CN118189870A - Bridge displacement prediction and early warning method and system - Google Patents

Abstract

The invention provides a bridge displacement prediction and early warning method and system, comprising the following steps: monitoring the bridge structure, acquiring monitoring data, and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement; performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, and acquiring a displacement main component as a prediction target; establishing a deep learning prediction model based on a long and short-time memory network, and summing the displacement prediction result with the rest components to obtain complete predicted displacement; and calculating a residual error value between the actual displacement and the predicted displacement, determining a probability density function, selecting a threshold value and carrying out real-time early warning. The bridge displacement prediction and early warning method and system provided by the invention can effectively solve the problem of health management of the bridge structure under the conditions of extreme temperature and strong wind.

Description

Bridge displacement prediction and early warning method and system

Technical Field

The invention belongs to the technical field of bridge structure monitoring, and particularly relates to a bridge displacement prediction and early warning method and system.

Background

Large span bridges are extremely susceptible to extreme weather (e.g., large temperature fluctuations and storms, etc.), which can accelerate the aging, damage and deformation process of the structure. In order to ensure safe and stable operation of the bridge under extreme temperature and strong wind weather conditions, the method is particularly important for real-time and accurate health monitoring of bridge structures. Under the background, various high-precision sensors and global navigation satellite systems are widely applied to bridge structure health monitoring, and real-time acquisition of multidimensional data such as bridge structure deformation, vibration, temperature and the like is realized.

In the existing research, bridge displacement prediction and early warning mainly focuses on building a health monitoring model by fusing and processing real-time bridge structure data. However, the following problems still remain when dealing with extreme weather: when nonlinear and time-varying bridge structure data are processed in practical application, the traditional prediction model has the problem of insufficient prediction precision. Under extreme weather conditions, the response of the bridge structure can change dramatically and complex. Traditional models are difficult to quickly adapt to such fast changing and highly uncertain environments, resulting in untimely or inaccurate predictions, leading to erroneous guidance for health monitoring. In this case, how to effectively cope with dynamic changes of bridge structures in extreme weather and to improve accuracy of displacement prediction becomes a current problem.

In order to solve the problems, the invention provides a bridge displacement prediction and early warning method and system.

Disclosure of Invention

The invention aims to provide a bridge displacement prediction and early warning method and system, and aims to solve the technical problems in the background technology.

In order to achieve the above purpose, the invention adopts the following technical scheme: the bridge displacement prediction and early warning method comprises the following steps:

Monitoring the bridge structure, acquiring monitoring data, and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement;

Performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, and acquiring a displacement main component as a prediction target;

establishing a deep learning prediction model based on a long and short-time memory network, and summing the displacement prediction result with the rest components to obtain complete predicted displacement;

And calculating a residual error value between the actual displacement and the predicted displacement, determining a probability density function, selecting a threshold value and carrying out real-time early warning.

Preferably, the preprocessing of the monitoring data comprises the steps of:

Removing abnormal zero values of data caused by instrument faults; unifying the time dimension according to the acquisition time of various data; obtaining a correlation coefficient between the temperature (X) and the displacement (Y), and removing a time lag effect caused by the temperature on the displacement, wherein the formula of the correlation coefficient is as follows:

Wherein X _i represents a temperature sample; /(I) Representing the average value of the temperature samples; y _i represents a displacement sample; /(I)Representing the mean value of the displacement samples.

Preferably, the high-frequency denoising of the alignment data includes the steps of:

Decomposing the displacement data signals to obtain approximate coefficients and detail coefficients, then selecting a soft threshold function to process the detail coefficients, and then reconstructing the signals according to the final approximate coefficients and the detail coefficients through wavelet inverse transformation, wherein the soft threshold function formula is as follows:

Wherein λ represents a threshold value; ω represents wavelet coefficients; ω _λ represents the wavelet coefficient after giving the threshold value.

