links to each other with the input of AD converter 6, the output of current signal 1 also links to each other with the input of AD conversion 6, voltage reference circuit 15 output+the 2.5V reference power source links to each other with the reference source input of AD converter 6 and DA converter 12, LCD display module 9 links to each other with microcontroller 7, RS485 communication module 10 links to each other with microcontroller 7, parameter storage 11 links to each other with microcontroller 7, DA converter 12 links to each other with microcontroller 7, the output of DA converter 12 links to each other with voltage and current converter (UI converter) 13, and system monitoring circuit 14 links to each other with microcontroller 7;
Power circuit 8 is input as+24V, is output as+15V-15V ,+5V ,-5V ,+3.3V.
With reference to shown in Figure 5, the signal input of sound transducer 2 comprises 2 road voice signals, wherein one the tunnel is the grinding machine noise, one the tunnel is background noise, AD620 in-phase input end in the two-way voice signal difference entering signal adaptation 3 is adjusted multiplication factor by potentiometer RG1, and the signal after AD620 amplification and impedance matching is input among the traffic filter MAX267, MAX267 is integrated 4 rank bandpass filters, can set centre frequency fo and quality factor q by digital port.Be input to the RMS-DC converter through the useful frequency band signals behind the bandpass filtering, this converter adopts AD637 to realize, input exchange signal can be calculated and convert virtual value to, with dc signaling output, for the AD sampling.The grinding machine current input signal is 4~20mA, after process resistance converts 0.5~2.5V voltage signal to, is input to the AD sampling and obtains current value.Voltage Reference employing+the 2.5V of AD conversion and DA converter is provided by MAX6102 in the system, and this voltage reference circuit is a three terminal device, and input+5V is output as+2.5V.
The supervisory circuit of system and parameter storage adopt X5043 to realize, the EEPROM of 4kb is arranged in it, are used for storing various parameters.All parameters all can be convenient to instrument and be adjusted by adorning under the upper machine communication mode.
Monitoring chip X5043 monitors system's operation and power supply situation, guarantees the reliable and stable operation of instrument; Under the situation of system in case of system halt, can reset rapidly, make instrument rework.The interface of it and microcontroller is 4 line system SPI interfaces, wherein/CS is a sheet choosing end, and SCK is the clock end, and SI is a data input pin, and SO is a data output end; X5043 is powering on and house dog time when overflowing, in/RST end output low level reset signal, this signal and microcontroller /RESET holds and links to each other.The display of system adopts the SMS0801 section-type LCD to realize, adopts the Serial Control mode between this lcd controller and the microcontroller, and wherein CLK is the clock end, and DI is a data terminal.The communicating circuit of system adopts MAX3485 to realize, adopts half-duplex mode, and it links to each other with microcontroller UART asynchronous communication mouth, wherein RXD is a data receiver, and TXD is a data sending terminal, and RTC is the transmitting-receiving control end, being the transmission state when RTC=1, is accepting state during RTC=0.The voltage output of system adopts the integrated DA converter of microcontroller to realize that output signal range is 0~2.5V, and as voltage way of output signal, this signal was input to the input of XTR110 simultaneously, is converted to 4~20mA electric current after process AD620 amplified 2 times.
With reference to shown in Figure 6, signal VIN process resistance R 5 is input to the amplifier input 4 among the filtering chip MAX267, contain two second-order bandpass filters among the MAX267, inner amplifier output feeds back to input 4 by resistance R 6, the signal input part 5 of first bandpass filter is received in output simultaneously, bandpass signal output 2 connects the input 1 of second bandpass filter, and output 24 feeds back to amplifier input 4 by resistance R 7, capacitor C 4.The clock of bandpass filter obtains by crystal Y1, and crystal Y1 two ends connect 11 ends of MAX267 and 12 ends, 18 ends respectively.Centre frequency fo is by F0~F4 totally 5 input adjustment, and these 5 terminals link to each other with toggle switch; Quality factor q is by Q0~Q6 totally 7 input adjustment, and these 7 terminals link to each other with toggle switch.The output signal BPB of bandpass filter links to each other with 13 ends of AD637 through behind the capacitance, and constant average time of AD637 realizes that by average capacitance C7 this electric capacity one end is connected with 8 ends of AD637, and the other end links to each other with 9 ends with 6 ends of AD637.Resistance R 8, C5, R9, the buffer among C10 and the AD637 constitutes wave filter, can effectively eliminate the ripple in the output signal.
