CN111695637B - Electromechanical system mathematical model identification method and system - Google Patents
Electromechanical system mathematical model identification method and system Download PDFInfo
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Abstract
The invention discloses a method and a system for identifying a mathematical model of an electromechanical system. The method comprises the following steps: collecting input and output data of an electromechanical system of an identified object; grouping the data into training set data and test set data; training set data are used for identifying mathematical models, different algorithms are adopted for training the training set data, a plurality of mathematical models are obtained, the mathematical models are tested and evaluated by using test set data, and the optimal mathematical models under different requirements are selected. The system comprises the embedded terminal and the cloud server host. The invention simplifies the hardware function of the identification system, and the system has configurability through the FPGA module. In addition, the cloud server host adopts a plurality of algorithms to identify mathematical models, and the optimal mathematical models under different requirements are selected for the user to select through model evaluation. The invention can greatly save the cost of the mathematical model identification system of the astronomical telescope electromechanical system, reduce the requirement on a user and increase the model identification precision.
Description
Technical Field
The invention relates to the field of astronomical telescope electromechanical system identification, in particular to an astronomical telescope electromechanical system mathematical model identification system and method based on an embedded terminal and a cloud server host.
Background
With the development of astronomical technology, higher and higher requirements are put on the light collecting capability and resolution of astronomical telescopes. In order to meet the requirement of astronomical observation, the operation of the telescope is challenged, and the telescope mainly has the following 3 aspects: (1) The caliber of the telescope is continuously increased, so that the rotational inertia of the electromechanical system of the telescope is increased, and larger time lag is generated when the electromechanical system operates. (2) Astronomical telescopes are very accurate in tracking stars, often on the order of an angle second or sub-angle second. (3) The operating speed of astronomical telescopes is very low, usually one revolution a day. Therefore, the characteristics of large inertia, low speed and high precision of the astronomical telescope greatly influence nonlinear factors such as friction, backlash, saturation and the like and various disturbances on the system precision. To achieve precise control of the telescope electromechanical system, a relatively precise mathematical model of the telescope electromechanical system needs to be established and a proper control method is adopted. At present, the control theory is deeply researched, and various control algorithms have been proposed. From conventional PID control, to adaptive control, fuzzy control, neural network control, etc. However, in the design of the control system, a mathematical model of the telescope electromechanical system is a precondition and basis for achieving accurate control. If the mathematical model is inaccurate, the accuracy, stability and rapidity of the control result are not ideal.
A mathematical model is a model that reflects the behavior of an actual process in terms of mathematical structures and forms. In control theory, mathematical models come in a variety of forms. The mathematical model commonly used in the time domain is a differential equation, a differential equation and a state equation, and the complex domain is a transfer function and a structure diagram, frequency characteristics in the frequency domain, and the like. There are two methods for establishing a mathematical model of the electromechanical system of the telescope. The first method is mechanism modeling, namely, by analyzing the motion law of the system, deriving by using theorem and mathematical methods, and establishing a mathematical model of the system. However, the mechanism modeling method needs to have clear understanding on the mechanism of the telescope electromechanical system, and can only be used for modeling of a simpler system. At present, the complexity of astronomical telescopes is higher and higher, and the mechanism modeling has the limitation that modeling errors are large or modeling cannot be performed. The second method is a system identification method, i.e., a mathematical model of the system is built using input and output data. The system identification does not need to deeply understand the mechanism of the system, and is very suitable for establishing a mathematical model of a complex system such as an astronomical telescope electromechanical system.
The mathematical model of the telescope electromechanical system is established through system identification, and a method of a special instrument is mainly adopted at present, namely a frequency characteristic analyzer, a dynamic signal analyzer or a servo analyzer is adopted. The output channels of these instruments are used to excite the system and the input channels of the instruments are used to collect the output of the system. And then obtaining a bird diagram, a Nickels diagram, a Nyquist diagram and the like of the system in the instrument through an algorithm. And then the user fits the transfer function of the system on a computer according to the frequency response functions to establish a mathematical model of the system. The use of a special instrument to identify a mathematical model of a system presents several problems:
1) The identification instrument is expensive, and the price is between tens of thousands and hundreds of thousands. The high price limits the application of special instruments.
2) The mechanism of the identification instrument is complex, and the technical requirement on the field user is high. The user will not only know the operating specifications of the instrument, but also the knowledge of signal processing, control theory, system analysis, which greatly limits the popularity of system identification.
3) The identification instrument can only identify the system of analog input and output, and for the system which is not the system of analog input and output, the system needs to be converted into analog by a special conversion instrument. Different signal forms require different conversion instruments and have no versatility.