Preferably, the performing a variant modal decomposition of the displacement data signal comprises the steps of:

Converting the denoised displacement data signal into a frequency domain by using Hilbert yellow transform to obtain a single-side frequency spectrum of each modal component;

The central frequency band of each modal component is moved to a baseband through an exponential function, the bandwidth of each IMF component is estimated through the square of a norm gradient, and the following constraint variation problem formula is obtained;

where { u _k}＝{u₁,...,u_k } and { ω _k}＝{ω₁,...,ω_k } represent the set of all IMF components and center frequencies, respectively; f is the decomposed signal; delta (t) is a dirac function; s.t. is expressed as a constraint term;

the quadratic penalty factor alpha and the Lagrange multiplier lambda (t) are introduced, the constraint variation problem is changed into the unconstrained variation problem, and the extended Lagrange expression is as follows:

wherein the penalty factor α represents an initial center constraint intensity of each modality; update/> And lambda ⁿ⁺¹ to satisfy the condition:

wherein epsilon is the discrimination precision; when the requirement of discrimination precision is met, k modal components are obtained:/>

And obtaining displacement components, then carrying out correlation calculation on the components with temperature and wind speed respectively, and taking the displacement component with the largest correlation coefficient as a prediction target.

Preferably, in the deep learning prediction model established based on the long-short-time memory network, the model performance is evaluated by using a decision coefficient R ², a mean square error MSE and a root mean square error RMSE, and the formulas are as follows:

Where y _i is the actual measurement value, Is a predictive value of the model.

Preferably, in the establishing a deep learning prediction model based on the long-short time memory network, the input variable is temperature; the output variable is the displacement component with the greatest correlation in the vertical displacement.

Preferably, in the establishing a deep learning prediction model based on the long-short time memory network, the input variable is wind speed; the output variable is the displacement component with the greatest correlation in the lateral displacement.

Preferably, the calculating the residual error value between the actual displacement and the predicted displacement, determining the probability density function thereof, selecting the threshold value and performing real-time early warning comprises the following steps:

calculating the posterior probability that each residual sample belongs to each gaussian distribution:

Where γ (z _nk) is the posterior probability that sample x _n belongs to the kth gaussian distribution; alpha _k is the mixing coefficient of the kth gaussian, representing the weight of the kth gaussian in the ensemble model; n (x _n|μ_k,∑_k) is a probability density function of a multidimensional gaussian distribution; mu _k represents the mean value of the gaussian distribution; sigma _k represents the covariance matrix; alpha _k represents the mixing coefficient.

Preferably, the calculating the residual error value between the actual displacement and the predicted displacement, determining the probability density function thereof, selecting the threshold value and performing real-time early warning comprises the following steps:

Re-evaluating the parameters using the posterior probability using the following formula;

wherein: n is the total number of residual samples; n _k is the number of residual samples belonging to the kth gaussian distribution.

A bridge displacement predictive warning system, comprising:

the bridge monitoring module is used for monitoring the bridge structure, acquiring monitoring data and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement;

the target selection module is used for performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, acquiring a displacement main component and taking the displacement main component as a prediction target;

The model construction module is used for establishing a deep learning prediction model based on the long-short-term memory network, and summing the displacement prediction result with the rest components to obtain complete prediction displacement;

the result output module is used for calculating the residual error value between the actual displacement and the predicted displacement, determining the probability density function, selecting the threshold value and carrying out real-time early warning

The bridge displacement prediction and early warning method and system provided by the invention have the beneficial effects that: compared with the prior art, the bridge displacement prediction and early warning method and system provided by the invention aim at the bridge displacement prediction and early warning precision problem under extreme weather conditions. Firstly, removing abnormal values of monitoring data and temperature time lag effects in displacement data, and cleaning irregularities in original data. And secondly, extracting displacement components directly related to temperature and wind speed by wavelet threshold denoising and variation modal decomposition technology, and accurately predicting by a long-short-term memory network model. And finally, selecting a threshold value according to engineering requirements based on the Gaussian mixture model and carrying out real-time early warning. The invention can effectively solve the problem of health management of the bridge structure under the conditions of extreme temperature and strong wind.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments or the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart diagram of a bridge displacement prediction and early warning method provided by an embodiment of the invention;

FIG. 2 is a flow chart of a method of acquiring a dataset based on a variational modal decomposition technique;

FIG. 3 is a flow chart of a high-precision bridge displacement prediction and early warning method under extreme temperature and strong wind conditions;

Fig. 4 is a structural block diagram of a bridge displacement prediction and early warning system provided by an embodiment of the invention; .

