CN116679026B - Self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method - Google Patents
Self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method Download PDFInfo
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Abstract
The invention relates to the technical field of sewage treatment, and discloses a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method, which comprises the following steps: establishing a mathematical model of a sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration; estimating a state value of a system by using an unbiased finite impulse response filter in a window interval, acquiring estimated values of system states of the unbiased finite impulse response filter under different window sizes, and selecting a window size corresponding to the window with highest estimated value precision as an optimal window size according to a Markov distance; and estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter under a window interval corresponding to the optimal window size. The invention can realize real-time estimation of the concentration of the dissolved oxygen in the sewage, reduce the estimation error of the filter and increase the estimation precision.
Description
Technical Field
The invention relates to the technical field of sewage treatment, in particular to a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method.
Background
Sewage treatment means that harmful substances in sewage are removed through a series of physical, chemical and biological treatment processes, so that the harmful substances reach the emission standards regulated by the national and local governments, and the influence on the environment and human health is reduced. The sewage treatment process generally comprises a plurality of stages of pretreatment, primary treatment, secondary treatment and tertiary treatment, wherein the pretreatment mainly comprises the removal of large-particle substances and sediments, the primary treatment mainly comprises the removal of suspended substances and biochemical oxygen demand through precipitation and filtration, the secondary treatment mainly comprises the removal of nutrient substances such as nitrogen and phosphorus through biodegradation, and the tertiary treatment mainly comprises the removal of refractory substances and trace pollutants through chemical treatment. The sewage treatment is an important environmental protection work, and can effectively reduce the pollution to the environment and the threat to human health.
The sewage treatment has the characteristics of large scale, multiple pollutant types, large water quality fluctuation, large treatment difficulty, high operation cost and the like in industry, and the characteristics of the sewage treatment increase the treatment difficulty and the cost to a certain extent, so that advanced technology and management means are needed to ensure the balance of treatment effect and economic benefit. By 2022, 3 months, there are ten thousands of wastewater treatment plants taking a pollution discharge license nationwide, wherein 98.6% of the wastewater treatment plants have published limit information on the total amount of self-pollutant discharge or the concentration of discharge. According to the sewage treatment capacity, the sewage treatment plant of 1-5 ten thousand tons/day is the most, and the ratio is 33.2%; a sewage treatment plant of 5000-10000 tons/day accounts for 11.7%; the sewage treatment plant of 1000-5000 tons/day accounts for 25.8%; a sewage treatment plant of 1000 tons/day or less accounts for 16.4%; the sewage treatment plant with the sewage treatment plant weight of less than 1 ten thousand tons/day accounts for 52.9 percent.
The sewage treatment process has the characteristics of nonlinearity, time variation, randomness and large time lag, the modeling and null value process of the sewage treatment process is still not easy at present, and in a specific sewage treatment field environment, the sensor can cause errors between the calculated state value and the actual value due to the interference effect. The quality of the water quality is directly determined by the quality of the control of the concentration of the dissolved oxygen in the sewage treatment process. Too little or too much dissolved oxygen concentration in the activated sludge basin can lead to deterioration of the sludge environment: the insufficient concentration of dissolved oxygen can cause the reduction of the growth rate of aerobic bacteria, thereby reducing the quality of effluent; conversely, if the concentration of dissolved oxygen is too high, the flocculant is destroyed, resulting in deterioration of the settling property of suspended solids and energy waste.
The finite impulse response is a popular research direction in recent years, and particularly in the unbiased finite impulse response filter, the body and shadow of which can be seen in many related fields, such as the fields of track tracing, transfer learning and the like, and the sensor can be used for measuring various parameters of water quality, such as PH value, temperature, dissolved oxygen, conductivity and the like, and the data can be input into the filter for predicting the future state of the water quality and controlling the future state of the water quality. However, the concentration of the dissolved oxygen in the sewage is a dynamic change process, and real-time monitoring and data acquisition are required to be carried out to ensure that the filter can timely and effectively process the dissolved oxygen signal, but the real-time monitoring and data acquisition cannot be realized by simply using an unbiased finite impulse response filter. In addition, the prior art lacks consideration and evaluation on stability, instantaneity and the like of the filter, and cannot ensure the application effect and stability of the filter, so that the estimation on the concentration of the dissolved oxygen in the sewage is inaccurate.
Disclosure of Invention
Therefore, the invention aims to solve the technical problems of overcoming the defects in the prior art, and providing the self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method which can realize real-time estimation of the sewage dissolved oxygen concentration, reduce filter estimation errors and increase estimation accuracy.