4) The mathematical model of the identification is single in form, basically the transfer function model of the identified system, and if the model of other forms is used, the user needs to do additional processing work.
The system identification instrument is high in price, and the mechanism is complex because the instrument integrates signal generation logic, data analysis and model identification functions. These functions not only have extremely high requirements on equipment hardware, but also increase the complexity of the embedded software of the instrument and prolong the development period, thereby increasing the instrument cost.
Disclosure of Invention
In order to establish an accurate mathematical model of an astronomical telescope electromechanical system, reduce complexity of a system identification instrument, reduce requirements on field users, improve universality of the instrument, overcome the problem of single mathematical model form and the like, the invention provides an astronomical telescope electromechanical system mathematical model identification method combining an embedded terminal and a cloud server host, and provides an astronomical telescope electromechanical system mathematical model identification system.
The invention adopts the following technical scheme:
a method for identifying a mathematical model of an electromechanical system, comprising:
s1: collecting input and output data of an electromechanical system of an identified object;
s2: grouping the data into training set data and test set data;
s3: training set data are used for identifying mathematical models, different algorithms are adopted for training the training set data, a plurality of mathematical models are obtained, the mathematical models are tested and evaluated by using test set data, and the optimal mathematical models under different requirements are selected, wherein the specific selection method is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is more than or equal to 0 and is a coefficient for adjusting training errors and complexity of a mathematical model;
according to the lambda difference, a plurality of selectable models are provided for a user, and the telescope electromechanical system can be accurately controlled based on the selectable models.
Still further, the recognized objects include two types:
the first type of identified objects do not have input and output data, the dynamic characteristics of the system are continuously excited by excitation signals in the identification time, and the output data of the system are acquired in real time, wherein the excitation signals and the acquired data are used for carrying out system identification;
the second class of identified objects has offline input and output data, and the offline data is directly used for system identification.
Still further, the selectable models include 4 types:
the 1 st model is the model with the minimum training error but the more complex mathematical model; the 2 nd mathematical model is the simplest model with larger training error; the 3 rd is a mathematical model with balanced training errors and model complexity; the 4 th is a mathematical model configured by the user;
and finally, 4 kinds of mathematical models and test set test results are transmitted to a user for selection through a communication interface.
Still further, the excitation signal comprises a sinusoidal sweep signal, a white noise signal, a Chirp signal, wherein:
the sine sweep frequency signal comprises a linear sweep frequency mode and a logarithmic sweep frequency mode;
the linear sweep mode is as follows:
A*sin(2*pi*(f 0 +(f 1 -f 0 )/T*t)*t)
wherein A is the amplitude of the output sinusoidal signal; f (f) 0 Is the lower limit frequency; f (f) 1 For the upper limit frequency f 1 -f 0 Is a frequency range; t is the duration of the test; t is the actual sweep frequency time;
the logarithmic sweep pattern is as follows:
A*sin(2*pi*(f 0 *exp(log(f 1 /f 0 )/T))*t)
the white noise signal is a stable random process with the mean value of 0 and the power spectral density of non-0 constant, and a pseudo random number is generated by recursive operation:
x i ＝Ax i-1 (modM)i＝1,2,…
wherein m=2 k The method comprises the steps of carrying out a first treatment on the surface of the k is an integer greater than 2; x is x i Is a random number; a is a sequence multiplier; mod is a remainder operation.
The Chirp signal is a continuous spectrum in the frequency domain, expressed as:
f in 0 For the Chirp signal start frequency, f 1 For the termination frequency of the Chirp signal, t 1 Is the total length of the Chirp signal.
Furthermore, the step S2 further includes a data noise reduction process, in which noise signals in the data are eliminated by filtering, and a low-pass filter is provided to filter out high-frequency noise signals according to a bandwidth configured by a user.
An electromechanical system mathematical model identification system, comprising:
and (3) an embedded terminal: the system comprises a signal measuring module, a man-machine interaction module and a communication module; the embedded terminal comprises a signal input/output interface, a man-machine interaction interface, a communication interface and a power interface, wherein the man-machine interaction interface is used for connecting man-machine interaction equipment, the signal input/output interface comprises an analog quantity input/output channel and a digital quantity input/output channel, and the communication interface comprises wireless communication and wired communication; the embedded terminal has no operation capability and is a passive executing mechanism;
cloud server host: the system comprises a mathematical model identification module and a model evaluation and selection module; the mathematical model identification module comprises frequency domain identification, neural network identification, fuzzy system identification, impulse response method identification and particle swarm optimization algorithm identification algorithms; the model evaluation and selection module adopts test set data to test the model, evaluates and selects various recognized mathematical models according to training errors of the training set data and model complexity, and a specific selection algorithm is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is more than or equal to 0 and is a coefficient for adjusting training errors and complexity of a mathematical model;
according to the lambda difference, a plurality of selectable models are provided for a user, and the telescope electromechanical system can be accurately controlled based on the selectable models.
