CN110967045A - Temperature effect error compensation system and design method of optical fiber sensor - Google Patents
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Abstract
The invention discloses a temperature effect error compensation system and a design method of an optical fiber sensor, comprising a temperature detection unit for detecting the temperature of the optical fiber sensor in real time; the synchronous error equivalent circuit receives a temperature signal of the temperature detection unit and synchronously simulates the temperature effect error of the optical fiber sensor according to the temperature signal; the error compensation output module is used for outputting according to the signal difference between the output signal of the optical fiber sensor and the temperature effect error signal output by the synchronous error equivalent circuit; the synchronous error equivalent circuit is an analog circuit, and the signal difference output by the error compensation output module is an analog signal. The design method is based on an equivalent temperature error fractional order model of the temperature error integer order model for design. The invention overcomes the limitation of error compensation depending on software, realizes hardware compensation, saves a large amount of calculation, and has the advantages of lower computer expense, higher speed, more effective error compensation and more accurate measurement result.
Description
Technical Field
The invention belongs to the field of optical fiber sensors, and particularly relates to the technical field of temperature error effect error compensation.
Background
The optical fiber sensor has the advantages of no mechanical rotating part, quick start, low cost and the like, has wide application prospect, and particularly has a great significance in the fields of inertial navigation, aerospace, robots and the like. However, the temperature effect is an important factor for restricting the development and application of the optical fiber sensor. The temperature effect is an important error source of the optical fiber sensor, and mainly refers to a phenomenon that the output of the optical fiber sensor drifts due to the change of temperature conditions. The error caused by the temperature effect is also the temperature effect error, in the actual working environment, the external temperature environment is always changed, a stable and unchangeable temperature field is hardly formed inside the optical fiber sensor, and the temperature effect error always exists. The improvement of the precision of the optical fiber sensor is generally realized by improving the process and an error compensation method, and the error compensation method has low cost and remarkable effect and is favored.
The cause of temperature effect error is complex: the optical fiber is in a complex temperature field due to factors such as environmental temperature change, self heating of a circuit board and the like, and a temperature effect error compensation model cannot be established from a temperature error mechanism basically due to factors such as optical fiber materials, winding process defects and the like.
An error model is established by measuring data, the rule of error characteristics is found out, and software compensation is a common method in the field of sensors. First, second, third, and even higher order differential equations are typically established that are shaped as:
of course, the lower the order, the easier the parameter identification, but the less effective the modeling, and the higher the order, the more difficult the parameter identification. These factors all result in poor modeling accuracy. Temperature effect errors often show strong nonlinear characteristics, a nonlinear system has parameter sensitivity, and errors are accumulated due to slight parameter difference, so that ideal effects are often difficult to obtain in engineering application.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a temperature effect error compensation system of an optical fiber sensor, which solves the technical problem of software compensation depending on a nonlinear error compensation model in the prior art.
In order to solve the technical problems, the technical scheme of the invention is as follows: a temperature effect error compensation system of an optical fiber sensor comprises a temperature detection unit for detecting the temperature of the optical fiber sensor in real time; the synchronous error equivalent circuit receives a temperature signal of the temperature detection unit and synchronously simulates the temperature effect error of the optical fiber sensor according to the temperature signal; the error compensation output module is used for outputting according to the signal difference between the output signal of the optical fiber sensor and the temperature effect error signal output by the synchronous error equivalent circuit; the synchronous error equivalent circuit is an analog circuit, and temperature signals and temperature effect error signals which are used as input and output signals of the synchronous error equivalent circuit are analog signals; the signal difference output by the error compensation output module is an analog signal.
Preferably, the synchronization error equivalent circuit comprises a frequency equivalent circuit formed by connecting a plurality of RC unit circuits in series; the frequency equivalent circuit takes a temperature signal as an input signal; the RC unit circuit comprises one or more of an RC low-pass filter circuit, an RC band-pass filter circuit and an RC high-pass filter circuit; correspondingly determining the type of each RC unit circuit according to each subfunction of an equivalent operator of a Laplace operator of the temperature error integer order model of the optical fiber sensor; the equivalence operator is equal to the product of each subfunction; and the equivalent operator is determined according to the differential order of the equivalent temperature error fractional order model of the temperature error integer order model.
Furthermore, the synchronous error equivalent circuit also comprises an amplifier, and the amplifier is used for amplifying the output signal of the frequency equivalent circuit according to the coefficient of the equivalent temperature error fractional order model.
Further, the error compensation output module outputs the following modes: and subtracting the temperature effect error signal output by the synchronous error equivalent circuit from the output signal of the optical fiber sensor to obtain a signal difference, and subtracting the fixed error of the optical fiber sensor from the signal difference and then outputting the signal difference.