In order to solve the technical problems, the invention provides a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method, which comprises the following steps:
Establishing a mathematical model of a sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration;
Estimating a state value of the system by using an unbiased finite impulse response filter in a window interval by combining a mathematical model of the system and an observation model of the sensor;
acquiring estimated values of system states of unbiased finite impulse response filters under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size;
and estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter under a window interval corresponding to the optimal window size.
In one embodiment of the invention, the mathematical model of the sewage dissolved oxygen concentration system according to the sewage treatment mechanism comprises the following steps:
The state space equation of the concentration of the dissolved oxygen is established according to the treatment mechanism of the sewage treatment by the activated sludge process and is as follows:
xk＝Axk-1+wk，
Wherein:
k is a time index, x k is a system state at k time, x k＝[x1,k,x2,k,x3,k]T; wherein x 1,k is the mass concentration of the microorganism, x 2,k is the mass concentration of the substrate, x 3,k is the mass concentration of the dissolved oxygen, and T represents the transposition;
w k is the system noise term at time k, w k -N (0, Q), where Q is the covariance matrix of the system noise term;
a is the state transition matrix of the system, Wherein u H is the maximum growth rate of the microorganism, k d is the endophytic hysteresis parameter, C' is the secondary sedimentation tank concentration factor, Q w is the flow of the sewage, V is the volume of the reactor, Y NH is the observed growth coefficient, Q in is the inflow, f is the factor linking the organic matter and the oxygen demand, f x is the water pump factor, and delta is the impulse coefficient set for the dissolved oxygen.
In one embodiment of the present invention, the method for modeling the observation of the sensor for dissolved oxygen concentration of sewage includes:
the method for establishing the observation model of the sensor comprises the following steps:
yk＝Cxk+vk，
Wherein y k is the observed value of the sewage dissolved oxygen measured by a sensor at the moment k, C is the observed matrix of the system, x k is the system state at the moment k, v k is the noise term of the observed value at the moment k, v k -N (0, R), wherein R is the covariance matrix of the observed noise term.
In one embodiment of the present invention, the estimating the state value of the system using the unbiased finite impulse response filter in the window section includes:
obtaining a system state estimated value at the moment k by using an estimated value of a standard least square batch processing unbiased finite impulse response filter in a window interval [ m, k ] The method comprises the following steps:
Wherein, H m,k represents a mapping matrix, Y m,k represents an extended observation vector, and T represents a transposition; m represents the initial time, m=k-n+1, N being the window size;
transforming the system state estimation value to obtain a recursive Kalman system state estimation value The method comprises the following steps:
Wherein, A k represents a state transition matrix of the system, G k represents a generalized noise power gain matrix, and C k represents an observation matrix of the system;
Prediction prior state estimation The method comprises the following steps:
Wherein, Is a priori state estimate, l is an auxiliary variable, iterating from l=m+k to l=k ending to obtain an estimate at the time scale K;
iteratively updating the prior state estimation to obtain the posterior state estimation The method comprises the following steps:
where K l is the offset correction gain, G l is the generalized noise power gain,Z l is the updated measurement residual,
In one embodiment of the present invention, the obtaining the estimated value of the system state of the unbiased finite impulse response filter under different window sizes, selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance, includes:
Randomly selecting an estimated value of a system state of the unbiased finite impulse response filter in a preset range of the window size, and primarily evaluating the basic set by using a mahalanobis distance to obtain an initial optimal window size;
expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at the moment as the final optimal window size.
In one embodiment of the present invention, the estimating values of the system states of the unbiased finite impulse response filter are randomly selected in groups within a preset range of window sizes to obtain a basic set, and the basic set is first estimated by using a mahalanobis distance to obtain an initial optimal window size, specifically:
setting a maximum value N max and a minimum value N min of a window size N preset range, equally dividing a section [ N min,Nmax ] into c+1 parts to obtain a set Wherein, The method comprises the steps of equally dividing a set into c+1 intervals, wherein i is { 1..c }, and c is a preset natural number;
At the collection Take on any value in each of the c+1 intervalsI.e { 1..c+1 }, runThe corresponding unbiased finite impulse response filter generates respective state estimation values, and the mahalanobis distance value of each state estimation value is calculated as:
Where y k is the measurement vector, Is the estimated vector, C k is the measurement matrix, R k is the measurement noise covariance;
And selecting the estimated value with the minimum Markov distance value as an initial optimal estimated value, and taking the window size corresponding to the initial optimal estimated value as the initial optimal window size.