In the figure: 1. a bridge monitoring module; 2. a target selection module; 3. a model building module; 4. and a result output module.

Detailed Description

In order to make the technical problems, technical schemes and beneficial effects to be solved more clear, the invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

Referring to fig. 1 to 4, a bridge displacement prediction and early warning method provided by the invention will now be described. The bridge displacement prediction and early warning method comprises the following steps:

S1, monitoring a bridge structure, acquiring monitoring data, and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement; and removing abnormal values and temperature time lag effects in displacement data through pretreatment.

The specific implementation process of the step S1 comprises the following steps:

S1.1, arranging a temperature sensor, an anemometer, a Beidou/global satellite navigation system and a real-time dynamic positioning receiver on the surface of a bridge, and collecting and monitoring temperature, wind speed and vertical and transverse displacement data of the bridge structure in real time. And removing abnormal zero values of data caused by instrument faults, and unifying time dimensions according to the acquisition time of various data.

S1.2, obtaining a Pearson correlation coefficient between temperature (X) and displacement (Y) by moving a time axis, taking a time interval of temperature sequence along the time axis according to monitoring data acquisition as a moving unit, realigning the temperature sequence and the displacement sequence, calculating the Pearson correlation coefficient between the temperature sequence and the displacement sequence, and obtaining the optimal lag time according to the time interval corresponding to the maximum value of the Pearson correlation coefficient; and (3) integrally moving the displacement data according to the obtained lag time, so as to remove the time lag effect of the temperature on the displacement, wherein the calculation formula of the pearson correlation coefficient is as follows:

Wherein X _i represents a temperature sample; /(I) Representing the average value of the temperature samples; y _i represents a displacement sample; /(I)Representing the mean value of the displacement samples.

S2, performing high-frequency denoising operation and variational modal decomposition operation on the displacement data, and acquiring a displacement main component and taking the displacement main component as a prediction target;

The specific implementation process of the step S2 comprises the following steps:

s2.1, removing high-frequency noise existing in displacement data (including vertical displacement and transverse displacement) by applying a wavelet threshold denoising method.

The specific process includes that a sym3 wavelet basis function is selected to decompose a displacement data signal to obtain an approximation coefficient and a detail coefficient; the approximation coefficients contain low frequency components of the signal, while the detail coefficients contain high frequency components of the signal, typically manifested as high frequency noise; by applying soft thresholding to the detail coefficients, smaller detail coefficients can be set to zero, effectively removing high frequency noise; and then reconstructing the signal according to the final approximate coefficient and the detail coefficient through wavelet inverse transformation, thereby eliminating high-frequency noise existing in the signal acquisition and transmission process and improving the signal quality. The soft threshold function formula is:

Wherein λ represents a threshold value; ω represents wavelet coefficients; ω _λ represents the wavelet coefficient after giving the threshold value.

S2.2, performing variation modal decomposition processing on the denoised bridge displacement data.

The specific process may be that the transform mode decomposition uses hilbert yellow transform to transform the denoised displacement data signal to the frequency domain, so as to obtain a single-side frequency spectrum of each mode component;

the central frequency band of each modal component is moved to a baseband through an exponential function, the bandwidth of each IMF (intrinsic modal function) component is estimated through the square of a norm gradient, and the following constraint variation problem formula is obtained;

where { u _k}＝{u₁,...,u_k } and { ω _k}＝{ω₁,...,ω_k } represent the set of all IMF components and center frequencies, respectively; f is the decomposed signal; delta (t) is a dirac function; s.t. is expressed as a constraint term;

the quadratic penalty factor alpha and the Lagrange multiplier lambda (t) are introduced, the constraint variation problem is changed into the unconstrained variation problem, and the extended Lagrange expression is as follows:

wherein the penalty factor α represents an initial center constraint intensity of each modality; update/> And lambda ⁿ⁺¹ to satisfy the condition:

wherein epsilon is the discrimination precision; when the requirement of discrimination precision is met, k modal components are obtained:/>

And obtaining displacement components, then carrying out correlation calculation on the components with temperature and wind speed respectively, and taking the displacement component with the largest correlation coefficient as a prediction target.