With reference to shown in Figure 7, the DAC output signal is 0~2.5V, and this signal links to each other with No. 3 ends of AD620, and after 2 times of AD620 amplifications, signal becomes 0~5V; Its multiplication factor is adjusted by potentiometer RG3.Because signal does not need direct current biasing, so the reference input REF ground connection of AD620.The signal output part 6 of AD620 is connected to the input 5 of voltage/current modular converter XTR110 simultaneously as the voltage output of instrument, and this termination is subjected to 0~5V signal.3 ends of XTR110 link to each other with 12 ends, 15 ends, and the accurate power supply of Nei Bu 10V can provide voltage bias for circuit like this.14 ends of XTR110 and the G of MOSFET end links to each other, links to each other with the S end of MOSFET behind 1 end of XTR110 and the 13 end short circuits, and the D of XTR110 holds and provides electric current to load, and maximum load is no more than 500 ohm.
Convenient in order to carry out parameter adjustment, adopt C Plus Plus to develop parameter tuning software, realize exchanges data with the load monitoring instrument by the RS485 communication, can carry out parameter tuning and adjustment to the load monitoring instrument easily.
This digital multifunctional mill load monitoring instrument is when grinding machine starts, grinding machine electric current when at first grinding and grinding machine noise according to sky, judge whether grinding machine lacks steel ball, in case lack steel ball, give the steel ball warning message of falling vacant, provide current steel ball loading capacity and the reference value that should replenish the steel ball amount according to the priori data of having stored simultaneously.When mill running, after grinding machine noise and background noise amplify by the adjustment of Signal Matching device, enter filtering and virtual value change-over circuit, obtain the energy information and the decibel information of noise, microprocessor receives these signals by sampling unit, calculate and obtain correlated results, and export by LCD, RS485 communication and voltage/current mode.
This digital multifunctional mill load monitor, the standard signal that converts interior coal load quantity signal to 4~20mA is input to DCS.And other input signal adopts the sensor and the transmitter of comparative maturity on the market.
The signal that is come by industry spot can comprise some noises unavoidably, so DCS carries out preliminary treatment at the different filtering algorithm of the dissimilar employings of this write signal, can implement accurately to guarantee the back control algolithm.Concrete filtering algorithm is as follows:
● mill load; At analogue collection module average value filtering (128 points are suitably adjusted according to picking rate) is set, the DPU acquisition rate is 500ms (as might improve as far as possible), and one order inertia filtering is set, and formula is:
y(k)=αx(k)+(1-α)y(k-1)
Wherein, y (k) is this final result, and y (k-1) is final result last time, and x (k) is this real-time measurement values, and α is a filter factor.Filter factor is set to 0.05 (can revise);
● entrance negative pressure; At analogue collection module average value filtering (128 points are suitably adjusted according to picking rate) is set, looks signal wave momentum size, moving average filter or one order inertia filtering (one order inertia filtering formula mill load) are set in DPU;
● outlet temperature; At analogue collection module average value filtering (64 points are suitably adjusted according to picking rate) is set;
● weighing-up wave; At analogue collection module average value filtering (64 points are suitably adjusted according to picking rate) is set;
● the pulverized coal preparation system ventilation; At analogue collection module average value filtering (64 points are suitably adjusted according to picking rate) is set.
The DCS configuration mainly realizes two parts, and one is adaptive searching optimal algorithm and a multidimensional FUZZY ALGORITHMS FOR CONTROL.The multidimensional FUZZY ALGORITHMS FOR CONTROL that lower floor uses, with the deviation of the deviation of the deviation of coal load quantity in the coal pulverizer, coal pulverizer outlet temperature and coal pulverizer entrance negative pressure as input quantity, deviation=setting value-measured value wherein, the setting value of current mill load is 80%, the setting value of outlet temperature is 61 ℃, and the setting value of entrance negative pressure is-300Pa.And output variable is coal-supplying amount (ton), hot blast door aperture (%) and recirculation air door aperture (%).
