RU2104495C1 - Process of measurement of physical quantities - Google Patents

Abstract

FIELD: information and measurement systems f aircraft and power plants. SUBSTANCE: process of measurement of physical quantity lies in its conversion to output signal of N pickups, in computation of optimal parameters of N filters and in their tuning. Output signals of pickups are filtered and value of measured physical quantity is obtained by summation of filtered signals. Characteristic feature of process consists in computation of N differences of output signals of pickups, in computation of correlation functions of difference signals for q a priori specified correlation intervals and in determination of a priori known correlation functions of errors of conversion of physical value by each pickup which are used for computation of optimal parameters of filters. EFFECT: increased precision of measurement of physical quantity.

Description

 The invention relates to the field of measurement technology and can be used in information-measuring systems of aircraft and power plants.

 A known method of measuring a physical quantity, based on measuring a physical quantity with two or more sensors, filtering the output signals of each sensor and summing the filtered signals [1]. The disadvantage of this method is the presence of measurement error due to the difference between the optimal filter parameters for the real current parameters of the measurement errors of individual sensors from the calculated obtained from a priori data on the parameters of the measurement errors.

 There is also a known method of measuring a physical quantity [2], which consists in measuring the physical quantity in series with two or more sensors, the number of which is N, calculating the correlation functions of the sensor output signals, calculating the optimal filter parameters from them, using which the sensor output signals are filtered , then the filtered signals are summed up and the value of the measured physical quantity is obtained, and after the measurement, the output signals of the sensors are converted to substantially stationary, and correlation function are separated into components, the first of which is equal to the correlation function of the useful signal, the second - the correlation function measurement error.

 The disadvantage of this method is the presence of measurement error due to the deviation of the filter parameters from optimal, since the separation of the correlation functions of the output signals of the sensors into the correlation functions of the useful signal and the measurement error is carried out without using any objective criterion, as well as the introduction of the conversion of signals to substantially stationary, which does not allow take into account the non-stationary nature of measurement errors when setting up filters.

 The problem to which the invention is directed is to increase the accuracy of measuring physical quantities by improving the quality of the filter.

где

- корреляционная функция разностного сигнала, полученного вычитанием выходного сигнала (i+1)-го датчика из выходного сигнала i-го датчика, определенная для интервала корреляции τ_j , где j = 1 ...q;

- корреляционная функция погрешности i-го датчика n_i, где i = 1 ...N.The problem is solved in that in the known method of measuring a physical quantity, which consists in sequentially measuring a physical quantity with two or more sensors, the number of which is equal to N, the correlation functions of the output signals of the sensors are calculated, the optimal filter parameters are calculated from them, with which they are filtered the output signals of the sensors, then the filtered signals are summed up and the value of the measured physical quantity is obtained, N differences of the output signals of the sensors are additionally calculated, forming their pairwise non-repeating aggregates, calculate the correlation functions of N differences of the output signals of the sensors, calculate the correlation functions of N difference signals for q fixed, successively increasing correlation intervals, calculate the values of the correlation functions of the measurement errors of each sensor by solving q linear equations

Where

- the correlation function of the difference signal obtained by subtracting the output signal of the (i + 1) th sensor from the output signal of the i-th sensor, defined for the correlation interval τ _j , where j = 1 ... q;

- correlation function of the error of the i-th sensor n _i , where i = 1 ... N.

относительно неизвестных a_ji для вычисления оптимальных параметров фильтров.Then, q unknown parameters of the correlation functions of the measurement errors of each sensor are calculated by solving a system of q non-linear equations of the form

relatively unknown a _ji to calculate the optimal filter parameters.

 The achieved technical result is justified as follows.

где x(t) - сигнал, отражающий значение измеряемой физической величины;
n_i(t) - аддитивная погрешность измерения i-го датчика, где i = 1 ...N.The physical quantity is measured by N sensors and the output signals of the sensors x _i (t), reduced to one level, are equal

where x (t) is a signal reflecting the value of the measured physical quantity;
n _i (t) is the additive measurement error of the i-th sensor, where i = 1 ... N.

где W _i(p) - передаточная функция фильтра выходного сигнала i-го датчика.Filtering of sensor signals should be performed provided that the sum of the transfer functions of the filters is constant

where W _i (p) is the transfer function of the filter of the output signal of the i-th sensor.

 The fulfillment of this dynamic condition leads to the absence of a dynamic error in the conversion of the useful signal.

 Such a measuring system will be effective if the root-mean-square error of the system’s measurements is several times smaller than the root-mean-square measurement error of the most accurate of the complexed sensors.

где

- спектральная плотность погрешности измерений i-го датчика;

- модуль амплитудно-частотной характеристики фильтра.The synthesis of optimal filter parameters is carried out from the condition that

Where

- spectral density of the measurement error of the i-th sensor;

- module of the frequency response of the filter.

Вид корреляционных погрешностей измерения известен априорно с точностью до параметров и в общем случае носит нелинейный характер

где τ - интервал корреляции;
a_ij - параметр корреляционной функции i-го датчика.Obviously, the filter parameters do not depend on the parameters of the useful signal, but are completely determined by the parameters of the spectral densities of the measurement errors or the corresponding correlation functions that are uniquely associated with the spectral densities of the inverse Fourier transforms

The form of the correlation errors of measurement is known a priori with an accuracy of up to parameters and, in the general case, is nonlinear

where τ is the correlation interval;
a _ij is the parameter of the correlation function of the i-th sensor.