A method for establishing the temperature effect error compensation system of the optical fiber sensor comprises the following steps:
step 1: establishing an equivalent temperature error fractional order model of a temperature error integer order model of the optical fiber sensor:
wherein t represents time, eTRepresenting the temperature effect error, c representing the fixed error, k representing the coefficient, a representing the order of differentiation;
step 2: designing a synchronous error equivalent circuit according to the differential order a and the coefficient k: calculating an equivalent operator of a Laplace operator of the temperature error integer order model according to the differential order a, and transforming the equivalent operator into products of all subfunctions; determining a transfer function of the RC unit circuit according to the subfunction of the equivalent operator, and designing the RC unit circuit according to the transfer function; determining the output amplification factor of the synchronous error equivalent circuit according to the coefficient k;
and step 3: designing a fixed error compensation module according to the fixed error c; the fixed error compensation module is configured in the error compensation output module in a functional module mode or designed in a synchronous error equivalent circuit in a hardware module mode.
Compared with the prior art, the invention has the following advantages:
1. according to the invention, the temperature effect error of the optical fiber sensor is synchronously simulated through the synchronous error equivalent circuit, and the error compensation output module outputs according to the signal difference between the output signal of the optical fiber sensor and the temperature effect error signal output by the synchronous error equivalent circuit, so that the temperature effect error signal in the output signal of the optical fiber sensor can be compensated, and the measurement precision of the optical fiber sensor is improved.
2. The synchronous error equivalent circuit is an analog circuit, input and output signals of the synchronous error equivalent circuit are analog signals, analog-to-digital signal conversion is not involved in the simulation of the temperature effect error signal, calculation does not need to be carried out by depending on an error compensation model, hardware compensation is achieved, a large amount of calculation is omitted, computer overhead is low, speed is high, error compensation is effective, and a measurement result is accurate. The defects that a software compensation mode in the prior art is difficult in parameter identification, low in precision and easy to generate error accumulation are effectively overcome.
3. The synchronous error equivalent circuit comprises a frequency equivalent circuit formed by connecting a plurality of RC unit circuits in series, the system function is equivalent, and the output is consistent with the temperature effect error of the optical fiber sensor at the same temperature. The structural type of the RC unit circuit is directly based on an equivalent operator, the basic basis is an equivalent temperature error fractional order model, and the parameter identification of the fractional order model is easy and can have higher precision. The integral model can improve modeling precision along with the increase of the order, but the parameter identification is difficult, and the temperature error integral model with higher order can be converted into the equivalent temperature error fractional model according to the intermediate equivalent process theory (any complex model can exist to simplify the equivalent fractional model).
4. Because no method for designing the circuit directly according to the fractional order model exists at present, the invention realizes the design of the synchronous error equivalent circuit by using the circuit design method of the integer order model through the conversion of an operator.
Drawings
FIG. 1 is a schematic diagram of the error compensation principle;
FIG. 2 is a block diagram of an RC low pass filter circuit;
FIG. 3 is a block diagram of an RC band-pass filter circuit;
fig. 4 is a schematic structural diagram of a synchronization error equivalent circuit in the present embodiment.
Detailed Description
Referring to fig. 1, a temperature effect error compensation system of an optical fiber sensor includes a temperature detection unit for detecting the temperature of the optical fiber sensor in real time; the synchronous error equivalent circuit receives a temperature signal of the temperature detection unit and synchronously simulates the temperature effect error of the optical fiber sensor according to the temperature signal; the error compensation output module is used for outputting according to the signal difference between the output signal of the optical fiber sensor and the temperature effect error signal output by the synchronous error equivalent circuit; the synchronous error equivalent circuit is an analog circuit, and temperature signals and temperature effect error signals which are used as input and output signals of the synchronous error equivalent circuit are analog signals; the error compensation output module outputs (for example, by using a subtraction operator) the signal difference as an analog signal.
The synchronous error equivalent circuit comprises a frequency equivalent circuit formed by connecting a plurality of RC unit circuits in series; the frequency equivalent circuit takes a temperature signal as an input signal; the RC unit circuit comprises one or more of an RC low-pass filter circuit, an RC band-pass filter circuit and an RC high-pass filter circuit; correspondingly determining the type of each RC unit circuit according to each subfunction of an equivalent operator of a Laplace operator of the temperature error integer order model of the optical fiber sensor; the equivalence operator is equal to the product of each subfunction; and the equivalent operator is determined according to the differential order of the equivalent temperature error fractional order model of the temperature error integer order model.
