Time series signal prediction method based on quantum filtering model

Abstract

The present invention provides a method for predicting a time series signal based on a quantum filtering model, which includes: setting filtering parameter values ​​and initial values ​​of each function, obtaining all time series signal data, calculating the difference function at each moment in turn and updating the weight function, calculating the potential energy function, calculating the wave function and the filtered time series signal data according to the Schrödinger equation in differential form, calculating the value of each quantile of the density matrix and regressing each quantile respectively, predicting the quantile value at each moment and predicting the time series signal data value at the next moment in turn, and then predicting the time series signal data that is greater than the last moment in the time series signal data in time. The present invention relies on the basic quantum filtering model, can realize filtering processing without making any assumptions about the distribution form of the noise signal, and realizes the prediction function of quantum filtering.

Description

Technical Field

[0001] The invention belongs to the technical field of signal filtering and prediction, and in particular to a time series signal prediction method based on a quantum filtering model. Background Art

[0002] In the field of filtering and prediction of time series signal data, most commonly used methods such as Kalman filtering, extended Kalman filtering and unscented Kalman filtering need to assume that the noise signal obeys Gaussian distribution, and the particle method needs to give the specific form of the noise distribution in advance. These methods are difficult to effectively filter out non-Gaussian noise signals in the data without knowing the form of the noise distribution.

[0003] Quantum filtering draws on the principle of "group response" of a large number of particles in physics to perform filtering processing. This method does not make any assumptions about the noise signal, so it is suitable for filtering and denoising signals when the noise distribution form is unknown. However, the existing quantum filtering model cannot realize the prediction function. The existing literature only proposes the abstract concept of "predictor" for the quantum filtering model, but does not realize the specific prediction function of the "predictor". Therefore, in order to take into account the prediction function, it is urgent and necessary to seek a time series signal prediction method based on the quantum filtering model so that the quantum filtering model can also have the prediction ability under the condition of being able to filter non-Gaussian noise signals. Summary of the invention

[0004] In view of the defects in the above-mentioned prior art, the present invention proposes a method for predicting time series signals based on a quantum filtering model. The method includes setting filter parameter values ​​and initial values ​​of each function, obtaining all time series signal data, calculating the difference function at each moment in turn and updating the weight function, calculating the potential energy function, calculating the wave function and the filtered time series signal data according to the Schrödinger equation in differential form, calculating the value of each quantile of the density matrix and regressing each quantile respectively, predicting the quantile value at each moment and predicting the time series signal data value at the next moment in turn, and then predicting the time series signal data that is greater than the last moment in the time series signal data in time. Relying on the basic quantum filtering model, the present invention can realize filtering processing without making any assumptions about the distribution form of the noise signal, and realizes the prediction function of quantum filtering.

[0005] The present invention provides a time series signal prediction method based on a quantum filtering model, which comprises the following steps:

[0006] S1. Set the filter parameter value and the initial value of each function, and calculate the predicted value of the time series signal data at time t1

[0007] S2, get the data from t1 to t TAll the time series signal data y(t1),y(t2),...,y(t T ), and input into step S3 in sequence;

[0008] S3, starting from time t1, according to t i Time series signal data predicted at the moment The timing signal data y(t i ) and wave function Calculate the difference function at time t1

[0009]

[0010]

[0011] Among them, x n represents the spatial position corresponding to the nth quantum filter neuron; N represents the number of quantum filter neurons; φ(x n ,t i ) indicates t i The difference function of the spatial position corresponding to the nth quantum filter neuron at the moment; σ f represents the input distribution variance; ψ(x n ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment;

[0012] S4. Update t i The weight function at the moment

[0013]

[0014]

[0015] Among them, W(x n ,t i ) indicates t i The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment; W(x n ,t i-1 ) indicates t i-1 The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment; β d represents the weight forgetting rate; β represents the weight updating rate;

[0016] S5. According to t i The difference function of time Weight function and potential energy coefficient ζ, calculate t i The potential energy function at time

[0017]

[0018] V(x n ,t i )=ζW(x n ,t i )φ(x n ,t i ) (7)

[0019] Among them, V(x n ,t i ) indicates t i The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment;

[0020] S6. Calculate t based on the difference form of the Schrödinger equation i Wave function at time

[0021]

[0022]