In one embodiment of the present invention, the expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at this time as the final optimal window size, which specifically includes:
at an initial optimal window size The basic filter bank is obtained by expanding the basic filter bank to the left and the right sides respectively, and the basic filter bank is integrated as follows:
Wherein, Respectively correspond toD is the expansion distance of window size;
Operation The corresponding unbiased finite impulse response filter generates respective state estimation values, and calculates the corresponding mahalanobis distance to obtainAccording toIs selected to the final optimal window size.
In one embodiment of the invention, the methodWhen the final optimal window size is selected, three conditions are selected, specifically:
First case: if it is The final optimal window size
Second case: if it isAn unbiased finite impulse response filter with a smaller window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window smaller unbiased finite impulse response filter is repeated with a window size ofContinuing to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance;
Third case: if it is An unbiased finite impulse response filter with a larger window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window larger unbiased finite impulse response filter is repeated with a window size ofThe mahalanobis distance is continued to be used to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance.
In one embodiment of the present invention, the following conditions are satisfied when the unbiased finite impulse response filter with smaller add window and the unbiased finite impulse response filter with larger add window are used simultaneously:
At time scale k, the window size of the unbiased finite impulse response filter must be smaller than k;
The mahalanobis distance calculated by adding a state estimation of an unbiased finite impulse response filter with a smaller or larger window needs to be smaller than the mahalanobis distance calculated from the previous state estimation;
The newly added window size must be within the initial preset range.
The invention also provides a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation system, which is characterized by comprising:
The modeling module is used for establishing a mathematical model of the sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration;
The estimated value acquisition module is used for estimating the state value of the system by using an unbiased finite impulse response filter in a window interval by combining the mathematical model of the system and the observation model of the sensor;
The optimal window size acquisition module is used for acquiring estimated values of the system states of the unbiased finite impulse response filter under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size;
And the real-time estimation module is used for estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter in a window interval corresponding to the optimal window size.
Compared with the prior art, the technical scheme of the invention has the following advantages:
The invention combines an unbiased finite impulse response filter and utilizes a sensor to obtain data, introduces the difference between the Marsdian distance estimated value and the measured value, updates the filter window on line, realizes the real-time estimation of the concentration of the dissolved oxygen in the sewage, reduces the estimation error of the filter and increases the estimation precision.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, in which:
Fig. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of a process for window size primary screening in accordance with the present invention.
FIG. 3 is a schematic diagram of a window size expansion reevaluation process in accordance with the present invention.
FIG. 4 is a graph showing the effect of the method of the present invention on the concentration of dissolved oxygen in sewage.
Fig. 5 is a graph showing a comparison of Root Mean Square Error (RMSE) of the concentration of dissolved oxygen in sewage estimated by using the method of the present invention, the kalman method, and the fixed window UFIR filtering in the example of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Referring to FIG. 1, the invention discloses a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method. In order to obtain more accurate dissolved oxygen concentration of sewage and solve the problem of environmental deterioration, the invention introduces an unbiased finite impulse response filter, and the filter needs to obtain an optimal estimation window firstly in the running process so as to drive an estimated value to approach to the optimal under the meaning of minimum mean square error. However, for the sewage oxygen concentration, when the characteristics of the sewage oxygen concentration are interfered by the outside or the modeling is inaccurate, the filter capable of adjusting the window on line is more advantageous than the filter with the fixed window, and can be better adapted to the actual situation of the complex and intricate, so that the accuracy of the sewage dissolved oxygen concentration estimation value can be improved by introducing the mahalanobis distance measurement estimation precision, and performing the two stages of primary screening and expansion and re-estimation, so that the optimal window at each moment can be selected and estimated on the premise of acceptable calculated quantity, the estimation of the sewage dissolved oxygen concentration at each moment can be obtained, and the accuracy of the sewage dissolved oxygen concentration estimation value can be improved. The method specifically comprises the following steps:
S1: and establishing a mathematical model of a sewage dissolved oxygen concentration system according to a sewage treatment mechanism.