Still further, the recognized objects include two types: the first type of identified object does not have input and output data; the second class of identified objects have offline input and output data;
for the first type of identified objects, the embedded terminal further comprises a signal excitation module, wherein the signal excitation module is used for continuously exciting dynamic characteristics of the system in an identification time, and the cloud server host further comprises an excitation signal generation module, and the excitation signal generation module is used for generating a signal sequence comprising sine sweep frequency, white noise and Chirp signals.
Further, the cloud server host also comprises a data preprocessing module, wherein the data preprocessing module is used for data noise reduction and data grouping; the noise signals in the data are eliminated in a filtering mode, and a low-pass filter is provided for filtering high-frequency noise signals according to the bandwidth configured by a user; the data are grouped into training sets and test sets, mathematical model identification is performed with the training sets, and the trained models are tested with the test sets.
Furthermore, the embedded terminal is provided with an FPGA board and a power interface, the FPGA board completes the functions of excitation signal output, signal measurement, man-machine interface and communication, and the power interface provides various levels of power for the whole terminal; the FPGA board includes:
the communication module is used for providing wireless and/or communication functions for the embedded terminal and the cloud server host;
the communication module is used for providing a communication channel for offline data transmission to the embedded terminal;
the analog quantity input channel and the analog quantity output channel are used for generating excitation signals for the identified system and collecting analog quantity information;
the digital quantity input channel and the digital quantity output channel are used for generating an excitation signal in a digital quantity form for the identified system and collecting digital quantity information.
Further, the mathematical model identification module comprises frequency domain identification, neural network identification, fuzzy system identification, impulse response method identification and particle swarm optimization algorithm identification.
Compared with the prior solution, the invention has the following beneficial effects:
1) Convenient and efficient: all data processing functions are completed in the cloud server host, so that the on-site embedded terminal only performs simple signal excitation, signal acquisition and communication functions, and the cost and complexity of the mathematical identification instrument are greatly reduced.
2) The universality is strong: the embedded terminal adopts the FPFA, and can adapt to the access of various sensors by utilizing the high configurability of the FPGA, so that the embedded terminal has high universality.
3) Modeling is accurate: a plurality of identification algorithms are integrated on the cloud server host, and an optimal mathematical model is automatically selected for a user to use according to the identification result, so that the accuracy of the mathematical model is greatly improved.
4) Simple and easy to use: the user does not need to be concerned with the mathematical principle and implementation of the model at all, but only needs to pay attention to the use of the sensor and the configuration of the model parameters. Meanwhile, the method can participate in the establishment of the mathematical model in a layered and deep manner according to the level of the field operator, so that the flexibility of the establishment of the mathematical model is ensured.
Drawings
FIG. 1 is a schematic diagram of a system of the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a schematic diagram of the structure of the present invention;
FIG. 4 is a schematic diagram of an embedded terminal human-machine interface of the present invention;
fig. 5 is a schematic view of a rear panel of an embedded terminal according to the present invention.
The marks in the figure: 1. a case; 2. two side panels; 3. an FPGA board; 4. a 5G communication module; 5. a power panel; 6. an information display screen; 7. a power button; 8. a keyboard; 9. an indicator light; 10. an input/output interface; 11. a net opening; 12. a USB interface; 13. a power interface; 14. an insulating rubber pad.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The present embodiment provides an electromechanical system mathematical model identification system, and the present embodiment uses an identification system of an astronomical telescope electromechanical system mathematical model as an example.
As shown in fig. 1, the electromechanical system mathematical model identification system of the present embodiment includes an embedded terminal and a cloud server host. The embedded terminal is provided with an excitation and output data acquisition device for the identified system and is provided with a signal input/output interface, a man-machine interaction interface, a communication interface and a power interface. The embedded terminal comprises a module developed based on the FPGA, and is mainly used for exciting the system and collecting data. The embedded terminal itself has no operational capability. The cloud server host completes excitation signal generation, data preprocessing, model identification and model evaluation and selection functions according to the user configuration data. The embedded terminal and the cloud server host interact through a wired or wireless communication interface.