[0023] Among them, ψ(x n ,t i ) indicates t i The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n+1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n+1th quantum filter neuron at the moment; ψ(x n-1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n-1th quantum filter neuron at the moment; V(x n ,t i-1 ) indicates t i-1 The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment; i represents the imaginary unit; Δx represents the difference between the positions of adjacent quantum neurons, that is, Δx = x n+1 -x n =x n -x n-1 ; m represents the diffusion coefficient;

[0024] S7. Calculate t i Time series signal data after moment filtering As output signal;

[0025] S8, wave function calculated according to step S6 Calculate t i The values ​​of each quantile of the density matrix at each moment;

[0026] S9. Regress each quantile and predict t i+1 The quantile value at the moment:

[0027] S10, prediction t i+1 The time series signal data value at the moment As input data;

[0028] S11, repeat steps S3 to S10, and complete all the timing signal data y(t1), y(t2), ..., y(t T-1 ) filtering and prediction of the corresponding next moment time series signal data value

[0029] S12, using t T Regression prediction results at time For a time greater than the last moment t in the time series signal data T The time t future The time series signal data at the moment is predicted:

[0030] S121, get t T The regression parameters of all quantiles at time instant;

[0031] S122, according to t T The regression parameters of each quantile at time t are calculated. future Data of each quantile at the time Where M represents the number of quantiles and is a natural number greater than 1;

[0032] S123, calculate t future The predicted value of the time series signal data at time

[0033]

[0034] in, Indicates t future The j-th quantile data at time; Indicates t future The j+1th quantile data at the moment; j represents the value of the wave function at the jth quantile; j+1 Represents the value of the wave function at the j+1th quantile.

[0035] Further, the step S1 specifically includes the following steps:

[0036] S011. Set the value of the filtering parameters, which include the weight update rate β, the weight forgetting rate β d , potential energy coefficient ζ, diffusion coefficient m and input distribution variance σ f ;

[0037] S012, setting the initial values ​​of other parts required in the filtering process, the initial values ​​of other parts including the number N of quantum filter neurons and the corresponding spatial position The value of the wave function Initial value of weight function All wave function quantiles that need to be calculated are percen1, percen2,…, percen M and the time length T for regression calculation regress ;

[0038] S013, based on the initial value of the wave function Calculate the predicted value of the time series signal data at time t1

[0039]

[0040] Among them, ψ(x n , t=0) represents the initial value of the wave function of the spatial position corresponding to the nth quantum filter neuron.

[0041] Further, the step S8 specifically includes the following steps:

[0042] S81. Calculate t i The density matrix at time

[0043]

[0044] ρ(x n ,t i )=|ψ(x n ,t i )| 2 (12)

[0045] Among them, ρ(x n ,t i ) indicates t i The density value of the spatial position corresponding to the nth quantum filter neuron at the moment;

[0046] S82. Calculate cumulative probability

[0047]

[0048]

[0049] Among them, c(x n ,t i ) indicates t i The cumulative probability of the spatial position corresponding to the nth quantum filter neuron at the moment; ρ(x s ,t i ) indicates t i The density value of the spatial position corresponding to the sth quantum filter neuron at the moment;

[0050] S83. Find the cumulative probability The first quantile that is greater than or equal to the jth quantile j The position x corresponding to the element percen (j,t i ), which requires:

[0051] c(x percen (j,t i ),t i )-ρ(x percen (j,t i ),t i )<percen j ≤c(x percen (j,t i ),t i ) (15)

[0052] Among them, c(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i ) is the cumulative probability; ρ(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i ) density value;

[0053] S84. Calculate the value of the quantile

[0054]

[0055] S85, repeat steps S83 to S84 to calculate all quantile values

[0056] Preferably, the step S9 specifically includes the following steps:

[0057] S91, find t i Time and before T regress The j-th quantile value at time

[0058] S92, for this T regress The quantile values ​​at each moment are regressed to estimate the regression parameters of the fitting curve;

[0059] S93. Estimate t based on the fitted regression parameters i+1 The jth quantile at the moment j The predicted value of

[0060] S94, repeat steps S91 to S93, and regress and calculate t i+1 All quantile forecast values ​​at time instant.

[0061] Preferably, in step S7, i Time series signal data after moment filtering for;

[0062]

[0063] Among them, |ψ(x n ,t i )| 2 Represents the relationship between ψ(x n ,t i ) modulo the square of the value.

[0064] Preferably, in step S10, t i+1 The predicted value of the time series signal data at time for;

[0065]

[0066] in, Indicates t i+1 The jth quantile at the moment j The predicted value of Indicates t i+1 The j+1th quantile at the moment j+1 The predicted value of .