The state space equation of the concentration of the dissolved oxygen is established according to the treatment mechanism of the sewage treatment by the activated sludge process and is as follows:
xk＝Axk-1+wk，
Wherein:
k is a time index, x k is a system state at k time, x k＝[x1,k,x2,k,x3,k]T; wherein x 1,k is the mass concentration of the microorganism, x 2,k is the mass concentration of the substrate, x 3,k is the mass concentration of the dissolved oxygen, and T represents the transposition;
w k is the system noise term at time k, w k obeys a gaussian distribution with zero mean, i.e. w k -N (0, Q), where Q is the covariance matrix of the system noise term;
a is the state transition matrix of the system, Wherein u H is the maximum growth rate of the microorganism, k d is the endophytic hysteresis parameter, C' is the secondary sedimentation tank concentration factor, Q w is the flow of the sewage, V is the volume of the reactor, Y NH is the observed growth coefficient, Q in is the inflow, f is the factor linking the organic matter and the oxygen demand, f x is the water pump factor, and delta is the impulse coefficient set for the dissolved oxygen.
S2: and monitoring the concentration of the dissolved oxygen in the sewage by using a sensor, and establishing an observation model of the sensor of the concentration of the dissolved oxygen in the sewage.
The method for establishing the observation model of the sensor comprises the following steps:
yk＝Cxk+vk，
Wherein y k is the observed value of the dissolved oxygen of the sewage measured by a sensor at the moment k, C is the observed matrix of the system, and in the embodiment, C= [0,1]; x k is the system state at time k, v k is the noise term of the observed value at time k, v k obeys a gaussian distribution with zero mean, i.e. v k -N (0, R), where R is the covariance matrix of the observed noise term.
S3: an Unbiased Finite Impulse Response (UFIR) filter is used to estimate a state value of the system within a window interval in combination with a mathematical model of the system and an observation model of the sensor.
The UFIR filter uses N measured values from the initial time m=k-N+1 to k to estimate, and the value of N is XX; no initial state x m and no initial error covariance matrix p m, nor noise covariance matrices Q i and R i are needed in the iteration interval, where i e m, k. UFIR filter can forget the measured value outside the window before m time, and determine the state estimated value at m+K-1 time in a batch processing modeWhere K is the dimension of the system state. The derivation process of the iterative form of the UFIR filter specifically comprises the following steps:
S3-1: obtaining a system state estimated value at the moment k by using an estimated value of a standard least square batch processing unbiased finite impulse response filter in a window interval [ m, k ] The method comprises the following steps:
Wherein, H m,k represents a mapping matrix, Y m,k represents an extended observation vector, and T represents a transposition; m represents the initial time, m=k-n+1, N being the window size;
S3-2: transforming the system state estimation value to obtain a recursive Kalman system state estimation value The method comprises the following steps:
Where a k represents the state transition matrix of the system, G k represents the generalized noise power gain matrix, and C k represents the observation matrix of the system.
S3-3: each recursion in the UFIR filter has two phases: prediction and updating. The UFIR algorithm does not require noise statistics, so the prediction stage only requires prediction of prior state estimationThe method comprises the following steps:
Wherein, Is a priori state estimate, l is an auxiliary variable, iterating from l=m+k to l=k ending to obtain an estimate at the time scale K.
S3-4: state estimation is improved by combining current state observation, prior state estimation is updated in an iterative mode, and posterior state estimation is obtainedThe method comprises the following steps:
where K l is the offset correction gain, G l is the generalized noise power gain (generalized noise power gain, GNPG),Z l is the updated measurement residual,
S4: and searching an optimal filtering window in real time. And acquiring estimated values of the system state of the unbiased finite impulse response filter under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size. The adjustment parameter required for this process is the window size N, which must be optimal, i.e., N opt, to ensure that MSE is minimized. Based on this, a UFIR (MUFIR) filter based on mahalanobis distance window adaptation is proposed, the basic idea is: using a filter bank, wherein the filter bank comprises UFIR filters with different window sizes, aiming at obtaining a plurality of estimates from the UFIR filters with different window sizes, measuring the estimation accuracy by using the Markov distance, and selecting the window size of the UFIR filter with the smallest Markov distance, i.e. the highest estimation accuracy, as N opt at the current moment, i.e.The method comprises the following steps:
s4-1: window size primary screening: and randomly selecting an estimated value of the system state of the unbiased finite impulse response filter in a preset range of the window size, and primarily evaluating the basic set by using the mahalanobis distance to obtain the initial optimal window size. As shown in fig. 2, specifically:
S4-1-1: first, design parameters are set, the maximum value N max and the minimum value N min of the preset range of the window size N are set, in order to minimize the dead zone, N min is generally set to the minimum allowable value (same level as the system), and for N max, it has a certain influence on the calculation burden of the system, so that it needs to be selected according to the specific system. After presetting the range of N [ N min,Nmax ], equally dividing the interval [ N min,Nmax ] into c+1 parts to obtain a set Wherein, For equally dividing the set into c+1 intervals as much as possible, i e { 1..c }; c is a preset natural number, and the value of c has a certain influence on the calculation load and the estimation precision, and in this embodiment, the value of c e [2,5].
