CN105335554A - Dissolved oxygen concentration soft measurement method based on improved extreme learning machine - Google Patents

Abstract

The invention discloses a dissolved oxygen concentration soft measurement method based on an improved extreme learning machine. The method comprises the following steps: S1, performing data acquisition on water factors which influence water quality; S2, performing outlier detection and filter processing operation on the acquired data; S3, using pre-processed batch historical data as input information of a soft-measuring model, using a detected dissolved oxygen concentration laboratory value as output data, establishing a dissolved oxygen concentration model; S4, establishing a model on-line correction mechanism to dynamically correct an aquaculture dissolved oxygen concentration model; based on real-time data information in an aquaculture production process, performing error comparison on the dissolved oxygen concentration laboratory value and the dissolved oxygen concentration value output by the soft-measuring model, and using an ellipsoidal bounding stable learning algorithm to learn and update the parameters of the dissolved oxygen concentration soft-measuring model. The ellipsoidal bounding stable learning algorithm can update the parameters of the model, and can ensure model errors to be stable and bounded.

Description

A kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine

Technical field

The present invention relates to soft sensor modeling field, particularly relating to a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine.

Background technology

For the prediction of dissolved oxygen concentration in aquaculture, be mostly the blackbox model based on neural network at present, utilize different optimized algorithms to improve the learning efficiency of network.Namely this hard measurement strategy does not carry out specificity analysis to problems such as the correlativity affected between each factor data of water quality and collinearities, rationally effective data preprocessing method is not set up yet, and major part lacks model tuning mechanism, learning algorithm can not ensure that error is stablized.Therefore, the precision of this class model constantly declines in time.Practice shows, neural network is difficult to separately for aquaculture process, because learning algorithm is accurate not, object response ratio learning process is fast, and long-play there will be phenomenons such as dispersing, unstable.Although the model parameter of prior art to neural network or extreme learning machine is optimized, can not ensure the stability of modeling error, As time goes on, model error may increase gradually.

Summary of the invention

According to prior art Problems existing, the invention discloses a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine, comprising the following steps:

S1: on the water temperature information, pH value information, the total ammonia nitrogen that affect water quality factors nitrite nitrogen and nitrate nitrogen information carries out data acquisition;

S2: Outliers detection, filtering process operation are carried out to the data collected: first adopt the robust data preprocess method of improvement identify the outlier in data and abnormal data and delete, process the data acquisition middle position value filtering technology of remainder, the inputoutput data of intermediate value as soft-sensing model of data is often organized in reservation again;

S3: adopt above-mentioned pretreated lot history data as the input information of soft-sensing model, sets up dissolved oxygen concentration model using the dissolved oxygen concentration laboratory values detected as output data;

Adopt the extreme learning machine flexible measurement method based on improving, namely ellipsoid is utilized to occur simultaneously theoretical, the Errors of extreme learning machine is defined as an ellipsoid, modeling error is defined as another ellipsoid, rebuild extreme learning machine model form, structure recursive identification algorithm, finds optimum soft-sensing model parameter, makes soft-sensing model export dissolved oxygen concentration value;

S4: Modling model on-line correction mechanism, the dynamic calibration of aquaculture dissolved oxygen concentration model: based on the real time data information in aquaculture production process, the dissolved oxygen concentration value that dissolved oxygen concentration laboratory values and soft-sensing model export is carried out application condition, adopts ellipsoidal bounding to stablize the soft-sensing model parameter of learning algorithm to dissolved oxygen concentration and learn and upgrade.

Further, rebuilding extreme learning machine model shape is following form:

${\hat{y}}_i\left(k\right)=B_k^T{\mathrm{\θ}}_i\left(k\right)---\left(1\right)$

Wherein: for the model output valve of extreme learning machine, $B_k^T$ For model Given information, θ _ik () is model parameter, set up learning algorithm according to the model after reconstruct, ensures the modeling error of definition

$e_i\left(k\right)=y_i\left(k\right)-{\hat{y}}_i\left(k\right)---\left(2\right)$

Stablize bounded, wherein y _ik () is true value, i.e. the laboratory values of dissolved oxygen DO.