[0067] Compared with the prior art, the technical effects of the present invention are:

[0068] 1. The present invention designs a time series signal prediction method based on a quantum filtering model. Relying on the basic quantum filtering model, the time series signal data wave function calculated by the quantum filtering model is used to calculate each quantile of the wave function, and regression and prediction are performed according to the quantiles at different times. The method is highly practical and simple and convenient.

[0069] 2. The present invention designs a time series signal prediction method based on a quantum filtering model. Compared with other filtering models for processing time series signal data, the proposed method can achieve filtering processing without making any assumptions about the distribution form of the noise signal; at the same time, compared with the existing quantum filtering model, the proposed method realizes the prediction function of quantum filtering by regressing and predicting each quantile of the wave function. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Other features, objects and advantages of the present application will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings.

[0071] Figure 1 It is a flow chart of a method for predicting a time series signal based on a quantum filtering model of the present invention;

[0072] Figure 2 is a graph showing the capacity of a lithium ion battery according to the present invention versus the number of cycles;

[0073] Figure 3 It is a graph showing the filtering and prediction results of the curve of lithium-ion battery capacity versus cycle number by the quantum filtering model of the present invention. DETAILED DESCRIPTION

[0074] The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the relevant invention, rather than to limit the invention. It should also be noted that, for ease of description, only the parts related to the relevant invention are shown in the accompanying drawings.

[0075] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0076] Figure 1 The present invention shows a method for predicting a time series signal based on a quantum filtering model, which comprises the following steps:

[0077] S1. Set the filter parameter value and the initial value of each function, and calculate the predicted value of the time series signal data at time t1

[0078] S011. Set the values ​​of the filtering parameters, including the weight update rate β and the weight forgetting rate β d , potential energy coefficient ζ, diffusion coefficient m and input distribution variance σ f .

[0079] S012. Set the initial values ​​of other parts required in the filtering process. The initial values ​​of other parts include the number of quantum filter neurons N and the corresponding spatial positions. The value of the wave function Initial value of weight function All wave function quantiles that need to be calculated are percen1, percen2,…, percen M and the time length T for regression calculation regress ; Where M represents the number of quantiles and is a natural number greater than 1.

[0080] S013, based on the initial value of the wave function Calculate the predicted value of the time series signal data at time t1

[0081]

[0082] Among them, x n represents the spatial position corresponding to the nth quantum filter neuron; ψ(x n , t=0) represents the initial value of the wave function of the spatial position corresponding to the nth quantum filter neuron.

[0083] S2, get the data from t1 to t T All the time series signal data y(t1),y(t2),...,y(t T ) and input them into step S3 in sequence.

[0084] S3, starting from time t1, according to t i Time series signal data predicted at the moment The timing signal data y(t i ) and wave function Calculate the difference function at time t1

[0085]

[0086]

[0087] Among them, φ(x n ,t i ) indicates t i The difference function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n ,ti-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at time.

[0088] S4. Update t i The weight function at the moment

[0089]

[0090]

[0091] Among them, W(x n ,t i ) indicates t i The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment; W(x n ,t i-1 ) indicates t i-1 The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment.

[0092] S5. According to t i The difference function of time Weight function and potential energy coefficient ζ, calculate t i The potential energy function at time

[0093]

[0094] V(x n ,t i )=ζW(x n ,t i )φ(x n ,t i ) (7)

[0095] Among them, V(x n ,t i ) indicates t i The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment.

[0096] S6. Calculate t based on the difference form of the Schrödinger equation i Wave function at time

[0097]

[0098]

[0099] Among them, ψ(x n ,t i ) indicates t iThe wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n+1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n+1th quantum filter neuron at the moment; ψ(x n-1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n-1th quantum filter neuron at the moment; V(x n ,t i-1 ) indicates t i-1 The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment; i represents the imaginary unit; Δx represents the difference between the positions of adjacent quantum neurons, that is, Δx = x n+1 -x n =x n -x n-1 .

[0100] S7. Calculate t i Time series signal data after moment filtering As output signal;

[0101]

[0102] Among them, |ψ(x n ,t i )| 2 Represents the relationship between ψ(x n ,t i ) modulo the square of the value.

[0103] S8, wave function calculated according to step S6 Calculate t i The values ​​of each quantile of the density matrix at the moment.