S2.3, decomposing through a variation mode to obtain each displacement component, calculating pearson correlation coefficients of each component with temperature and wind speed, and taking the displacement component with the largest correlation coefficient as a prediction target; wherein, the main component obtained by decomposing the temperature and the vertical displacement has the maximum correlation, and the main component obtained by decomposing the wind speed and the lateral displacement has the maximum correlation.

S3, establishing a deep learning prediction model based on a long-short-time memory network, and summing a displacement prediction result with the rest components to obtain complete prediction displacement; the prediction target obtained in the step 2 provides data for the deep learning prediction model in the step 3.

In this step, the network module unit of the deep learning prediction model includes: forget gate unit, input gate unit, cell state update unit, output gate unit.

The specific implementation process of the step S3 comprises the following steps:

S3.1, determining input and output parameters of the model. According to the applicable conditions, the environmental data and the displacement data are divided into a training set, a verification set and a test set, wherein the ratio of the training set to the verification set to the test set is 8:1:1.

The specific process is that when the deep learning prediction model is suitable for the extreme temperature condition prediction environment, the input variable is temperature; the output variable is the displacement component with the greatest correlation in the vertical displacement. When the deep learning prediction model is suitable for a strong wind condition prediction environment, the input variable is wind speed; the output variable is the displacement component with the greatest correlation in the lateral displacement.

S3.2, forward propagation is carried out through training data, prediction output is calculated, the difference between the prediction output and an actual target is calculated by using a mean square error loss function, and model parameters are updated through a backward propagation and optimizer;

in the forward propagation process, the model receives input data and calculates the input data through a long-short-time memory network to generate prediction output.

The forward propagation calculation process can be expressed as:

in the formula, X is model input data, For prediction output, the parameter W represents a weight matrix, b represents a bias vector, and f is an activation function Sigmoid.

The loss function is used for measuring the difference between the model prediction output and the actual target, and the calculation formula of the mean square error loss (RMSE) function is as follows:

Where y _i is the actual measurement value, Is a predictive value of the model;

The back propagation is used to calculate the gradient of the loss function to the model parameters for subsequent updating of the parameters using the optimizer. By means of the chain law, gradients can be efficiently calculated and model parameters updated using an optimizer.

The formula for parameter update is typically:

θ represents model parameters, i.e., a set of individual connection weights and offsets in the neural network; alpha is learning rate, and the step length is updated by control parameters; representing the gradient of the loss function with respect to the model parameters, i.e. the parameter gradient.

And S3.3, verifying the performance of the long-time and short-time memory network model by using the verification set data, and performing 10 times of cross verification on the test set data to verify.

S3.4, evaluating the model performance by using a decision coefficient R ², a mean square error MSE and a root mean square error RMSE, wherein the formulas are as follows:

Where y _i is the actual measurement value, Is a predictive value of the model.

S3.5, recording residual errors of the predicted value and the actual value after training is completed;

And S3.6, adding the prediction result and the rest displacement components decomposed by the variation mode to obtain complete real-time prediction displacement, wherein the method is suitable for displacement prediction under extreme air temperature and strong wind conditions.

S4, calculating residual error values between the actual displacement and the predicted displacement, determining probability density functions, selecting threshold values and carrying out real-time early warning

The specific implementation process of the step S4 comprises the following steps:

S4.1, initializing a mean value, a covariance matrix and a mixing coefficient of Gaussian distribution;

S4.2, calculating the posterior probability that each residual sample belongs to each Gaussian distribution:

Where γ (z _nk) is the posterior probability that sample x _n belongs to the kth gaussian distribution; alpha _k is the mixing coefficient of the kth gaussian, representing the weight of the kth gaussian in the ensemble model; n (x _n|μ_k,∑_k) is a probability density function of a multidimensional gaussian distribution; mu _k represents the mean value of the gaussian distribution; sigma _k represents the covariance matrix; alpha _k represents the mixing coefficient.