The deviation of coal load quantity is that the deviation of fhe, coal pulverizer outlet temperature is cwe in the note coal pulverizer, and the deviation of coal pulverizer entrance negative pressure is rfe, and coal-supplying amount is that gm, hot blast door aperture are hf, and recirculation air door aperture is zf.The pairing linguistic variable of above variable be respectively FHE, CWE, RFE, GM; HF and ZF.The codomain of input variable and output variable is different, and the domain of the linguistic variable of each variable correspondence is all selected [2 ,-1,0,1,2], and concrete variation formula is as follows:
Wherein, [] is for rounding operator.
The language value of the linguistic variable of each variable correspondence is all selected [NB, NS, ZO, PS, PB], and representative is negative big, negative little, zero, just little, honest respectively.The selection of fuzzy rule and degree of membership is all set up according to expert's knowledge and technology personnel's experience.Membership function has continuously and discrete two kinds of forms, for the DCS system, adopts the membership function of discrete form to be easier to writing on the program.For the ease of realizing, the aperture of deviation, coal-supplying amount, hot blast door aperture and the recirculation air door of the deviation of the deviation of coal load quantity in the coal pulverizer, coal pulverizer outlet temperature, coal pulverizer entrance negative pressure all can be adopted unified discrete type membership function, shown in table 1~6.
Table 1FHE degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
0 |
0 |
0 |
0 |
1 |
PS |
0 |
0 |
0 |
1 |
0 |
Z0 |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
1 |
0 |
0 |
0 |
NB |
1 |
0 |
0 |
0 |
0 |
Table 2CWE degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
0 |
0 |
0 |
0.6 |
1 |
PS |
0 |
0 |
0.4 |
1 |
0 |
ZO |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
1 |
0.4 |
0 |
0 |
NB |
1 |
0.6 |
0 |
0 |
0 |
Table 3RFE degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
1 |
0.7 |
0 |
0 |
0 |
PS |
0 |
1 |
0.3 |
0 |
0 |
ZO |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
0 |
0.3 |
1 |
0 |
NB |
0 |
0 |
0 |
0.7 |
1 |
Table 4GM degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
0 |
0 |
0 |
0 |
1 |
PS |
0 |
0 |
0 |
1 |
0 |
ZO |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
1 |
0 |
0 |
0 |
NB |
1 |
0 |
0 |
0 |
0 |
Table 5HF degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
0 |
0 |
0 |
0.9 |
1 |
PS |
0 |
0 |
0.2 |
1 |
0 |
ZO |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
1 |
0.2 |
0 |
0 |
NB |
1 |
0.9 |
0 |
0 |
0 |
Table 6SF degree of membership assignment table
|
-2 |
-1 |
0 |
1 |
2 |
PB |
0 |
0 |
0 |
0.9 |
1 |
PS |
0 |
0 |
0.2 |
1 |
0 |
ZO |
0 |
0 |
1 |
0 |
0 |
NS |
0 |
1 |
0.2 |
0 |
0 |
NB |
1 |
0.9 |
0 |
0 |
0 |
Common fuzzy control rule is the form appearance with form, and because the input of the fuzzy controller among the present invention is three variablees, then its fuzzy rule is a regular cube in fact, can obtain this rule cube according to expert's knowledge and operations staff's experience, but regular cube is more complicated in statement, so with this cube is converted into a series of " If ... Then ... " statement is shown in appendix 1.Use maximum membership degree method de-fuzzy then, can obtain fuzzy polling list, shown in appendix 2.At last, will control question blank, the program configuration by DCS can realize.During working control, the input model by inquiry control question blank, can obtain the language grade point of output quantity through after changing immediately, again with grade point, according to following formula:
Obtain actual use value, export to corresponding executing agency then.