[0104] S81. Calculate t i The density matrix at time

[0105]

[0106] ρ(x n ,t i )=|ψ(x n ,t i )| 2 (12)

[0107] Among them, ρ(x n ,ti ) indicates t i The density value of the spatial position corresponding to the nth quantum filter neuron at the moment.

[0108] S82. Calculate cumulative probability

[0109]

[0110]

[0111] Among them, c(x n ,t i ) indicates t i The cumulative probability of the spatial position corresponding to the nth quantum filter neuron at the moment; ρ(x s ,t i ) indicates t i The density value of the spatial position corresponding to the sth quantum filter neuron at the moment.

[0112] S83. Find the cumulative probability The first quantile that is greater than or equal to the jth quantile j The position x corresponding to the element percen (j,t i ), which requires:

[0113] c(x percen (j,t i ),t i )-ρ(x percen (j,t i ),t i )<percen j ≤c(x percen (j,t i ),t i ) (15)

[0114] Among them, c(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i ) is the cumulative probability; ρ(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i ) density value.

[0115] S84. Calculate the value of the quantile

[0116]

[0117] S85, repeat steps S83 to S84 to calculate all quantile values

[0118] S9. Regress each quantile and predict t i+1 The quantile value at the moment.

[0119] S91, find t i Time and before T regress The j-th quantile value at time

[0120] S92, for this T regress The quantile values ​​at each moment are regressed to estimate the regression parameters of the fitting curve.

[0121] S93. Estimate t based on the fitted regression parameters i+1 The jth quantile at the moment j The predicted value of

[0122] S94, repeat steps S91 to S93, and regress and calculate t i+1 All quantile forecast values ​​at time instant.

[0123] S10, prediction t i+1 The time series signal data value at the moment As input data;

[0124]

[0125] in, Indicates t i+1 The jth quantile at the moment j The predicted value of Indicates t i+1 The j+1th quantile at the moment j+1 The predicted value of .

[0126] S11, repeat steps S3 to S10, and complete all the timing signal data y(t1), y(t2), ..., y(t T-1 ) filtering and prediction of the corresponding next moment time series signal data value

[0127] S12, using t T Regression prediction results at time For a time greater than the last moment t in the time series signal data T The time tfuture The time series signal data at the moment is predicted.

[0128] S121, get t T The regression parameters for all quantiles at time t.

[0129] S122, according to t T The regression parameters of each quantile at time t are calculated. future Data of each quantile at the time

[0130] S123, calculate t future The predicted value of the time series signal data at time

[0131]

[0132] in, Indicates t future The j-th quantile data at time; Indicates t future The j+1th quantile data at the moment; j represents the value of the wave function at the jth quantile; j+1 Represents the value of the wave function at the j+1th quantile.

[0133] The present invention is further described in detail below with reference to specific cases.

[0134] Taking a lithium-ion battery as the research object, a time series signal prediction method based on quantum filtering model is implemented. Figure 2 It is a curve of the capacity of a selected lithium-ion battery changing with the number of cycles. This data can be used as time series signal data for filtering and prediction. This method selects the data of the capacity changing with the number of cycles from the 1st to the 500th cycle as the input data of the quantum filter model, and predicts the data value of the capacity changing with the number of cycles after 500 cycles based on the input time series signal data. The specific implementation steps are as follows:

[0135] S1. Set weight update rate β = 0.1, weight forgetting rate β d =0.85, potential energy coefficient ζ = 1, diffusion coefficient m = 1, input distribution variance σ f =1; Set the number of quantum filter neurons N to 1001, and the spatial position corresponding to each neuron The values ​​of are x1=742, x2=744, x3=746, ..., x 1000 =2740, x 1001 =2742, set the initial value of the wave function Each of the items is Set the initial value of the weight function Each item in is 1. Suppose the number of quantile values ​​to be calculated is M = 21, where percen1 = 0.01%, percen 21 =99.99%, percen2 to percen 20 5%, 10%, 15% to 95%, respectively. The time length T for regression calculation is regress =100; the predicted value of the time series signal data at time t1 can be obtained by calculation

[0136] S2, get the data from t1 to t 500 The capacity data at each moment is taken as the time series signal data y(t1),y(t2),...,y(t 500 ), and input into step S3 in sequence;

[0137] S3. Calculate t i The difference function of time in Including 1001 elements, taking time t1 as an example, we can get y(t1)=1741.3, from which we can calculate φ(x1,t1), ..., φ(x 1001 ,t1).