The synchronous error equivalent circuit also comprises an amplifier, and the amplifier is used for amplifying the output signal of the frequency equivalent circuit according to the coefficient of the equivalent temperature error fractional order model.
The error compensation output module outputs the following modes: and subtracting the temperature effect error signal output by the synchronous error equivalent circuit from the output signal of the optical fiber sensor to obtain a signal difference, and subtracting the fixed error of the optical fiber sensor from the signal difference and then outputting the signal difference.
The temperature effect error compensation system of the optical fiber sensor in the present embodiment is established as follows:
step 1: establishing an equivalent temperature error fractional order model of a temperature error integer order model of the optical fiber sensor:
wherein t represents time, eTRepresenting the temperature effect error, c representing the fixed error, k representing the coefficient, a representing the order of differentiation;
step 2: designing a synchronous error equivalent circuit according to the differential order a and the coefficient k: calculating an equivalent operator of a Laplace operator of the temperature error integer order model according to the differential order a, and transforming the equivalent operator into products of all subfunctions; determining a transfer function of the RC unit circuit according to the subfunction of the equivalent operator, and designing the RC unit circuit according to the transfer function; determining the output amplification factor of the synchronous error equivalent circuit according to the coefficient k;
and step 3: designing a fixed error compensation module according to the fixed error c; the fixed error compensation module is configured in the error compensation output module in a functional module mode or designed in a synchronous error equivalent circuit in a hardware module mode.
The establishment of the equivalent temperature error fractional order model comprises the following steps:
step 101: establishing an initial temperature error fractional order model:
wherein T represents time, T represents temperature, eTRepresenting temperature effect error, c representing fixed error, k 'representing quasi-coefficient, a' representing quasi-differential order;
step 102: performing an isothermal experiment, then
Determining the value of the fixed error c according to the measurement error;
step 103: iterating the quasi-differential order a ', a' belongs to (0,1), and calculating a quasi-coefficient k 'corresponding to each quasi-differential order a' according to the measurement data of the temperature-varying experiment; the measurement data of the temperature-changing experiment comprises temperature data and an output signal of the optical fiber sensor; the optical fiber sensor in the temperature-varying experiment has no input signal, but different output signals are generated along with the change of the temperature, so that the output signal of the optical fiber sensor in the temperature-varying experiment is the temperature effect error of the optical fiber sensor.
Step 104: and calculating the mean square error according to the measurement data of the temperature-varying experiment, and taking the quasi-differential order a 'and the quasi-coefficient k' corresponding to the minimum mean square error as the differential order a and the coefficient k of the equivalent temperature error fractional order model.
The differential order a and the coefficient k obtained through the iteration process are substituted into the initial temperature error fractional order model to obtain an equivalent temperature error fractional order model, so that the equivalent temperature error fractional order model can simulate an error which is closer to a real error, and the output precision of the synchronous error equivalent circuit is improved.
The quasi-coefficient k' is calculated as follows:
first, it is calculated according to the following formula
Wherein Γ represents a gamma function, n represents an integer, and n-1 < a < n.
Then, the measured data of the temperature-changing experiment are utilized and are based on
And (6) fitting. The quasi-coefficient k' is determined based on a minimum variance criterion. e.g. of the typeTK 'can be determined if a', T and c are known.
Because there is no method for designing circuit directly according to fractional order model, the invention realizes the design of synchronous error equivalent circuit by using integer order model circuit design method through operator conversion, the operator conversion method adopts the prior art, and converts according to the differential order of fractional order model, and the conversion relation of part operators is as follows:
in the formula, s represents the laplacian of the integer order model, and the decimal in the upper right corner of s is the differential order of the fractional order model.
In the present embodiment, the differential order a is 0.9,
for example, the equivalence operator is as follows:
decomposing the equivalence operator into several subfunctions of the multiplications:
the transfer functions corresponding to the subfunctions with the laplacian s in the denominator are as follows:
the RC unit circuit corresponding to the sub-function is a low-pass filter circuit, as shown in fig. 2.
The transfer functions corresponding to the subfunctions with laplacian s in both the numerator and denominator are as follows:
the RC unit circuit corresponding to the sub-function is a low-pass filter circuit, as shown in fig. 3.