Adopt the extreme learning machine flexible measurement method concrete steps based on improving as follows:

In S3, concrete mode is as follows: the Errors ellipsoid E first defining extreme learning machine _kfor:

$E_k=\left\{{\mathrm{\θ}}_i\left(k\right)\right|{\widetilde{\mathrm{\θ}}}_i^T\left(k\right)P_k^{-1}{\widetilde{\mathrm{\θ}}}_i\left(k\right)\≤1\}---\left(3\right)$

Wherein the unknown best initial weights minimizing modeling error, for positive semidefinite symmetric matrix, modeling error be defined as another ellipsoid S _k, its form is:

$S_k=\left\{B_k^T{\mathrm{\θ}}_i^{*}\right|\frac{1}{{\mathrm{\γ}}_i}\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\θ}}_i^{*}|{|}^2\≤1\}---\left(4\right)$

Wherein γ _ibe a normal number, i=1 ... n, ellipsoid collection S ₁, S ₂center be suppose that initial parameter error is at ellipsoid E ₁within:

$E_1=\left\{{\mathrm{\θ}}_i\left(1\right)\right|{\widetilde{\mathrm{\θ}}}_i^T\left(1\right)P_1^{-1}{\widetilde{\mathrm{\θ}}}_i\left(1\right)\≤1\}---\left(5\right)$

Wherein P ₁given diagonal angle positive definite matrix, P ₁=P ₁ ^t>0, P ₁∈ R ^{2m × 2m}, m refers to the dimension of input variable, ellipsoid set E ₁, E ₂common center, two ellipsoid E _kand S _kcommon factor (1-λ _k) E _k+ λ _ks _k, meet

$(1-{\mathrm{\λ}}_k){\widetilde{\mathrm{\θ}}}_i^T\left(k\right)P_k^{-1}{\widetilde{\mathrm{\θ}}}_i\left(k\right)+\frac{1}{{\mathrm{\γ}}_i}{\mathrm{\λ}}_k\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\θ}}_i^{*}|{|}^2\≤1---\left(6\right)$

Wherein 0≤λ _k≤ 1, according to E _kwhen being a bounding ellipsoid collection, E _k+1also be the principle of bounding ellipsoid collection, design recursive identification algorithm makes the new ellipsoid area of two oval common factor compositions more and more less, finally finds the minimal set satisfied condition.

Adopt ellipsoidal bounding to stablize learning algorithm in S4 learn soft-sensing model parameter and upgrade in the following way:

Following recursive identification algorithm is adopted to upgrade P _kand θ _i(k)

${\mathrm{\θ}}_i(k+1)={\mathrm{\θ}}_i\left(k\right)+\frac{{\mathrm{\λ}}_k}{{\mathrm{\γ}}_i}{P}_k{B}_k{e}_i\left(k\right)---\left(6\right)$

${\mathrm{\λ}}_k=\frac{{\mathrm{\λ\γ}}_i}{1+B_k^T{P}_{k+1}{B}_k}---\left(7\right)$

$(1-{\mathrm{\λ}}_k)P_{k+1}=P_k-\frac{{\mathrm{\λ}}_k}{(1-{\mathrm{\λ}}_k){\mathrm{\γ}}_i+{\mathrm{\λ}}_k{B}_k^T{P}_k{B}_k}{P}_k{B}_k{B}_k^T{P}_k---\left(8\right)$

Wherein, 0< λ <1, and λ _k>0, then E _k+1for ellipsoid collection, meet

$\begin{array}{c}{E}_{k+1}=\left\{{\mathrm{\&theta;}}_i(k+1)\right|{\widetilde{\mathrm{\&theta;}}}_i^T(k+1)P_{k+1}^{-1}{\widetilde{\mathrm{\&theta;}}}_i(k+1)\\ \&le;1-\frac{{\mathrm{\&lambda;}}_k}{{\mathrm{\&gamma;}}_i}(1-\mathrm{\&lambda;})e_i^2\left(k\right)\&le;1\}\end{array}$

The normalized modeling error of soft-sensing model approach

$\underset{k\&RightArrow;\mathrm{\&infin;}}{\lim \sup }\frac{1}{T}\underset{k=1}{\overset{T}{\&Sigma;}}{\hat{e}}_i^2\left(k\right)\&le;\frac{1}{1-\mathrm{\&lambda;}}---\left(9\right)$

Wherein 0< λ <1.