The flow chart that the establishment of adaptive searching optimal algorithm is represented according to Fig. 3.The upper strata adaptive searching optimal algorithm changes the setting value of coal load quantity, coal pulverizer outlet temperature value and coal pulverizer entrance negative pressure in the coal pulverizer simultaneously, and lower floor controls according to these three setting values.The setting value of current mill load is 80%, and the setting value of outlet temperature is 58 ℃, and the setting value of entrance negative pressure is-400Pa.Measure mill load, outlet temperature and entrance negative pressure in real time, the deviation of these three amounts carried out normalization:
Then, whether judge three data all less than threshold value 0.1 (can revise), if less than, proof system is stable under current setting value.
Then under the situation of system stability, the coal-supplying amount (ton), outlet temperature of accumulative total feeder (℃) and ventilation (standard cubic meter/hour), measurement period is 5 minutes (can revise), is averaged then, characterizes with mean value that coal-grinding is exerted oneself, drying is exerted oneself and ventilation is exerted oneself.To weigh again mean value, outlet temperature mean value and ventilation mean value carries out normalized, and the normalization formula is as follows:
With the data computation pulverizer capacity composite evaluation function after the normalization.
The weighted average that the composite evaluation function of exerting oneself equals that coal-grinding is exerted oneself, drying is exerted oneself and ventilates and exert oneself, the composite evaluation function of exerting oneself formula is as follows:
In the formula: P is the composite evaluation function of exerting oneself, P
MmFor coal-grinding is exerted oneself, p
GzFor drying is exerted oneself and p
TfFor ventilation is exerted oneself, k
1, k
2And k
3Be respectively coal-grinding power factor, dry power factor and be the ventilation power factor.The coal-grinding power factor is set to 0.6, dry power factor is set to 0.2 and be set to 0.2 (can finely tune according to actual) for the ventilation power factor.
Then, the variation of the composite evaluation function of relatively exerting oneself numerical value, if exert oneself the more last no change of overall merit numerical value, then setting value is not made an amendment.Overall merit numerical value is less than the last time if exert oneself, and the operation that present system then is described need revise the setting value of lower floor's control algolithm with fixing optimizing step-length not at optimum state.The optimizing step-length of mill load setting value is 3% (can revise), and the optimizing step-length of outlet temperature is 0.5 ℃ (can revise), and the optimizing step-length of entrance negative pressure is 30Pa (can revise).
Adaptive searching optimal algorithm when initial, increases (or minimizing) three setting values in each cycle, will revise the back setting value and send to lower floor's controller, and the multi-dimensional fuzzy controller of lower floor is then regulated relevant variable as controlling target with new setting value.After treating system stability, calculate the composite evaluation function of exerting oneself,, illustrate that the direction of setting value modification is improper, then reduce (or increasing) setting value at needs if numerical value diminishes; Composite evaluation function numerical value becomes big if exert oneself, and then continuing increases setting value, knows to search out best setting value.
Like this, the DCS system finds out the coal pulverizer outlet temperature value and the best coal pulverizer entrance negative pressure value of best coal pulverizer internal memory coal value, the best by adaptive searching optimal algorithm, and serve as control setting value with these three optimal values, by the multidimensional FUZZY ALGORITHMS FOR CONTROL simultaneously to coal-supplying amount, hot blast door aperture and recirculation air door aperture (steam generator system is the pulverized coal carried by hot air system) or cold-air flap aperture (steam generator system is the transporting pulverized coal with exhaust gas system) automatically adjust, and pulverized coal preparation system is moved under optimum condition always.
For the thermal power plant that does not adopt the DCS scheme, can adopt PLC or control module and industrial computer to form small-sized DCS system, in PLC or control module, realize the multidimensional FUZZY ALGORITHMS FOR CONTROL, in industrial computer, use configuration software and realize adaptive searching optimal algorithm.