S4-1-2: at the collectionTake on any value in each of the c+1 intervalsThen there isI.e. { 1..c+1 }. OperationCorresponding unbiased finite impulse response filters produce respective state estimatesThe mahalanobis distance value of each state estimation value is calculated as follows:
Where y k is the measurement vector, Is the estimated vector, C k is the measurement matrix, R k is the measurement noise covariance;
s4-1-3: selecting the estimated value with the minimum Markov distance value as an initial optimal estimated value, and taking the window size corresponding to the initial optimal estimated value as an initial optimal window size, namely the initial optimal window size
S4-2: window size expansion reevaluation: expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at the moment as the final optimal window size. As shown in fig. 3, in particular
S4-2-1: in order to expand, a basic window needs to be obtained first, and the basic window is obtained at the end of the operation of the processAt an initial optimal window sizeThe basic filter bank is obtained by expanding the basic filter bank to the left and the right sides respectively, and the basic filter bank is integrated as follows:
Wherein, Respectively correspond toD is the expansion distance of window size; d is a design parameter, typically set to 1 or 2.
S4-2-2: operationThe corresponding unbiased finite impulse response filter generates respective state estimation values, and calculates the corresponding mahalanobis distance to obtain
S4-2-3: according toIs selected to the final optimal window size. The selection is carried out in three cases, specifically:
First case: if it is The final optimal window size
Second case: if it isAn unbiased finite impulse response filter with a smaller window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window smaller unbiased finite impulse response filter is repeated with a window size ofContinuing to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance;
Third case: if it is An unbiased finite impulse response filter with a larger window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window larger unbiased finite impulse response filter is repeated with a window size ofThe mahalanobis distance is continued to be used to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance.
In short, if the D k calculated by the added new UFIR filter is smaller than the D k calculated by the original UFIR filter, adding a UFIR filter with a new window size to the filter bank; otherwise, stopping expanding, selecting the window corresponding to the minimum D k at the current time as N opt at the current time, selecting the corresponding UFIR filter as the current time filter, and selecting the corresponding state estimation as the current time optimal estimation.
In adding an unbiased finite impulse response filter with a smaller window and adding an unbiased finite impulse response filter with a larger window, the following conditions need to be satisfied at the same time:
(1) At time scale k, the window size of the unbiased finite impulse response filter must be smaller than k;
(2) The mahalanobis distance calculated by adding a state estimation of an unbiased finite impulse response filter with a smaller or larger window needs to be smaller than the mahalanobis distance calculated from the previous state estimation;
(3) The newly added window size N new must be within the initial preset range, i.e., N new∈[Nmin,Nmax.
When any of the above conditions is not satisfied, the expansion is stopped, and N opt is obtained.
S5: and finally estimating online. And estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter under a window interval corresponding to the optimal window size. The unbiased finite impulse response filter capable of adaptively changing the window on line can be obtained by searching the optimal window size, and the filter can estimate the state value of the dissolved oxygen concentration of the sewage in a complex sewage environment, so that on-line evaluation is realized.
The invention also discloses a self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation system, which comprises a modeling module, an estimated value acquisition module, an optimal window size acquisition module and a real-time estimation module. The modeling module is used for establishing a mathematical model of the sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration. The estimated value acquisition module is used for estimating the state value of the system by using an unbiased finite impulse response filter in a window interval in combination with the mathematical model of the system and the observation model of the sensor. The optimal window size acquisition module is used for acquiring estimated values of the system states of the unbiased finite impulse response filter under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size. The real-time estimation module is used for estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter under the window interval corresponding to the optimal window size.
The invention also discloses a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, realizes the self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method.
The invention also discloses a device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the self-adaptive unbiased finite impulse response filtering sewage dissolved oxygen concentration estimation method when executing the computer program.