[0138] S4. Update t i The weight function at the moment in Contains 1001 elements, at time t1 The nth spatial position x in n For example, we can get φ(x n ,t1), which can be used to calculate different x n W(x n ,t1).

[0139] S5. Calculate t i Potential energy function at time in Contains 1001 elements, which can be obtained by and Calculated.

[0140] S6. Calculate t i Wave function at time in Contains 1001 elements, with the time t1 The nth spatial position x in n For example, according to the last moment The value of and the value calculated in step S5 To calculate

[0141] S7. Calculate t i The filtered time series signal data at the moment

[0142] S8. Calculate t i The values ​​of each quantile of the moment density matrix

[0143] S9. Regress each quantile and predict t i+1 The quantile value at the moment. regress =100, so this step is only performed at t 100 and later. 100 Take the moment as an example, find the moment t1, moment t2, ... to moment t 100 The jth quantile data at time t is regressed into a straight line by fitting the quantile data at t t and obtaining the parameters of the straight line. Substitute the fitted straight line parameters into t 101 moment, in order to obtain the predicted value of the j-th quantile data at the 101st moment

[0144] S10, prediction t i+1 The time series signal data value at the moment

[0145] S11, repeat steps S3 to S10, and complete all the timing signal data y(t1), y(t2), ..., y(t 499 ) filtering and prediction of the corresponding next moment time series signal data value

[0146] S12, using t 500 The regression prediction result at time t future The time series signal data at time is predicted. future Time greater than t 500 time.

[0147] Figure 3 The results of filtering and predicting the capacity of a lithium-ion battery as a function of the number of cycles are shown in the quantum filtering model. The image results show that this method has done a good job of removing the fluctuations in the curve during the filtering stage, and also accurately predicted the capacity change after 500 cycles during the prediction stage.

[0148] The present invention also analyzes the capacity cycle curves of a batch of lithium-ion batteries, and uses 1 to 500 cycles as filter data to predict the capacity change of subsequent cycles. The standard deviation (s Q ), and its calculation formula is as follows.

[0149]

[0150]

[0151] Among them, s Q,i represents the standard deviation of the difference between the predicted capacity and the actual capacity of the ith battery; T i represents the predicted number of cycles for the ith battery; Q i,t represents the real capacity of the ith battery at the tth cycle; represents the predicted capacity value of the ith battery at the tth cycle; N bat is the total number of lithium-ion batteries predicted.

[0152] In order to compare with the existing lithium-ion battery capacity prediction methods, the present invention also calculates the capacity prediction standard deviation of the common Kalman filter and particle filter methods. Since the capacity degradation curve of a normally degraded lithium-ion battery is a straight line, the unscented Kalman filter and the extended Kalman filter are mainly improvements on the conventional Kalman filter method to achieve a good filtering effect on nonlinear curves. Therefore, the prediction effect of the two types of improved Kalman filter methods will not be better than the fitting effect of the conventional Kalman filter on the linear degradation curve, so the present invention only uses the conventional Kalman filter method and the particle filter method for prediction. In addition, the present invention also tried two common filtering models, the smoothing filter method and the low-pass filter method, to predict the cycle capacity of lithium-ion batteries, and also calculated the corresponding s Q , in order to compare the prediction effects of various models. The specific results can be seen in Table 1.

[0153]

[0154] Table 1

[0155] As can be seen from Table 1, the average prediction standard deviation of quantum filtering is 10.801mAh, while the capacity prediction standard deviations of Kalman filtering and particle filtering are both above 11mAh. It can be seen that the two common filtering methods have large fluctuations in the prediction of lithium-ion battery capacity, while the capacity prediction of quantum filtering is relatively closer to the original curve, so the prediction standard deviation is relatively low. In addition, it can be seen that the standard deviation of smoothing filtering is above 11mAh under the conditions of various parameter values, and it is observed that when the number of smoothing filters increases from 10 to 25, the standard deviation of prediction is constantly decreasing, and when the number of smoothing starts from 35, the standard deviation of prediction increases successively. It can be seen that when the number of smoothing is too large, the gap between the filtered signal and the original signal increases due to the excessive number of averages involved. Therefore, it can be explained that the prediction accuracy of the smoothing filtering method for capacity is not as good as the prediction accuracy of quantum filtering. Similarly, after selecting appropriate low-pass filtering parameters, it can be found that the prediction accuracy of low-pass filtering for cycle capacity is relatively worse (the standard deviation reaches 14.339mAh), so it can also be explained that the capacity prediction accuracy of low-pass filtering is not as good as that of quantum filtering.