Appendix 1 fuzzy reasoning table
Sequence number |
If[FHE=?,CWE=?,RFE=?] |
Then[GM=?,HF=?,SF=?] |
1 |
[PB,PB,PB] |
[NB,NB,NB] |
2 |
[PS,PB,PB] |
[NS,NB,NB] |
3 |
[ZO,PB,PB] |
[ZO,NB,NB] |
4 |
[NS,PB,PB] |
[PS,NB,NB] |
5 |
[NB,PB,PB] |
[PB,NB,NB] |
6 |
[PB,PS,PB] |
[NB,NS,NB] |
7 |
[PS,PS,PB] |
[NS,NS,NB] |
8 |
[ZO,PS,PB] |
[ZO,NS,NB] |
9 |
[NS,PS,PB] |
[PS,NS,NB] |
10 |
[NB,PS,PB] |
[PB,NS,NB] |
11 |
[PB,ZO,PB] |
[NB,ZO,NB] |
12 |
[PS,ZO,PB] |
[NS,ZO,NB] |
13 |
[ZO,ZO,PB] |
[ZO,ZO,NB] |
14 |
[NS,ZO,PB] |
[PS,ZO,NB] |
15 |
[NB,ZO,PB] |
[PB,ZO,NB] |
16 |
[PB,NS,PB] |
[NB,PS,NB] |
17 |
[PS,NS,PB] |
[NS,PS,NB] |
18 |
[ZO,NS,PB] |
[ZO,PS,NB] |
19 |
[NS,NS,PB] |
[PS,PS,NB] |
20 |
[NB,NS,PB] |
[PB,PS,NB] |
21 |
[PB,NB,PB] |
[NB,PB,NB] |
22 |
[PS,NB,PB] |
[NS,PB,NB] |
23 |
[ZO,NB,PB] |
[ZO,PB,NB] |
24 |
[NS,NB,PB] |
[PS,PB,NB] |
25 |
[NB,NB,PB] |
[PB,PB,NB] |
26 |
[PB,PB,PS] |
[NB,NB,NS] |
27 |
[PS,PB,PS] |
[NS,NB,NS] |
28 |
[ZO,PB,PS] |
[ZO,NB,NS] |
29 |
[NS,PB,PS] |
[PS,NB,NS] |
30 |
[NB,PB,PS] |
[PB,NB,NS] |
31 |
[PB,PS,PS] |
[NB,NS,NS] |
32 |
[PS,PS,PS] |
[NS,NS,NS] |
33 |
[ZO,PS,PS] |
[ZO,NS,NS] |
34 |
[NS,PS,PS] |
[PS,NS,NS] |
35 |
[NB,PS,PS] |
[PB,NS,NS] |
36 |
[PB,ZO,PS] |
[NB,ZO,NS] |
37 |
[PS,ZO,PS] |
[NS,ZO,NS] |
38 |
[ZO,ZO,PS] |
[ZO,ZO,NS] |
39 |
[NS,ZO,PS] |
[PS,ZO,NS] |
40 |
[NB,ZO,PS] |
[PB,ZO,NS] |
41 |
[PB,NS,PS] |
[NB,PS,NS] |
42 |
[PS,NS,PS] |
[NS,PS,NS] |
43 |
[ZO,NS,PS] |
[ZO,PS,NS] |
44 |
[NS,NS,PS] |
[PS,PS,NS] |
45 |
[NB,NS,PS] |
[PB,PS,NS] |
46 |
[PB,NB,PS] |
[NB,PB,NS] |
47 |
[PS,NB,PS] |
[NS,PB,NS] |
48 |
[ZO,NB,PS] |
[ZO,PB,NS] |
49 |
[NS,NB,PS] |
[PS,PB,NS] |
50 |
[NB,NB,PS] |
[PB,PB,NS] |
51 |
[PB,PB,ZO] |
[NB,NB,ZO] |
52 |
[PS,PB,ZO] |
[NS,NB,ZO] |
53 |
[ZO,PB,ZO] |
[ZO,NB,ZO] |
54 |
[NS,PB,ZO] |
[PS,NB,ZO] |
55 |
[NB,PB,ZO] |
[PB,NB,ZO] |
56 |
[PB,PS,ZO] |
[NB,NS,ZO] |
57 |
[PS,PS,ZO] |
[NS,NS,ZO] |
58 |
[ZO,PS,ZO] |
[ZO,NS,ZO] |