Owing to have employed technique scheme, provided by the invention based on improving the dissolved oxygen concentration flexible measurement method of extreme learning machine, the ellipsoidal bounding of employing stablizes learning algorithm, can not only Renewal model parameter, and can ensure that modeling error stablizes bounded.Because aquaculture process is slow, and affect the many factors of aquaculture process, the interphase interaction of parameter influences each other again, has uncertainty, and error easily occurs Divergent Phenomenon.And stability is the prerequisite ensureing that model is permanently effective, it is the basis that algorithm carries out application on site.This algorithm covers the operation of the data prediction such as Outliers detection, filtering, and comprise stable learning algorithm, the on-line measurement of dissolved oxygen concentration can not only be realized, and can make error within technological requirement scope, experimental result shows that this method learning ability is strong, and generalization ability is good.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present application or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, the accompanying drawing that the following describes is only some embodiments recorded in the application, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is the process flow diagram of method disclosed by the invention;

The display figure that predicts the outcome that Fig. 2 is the flexible measurement method of dissolved oxygen concentration disclosed in the present invention.

Embodiment

For making technical scheme of the present invention and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, clear complete description is carried out to the technical scheme in the embodiment of the present invention:

A kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine as shown in Figure 1, the following scheme of concrete employing:

S1: on the water temperature information, pH value information, the total ammonia nitrogen that affect water quality factors nitrite nitrogen and nitrate nitrogen information carries out data acquisition, can gather other information in real process, only illustrates the above-mentioned five kinds of water quality factors information of book here.

S2: Outliers detection, filtering process operation are carried out to the above-mentioned data collected, profit group puts identification and filtering operation does not have sequencing, first we can adopt the robust data preprocess method of improvement identify the outlier in data and abnormal data and delete, process the data acquisition middle position value filtering technology of remainder, the inputoutput data of intermediate value as soft-sensing model of data is often organized in reservation again.Namely filtering process adopts conventional middle position value filtering technology.

S3: as shown in Figure 2, the dissolved oxygen concentration laboratory values detected, as the input information of soft-sensing model, is set up dissolved oxygen concentration model as output data by the lot history data adopting S2 pretreated.Concrete scheme is: adopt the extreme learning machine flexible measurement method based on improving, namely ellipsoid is utilized to occur simultaneously theoretical, the Errors of extreme learning machine is defined as an ellipsoid, modeling error is defined as another ellipsoid, rebuild extreme learning machine model form, structure recursive identification algorithm, then finds optimum soft-sensing model parameter, makes soft-sensing model export dissolved oxygen concentration value.

S4: Modling model on-line correction mechanism, the dynamic calibration of aquaculture dissolved oxygen concentration model: based on the real time data information in aquaculture production process, the dissolved oxygen concentration value that dissolved oxygen concentration laboratory values and soft-sensing model export is carried out application condition, adopts ellipsoidal bounding to stablize the soft-sensing model parameter of learning algorithm to dissolved oxygen concentration and learn and upgrade.Here by when detecting that dissolved oxygen concentration value and the actual value detected compare, when two values according to the requirement of reality in error range or the dissolved oxygen concentration value that exports of soft-sensing model and actual detected value relatively time then model is this moment the model that we create.

Further, rebuilding extreme learning machine model shape is following form:

${\hat{y}}_i\left(k\right)=B_k^T{\mathrm{\&theta;}}_i\left(k\right)---\left(1\right)$

Wherein: for the model output valve of extreme learning machine, for model Given information, θ _ik () is model parameter, set up learning algorithm according to the model after reconstruct, ensures the modeling error of definition

$e_i\left(k\right)=y_i\left(k\right)-{\hat{y}}_i\left(k\right)---\left(2\right)$

Stablize bounded, wherein y _ik () is true value, i.e. the laboratory values of dissolved oxygen DO.