Compared with infinite impulse response (such as Kalman filtering) and an unbiased finite impulse response filtering method using a fixed window, the method combines an unbiased finite impulse response filter and utilizes a sensor to obtain data, and the filter window is updated online by introducing the difference between the Mars distance estimated value and the measured value, so that the real-time estimation of the concentration of the dissolved oxygen in the sewage is realized, the estimation error of the filter is reduced, the estimation precision is increased, and the method has very important significance for accurately estimating the concentration of the dissolved oxygen.
In order to further prove the beneficial effects of the invention, simulation experiments are carried out by taking the following parameter settings as examples in the embodiment:
The parameters of the sensor are respectively as follows: the system has 3 states, namely the first state: mass concentration of microorganisms mg/L, second state: mass concentration of substrate mg/L and third state: the concentration of dissolved oxygen in sewage is mg/L. The initial values for the 3 states were all set to 0mg/L.
The method of the invention is used for tracking the concentration state of the dissolved oxygen in the sewage, and the tracking effect is shown in figure 4. MUFIR in fig. 4 shows the results using the present invention, and TURE shows the true value. It can be seen that the estimated value of the present invention substantially coincides with the actual value.
The method, the Kalman method and the fixed window UFIR filter are respectively used for estimating the concentration state of the dissolved oxygen in the sewage, and the Root Mean Square Error (RMSE) between each method and the actual value is calculated, and the result is shown in figure 5. KF in fig. 5 shows the result using the kalman method, MUFIR shows the result using the method of the present invention, UFIR shows the result using fixed window UFIR filtering. It can be seen that the root mean square error of the invention is minimum, the difference between the root mean square error and the actual value is minimum, and the estimation accuracy is effectively improved.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (5)
1. The method for estimating the concentration of the dissolved oxygen in the sewage by self-adaptive unbiased finite impulse response filtering is characterized by comprising the following steps of:
Establishing a mathematical model of a sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration;
Estimating a state value of the system by using an unbiased finite impulse response filter in a window interval by combining a mathematical model of the system and an observation model of the sensor;
acquiring estimated values of system states of unbiased finite impulse response filters under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size;
estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter under a window interval corresponding to the optimal window size;
The mathematical model for establishing a sewage dissolved oxygen concentration system according to a sewage treatment mechanism comprises the following steps:
The state space equation of the concentration of the dissolved oxygen is established according to the treatment mechanism of the sewage treatment by the activated sludge process and is as follows:
xk＝Axk-1+wk，
Wherein:
k is a time index, x k is a system state at k time, x k＝[x1,k,x2,k,x3,k]T; wherein x 1,k is the mass concentration of the microorganism, x 2,k is the mass concentration of the substrate, x 3,k is the mass concentration of the dissolved oxygen, and T represents the transposition;
w k is the system noise term at time k, w k -N (0, Q), where Q is the covariance matrix of the system noise term;
a is the state transition matrix of the system, Wherein u H is the maximum growth rate of the microorganism, k d is the endophytic hysteresis parameter, C' is the secondary sedimentation tank concentration factor, Q w is the flow of the sewage, V is the volume of the reactor, Y NH is the observed growth coefficient, Q in is the inflow, f is the factor for connecting the organic matter and the oxygen demand, f x is the water pump factor, and delta is the impulse coefficient set for the dissolved oxygen;
the observation model for establishing the sensor of the dissolved oxygen concentration of the sewage comprises the following steps:
the method for establishing the observation model of the sensor comprises the following steps:
yk＝Cxk+vk，
Wherein y k is the observed value of the sewage dissolved oxygen measured by a sensor at the moment k, C is the observed matrix of the system, x k is the system state at the moment k, v k is the noise term of the observed value at the moment k, v k -N (0, R), wherein R is the covariance matrix of the observed noise term;
The estimating a state value of the system using an unbiased finite impulse response filter within a window interval includes:
obtaining a system state estimated value at the moment k by using an estimated value of a standard least square batch processing unbiased finite impulse response filter in a window interval [ m, k ] The method comprises the following steps:
Wherein, H m,k represents a mapping matrix, Y m,k represents an extended observation vector, and T represents a transposition; m represents the initial time, m=k-n+1, N being the window size;