1. Embedded terminal
The embedded terminal mainly comprises a signal input/output interface, a man-machine interaction interface, a communication interface and a power interface.
1.1, signal input/output interface
In this embodiment, the embedded terminal provides 4 signal input/output modes, which are respectively analog quantity output, digital quantity output, analog quantity input and digital quantity input. The analog output is 8 paths, the signal amplitude is +/-10V, and the bandwidth is 100kHz. The number output is 8 paths, the resolution is 16 bits, and the highest frequency is 100kHz. The analog quantity is input into 8 paths, the voltage range is +/-10V, and the sampling frequency is 100kHz. The digital quantity input is 8 paths in total, and the sampling frequency of the digital quantity signal is 100kHz. Any 4 bits in the digital quantity input can be configured into an input interface of the encoder through the FPGA, and the input interface corresponds to A+, A-, B+ and B-input by the encoder respectively. The analog input channel not only can collect analog voltage signals, but also can collect thermal resistance, thermocouple and IEPE vibration signals through the FPGA.
1.2 human-computer interaction interface
The man-machine interaction interface mainly completes the input of data and configuration information and displays the result.
In this embodiment, the user configures the identification model, the excitation signal and the communication mode through the man-machine interaction interface. Configuration information is input through a keyboard and displayed through an LCD screen (the input mode of the invention is not limited to the keyboard, and can also be a touch screen, etc., the output equipment of the invention is not limited to the LCD screen display, and only has a display function), and the final mathematical model is also displayed to a user through the LCD screen. The configurable information includes: model form, model order, excitation signal form, signal bandwidth, signal amplitude, communication mode, etc. All configuration information appears sequentially on the LCD screen, and the user only needs to input corresponding information through the keyboard, and if it is unclear how to select, the default item provided by the system can be selected.
In this embodiment, the recognition model forms share 4 forms of differential equation, transfer function and polynomial, and the default form is a transfer function model. The model order may be configured from 1 order to 10 order, with the default order being 2 order. In this embodiment, the excitation signal has 3 forms of sinusoidal sweep, white noise and Chirp signal, and the default form is sinusoidal sweep. After the user is configured, the configuration information is uploaded to the cloud server host through the selected communication mode.
The invention is suitable for the mathematical model identification of two types of systems, namely A type and B type. Class a is a system that requires real-time excitation and acquisition of system signals without input and output data. Class B is a system that has offline input and output data. For class a systems, the user needs to configure the identification model, stimulus signals, and communication means. For the class B system, the user only needs to configure the identification model and the communication mode.
1.3 communication interface
In this embodiment, the embedded terminal has two communication modes, that is, an ethernet wired communication mode and a 5G wireless communication mode, so that a user can freely select any one of the communication modes according to the field situation.
1.4 Power interface
The power interface provides an accurate level for all components of the embedded terminal. In this embodiment, the input power to the embedded terminal is 220VAC, and the input power is rectified, filtered and converted by the independent power module to produce ±24VDC, ±15VDC, ±5VDC, and 3.3VDC to supply the required modules.
2. Cloud server host
In this embodiment, the cloud server host is divided into 4 modules, namely, an excitation signal generation module, a data preprocessing module, a mathematical model identification module and a model evaluation and selection module.
2.1 excitation Signal Generation Module
In order to accurately acquire the mathematical model of the system, the dynamic characteristics of the system must be continuously excited by the input signal in the identification time, so that high requirements are placed on the form and the precision of the excitation signal. In this embodiment, according to different systems, the cloud server host provides three excitation signals, which are respectively sinusoidal sweep, white noise, and Chirp signals. All signals are output according to the bandwidth and amplitude of the user input. The digital quantity is directly output through a digital interface of the FPGA, and the analog quantity is output after DA conversion.
Sinusoidal sweep frequency signal: the system provides 2 sweep modes, namely a linear sweep and a logarithmic sweep. The frequency variation of a linear sweep is linear, i.e. how many hertz is swept per unit time, in Hz/s. The frequency changes logarithmically when the frequency sweeps logarithmically, and the sweep rate can be oct/s, and oct is an octave. Logarithmic sweep means that the number of frequency doubling passes swept at the same time is the same, with low frequency sweep being slow and high frequency sweep being fast for logarithmic sweep.
The linear sweep frequency formula is as follows:
A*sin(2*pi*(f 0 +(f 1 -f 0 )/T*t)*t)
wherein A is the amplitude of the output sinusoidal signal; f (f) 0 Is the lower limit frequency; f (f) 1 For the upper limit frequency f 1 -f 0 Is a frequency range; t is the duration of the test; t is the actual sweep time.