Due to extreme learning machine and neural networks with single hidden layer similar, can be write as following form:

$\hat{y}\left(k\right)=V_k\mathrm{\&phi;}\&lsqb;W_{k}x\left(k\right)\&rsqb;$

Wherein x (k) ∈ R ^mrepresent input variable, represent output variable, V _k∈ R ^{1 × m}represent the output layer weight vector of neural network, W _k∈ R ^{m × n}represent the hidden layer weight matrix of neural network, φ ∈ R ^mrepresent the activation function of hidden layer, generally get Sigmoid function.

Re-constructed as following form:

${\hat{y}}_i\left(k\right)=B_k^T{\mathrm{\&theta;}}_i\left(k\right)$

$B_k^T=\&lsqb;\mathrm{\&phi;},{\mathrm{\&phi;}}^{\&prime;}{V}_1^{T}x\&rsqb;$

θ(k)＝[θ ₁(k)，…θ _n(k)] ^T

Further, adopt the extreme learning machine flexible measurement method concrete steps based on improving as follows:

In S3, concrete mode is as follows: the Errors ellipsoid E first defining extreme learning machine _kfor:

$E_k=\left\{{\mathrm{\&theta;}}_i\left(k\right)\right|{\widetilde{\mathrm{\&theta;}}}_i^T\left(k\right)P_k^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(k\right)\&le;1\}---\left(3\right)$

Wherein the unknown best initial weights minimizing modeling error, for positive semidefinite symmetric matrix, modeling error be defined as another ellipsoid S _k, its form is:

$S_k=\left\{B_k^T{\mathrm{\&theta;}}_i^{*}\right|\frac{1}{{\mathrm{\&gamma;}}_i}\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\&theta;}}_i^{*}|{|}^2\&le;1\}---\left(4\right)$

Wherein γ _ibe a normal number, i=1 ... n, ellipsoid collection S ₁, S ₂center be suppose that initial parameter error is at ellipsoid E ₁within:

$E_1=\left\{{\mathrm{\&theta;}}_i\left(1\right)\right|{\widetilde{\mathrm{\&theta;}}}_i^T\left(1\right)P_1^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(1\right)\&le;1\}---\left(5\right)$

Wherein P ₁given diagonal angle positive definite matrix, P ₁=P ₁ ^t>0, P ₁∈ R ^{2m × 2m}, m is the dimension of input variable, ellipsoid set E ₁, E ₂common center, two ellipsoid E _kand S _kcommon factor (1-λ _k) E _k+ λ _ks _k, meet

$(1-{\mathrm{\&lambda;}}_k){\widetilde{\mathrm{\&theta;}}}_i^T\left(k\right)P_k^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(k\right)+\frac{1}{{\mathrm{\&gamma;}}_i}{\mathrm{\&lambda;}}_k\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\&theta;}}_i^{*}|{|}^2\&le;1---\left(6\right)$

Wherein 0≤λ _k≤ 1, according to E _kwhen being a bounding ellipsoid collection, E _k+1also be the principle of bounding ellipsoid collection, design recursive identification algorithm makes the new ellipsoid area of two oval common factor compositions more and more less, finally finds the minimal set satisfied condition.

Adopt ellipsoidal bounding to stablize learning algorithm in S4 learn soft-sensing model parameter and upgrade in the following way:

Following recursive identification algorithm is adopted to upgrade P _kand θ _i(k)

${\mathrm{\&theta;}}_i(k+1)={\mathrm{\&theta;}}_i\left(k\right)+\frac{{\mathrm{\&lambda;}}_k}{{\mathrm{\&gamma;}}_i}{P}_k{B}_k{e}_i\left(k\right)---\left(7\right)$

${\mathrm{\&lambda;}}_k=\frac{{\mathrm{\&lambda;\&gamma;}}_i}{1+B_k^T{P}_{k+1}{B}_k}---\left(8\right)$

$(1-{\mathrm{\&lambda;}}_k)P_{k+1}=P_k-\frac{{\mathrm{\&lambda;}}_k}{(1-{\mathrm{\&lambda;}}_k){\mathrm{\&gamma;}}_i+{\mathrm{\&lambda;}}_k{B}_k^T{P}_k{B}_k}{P}_k{B}_k{B}_k^T{P}_k---\left(9\right)$