transforming the system state estimation value to obtain a recursive Kalman system state estimation value The method comprises the following steps:
Wherein, A k represents a state transition matrix of the system, G k represents a generalized noise power gain matrix, and C k represents an observation matrix of the system;
Prediction prior state estimation The method comprises the following steps:
Wherein, Is a priori state estimate, l is an auxiliary variable, iterating from l=m+k to l=k ending to obtain an estimate at the time scale K;
iteratively updating the prior state estimation to obtain the posterior state estimation The method comprises the following steps:
where K l is the offset correction gain, G l is the generalized noise power gain,Z l is the updated measurement residual,
The obtaining the estimated value of the system state of the unbiased finite impulse response filter under different window sizes, selecting the corresponding window size with the highest estimated value precision according to the mahalanobis distance, including:
Randomly selecting an estimated value of a system state of the unbiased finite impulse response filter in a preset range of the window size, and primarily evaluating the basic set by using a mahalanobis distance to obtain an initial optimal window size;
Expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at the moment as the final optimal window size;
The method comprises the steps of randomly selecting an estimation value of a system state of an unbiased finite impulse response filter in a preset range of window sizes, and obtaining an initial optimal window size by using a primary estimation basic set of a mahalanobis distance, wherein the method comprises the following steps of:
setting a maximum value N max and a minimum value N min of a window size N preset range, equally dividing a section [ N min,Nmax ] into c+1 parts to obtain a set Wherein, The method comprises the steps of equally dividing a set into c+1 intervals, wherein i is { 1..c }, and c is a preset natural number;
At the collection Take on any value in each of the c+1 intervalsOperationThe corresponding unbiased finite impulse response filter generates respective state estimation values, and the mahalanobis distance value of each state estimation value is calculated as:
Where y k is the measurement vector, Is the estimated vector, C k is the measurement matrix, R k is the measurement noise covariance;
And selecting the estimated value with the minimum Markov distance value as an initial optimal estimated value, and taking the window size corresponding to the initial optimal estimated value as the initial optimal window size.
2. The adaptive unbiased finite impulse response filtered sewage dissolved oxygen concentration estimation method as claimed in claim 1, characterized in that: expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at the moment as the final optimal window size, wherein the method specifically comprises the following steps:
at an initial optimal window size The basic filter bank is obtained by expanding the basic filter bank to the left and the right sides respectively, and the basic filter bank is integrated as follows:
Wherein, Respectively correspond toD is the expansion distance of window size;
Operation The corresponding unbiased finite impulse response filter generates respective state estimation values, and calculates the corresponding mahalanobis distance to obtainAccording toIs selected to the final optimal window size.
3. The adaptive unbiased finite impulse response filtered sewage dissolved oxygen concentration estimation method as claimed in claim 2, characterized in that: said basis isWhen the final optimal window size is selected, three conditions are selected, specifically:
First case: if it is The final optimal window size
Second case: if it isAn unbiased finite impulse response filter with a smaller window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window smaller unbiased finite impulse response filter is repeated with a window size ofContinuing to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance;
Third case: if it is An unbiased finite impulse response filter with a larger window is added, the window size beingContinuing to evaluate the Markov distance to obtain
If it isThen consider asCorresponding toThe optimal window size at the current moment is obtained, the expansion is stopped, and the final optimal window size is obtained
If it isThen the "add window larger unbiased finite impulse response filter is repeated with a window size ofThe mahalanobis distance is continued to be used to evaluate the operation until the current mahalanobis distance is greater than the last mahalanobis distance.
4. The adaptive unbiased finite impulse response filtered sewage dissolved oxygen concentration estimation method as claimed in claim 3, characterized in that: when the unbiased finite impulse response filter with smaller adding window and the unbiased finite impulse response filter with larger adding window are used, the following conditions are satisfied at the same time:
At time scale k, the window size of the unbiased finite impulse response filter must be smaller than k;
The mahalanobis distance calculated by adding a state estimation of an unbiased finite impulse response filter with a smaller or larger window needs to be smaller than the mahalanobis distance calculated from the previous state estimation;
The newly added window size must be within the initial preset range.