The logarithmic sweep formula is as follows:
A*sin(2*pi*(f 0 *exp(log(f 1 /f 0 )/T))*t)
all symbols have the same meaning as a linear sweep.
White noise signal: white noise is the simplest random process, being a smooth random process with an average value of 0 and a power spectral density of non-0 constant. A pseudo-random number is generated by a recursive operation.
x i ＝Ax i-1 (modM)i＝1,2,…
Wherein m=2 k The method comprises the steps of carrying out a first treatment on the surface of the k is an integer greater than 2; x is x i Is a random number; a is a sequence multiplier; mod is a remainder operation.
Chirp signal: the Chirp signal has the characteristic of continuous frequency spectrum in the frequency domain, and is suitable for the occasion of fast mathematical model identification. The formula is as follows:
f in 0 For the Chirp signal start frequency, f 1 For the termination frequency of the Chirp signal, t 1 Is the total length of the Chirp signal.
2.2 data preprocessing module
The data noise reduction and the data grouping are mainly completed. And eliminating noise signals in the data in a filtering mode, and providing a low-pass filter for filtering high-frequency noise signals according to the bandwidth configured by a user. To verify the accuracy of the recognition model, the data needs to be grouped into training and testing sets. Mathematical model identification is performed with the training set, and the trained model is tested with the test set.
2.3, mathematical model identification Module
The mathematical model recognition module integrates the mainstream system recognition algorithms. The method mainly comprises frequency domain identification, neural network identification, fuzzy system identification, impulse response method identification and particle swarm optimization algorithm identification.
Frequency domain identification: the expression of the frequency characteristic of the controlled object is:
wherein Y(s) is Lawster's transformation of the input quantity of the identification object, and U(s) is Lawster's transformation of the input quantity of the identification object. Drawing a frequency characteristic of the system into a logarithmic frequency characteristic curve according to the measured input output quantity of the system, and obtaining a Bode diagram of the system. In order to obtain the transfer function of the system from the Bode diagram, the transfer function parameters are obtained by least square method according to the order identification input by the user.
Neural network identification: and identifying the mathematical model of the system by utilizing the nonlinear processing capacity of the neural network. Mathematical model identification is performed by using the most classical BP neural network, and the algorithm consists of forward propagation and error back propagation. The whole neural network is divided into 3 layers, namely an input layer, an intermediate layer and an output layer. The neurons of each layer adopt a full-connection mode, and the number of the neurons is adjustable.
Let the identified system be M input N output system, the output of the identified system be:
Y＝[y 1 …y N ] T
inputs to the identified system are:
U＝[u 1 …u M ] T
the output of the neural network is:
the activation function is a Softmax function:
the error performance index function is:
the weight between layers is adjusted by gradient descent method.
And (3) fuzzy system identification: for complex systems with a plurality of influencing factors, and when a large number of nonlinear and time-varying characteristics exist in the system, fuzzy recognition is adopted to model the complex system. Different recognition models are selected according to different input variables. The input ambiguity set = { negative large, negative medium, negative small, zero, positive small, medium, positive large } = { NB, NM, NS, ZR, PS, PM, PB }. The membership functions select the following 5 membership functions. The blurring operator includes an intersection operator AND a union operator OR. The fuzzy system identification process is as follows: establishing an input fuzzy set according to the magnitude of the input quantity amplitude; mapping the input to the [0,1] interval by a membership function; the fuzzy rule IF … THEN is used for selecting a linear function from output alternative functions according to input variables and operators, wherein the linear function can be a function input by a user or a function identified by other identification methods.
Impulse response method: impulse response methods are commonly used to measure the modal frequencies of a system by hammering. Based on input x of the system p (t) and output response y l (t) Fourier transforming the input and output to obtain the transfer function H of the system lp (s). The system is a time-invariant system with N-order degrees of freedom, and has viscous damping, and the p point causes a frequency response function expression of the l point:
in which A rlp Sum s r The mode remainder and the mode pole of the r-th order are respectively, and the symbol represents conjugation.
Particle swarm identification: if the structure of the mathematical model is known through mechanism modeling, but the parameters are unknown, the particle swarm algorithm is used to identify the system model parameters. The particle swarm optimization algorithm belongs to one of the swarm intelligent algorithms, and a swarm optimal solution is found by continuously searching a plurality of unqualified particles in a solution space. The specific flow is as follows:
1) Initializing a particle swarm, wherein the number of selected particles is N, and the parameter of the system model to be identified is M.