59 |
[NS,PS,ZO] |
[PS,NS,ZO] |
60 |
[NB,PS,ZO] |
[PB,NS,ZO] |
61 |
[PB,ZO,ZO] |
[NB,ZO,ZO] |
62 |
[PS,ZO,ZO] |
[NS,ZO,ZO] |
63 |
[ZO,ZO,ZO] |
[ZO,ZO,ZO] |
64 |
[NS,ZO,ZO] |
[PS,ZO,ZO] |
65 |
[NB,ZO,ZO] |
[PB,ZO,ZO] |
66 |
[PB,NS,ZO] |
[NB,PS,ZO] |
67 |
[PS,NS,ZO] |
[NS,PS,ZO] |
68 |
[ZO,NS,ZO] |
[ZO,PS,ZO] |
69 |
[NS,NS,ZO] |
[PS,PS,ZO] |
70 |
[NB,NS,ZO] |
[PB,PS,ZO] |
71 |
[PB,NB,ZO] |
[NB,PB,ZO] |
72 |
[PS,NB,ZO] |
[NS,PB,ZO] |
73 |
[ZO,NB,ZO] |
[ZO,PB,ZO] |
74 |
[NS,NB,ZO] |
[PS,PB,ZO] |
75 |
[NB,NB,ZO] |
[PB,PB,ZO] |
76 |
[PB,PB,NS] |
[NB,NB,PS] |
77 |
[PS,PB,NS] |
[NS,NB,PS] |
78 |
[ZO,PB,NS] |
[ZO,NB,PS] |
79 |
[NS,PB,NS] |
[PS,NB,PS] |
80 |
[NB,PB,NS] |
[PB,NB,PS] |
81 |
[PB,PS,NS] |
[NB,NS,PS] |
82 |
[PS,PS,NS] |
[NS,NS,PS] |
83 |
[ZO,PS,NS] |
[ZO,NS,PS] |
84 |
[NS,PS,NS] |
[PS,NS,PS] |
85 |
[NB,PS,NS] |
[PB,NS,PS] |
86 |
[PB,ZO,NS] |
[NB,ZO,PS] |
87 |
[PS,ZO,NS] |
[NS,ZO,PS] |
88 |
[ZO,ZO,NS] |
[ZO,ZO,PS] |
89 |
[NS,ZO,NS] |
[PS,ZO,PS] |
90 |
[NB,ZO,NS] |
[PB,ZO,PS] |
91 |
[PB,NS,NS] |
[NB,PS,PS] |
92 |
[PS,NS,NS] |
[NS,PS,PS] |
93 |
[ZO,NS,NS] |
[ZO,PS,PS] |
94 |
[NS,NS,NS] |
[PS,PS,PS] |
95 |
[NB,NS,NS] |
[PB,PS,PS] |
96 |
[PB,NB,NS] |
[NB,PB,PS] |
97 |
[PS,NB,NS] |
[NS,PB,PS] |
98 |
[ZO,NB,NS] |
[ZO,PB,PS] |
99 |
[NS,NB,NS] |
[PS,PB,PS] |
100 |
[NB,NB,NS] |
[PB,PB,PS] |
101 |
[PB,PB,NB] |
[NB,NB,PB] |
102 |
[PS,PB,NB] |
[NS,NB,PB] |
103 |
[ZO,PB,NB] |
[ZO,NB,PB] |
104 |
[NS,PB,NB] |
[PS,NB,PB] |
105 |
[NB,PB,NB] |
[PB,NB,PB] |
106 |
[PB,PS,NB] |
[NB,NS,PB] |
107 |
[PS,P?S,NB] |
[NS,NS,PB] |
108 |
[ZO,PS,NB] |
[ZO,NS,PB] |
109 |
[NS,PS,NB] |
[PS,NS,PB] |
110 |
[NB,PS,NB] |
[PB,NS,PB] |
111 |
[PB,ZO,NB] |
[NB,ZO,PB] |
112 |
[PS,ZO,NB] |
[NS,ZO,PB] |
113 |
[ZO,ZO,NB] |
[ZO,ZO,PB] |
114 |
[NS,ZO,NB] |
[PS,ZO,PB] |
115 |
[NB,ZO,NB] |
[PB,ZO,PB] |
116 |
[PB,NS,NB] |
[NB,PS,PB] |
117 |
[PS,NS,NB] |
[NS,PS,PB] |
118 |
[ZO,NS,NB] |
[ZO,PS,PB] |