S4.3, re-evaluating parameters by using the posterior probability by adopting the following formula;

wherein: n is the total number of residual samples; n _k is the number of residual samples belonging to the kth gaussian distribution.

S4.4, repeating the two steps until the parameters are converged;

S4.5, determining a threshold value used for real-time displacement prediction early warning under two conditions of extreme temperature and strong wind, wherein the threshold value is considered to be selected, namely, the setting of the threshold value can be adjusted according to factors such as specific application scenes, risk bearing capacity and the like;

S4.6, substituting residual data obtained through real-time monitoring into the probability density function according to the obtained probability density function, calculating posterior probability of each residual sample, and marking samples with posterior probability higher than the threshold as abnormal or performing corresponding early warning operation.

Compared with the prior art, the bridge displacement prediction and early warning method provided by the invention aims at the problem of bridge displacement prediction and early warning precision under extreme weather conditions. Firstly, removing abnormal values of monitoring data and temperature time lag effects in displacement data, and cleaning irregularities in original data. And secondly, extracting displacement components directly related to temperature and wind speed by wavelet threshold denoising and variation modal decomposition technology, and accurately predicting by a long-short-term memory network model. And finally, selecting a threshold value according to engineering requirements based on the Gaussian mixture model and carrying out real-time early warning. The invention can effectively solve the problem of health management of the bridge structure under the conditions of extreme temperature and strong wind.

The invention also provides a bridge displacement prediction and early warning system, please refer to fig. 1 to 4 together, comprising: the bridge monitoring system comprises a bridge monitoring module 1, a target selecting module 2, a model constructing module 3 and a result output module 4, wherein the bridge monitoring module 1 is used for monitoring a bridge structure, acquiring monitoring data and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement; the target selection module 2 is used for performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, acquiring a displacement main component and taking the displacement main component as a prediction target; the model construction module 3 is used for establishing a deep learning prediction model based on a long and short time memory network, and summing displacement prediction results with the rest components to obtain complete prediction displacement; the result output module 4 is used for calculating the residual error value between the actual displacement and the predicted displacement, determining the probability density function, selecting the threshold value and carrying out real-time early warning.

The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (10)

1. The bridge displacement prediction and early warning method is characterized by comprising the following steps of:

Monitoring the bridge structure, acquiring monitoring data, and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement;

Performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, and acquiring a displacement main component as a prediction target;

establishing a deep learning prediction model based on a long and short-time memory network, and summing the displacement prediction result with the rest components to obtain complete predicted displacement;

And calculating a residual error value between the actual displacement and the predicted displacement, determining a probability density function, selecting a threshold value and carrying out real-time early warning.

2. The bridge displacement prediction and early warning method according to claim 1, wherein the preprocessing of the monitoring data comprises the following steps:

Removing abnormal zero values of data caused by instrument faults; unifying the time dimension according to the acquisition time of various data; obtaining a correlation coefficient between the temperature (X) and the displacement (Y), and removing a time lag effect caused by the temperature on the displacement, wherein the formula of the correlation coefficient is as follows:

Wherein X _i represents a temperature sample; /(I) Representing the average value of the temperature samples; y _i represents a displacement sample; /(I)Representing the mean value of the displacement samples.

3. The bridge displacement prediction and early warning method according to claim 1, wherein the high-frequency denoising of the displacement data comprises the following steps:

Decomposing the displacement data signals to obtain approximate coefficients and detail coefficients, then selecting a soft threshold function to process the detail coefficients, and then reconstructing the signals according to the final approximate coefficients and the detail coefficients through wavelet inverse transformation, wherein the soft threshold function formula is as follows:

Wherein λ represents a threshold value; ω represents wavelet coefficients; ω _λ represents the wavelet coefficient after giving the threshold value.

