| Displacement measurement is one of the most basic and common physical measurement.Precision displacement measurement cover many areas such as space navigation, satellite sounding,super-large-scale integration production, material structure study and nanometer technology. Gratingtyped displacement sensors, such as optical grating sensors, are most widely applied in precisiondisplacement measurement. However, such high precision displacement sensors mainly depend onimport in our country. These high precision displacement sensors cost too much and are usuallyrestricted to import. These negative factors directly influence the development of our nationalmanufacturing industry and national defense industry.Our research team have been involving in precision displacement study since1995, and a novelprecision displacement sensors named time grating sensors with proprietary intellectual propertyrights have been invented. Time grating displacement sensors adopt time quantity as measurementstandard to measurement spatial value. Because time pulses in time grating sensors have a specialspatial equivalent, a new measurement principle, special measurement using time as measurementstandard, can be realized. The measurement precision of existing field typed circular time gratingsensors can reach±0.8″, and that of linear time grating sensors can reach±0.5μm/m. And theresolution of time grating sensors can reach0.1″and0.1μm, respectively.Time grating sensors adopt time to measure spatial value, i.e. time grating sensors measurespatial value every equal time interval. Therefore, time grating sensors are mainly used in staticalmeasurement state. However, sampling equal spatial interval is needed in many applications. Inorder to adopt time grating sensors as position detectors in dynamic measurement for suchapplications, original absolute time grating signal should be transformed into incremental pulseswith equal spatial value. Funded by three National Natural Science Foundation of China (NSFC),this study adopts forecast theory to realize the dynamic measurement of time grating sensors and thesignal subdivision of traditional grating typed displacement sensors. Furthermore, forecast theory,algorithm and related experiments are also studied. The main research content and innovations are asfollows:（1）Two displacement measurement models are analyzed from spatial quantity and timequantity. After analyzing the measurement models and principles of grating typed displacementsensors and time grating sensors deeply, the correlation and variation in physical meaning betweenthem are discussed. （2）Forecast theory is presented for precision displacement measurement. Some classicalforecast theory are analyzed and discussed with mathematics, and the optimal forecast theory isobtained, which validates the effectiveness and availability of forecast theory for precisiondisplacement measurement.（3）The principle of continuous spatial position signal generation is presented in time order fora new principle of full closed loop control. Combing with forecast theory and the measurementprinciples of time grating, the principles of identification, checkout, optimization of forecastregression model are presented, as well as the model ordering and parameter estimation withmathematics and kinematics. In order to obtain optimal forecast results, adaptive forecast model withtime order is presented. As a result, the time variation of model parameters can be realized. Thepurpose is to forecast the displacement of time grating sensors during the next measurement periodbased on series of past measured absolute displacement values. The forecast incrementaldisplacement values are transformed into continuous equal spatial forecast pulses with pulse widthmodulation (PWM). Therefore, time grating sensors applied for statical measurement can be adoptedas position dectors for dynamic position feedback of a full closed loop numerical control system.And the problems of feedback errors and compatible interface of numerical control system can besolved.（4）Forecast technology are pesented for transmission error measurement of gear-hobbingmachine. Time grating sensors are adopted as position detectors for transmission error measurementof gear-hobbing machine. A soft synchronization technology is presented based on forecasttechnology for time grating sensors equipped in the high speed terminal and low speed terminal oftransmission chain. In this way, the problems of time-time asynchronization, time-spaceasynchronization and space-space asynchronization can be solved, and precision transmission errorscan be measured synchronously.（5）The principles of time series signal generation which represent spatial position values arepresented in spatial order. Spatial series theory is established using time series with a time-spacecorresponding method. State-time model and space series model will be established to forecastprecise time quantity. Therefore, a novel subdivision technology based on time space transformationmethod for grating typed sensors is proposed. This subdivision technology broaden out thetranditional think model of subdivision technology and bring some innovations for the signalsubdivision of grating typed sensors. This method has nothing to do with the orthogonal and equalamplitude of signal outputted from grating typed sensors.（6）The principle of time pulse generation with spatial value based on time-space transformation of measurement standard is presented. The real time subdivision technology arepresented for spatial pulses of time gratings and grating typed displacement sensors, and real timeerror correction technology are also presented for calibrating subdivision errors.（7） Error correction methods are presented for statical measurement and dynamicmeasurement. The methods of multi-probe and harmonic correction based on fourier series arepresented for statical measurement, and discrete standard quantity interpolation method is presentedfor dynamic error correction. Therefore, a set of error correction theory and methods are establishedbased on mathematics and kinematics.Among the mentioned research works, the most successful achievements of theory andtechnology are as follows:（1）A self-adaptive regression forecast theory is established for precision displacementmeasurement. Combining with precision displacement measurement and forecast theory, themulti-statistical regression model, time theory and support vector regression machine which areadopted most widely are discussed. And a self-adaptive regression forecast theory is presented basedon the deep analysis on the binifits and drawbacks of three classic forecast theory, which provides apowerful theoretical foundation for precision displacement measurement.（2）Error correction technology are established for statical and dynamic measurement. Staticalerrors of the time gating sensor are calibricated within1″with a multi-probe method and a harmoniccorrection technique based on fourier series, which realizes precision measurement without precisionmechnical fabrication. In addition, the next future displacement value is forecasted with standardquantity interpolation method. In order to ensure forecasting precision and eliminate accumulativeforecasting errors, the forecasting errors during the last measurement period are deducted from theoriginal forecasting value.（3）The experiment study of dynamic precision angular displacement measurement arerealized, and related products are designed.①A full closed loop numerical control rotary tablewith time grating sensors as position detectors based on time series theory is designed. A self-adaptive regression forecast model is adopted to forcast the effective displacement value of nextmeasurement period in real time. And the forecasting incremental angular displacement istransformed into continuous forecasting pulses with equal spatial value using embedded technology.Therefore, time grating sensors can be used as a position feedback sensors for full closed loopnumerical control rotary table. The forecasting precision can reach±2″.②A soft synchronizationtechnology is realized based on forecast technology for transmission error measurement oftransmission chain. A soft synchronization technology is presented based on forecast technology for time grating sensors equipped in the high speed terminal and low speed terminal of transmissionchain. In this way, the problems of time-time asynchronization, time-space asynchronization andspace-space asynchronization can be solved, and precision transmission errors can be measuredsynchronously, and the synchronized transmission errors can be measured with time grating sensors.③The novel signal subdivision devices of traditional grating typed displacement sensors aredesigned based on space series theory. Space series theory is presented. And state-time model andspace series model will be established to forecast precise moving time quantity of line-space ofgrating using time series with a time-space corresponding method. And maximum subdivisionnumber can achieve400, and the subdivision accuracy of angular displacement measurement ishigher than±4％of the original signal period. And forecasting errors are limited within±1.3″. |
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