119 |
[NS,NS,NB] |
[PS,PS,PB] |
120 |
[NB,NS,NB] |
[PB,PS,PB] |
121 |
[PB,NB,NB] |
[NB,PB,PB] |
122 |
[PS,NB,NB] |
[NS,PB,PB] |
123 |
[ZO,NB,NB] |
[ZO,PB,PB] |
124 |
[NS,NB,NB] |
[PS,PB,PB] |
125 |
[NB,NB,NB] |
[PB,PB,PB] |
Appendix 2 fuzzy polling list
Sequence number |
If[fhe=?,cwe=?,rfe=?] |
Then[gm=?,hf=?,sf=?] |
1 |
[2,2,2] |
[-2,-2,-2] |
2 |
[1,2,2] |
[-1,-2,-2] |
3 |
[0,2,2] |
[0,-2,-2] |
4 |
[-1,2,2] |
[1,-2,-2] |
5 |
[-2,2,2] |
[2,-2,-2] |
6 |
[2,1,2] |
[-2,-1,-2] |
7 |
[1,1,2] |
[-1,-1,-2] |
8 |
[0,1,2] |
[0,-1,-2] |
9 |
[-1,1,2] |
[1,-1,-2] |
10 |
[-2,1,2] |
[2,-1,-2] |
11 |
[2,0,2] |
[-2,0,-2] |
12 |
[1,0,2] |
[-1,0,-2] |
13 |
[0,0,2] |
[0,0,-2] |
14 |
[-1,0,2] |
[1,0,-2] |
15 |
[-2,0,2] |
[2,0,-2] |
16 |
[2,-1,2] |
[-2,1,-2] |
17 |
[1,-1,2] |
[-1,1,-2] |
18 |
[0,-1,2] |
[0,1,-2] |
19 |
[-1,-1,2] |
[1,1,-2] |
20 |
[-2,-1,2] |
[2,1,-2] |
21 |
[2,-2,2] |
[-2,2,-2] |
22 |
[1,-2,2] |
[-1,2,-2] |
23 |
[0,-2,2] |
[0,2,-2] |
24 |
[-1,-2,2] |
[1,2,-2] |
25 |
[-2,-2,2] |
[2,2,-2] |
26 |
[2,2,1] |
[-2,-2,-1] |
27 |
[1,2,1] |
[-1,-2,-1] |
28 |
[0,2,1] |
[0,-2,-1] |
29 |
[-1,2,1] |
[1,-2,-1] |
30 |
[-2,2,1] |
[2,-2,-1] |
31 |
[2,1,1] |
[-2,-1,-1] |
32 |
[1,1,1] |
[-1,-1,-1] |
33 |
[0,1,1] |
[0,-1,-1] |
34 |
[-1,1,1] |
[1,-1,-1] |
35 |
[-2,1,1] |
[2,-1,-1] |
36 |
[2,0,1] |
[-2,0,-1] |
37 |
[1,0,1] |
[-1,0,-1] |
38 |
[0,0,1] |
[0,0,-1] |
39 |
[-1,0,1] |
[1,0,-1] |
40 |
[-2,0,1] |
[2,0,-1] |
41 |
[2,-1,1] |
[-2,1,-1] |
42 |
[1,-1,1] |
[-1,1,-1] |
43 |
[0,-1,1] |
[0,1,-1] |
44 |
[-1,-1,1] |
[1,1,-1] |
45 |
[-2,-1,1] |
[2,1,-1] |
46 |
[2,-2,1] |
[-2,2,-1] |
47 |
[1,-2,1] |
[-1,2,-1] |
48 |
[0,-2,1] |
[0,2,-1] |
49 |
[-1,-2,1] |
[1,2,-1] |
50 |
[-2,-2,1] |
[2,2,-1] |
51 |
[2,2,0] |
[-2,-2,0] |
52 |
[1,2,0] |
[-1,-2,0] |
53 |
[0,2,0] |
[0,-2,0] |
54 |
[-1,2,0] |
[1,-2,0] |
55 |
[-2,2,0] |
[2,-2,0] |
56 |
[2,1,0] |
[-2,-1,0] |
57 |
[1,1,0] |
[-1,-1,0] |