4. The bridge displacement prediction and early warning method according to claim 3, wherein the performing of the variation modal decomposition on the displacement data signal comprises the steps of:

Converting the denoised displacement data signal into a frequency domain by using Hilbert yellow transform to obtain a single-side frequency spectrum of each modal component;

The central frequency band of each modal component is moved to a baseband through an exponential function, the bandwidth of each IMF component is estimated through the square of a norm gradient, and the following constraint variation problem formula is obtained;

where { u _k}＝{u₁,...,u_k } and { ω _k}＝{ω₁,...,ω_k } represent the set of all IMF components and center frequencies, respectively; f is the decomposed signal; delta (t) is a dirac function; s.t. is expressed as a constraint term;

the quadratic penalty factor alpha and the Lagrange multiplier lambda (t) are introduced, the constraint variation problem is changed into the unconstrained variation problem, and the extended Lagrange expression is as follows:

; wherein the penalty factor α represents an initial center constraint intensity of each modality; updating And lambda ⁿ⁺¹ to satisfy the condition:

Wherein epsilon is the discrimination precision; when the requirement of discrimination precision is met, k modal components are obtained:

and obtaining displacement components, then carrying out correlation calculation on the components with temperature and wind speed respectively, and taking the displacement component with the largest correlation coefficient as a prediction target.

5. The bridge displacement prediction and early warning method according to claim 4, wherein the model performance is evaluated by using a decision coefficient R ², a mean square error MSE and a root mean square error RMSE in the establishment of the deep learning prediction model based on the long short time memory network, and the formulas are as follows:

Where y _i is the actual measurement value, Is a predictive value of the model.

6. The bridge displacement prediction and early warning method according to claim 5, wherein in the deep learning prediction model established based on the long and short time memory network, the input variable is temperature; the output variable is the displacement component with the greatest correlation in the vertical displacement.

7. The bridge displacement prediction early warning method according to any one of claims 5 or 6, wherein in the deep learning prediction model established based on the long and short time memory network, the input variable is wind speed; the output variable is the displacement component with the greatest correlation in the lateral displacement.

8. The bridge displacement prediction and early warning method according to claim 1, wherein the calculating of the residual value between the actual displacement and the predicted displacement, determining the probability density function thereof, selecting the threshold value and performing the real-time early warning comprises the following steps:

calculating the posterior probability that each residual sample belongs to each gaussian distribution:

Where γ (z _nk) is the posterior probability that sample x _n belongs to the kth gaussian distribution; alpha _k is the mixing coefficient of the kth gaussian, representing the weight of the kth gaussian in the ensemble model; n (x _n|μ_k,∑_k) is a probability density function of a multidimensional gaussian distribution; mu _k represents the mean value of the gaussian distribution; sigma _k represents the covariance matrix; alpha _k represents the mixing coefficient.

9. The bridge displacement prediction and early warning method according to claim 8, wherein the calculating the residual value between the actual displacement and the predicted displacement, determining the probability density function thereof, selecting the threshold value and performing real-time early warning comprises the following steps:

Re-evaluating the parameters using the posterior probability using the following formula;

wherein: n is the total number of residual samples; n _k is the number of residual samples belonging to the kth gaussian distribution.

10. The bridge displacement prediction early warning system is characterized by comprising:

the bridge monitoring module is used for monitoring the bridge structure, acquiring monitoring data and preprocessing the monitoring data; the monitoring data comprise temperature, wind speed, vertical displacement and transverse displacement;

the target selection module is used for performing high-frequency denoising operation and variation modal decomposition operation on the displacement data, acquiring a displacement main component and taking the displacement main component as a prediction target;

The model construction module is used for establishing a deep learning prediction model based on the long-short-term memory network, and summing the displacement prediction result with the rest components to obtain complete prediction displacement;

And the result output module is used for calculating the residual error value between the actual displacement and the predicted displacement, determining the probability density function, selecting a threshold value and carrying out real-time early warning.