[0156] It is necessary to further explain that although the predicted standard deviations of the capacity of several methods are all above 10, quantum filtering cannot be reduced in magnitude compared with the other four prediction methods. Figure 2 It can be clearly seen that the original capacity cycle data curve has obvious volatility. These fluctuations in the curve, as part of the noise of the capacity curve, have an amplitude of more than ten or even dozens of mAh. Therefore, the capacity prediction standard deviation of the filter model itself is around 10 mAh. It can be seen that quantum filtering has a good effect on improving the prediction performance.

[0157] The present invention also predicts the life of lithium-ion batteries and compares it with the life when the capacity reaches 80% threshold in the actual test, and calculates the relative error ε of the predicted life life , and its calculation formula is as follows:

[0158]

[0159] Among them, l i is the actual life of the ith battery; is the estimated lifespan of the ith battery.

[0160] The present invention also uses the common Kalman filter method, particle filter method, smoothing filter method and low-pass filter method to predict the life value of the lithium-ion battery and calculate the corresponding relative error ε life , in order to compare the prediction effects of different models, the specific results can be seen in Table 2.

[0161]

[0162] Table 2

[0163] As can be seen from Table 2, the relative error of life prediction of quantum filtering is 2.13%, which has higher capacity prediction accuracy than the other four filter models. As the number of smoothing increases, the relative error of the life of lithium-ion batteries predicted by the smoothing filter method also increases. The reason for this phenomenon is that as the number of smoothing increases, the delay effect of the filter model will become more obvious, and the prediction accuracy will also decrease, making the relative error larger. The low-pass filter model has the worst life prediction accuracy, with a deviation of more than 11%.

[0164] The present invention designs a time series signal prediction method based on a quantum filtering model. Relying on the basic quantum filtering model, the time series signal data wave function calculated by the quantum filtering model is used to calculate each quantile of the wave function, and regression and prediction are performed according to the quantiles at different times. The method is highly practical and simple and convenient. Compared with other filtering models for processing time series signal data, the proposed method can realize filtering processing without making any assumptions about the distribution form of the noise signal. At the same time, compared with the existing quantum filtering model, the proposed method realizes the prediction function of quantum filtering by regressing and predicting each quantile of the wave function.

[0165] Finally, it should be noted that the above embodiments are only intended to illustrate rather than limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the present invention can still be modified or replaced by equivalents. Any modification or partial replacement that does not depart from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A time series signal prediction method based on quantum filtering model, It is characterized in that It includes the following steps: S1. Set the filter parameter values ​​and the initial values ​​of each function, and calculate the tth 1 The predicted value of the time series signal data at the moment S2, get from t 1 to T All time series signal data y(t 1 ),y(t 2 ),...,y(t T ), and input into step S3 in sequence; S3, since the tth 1 Starting from time t i Time series signal data predicted at the moment The timing signal data y(t i ) and wave function Calculate t 1 The difference function of time Among them, x n represents the spatial position corresponding to the nth quantum filter neuron; N represents the number of quantum filter neurons; φ(x n ,t i ) indicates t i The difference function of the spatial position corresponding to the nth quantum filter neuron at the moment; σ f represents the input distribution variance; ψ(x n ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; S4. Update t i The weight function at the moment Among them, W(x n ,t i ) indicates t i The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment; W(x n ,t i-1 ) indicates t i-1 The weight function of the spatial position corresponding to the nth quantum filter neuron at the moment; β d represents the weight forgetting rate; β represents the weight updating rate; S5. According to t i The difference function of time Weight function and potential energy coefficient ζ, calculate t i The potential energy function at time V(x n ,t i )=ζW(x n ,t i )φ(x n ,t i ) (7) Among them, V(x n ,t i ) indicates t i The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment; S6. Calculate t based on the difference form of the Schrödinger equation i Wave function at time Among them, ψ(x n ,t i ) indicates t i The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the nth quantum filter neuron at the moment; ψ(x n+1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n+1th quantum filter neuron at the moment; ψ(x n-1 ,t i-1 ) indicates t i-1 The wave function of the spatial position corresponding to the n-1th quantum filter neuron at the moment; V(x n ,t i-1 ) indicates t i-1 The potential energy function of the spatial position corresponding to the nth quantum filter neuron at the moment; i represents the imaginary unit; Δx represents the difference between the positions of adjacent quantum neurons, that is, Δx = x n+1 -x n =x n -x n-1 ; m represents the diffusion coefficient; S7. Calculate t i Time series signal data after moment filtering As output signal; S8, wave function calculated according to step S6 Calculate t i The values ​​of each quantile of the density matrix at each moment; S9. Regress each quantile and predict t i+1 The quantile value at the moment: S10, prediction t i+1 The time series signal data value at the moment As input data; S11, repeat steps S3 to S10, and complete all the timing signal data y(t 1 ),y(t 2 ),...,y(t T-1 ) and the prediction of the corresponding next moment time series signal data value S12, using t T Regression prediction results at time For a time greater than the last moment t in the time series signal data T The time t future The time series signal data at the moment is predicted: S121, get t T The regression parameters of all quantiles at time instant; S122, according to t T The regression parameters of each quantile at time t are calculated. future Data of each quantile at the time Where M represents the number of quantiles and is a natural number greater than 1; S123, calculate t future The predicted value of the time series signal data at time in, Indicates t future The j-th quantile data at time; Indicates t future The j+1th quantile data at the moment; j represents the value of the wave function at the jth quantile; j+1 Represents the value of the wave function at the j+1th quantile.