5. An adaptive unbiased finite impulse response filtered sewage dissolved oxygen concentration estimation system, comprising:
The modeling module is used for establishing a mathematical model of the sewage dissolved oxygen concentration system according to a sewage treatment mechanism, monitoring the sewage dissolved oxygen concentration by using a sensor, and establishing an observation model of the sensor of the sewage dissolved oxygen concentration;
The estimated value acquisition module is used for estimating the state value of the system by using an unbiased finite impulse response filter in a window interval by combining the mathematical model of the system and the observation model of the sensor;
The optimal window size acquisition module is used for acquiring estimated values of the system states of the unbiased finite impulse response filter under different window sizes, and selecting the window size corresponding to the highest estimated value precision according to the mahalanobis distance as the optimal window size;
the real-time estimation module is used for estimating the state value of the dissolved oxygen concentration of the sewage in real time by using an unbiased finite impulse response filter in a window interval corresponding to the optimal window size;
The mathematical model for establishing a sewage dissolved oxygen concentration system according to a sewage treatment mechanism comprises the following steps:
The state space equation of the concentration of the dissolved oxygen is established according to the treatment mechanism of the sewage treatment by the activated sludge process and is as follows:
xk＝Axk-1+wk，
Wherein:
k is a time index, x k is a system state at k time, x k＝[x1,k,x2,k,x3,k]T; wherein x 1,k is the mass concentration of the microorganism, x 2,k is the mass concentration of the substrate, x 3,k is the mass concentration of the dissolved oxygen, and T represents the transposition;
w k is the system noise term at time k, w k -N (0, Q), where Q is the covariance matrix of the system noise term;
a is the state transition matrix of the system, Wherein u H is the maximum growth rate of the microorganism, k d is the endophytic hysteresis parameter, C' is the secondary sedimentation tank concentration factor, Q w is the flow of the sewage, V is the volume of the reactor, Y NH is the observed growth coefficient, Q in is the inflow, f is the factor for connecting the organic matter and the oxygen demand, f x is the water pump factor, and delta is the impulse coefficient set for the dissolved oxygen;
the observation model for establishing the sensor of the dissolved oxygen concentration of the sewage comprises the following steps:
the method for establishing the observation model of the sensor comprises the following steps:
yk＝Cxk+vk，
Wherein y k is the observed value of the sewage dissolved oxygen measured by a sensor at the moment k, C is the observed matrix of the system, x k is the system state at the moment k, v k is the noise term of the observed value at the moment k, v k -N (0, R), wherein R is the covariance matrix of the observed noise term;
The estimating a state value of the system using an unbiased finite impulse response filter within a window interval includes:
obtaining a system state estimated value at the moment k by using an estimated value of a standard least square batch processing unbiased finite impulse response filter in a window interval [ m, k ] The method comprises the following steps:
Wherein, H m,k represents a mapping matrix, Y m,k represents an extended observation vector, and T represents a transposition; m represents the initial time, m=k-n+1, N being the window size;
transforming the system state estimation value to obtain a recursive Kalman system state estimation value The method comprises the following steps:
Wherein, A k represents a state transition matrix of the system, G k represents a generalized noise power gain matrix, and C k represents an observation matrix of the system;
Prediction prior state estimation The method comprises the following steps:
Wherein, Is a priori state estimate, l is an auxiliary variable, iterating from l=m+k to l=k ending to obtain an estimate at the time scale K;
iteratively updating the prior state estimation to obtain the posterior state estimation The method comprises the following steps:
where K l is the offset correction gain, G l is the generalized noise power gain,Z l is the updated measurement residual,
The obtaining the estimated value of the system state of the unbiased finite impulse response filter under different window sizes, selecting the corresponding window size with the highest estimated value precision according to the mahalanobis distance, including:
Randomly selecting an estimated value of a system state of the unbiased finite impulse response filter in a preset range of the window size, and primarily evaluating the basic set by using a mahalanobis distance to obtain an initial optimal window size;
Expanding the initial optimal window size, re-evaluating the estimated value of the system state corresponding to the expanded initial optimal window size by using the mahalanobis distance, and selecting the window size corresponding to the highest estimated value precision at the moment as the final optimal window size;
The method comprises the steps of randomly selecting an estimation value of a system state of an unbiased finite impulse response filter in a preset range of window sizes, and obtaining an initial optimal window size by using a primary estimation basic set of a mahalanobis distance, wherein the method comprises the following steps of:
setting a maximum value N max and a minimum value N min of a window size N preset range, equally dividing a section [ N min,Nmax ] into c+1 parts to obtain a set Wherein, The method comprises the steps of equally dividing a set into c+1 intervals, wherein i is { 1..c }, and c is a preset natural number;
At the collection Take on any value in each of the c+1 intervalsOperationThe corresponding unbiased finite impulse response filter generates respective state estimation values, and the mahalanobis distance value of each state estimation value is calculated as:
Where y k is the measurement vector, Is the estimated vector, C k is the measurement matrix, R k is the measurement noise covariance;
And selecting the estimated value with the minimum Markov distance value as an initial optimal estimated value, and taking the window size corresponding to the initial optimal estimated value as the initial optimal window size.
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