Wherein, 0< λ <1, and λ _k>0, then E _k+1for ellipsoid collection, meet

$\begin{array}{c}{E}_{k+1}=\left\{{\mathrm{\&theta;}}_i(k+1)\right|{\widetilde{\mathrm{\&theta;}}}_i^T(k+1)P_{k+1}^{-1}{\widetilde{\mathrm{\&theta;}}}_i(k+1)\\ \&le;1-\frac{{\mathrm{\&lambda;}}_k}{{\mathrm{\&gamma;}}_i}(1-\mathrm{\&lambda;})e_i^2\left(k\right)\&le;1\}\end{array}$

The normalized modeling error of soft-sensing model approach

$\underset{k\&RightArrow;\mathrm{\&infin;}}{\lim \sup }\frac{1}{T}\underset{k=1}{\overset{T}{\&Sigma;}}{\hat{e}}_i^2\left(k\right)\&le;\frac{1}{1-\mathrm{\&lambda;}}---\left(10\right)$

Wherein 0< λ <1.

The above; be only the present invention's preferably embodiment; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses; be equal to according to technical scheme of the present invention and inventive concept thereof and replace or change, all should be encompassed within protection scope of the present invention.

Claims (5)

1., based on the dissolved oxygen concentration flexible measurement method improving extreme learning machine, it is characterized in that: comprise the following steps:

S1: on the water temperature information, pH value information, the total ammonia nitrogen that affect water quality factors nitrite nitrogen and nitrate nitrogen information carries out data acquisition;

S2: Outliers detection, filtering process operation are carried out to the data collected: first adopt the robust data preprocess method of improvement identify the outlier in data and abnormal data and delete, process the data acquisition middle position value filtering technology of remainder, the inputoutput data of intermediate value as soft-sensing model of data is often organized in reservation again;

S3: adopt above-mentioned pretreated lot history data as the input information of soft-sensing model, sets up dissolved oxygen concentration model using the dissolved oxygen concentration laboratory values detected as output data;

Adopt the extreme learning machine flexible measurement method based on improving, namely ellipsoid is utilized to occur simultaneously theoretical, the Errors of extreme learning machine is defined as an ellipsoid, modeling error is defined as another ellipsoid, rebuild extreme learning machine model form, structure recursive identification algorithm, finds optimum soft-sensing model parameter, makes soft-sensing model export dissolved oxygen concentration value;

S4: Modling model on-line correction mechanism, the dynamic calibration of aquaculture dissolved oxygen concentration model: based on the real time data information in aquaculture production process, the dissolved oxygen concentration value that dissolved oxygen concentration laboratory values and soft-sensing model export is carried out application condition, adopts ellipsoidal bounding to stablize the soft-sensing model parameter of learning algorithm to dissolved oxygen concentration and learn and upgrade.

2. a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine according to claim 1, is further characterized in that:

Rebuilding extreme learning machine model shape is following form:

${\hat{y}}_i\left(k\right)=B_k^T{\mathrm{\&theta;}}_i\left(k\right)---\left(1\right)$

Wherein: for the model output valve of extreme learning machine, for model Given information, θ _ik () is model parameter, set up learning algorithm according to the model after reconstruct, ensures the modeling error of definition

$e_i\left(k\right)=y_i\left(k\right)-{\hat{y}}_i\left(k\right)---\left(2\right)$

Stablize bounded, wherein y _ik () is true value, i.e. the laboratory values of dissolved oxygen DO.