Randomly initializing a position information matrix of the particles:
randomly initializing a velocity information matrix of the particles:
the maximum speed, minimum speed, maximum position, minimum position of the particles are set.
2) And calculating the current fitness of all particles of the t-th iteration of the particle swarm.
3) According to the current fitness of each particle
Updating a historical optimal fitness set of each particle:
Jbest＝[Jbest 1 …Jbest N ] T
if it is
Less than the historically optimal fitness Jbest of the particle i Then update Jbest i Otherwise, jbest i Remain unchanged.
4) And searching for the global optimal fitness. Selecting the best fit of the Jbest i As the current global optimum fitness G, if G is better than the historical global optimum fitness Gbest, the Gbest is updated, otherwise the Gbest remains unchanged.
5) The velocity information and the position information of each particle are updated.
Wherein, the liquid crystal display device comprises a liquid crystal display device,w is the inertial weight. c 1 ，c 2 R1 is a learning factor i,j ，r2 i,j Is [0-1]Random numbers in between. jbest i,j Is each element of particle corresponding to each fitness in the JBest, gbest j And each element of the particle corresponding to the global optimal fitness Gbest.
Repeating the processes 2) to 5) until the precision requirement is met or the iteration number reaches the upper limit, and obtaining the position information of the particles corresponding to the Gbest.
2.4 model evaluation and selection Module
Mathematical models identified by various algorithms vary in complexity and training error. However, due to the finite nature of the training set samples and the test set samples, the recognized mathematical model may have an overfitting phenomenon, i.e., the training error is minimum, while the test error is very large, which ultimately results in a finite generalization capability of the mathematical model. In order to solve the problem, the evaluation and selection of the mathematical model are completed on the cloud server host through an integrated idea, and a specific selection algorithm is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is greater than or equal to 0 and is a coefficient for adjusting training errors and complexity of the mathematical model.
The user is provided with 4 models according to lambda. The 1 st model is the model with the minimum training error but the more complex mathematical model; the 2 nd mathematical model is the simplest model with larger training error; the 3 rd is a mathematical model with balanced training errors and model complexity; the 4 th is a mathematical model configured by the user. Finally, 4 mathematical models under different requirements are transmitted to a user for selection through a communication interface.
As shown in fig. 2, the present embodiment further provides a method for identifying a mathematical model of an electromechanical system, including:
s1: collecting electromechanical system data of an identified object;
s2: grouping the data into training set data and test set data;
s3: training set data are used for identifying mathematical models, different algorithms are adopted for training the training set data, a plurality of mathematical models are obtained, the mathematical models are tested and evaluated by using test set data, and the optimal mathematical models under different requirements are selected, wherein the specific selection method is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is more than or equal to 0 and is a coefficient for adjusting training errors and complexity of a mathematical model;
according to the lambda difference, a plurality of selectable models are provided for a user, so that the electromechanical system of the telescope is accurately controlled.
As shown in fig. 3-5, a device for implementing the system and the method of the present invention includes an embedded terminal box 1, slots are formed in two side panels 2 of the box 1 for heat dissipation of the box, an FPGA board 3 is mounted in the box 1, and a 5G communication module 4 is mounted on the FPGA board for wireless communication between the embedded terminal and a cloud server host. A power board 5 is simultaneously installed in the case 1 to provide high-precision level to each part of the embedded terminal. The top surface of the box body 1 is a human-computer interface, and comprises an information display screen 6, a power button 7, a keyboard 8 and an indicator light 9, wherein the display screen 6 is used for displaying configuration information and a final identification model. The keyboard 8 is used for the user to input configuration information. In addition, 3 indicator lamps are arranged on the box body 1, namely yellow, green and red, and yellow represents that the embedded terminal has an alarm, but can be used continuously. Green represents that the embedded terminal works normally, and red represents that the embedded terminal has a fault and stops operating. The rear panel of the box body 1 is provided with 4 rows of input and output interfaces 10 which are respectively analog quantity input, analog quantity output, digital quantity input and digital quantity output, and the 4 rows of signal interfaces are mainly used for the output of an excitation system and an acquisition system. And the two network ports 11 are used for uploading the acquired signals to the cloud server host and receiving instruction information of the cloud server host. And the two USB interfaces 12 are used for transmitting the existing offline data to the embedded terminal and uploading the offline data to the cloud server host through the embedded terminal. And the power interface 13 is used for providing 220VAC power for the case. An insulating rubber pad 14 for insulation and vibration prevention of the cabinet.