2. The method for predicting time series signals based on a quantum filtering model according to claim 1, It is characterized in that The step S1 specifically includes the following steps: S011. Set the value of the filtering parameters, which include the weight update rate β, the weight forgetting rate β d , potential energy coefficient ζ, diffusion coefficient m and input distribution variance σ f ; S012, setting the initial values ​​of other parts required in the filtering process, the initial values ​​of other parts including the number N of quantum filter neurons and the corresponding spatial position The value of the wave function Initial value of weight function All wave function quantiles that need to be calculated take the value of percen 1 ,percen 2 ,…,percen M and the time length T for regression calculation regress ; S013, based on the initial value of the wave function Calculate the tth 1 The predicted value of the time series signal data at the moment Among them, ψ(x n , t=0) represents the initial value of the wave function of the spatial position corresponding to the nth quantum filter neuron.

3. The method for predicting time series signals based on a quantum filtering model according to claim 1, It is characterized in that The step S8 specifically includes the following steps: S81. Calculate t i The density matrix at time p(x n ,t i )=|ψ(x n ,t i )| 2 (12) Among them, ρ(x n ,t i ) indicates t i The density value of the spatial position corresponding to the nth quantum filter neuron at the moment; S82. Calculate cumulative probability Among them, c(x n ,t i ) indicates t i The cumulative probability of the spatial position corresponding to the nth quantum filter neuron at the moment; ρ(x s ,t i ) indicates t i The density value of the spatial position corresponding to the sth quantum filter neuron at the moment; S83. Find the cumulative probability The first quantile that is greater than or equal to the jth quantile j The position x corresponding to the element percen (j,t i ), which requires: c(x percen (j,t i ),t i )-ρ(x percen (j,t i ),t i )<percen j ≤c(x percen (j,t i ),t i ) (15) Among them, c(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i ) is the cumulative probability; ρ(x percen (j,t i ),t i ) indicates t i Time x percen (j,t i )’s density value; S84. Calculate the value of the quantile S85, repeat steps S83 to S84 to calculate all quantile values 4. The method for predicting time series signals based on a quantum filtering model according to claim 1, It is characterized in that The step S9 specifically includes the following steps: S91, find t i Time and before T regress The j-th quantile value at time S92, for this T regress The quantile values ​​at each moment are regressed to estimate the regression parameters of the fitting curve; S93. Estimate t based on the fitted regression parameters i+1 The jth quantile at the moment j The predicted value of S94, repeat steps S91 to S93, and regress and calculate t i+1 All quantile forecast values ​​at time instant.

5. The method for predicting time series signals based on a quantum filtering model according to claim 1, It is characterized in that In step S7, i Time series signal data after moment filtering for; Among them, |ψ(x n ,t i )| 2 Represents the relationship between ψ(x n ,t i ) modulo square value.

6. The method for predicting time series signals based on a quantum filtering model according to claim 1, It is characterized in that In step S10, i+1 The predicted value of the time series signal data at time for; in, Indicates t i+1 The jth quantile at the moment j The predicted value of Indicates t i+1 The j+1th quantile at the moment j+1 The predicted value of .

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