3. a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine according to claim 1, is further characterized in that: adopt the extreme learning machine flexible measurement method concrete steps based on improving as follows:

In S3, concrete mode is as follows: the Errors ellipsoid E first defining extreme learning machine _kfor:

$E_k=\left\{{\mathrm{\&theta;}}_i\left(k\right)\right|{{\widetilde{\mathrm{\&theta;}}}_i}^T\left(k\right){P_k}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(k\right)\&le;1\}---\left(3\right)$

Wherein the unknown best initial weights minimizing modeling error, for positive semidefinite symmetric matrix, modeling error be defined as another ellipsoid S _k, its form is:

$S_k=\left\{B_k^T{\mathrm{\&theta;}}_i^{*}\right|\frac{1}{{\mathrm{\&gamma;}}_i}\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\&theta;}}_i^{*}|{|}^2\&le;1\}---\left(4\right)$

Wherein γ _ibe a normal number, i=1 ... n, ellipsoid collection S ₁, S ₂center be suppose that initial parameter error is at ellipsoid E ₁within:

$E_1=\left\{{\mathrm{\&theta;}}_i\left(1\right)\right|{{\widetilde{\mathrm{\&theta;}}}_i}^T\left(1\right){P_1}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(1\right)\&le;1\}---\left(5\right)$

Wherein P ₁given diagonal angle positive definite matrix, p ₁∈ R ^{2m × 2m}, m is the dimension of input variable, ellipsoid set E ₁, E ₂common center, two ellipsoid E _kand S _kcommon factor (1-λ _k) E _k+ λ _ks _k, meet

$(1-{\mathrm{\&lambda;}}_k){{\widetilde{\mathrm{\&theta;}}}_i}^T\left(k\right){P_k}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(k\right)+\frac{1}{{\mathrm{\&gamma;}}_i}{\mathrm{\&lambda;}}_k\left|\right|y_i\left(k\right)-B_k^T{\mathrm{\&theta;}}_i^{*}|{|}^2\&le;1---\left(6\right)$

Wherein 0≤λ _k≤ 1, according to E _kwhen being a bounding ellipsoid collection, E _k+1also be the principle of bounding ellipsoid collection, design recursive identification algorithm makes the new ellipsoid area of two oval common factor compositions more and more less, finally finds the minimal set satisfied condition.

4. a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine according to claim 1, is further characterized in that: adopt ellipsoidal bounding to stablize learning algorithm in S4 and learn soft-sensing model parameter and upgrade in the following way:

Following recursive identification algorithm is adopted to upgrade P _kand θ _i(k)

${\mathrm{\&theta;}}_i(k+1)={\mathrm{\&theta;}}_i\left(k\right)+\frac{{\mathrm{\&lambda;}}_k}{{\mathrm{\&gamma;}}_i}{P}_k{B}_k{e}_i\left(k\right)---\left(6\right)$

${\mathrm{\&lambda;}}_k=\frac{{\mathrm{\&lambda;\&gamma;}}_i}{1+B_k^T{P}_{k+1}{B}_k}---\left(7\right)$

$(1-{\mathrm{\&lambda;}}_k)P_{k+1}=P_k-\frac{{\mathrm{\&lambda;}}_k}{(1-{\mathrm{\&lambda;}}_k){\mathrm{\&gamma;}}_i+{\mathrm{\&lambda;}}_k{B}_k^T{P}_k{B}_k}{P}_k{B}_k{B}_k^T{P}_k---\left(8\right)$

Wherein, 0< λ <1, and λ _k>0, then E _k+1for ellipsoid collection, meet

$\begin{array}{c}{E}_{k+1}=\left\{{\mathrm{\&theta;}}_i(k+1)\right|{{\widetilde{\mathrm{\&theta;}}}_i}^T(k+1)P_{k+1}^{-1}{\widetilde{\mathrm{\&theta;}}}_i(k+1)\\ \&le;1-\frac{{\mathrm{\&lambda;}}_k}{{\mathrm{\&gamma;}}_i}\left(1-\mathrm{\&lambda;}\right)e_i^2\left(k\right)\&le;1\}\end{array}.$

5. a kind of dissolved oxygen concentration flexible measurement method based on improving extreme learning machine according to claim 1, is further characterized in that: the normalized modeling error of soft-sensing model approach

$\underset{k\&RightArrow;\mathrm{\&infin;}}{\lim sup}\frac{1}{T}\underset{k=1}{\overset{T}{\&Sigma;}}{\hat{e}}_i^2\left(k\right)\&le;\frac{1}{1-\mathrm{\&lambda;}}---\left(9\right)$

Wherein 0< λ <1.