The invention can aim at two identified objects, A type is a system which has no input and output data and needs to excite and collect system signals in real time. The method comprises the steps of exciting the identified system through an output interface of the embedded terminal, and collecting an output signal of the identified system through an input interface. Class B is a system for inputting and outputting data offline, which is input into the embedded terminal through the USB interface 12 of the embedded device.
For class a objects, the excitation signals, mathematical models and communication modes need to be configured before the system is identified, while for class B objects, only the mathematical models and communication modes need to be configured. During configuration, the required configuration information is displayed on the LCD screen one by one, and a user needs to configure the information according to the actual situation of the identified system through the keyboard 8. After the configuration is completed, the configuration information is transmitted to the cloud server host through the network port 11 or 5G wireless communication. The cloud server host generates a sequence of excitation signals according to the configuration information and transmits the sequence to the embedded terminal through the communication interface, and the embedded terminal excites the identified system through the input/output interface 10 and acquires system output data in real time. The excitation signals and the collected data are transmitted to the cloud server host through the communication interface. The cloud server host firstly stores the signals, and then carries out system identification on the signals after all the tests are finished. The cloud server host firstly preprocesses the data, namely removes noise existing in the data, groups the data and divides the data into a training set and a testing set. The training set is used for mathematical model building, and the test set is used for model evaluation and selection. After the data grouping is completed, the training set data is input into a mathematical model identification module, and the training set data is trained by using all algorithms in the module to obtain a series of mathematical models. After a series of mathematical models are established, the models are tested and evaluated by using test set data in a model evaluation and selection module, and 4 models are provided for a user according to the evaluation result. The 1 st model is the model with the minimum training error but the more complex mathematical model; the 2 nd mathematical model is the simplest model with larger training error; the 3 rd is a mathematical model with balanced training errors and model complexity; the 4 th is a mathematical model configured by the user. And finally, transmitting the test results of the 4 mathematical models and the test set to the embedded terminal through the communication interface, and displaying the test results on the LCD screen for the user to select.
In summary, the invention provides a system and a method for identifying a mathematical model of an electromechanical system, and the whole system comprises an embedded terminal and a cloud server host. The embedded terminal is provided with a signal input/output interface, a man-machine interaction interface, a communication interface and a power interface. The embedded terminal is mainly used for exciting and collecting data of the telescope electromechanical system, has no calculation capability, and has all calculation functions on a cloud server host. The cloud server host completes excitation signal generation, data preprocessing, mathematical model identification and model evaluation and selection functions. The invention simplifies the hardware function of the identification system, and the system has configurability through the FPGA module. In addition, the cloud server host adopts a plurality of algorithms to identify mathematical models, and the optimal mathematical models under different requirements are selected for the user to select through model evaluation. The invention can greatly save the cost of the mathematical model identification system of the astronomical telescope electromechanical system, reduce the requirement on a user and increase the model identification precision.
The above description is only of the preferred embodiments of the present invention, and is not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A method for identifying a mathematical model of an electromechanical system, comprising:
s1: collecting input and output data of an electromechanical system of an identified object;
s2: grouping the data into training set data and test set data;
s3: training set data are used for identifying mathematical models, different algorithms are adopted for training the training set data, a plurality of mathematical models are obtained, the mathematical models are tested and evaluated by using test set data, and the optimal mathematical models under different requirements are selected, wherein the specific selection method is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is more than or equal to 0 and is a coefficient for adjusting training errors and complexity of a mathematical model;
according to the lambda difference, a plurality of selectable models are provided for a user, and the telescope electromechanical system can be accurately controlled based on the selectable models.
2. The method of claim 1, wherein the identified objects comprise two types:
the first type of identified objects do not have input and output data, the dynamic characteristics of the system are continuously excited by excitation signals in the identification time, and the output data of the system are acquired in real time, wherein the excitation signals and the acquired data are used for carrying out system identification;
the second class of identified objects has offline input and output data, and the offline data is directly used for system identification.
3. The method of claim 1, wherein the selectable models comprise 4 types:
the 1 st model is the model with the minimum training error but the more complex mathematical model; the 2 nd mathematical model is the simplest model with larger training error; the 3 rd is a mathematical model with balanced training errors and model complexity; the 4 th is a mathematical model configured by the user;
and finally, 4 kinds of mathematical models and test set test results are transmitted to a user for selection through a communication interface.