Design of
The circuit is shown in FIG. 4, where V4And VoThe amplifier is composed of the structure of the first and the second temperature difference, and the amplification coefficient of the amplifier is the coefficient k of an equivalent temperature error fractional order model. Output of the temperature detection unit as Vi，R1＝10KΩ，R2＝2KΩ，C1＝7.73994mF，C2＝464.25mF，C3＝773.99mF，C4＝2.78mFC5＝4.6425mF，K＝52.65。
Claims (7)
1. A temperature effect error compensation system for an optical fiber sensor, comprising: the temperature detection unit is used for detecting the temperature of the optical fiber sensor in real time; the synchronous error equivalent circuit receives a temperature signal of the temperature detection unit and synchronously simulates the temperature effect error of the optical fiber sensor according to the temperature signal; the error compensation output module is used for outputting according to the signal difference between the output signal of the optical fiber sensor and the temperature effect error signal output by the synchronous error equivalent circuit; the synchronous error equivalent circuit is an analog circuit, and temperature signals and temperature effect error signals which are used as input and output signals of the synchronous error equivalent circuit are analog signals; the signal difference output by the error compensation output module is an analog signal.
2. The system for compensating for temperature effect error of an optical fiber sensor according to claim 1, wherein: the synchronous error equivalent circuit comprises a frequency equivalent circuit formed by connecting a plurality of RC unit circuits in series; the frequency equivalent circuit takes a temperature signal as an input signal; the RC unit circuit comprises one or more of an RC low-pass filter circuit, an RC band-pass filter circuit and an RC high-pass filter circuit; correspondingly determining the type of each RC unit circuit according to each subfunction of an equivalent operator of a Laplace operator of the temperature error integer order model of the optical fiber sensor; the equivalence operator is equal to the product of each subfunction; and the equivalent operator is determined according to the differential order of the equivalent temperature error fractional order model of the temperature error integer order model.
3. The system for compensating for temperature effect error of an optical fiber sensor according to claim 2, wherein: the synchronous error equivalent circuit also comprises an amplifier, and the amplifier is used for amplifying the output signal of the frequency equivalent circuit according to the coefficient of the equivalent temperature error fractional order model.
4. The system for compensating for temperature effect error of an optical fiber sensor according to claim 1, wherein: the error compensation output module outputs the following modes: and subtracting the temperature effect error signal output by the synchronous error equivalent circuit from the output signal of the optical fiber sensor to obtain a signal difference, and subtracting the fixed error of the optical fiber sensor from the signal difference and then outputting the signal difference.
5. A method of establishing a temperature effect error compensation system for an optical fiber sensor according to claim 2, wherein: the method comprises the following steps:
step 1: establishing an equivalent temperature error fractional order model of a temperature error integer order model of the optical fiber sensor:
wherein t represents time, eTRepresenting the temperature effect error, c representing the fixed error, k representing the coefficient, a representing the order of differentiation;
step 2: designing a synchronous error equivalent circuit according to the differential order a and the coefficient k: calculating an equivalent operator of a Laplace operator of the temperature error integer order model according to the differential order a, and transforming the equivalent operator into products of all subfunctions; determining a transfer function of the RC unit circuit according to the subfunction of the equivalent operator, and designing the RC unit circuit according to the transfer function; determining the output amplification factor of the synchronous error equivalent circuit according to the coefficient k;
and step 3: designing a fixed error compensation module according to the fixed error c; the fixed error compensation module is configured in the error compensation output module in a functional module mode or designed in a synchronous error equivalent circuit in a hardware module mode.
6. The method for establishing the temperature effect error compensation system of the optical fiber sensor according to claim 5, wherein: the establishment of the equivalent temperature error fractional order model comprises the following steps:
step 101: establishing an initial temperature error fractional order model:
wherein T represents time, T represents temperature, eTRepresenting temperature effect error, c representing fixed error, k 'representing quasi-coefficient, a' representing quasi-differential order;
step 102: performing an isothermal experiment, then
Determining the value of the fixed error c according to the measurement error;
step 103: iterating the quasi-differential order a ', a' belongs to (0,1), and calculating a quasi-coefficient k 'corresponding to each quasi-differential order a' according to the measurement data of the temperature-varying experiment; the measurement data of the temperature-changing experiment comprises temperature data and output signals of the optical fiber sensor, and the output signals of the optical fiber sensor in the temperature-changing experiment are temperature effect errors of the optical fiber sensor;
step 104: and calculating the mean square error according to the measurement data of the temperature-varying experiment, and taking the quasi-differential order a 'and the quasi-coefficient k' corresponding to the minimum mean square error as the differential order a and the coefficient k of the equivalent temperature error fractional order model.
7. The method for establishing the temperature effect error compensation system of the optical fiber sensor according to claim 6, wherein: the quasi-coefficient k' is calculated as follows:
first, it is calculated according to the following formula
Where Γ represents a gamma function, n represents an integer, and n-1 < a < n, and τ represents an integral variable.
Then, the measured data of the temperature-changing experiment are utilized and are based on
Curve fitting is performed and the quasi-coefficient k' is determined based on the least square error criterion.
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