соответствующая случайному процессу типа "нерегулярная качка".If the form of the function is a priori unknown, then it is possible to approximate the unknown function by a polynomial of the form

corresponding to a random process such as "irregular rolling".

при a_5i = 0

при a_5i = 0, a_4i = 0

и так далее.Then for a _5i = 0, a _3i = 0

for a _5i = 0

for a _5i = 0, a _4i = 0

and so on.

 Depending on the capabilities of computing devices, you can use an implicit method of setting the type of correlation function in the form of a power or functional series.

Сравниваемые выходные сигналы датчиков образуют попарно неповторяющиеся совокупности, а число вычисляемых разностей равно числу используемых датчиков. Корреляционная функция разностного сигнала e_i(t) равна сумме корреляционных функций погрешностей i-го и (i+1)-го датчика, при условии их некоррелированности для любого фиксированного интервала корреляции τ_j .The difference signals e _i (t) obtained by subtracting the output signal of the (i + 1) th sensor from the output signal of the i-th sensor do not contain the components of the useful signal and are observable signals determined by the current values of the measurement errors:

The compared output signals of the sensors form pairwise non-repeating aggregates, and the number of calculated differences is equal to the number of sensors used. The correlation function of the difference signal e _i (t) is equal to the sum of the correlation functions of the errors of the i-th and (i + 1) -th sensors, provided they are uncorrelated for any fixed correlation interval τ _j .

Вычисление корреляционных функций всех разностей позволит определить однозначно значения корреляционных функций погрешности каждого датчика для фиксированного интервала времени τ_j решением системы линейных однородных уравнений.

The calculation of the correlation functions of all the differences will allow us to uniquely determine the values of the correlation functions of the error of each sensor for a fixed time interval τ _j by solving a system of linear homogeneous equations.

В результате корреляционная функция погрешности каждого датчика определена в одной точке.

As a result, the correlation function of the error of each sensor is determined at one point.

If the number of unknown parameters a _{ij of the} correlation function is q, then their determination requires q values of the correlation function for q fixed, successively increasing correlation intervals τ _j , where j = 1 ... q.

Величина интервала корреляции τ_q должна быть при этом наибольшей. Эта система может быть решена относительно

, если математическое ожидание погрешности хотя бы одного из датчиков известно.If the measurement errors contain systematic components, then the values of the correlation functions of the difference signals are equal

The value of the correlation interval τ _q should be the largest. This system can be solved in relation to

if the mathematical expectation of the error of at least one of the sensors is known.

Thus, when using the proposed method, it is not necessary to separate the correlation functions of the output signals of the sensors into the correlation functions of the useful signal and interference, it is not necessary to convert the signals to substantially stationary, which reduces the measurement error, which causes deviations of the filter parameters from the optimal ones. The method also allows you to take into account the non-stationary nature of the measurement errors when setting up the filters, since the optimal values of the parameters of the controlled filter are functions of time and are calculated as functions of the parameters of the measurement errors, which are a priori unknown, and the considered method realizes the possibility of calculating the parameters of measurement errors by determining the values of the correlation functions of difference signals. This allows you to uniquely determine the values of the correlation functions of the error of each sensor for a fixed time interval τ _j and then determine the a priori unknown parameters of the correlation functions of the errors and more accurately calculate the optimal filter parameters.

 An example of a specific implementation of the method.

 Consider a two-component integrated system for assessing the temperature state of a gas turbine engine, consisting of a thermocouple and an optical pyrometric converter.

термопары

Значения A², B² и ω являются априорно неизвестными. Для их оценки определим значение корреляционной функции разностного сигнала R_e(τ) для трех фиксированных интервалов корреляции τ_o= 0, τ₁= τ, τ₂= 2τ.

Решим систему уравнений (11), при этом для удобства введем следующие обозначения R_e(τ_o)= N₁;R_e(τ)=N₂;R_e(2τ)= N₃.The correlation functions of the errors of the transducers are as follows:
pyromerte

thermocouples

The values of A ² , B ^2, and ω are a priori unknown. To evaluate them, we determine the value of the correlation function of the difference signal R _e (τ) for three fixed correlation intervals τ _o = 0, τ ₁ = τ, τ ₂ = 2τ.

We solve the system of equations (11), while for convenience we introduce the following notation R _e (τ _o ) = N ₁ ; R _e (τ) = N ₂ ; R _e (2τ) = N ₃ .

Решением системы уравнений (12) являются:

Зная корреляционные функции погрешности датчиков и определив параметры погрешностей измерения A², B² и ω, возможно провести синтез оптимальных параметров фильтра, исходя из условия (3) и используя преобразование (4).We rewrite (11) as follows:

The solution to the system of equations (12) are:

Knowing the correlation functions of the error of the sensors and determining the parameters of the measurement errors A ² , B ² and ω, it is possible to synthesize the optimal filter parameters based on condition (3) and using transformation (4).

Claims (1)

 The method of measuring a physical quantity, which consists in converting the measured physical quantity into the output signals of N sensors (N ≥ 2), calculate the optimal parameters of N filters and adjust them, filter the output signals of the sensors with appropriate filters and obtain the value of the measured physical quantity by summing the filtered signals characterized in that N differences of the output signals of the sensors are calculated, forming pairwise non-repeating aggregates, each output signal being used when calculating the mentioned differences at least two times, at the same time calculating the correlation functions of the difference signals for q a priori defined correlation intervals, they determine q parameters of a priori known correlation functions of physical quantity conversion errors by each sensor, which are used to calculate the optimal filter parameters.