4. The method of claim 2, wherein the excitation signal comprises a sinusoidal sweep signal, a white noise signal, a Chirp signal, wherein:
the sine sweep frequency signal comprises a linear sweep frequency mode and a logarithmic sweep frequency mode;
the linear sweep mode is as follows:
A*sin(2*pi*(f 0 +(f 1 -f 0 )/T*t)*t)
wherein A is the amplitude of the output sinusoidal signal; f (f) 0 Is the lower limit frequency; f (f) 1 For the upper limit frequency f 1 -f 0 Is a frequency range; t is the duration of the test; t is the actual sweep frequency time;
the logarithmic sweep pattern is as follows:
A*sin(2*pi*(f 0 *exp(log(f 1 /f 0 )/T))*t)
the white noise signal is a stable random process with the mean value of 0 and the power spectral density of non-0 constant, and a pseudo random number is generated by recursive operation:
x i ＝Ax i-1 (modM)i＝1,2,…
wherein m=2 k The method comprises the steps of carrying out a first treatment on the surface of the k is an integer greater than 2; x is x i Is a random number; a is a sequence multiplier; mod is a remainder operation;
the Chirp signal is a continuous spectrum in the frequency domain, expressed as:
f in 0 For the Chirp signal start frequency, f 1 For the termination frequency of the Chirp signal, t 1 Is the total length of the Chirp signal.
5. The method of claim 2, wherein S2 further comprises a data noise reduction process, wherein noise signals in the data are eliminated by filtering, and a low-pass filter is provided to filter out high-frequency noise signals according to a bandwidth configured by a user.
6. An electromechanical system mathematical model identification system, comprising:
and (3) an embedded terminal: the system comprises a signal measuring module, a man-machine interaction module and a communication module; the embedded terminal comprises a signal input/output interface, a man-machine interaction interface, a communication interface and a power interface, wherein the man-machine interaction interface is used for connecting man-machine interaction equipment, the signal input/output interface comprises an analog quantity input/output channel and a digital quantity input/output channel, and the communication interface comprises wireless communication and wired communication; the embedded terminal has no operation capability and is a passive executing mechanism;
cloud server host: the system comprises a mathematical model identification module and a model evaluation and selection module; the mathematical model identification module comprises frequency domain identification, neural network identification, fuzzy system identification, impulse response method identification and particle swarm optimization algorithm identification algorithms; the model evaluation and selection module adopts test set data to test the model, evaluates and selects various recognized mathematical models according to training errors of the training set data and model complexity, and a specific selection algorithm is as follows:
wherein N is the sample capacity of the training set; y is the output value of the training set; f (x) is an expression of a mathematical model; x is the input quantity of the training set; w is a parameter vector of the mathematical model; lambda is more than or equal to 0 and is a coefficient for adjusting training errors and complexity of a mathematical model;
according to the lambda difference, a plurality of selectable models are provided for a user, and the telescope electromechanical system can be accurately controlled based on the selectable models.
7. An electromechanical systems mathematical model recognition system according to claim 6, wherein the recognized objects of the recognition system include two types: the first type of identified object does not have input and output data; the second class of identified objects have offline input and output data;
for the first type of identified objects, the embedded terminal further comprises a signal excitation module, wherein the signal excitation module is used for continuously exciting dynamic characteristics of the system in an identification time, and the cloud server host further comprises an excitation signal generation module, and the excitation signal generation module is used for generating a signal sequence comprising sine sweep frequency, white noise and Chirp signals.
8. The system of claim 6, wherein the cloud server host further comprises a data preprocessing module for data noise reduction and data grouping; the noise signals in the data are eliminated in a filtering mode, and a low-pass filter is provided for filtering high-frequency noise signals according to the bandwidth configured by a user; the data are grouped into training sets and test sets, mathematical model identification is performed with the training sets, and the trained models are tested with the test sets.
9. The system of claim 6, wherein the embedded terminal is provided with an FPGA board and a power interface, the FPGA board performs the functions of excitation signal output, signal measurement, man-machine interface and communication, and the power interface provides power of various levels for the whole terminal; the FPGA board includes:
the communication module is used for providing wireless and/or wired communication functions for the embedded terminal and the cloud server host;
the communication module is used for providing a communication channel for offline data transmission to the embedded terminal;
the analog quantity input channel and the analog quantity output channel are used for generating excitation signals for the identified system and collecting analog quantity information;
the digital quantity input channel and the digital quantity output channel are used for generating an excitation signal in a digital quantity form for the identified system and collecting digital quantity information.
10. The system of claim 6, wherein the mathematical model identification module comprises frequency domain identification, neural network identification, fuzzy system identification, impulse response method identification, and particle swarm optimization algorithm identification.
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