58 |
[0,1,0] |
[0,-1,0] |
59 |
[-1,1,0] |
[1,-1,0] |
60 |
[-2,1,0] |
[2,-1,0] |
61 |
[2,0,0] |
[-2,0,0] |
62 |
[1,0,0] |
[-1,0,0] |
63 |
[0,0,0] |
[0,0,0] |
64 |
[-1,0,0] |
[1,0,0] |
65 |
[-2,0,0] |
[2,0,0] |
66 |
[2,-1,0] |
[-2,1,0] |
67 |
[1,-1,0] |
[-1,1,0] |
68 |
[0,-1,0] |
[0,1,0] |
69 |
[-1,-1,0] |
[1,1,0] |
70 |
[-2,-1,0] |
[2,1,0] |
71 |
[2,-2,0] |
[-2,2,0] |
72 |
[1,-2,0] |
[-1,2,0] |
73 |
[0,-2,0] |
[0,2,0] |
74 |
[-1,-2,0] |
[1,2,0] |
75 |
[-2,-2,0] |
[2,2,0] |
76 |
[2,2,-1] |
[-2,-2,1] |
77 |
[1,2,-1] |
[-1,-2,1] |
78 |
[0,2,-1] |
[0,-2,1] |
79 |
[-1,2,-1] |
[1,-2,1] |
80 |
[-2,2,-1] |
[2,-2,1] |
81 |
[2,1,-1] |
[-2,-1,1] |
82 |
[1,1,-1] |
[-1,-1,1] |
83 |
[0,1,-1] |
[0,-1,1] |
84 |
[-1,1,-1] |
[1,-1,1] |
85 |
[-2,1,-1] |
[2,-1,1] |
86 |
[2,0,-1] |
[-2,0,1] |
87 |
[1,0,-1] |
[-1,0,1] |
88 |
[0,0,-1] |
[0,0,1] |
89 |
[-1,0,-1] |
[1,0,1] |
90 |
[-2,0,-1] |
[2,0,1] |
91 |
[2,-1,-1] |
[-2,1,1] |
92 |
[1,-1,-1] |
[-1,1,1] |
93 |
[0,-1,-1] |
[0,1,1] |
94 |
[-1,-1,-1] |
[1,1,1] |
95 |
[-2,-1,-1] |
[2,1,1] |
96 |
[2,-2,-1] |
[-2,2,1] |
97 |
[1,-2,-1] |
[-1,2,1] |
98 |
[0,-2,-1] |
[0,2,1] |
99 |
[-1,-2,-1] |
[1,2,1] |
100 |
[-2,-2,-1] |
[2,2,1] |
101 |
[2,2,-2] |
[-2,-2,2] |
102 |
[1,2,-2] |
[-1,-2,2] |
103 |
[0,2,-2] |
[0,-2,2] |
104 |
[-1,2,-2] |
[1,-2,2] |
105 |
[-2,2,-2] |
[2,-2,2] |
106 |
[2,1,-2] |
[-2,-1,2] |
107 |
[1,1,-2] |
[-1,-1,2] |
108 |
[0,1,-2] |
[0,-1,2] |
109 |
[-1,1,-2] |
[1,-1,2] |
110 |
[-2,1,-2] |
[2,-1,2] |
111 |
[2,0,-2] |
[-2,0,2] |
112 |
[1,0,-2] |
[-1,0,2] |
113 |
[0,0,-2] |
[0,0,2] |
114 |
[-1,0,-2] |
[1,0,2] |
115 |
[-2,0,-2] |
[2,0,2] |
116 |
[2,-1,-2] |
[-2,1,2] |
117 |
[1,-1,-2] |
[-1,1,2] |
118 |
[0,-1,-2] |
[0,1,2] |
119 |
[-1,-1,-2] |
[1,1,2] |
120 |
[-2,-1,-2] |
[2,1,2] |
121 |
[2,-2,-2] |
[-2,2,2] |
122 |
[1,-2,-2] |
[-1,2,2] |
123 |
[0,-2,-2] |
[0,2,2] |
124 |
[-1,-2,-2] |
[1,2,2] |
125 |
[-2,-2,-2] |
[2,2,2] |