Full-dynamic non-invasive blood glucose detection method based on full-spectrum peak segment optimization algorithm

Abstract

The invention provides a full-dynamic non-invasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm. The method comprises the following steps: step S1, performing blood glucose testing on a nail bed part of a human little finger by matching an infrared dual-wavelength semiconductor laser with a spectrograph, and recording blood glucose Raman spectrum data obtained in each blood glucose testing; step S2, carrying out pretreatment on the obtained blood glucose Raman spectrum data; s3, dividing the preprocessed blood glucose Raman spectrum data into a training set and a prediction set, analyzing through a principal component analysis method and a partial least square regression analysis method, and establishing a model; s4, inputting the preprocessed blood glucose Raman spectrum data as an independent variable into the model in the step S3, analyzing the blood glucose concentration of the human body, and giving a reference value; according to the full-dynamic non-invasive blood glucose detection method based on the full-spectrum peak segment optimization algorithm, the accuracy of quantitative analysis of a high-fluorescence background sample through a Raman spectrum is achieved, complex treatment on the sample is not needed, and the accuracy of human body non-invasive blood glucose detection is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of rapid extraction of characteristic peaks of human blood glucose Raman spectrum, in particular to a full-dynamic non-invasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm. Background Art

[0002] Diabetes, a chronic disease, can cause complications such as cancer, cardiovascular disease, and diabetic nephropathy, and currently has no cure. As people's quality of life improves, the number of diabetic patients and the cost of their treatment are increasing. Despite patients' awareness of the importance of controlling blood sugar levels, over 50.1% of diabetic patients still do not perform daily self-monitoring. Therefore, reliable non-invasive blood glucose monitoring technologies are urgently needed to provide painless, convenient, continuous, or frequent blood glucose monitoring for those in need.

[0003] Over the past few decades, people have been seeking various non-invasive blood glucose monitoring technologies. Among the many methods, optical methods have attracted considerable attention. Raman spectroscopy is a scattering spectrum, and the energy change of its photons usually originates from the superposition of molecular vibration energy and incident photon energy. Therefore, Raman scattered light contains rich information on molecular vibration structure and can be used as a "fingerprint" spectrum for molecular identification, including glucose molecules. So far, it has been reported that various biological samples (such as serum, blood, tissue and skin) have diagnostic feasibility of quantitative blood glucose analysis using Raman spectroscopy. These characteristics make it possible for Raman spectroscopy to perform quantitative analysis of human blood glucose levels non-invasively, and it is considered to be one of the most promising technologies for non-invasive detection of human blood glucose. However, the existing Raman spectroscopy technology has the following prominent problems:

[0004] The weak Raman spectral signal is easily affected by Rayleigh light and spatial stray light, causing the obtained glucose characteristic peak to be annihilated in the background spectrum; the Raman spectral signal of biological samples is weak, and artifacts caused by movement will appear during human testing; the existing Raman spectral testing system is bulky, cumbersome to operate, and requires high professionalism, making it unsuitable for integrated and portable systems.

[0005] This paper proposes a fully dynamic non-invasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm. Its innovation lies in: developing an integrated, mature, portable non-invasive blood glucose device; improving the algorithm by adding spike removal, peak shape search, and PCA-PLSR algorithms to the previous multiple-iteration deconvolution reduction algorithm, optimizing and adapting the full-spectrum peak segment of the human finger Raman spectrum and performing high-sensitivity PLS prediction of full-dynamic blood glucose concentration;

[0006] The device was taken to the hospital for testing, and its predictive effectiveness was good for extremely high and normal blood sugar concentrations, as well as for the lower blood sugar concentration range. Summary of the Invention

[0007] The present invention aims to provide a fully dynamic, non-invasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm, achieving the accuracy of Raman spectroscopy quantitative analysis of samples with high fluorescence backgrounds without requiring complex sample processing. This improves the portability and accuracy of blood glucose detection.

[0008] To achieve the above objectives, the present invention provides a fully dynamic non-invasive blood glucose detection method based on a full spectrum peak segment optimization algorithm, comprising the following steps:

[0009] Step S1, performing a blood glucose test on the nail bed of a human little finger using an infrared dual-wavelength semiconductor laser in conjunction with a spectrometer and recording blood glucose Raman spectrum data obtained from each blood glucose test;

[0010] Step S2, preprocessing the obtained blood glucose Raman spectrum data;

[0011] Step S3, dividing the pre-processed blood glucose Raman spectroscopy data into a training set and a prediction set model, analyzing them by principal component analysis and partial least squares regression analysis to establish a model;

[0012] Step S4: input the pre-processed blood glucose Raman spectrum data as an independent variable into the model of step S3, analyze the blood glucose concentration of the human body and provide a reference value.

[0013] Preferably, in step S1, the laser dual wavelengths of the selected infrared dual-wavelength semiconductor laser are 784nm and 785nm, the power of the selected infrared dual-wavelength semiconductor laser is 550mW, and the fixed focusing distance of the selected infrared dual-wavelength semiconductor laser is 1.5mm, so as to obtain the Raman spectra of blood glucose at different wavelengths; the magnification of the objective lens is 100, the numerical aperture NA=0.8, the selected spectrometer wavelength range is 780-1010nm, and the resolution is 0.2nm.

[0014] Preferably, in step S2, the area integral of each blood glucose Raman spectrum obtained in step S1 is obtained, and the product of the coefficient ratio and the subtraction spectrum is used as the difference spectrum, and the constraint factors α, β, and γ are added to perform a multiple iterative deconvolution restoration algorithm;

[0015] Preferably, in step S2, the blood glucose Raman spectrum is denoised using moving average filtering, Savitzky-Golay filtering, and peak denoising methods; the above methods are combined with a peak shape search method to further preprocess the blood glucose Raman spectrum; wherein the constraint factors α, β, and γ are selected as 100, 1000, and 1, respectively.

[0016] Preferably, in step S2, moving average filtering, Savitzky-Golay filtering, and wavelet transform denoising are used to remove noise from the blood glucose Raman spectrum; and an auxiliary peak shape search method is used to further pre-process the blood glucose Raman spectrum.

[0017] Preferably, in step S2, a peak shape search method is used to accurately identify the position of the peak from the blood glucose Raman spectrum data, and the intensity of the peak shape correlated with the characteristic peak is extracted; a threshold is set, and when the intensity of a data point in the blood glucose Raman spectrum data is greater than the threshold, the blood glucose Raman spectrum is reduced in dimension by PCA.

[0018] Preferably, in step S3, the number of principal components of the model is found by principal component analysis method, so that the cumulative contribution rate of the independent variable and the dependent variable to the model reaches more than 95%, and partial least squares regression analysis is performed, and multiple iterations are performed to find R 2 , RMSEP and MAPE optimal model;

[0019] Using the coefficient of determination R 2 , root mean square prediction error RMSEP and mean absolute percentage error MAPE to evaluate the goodness of fit of the model;

[0020]

[0021] Where n is the number of samples, y i is the true value of the ith observation, is the model prediction value for the i-th observation;

[0022] is the mean of the true values;

[0023]

[0024] The root mean square prediction error RMSEP reflects the average error between the model prediction value and the true value, and takes the square root of its average value;

[0025]

[0026] The mean absolute percentage error (MAPE) represents the prediction error as a percentage. Therefore, the present invention utilizes the aforementioned fully dynamic, noninvasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm to achieve the accuracy of Raman spectroscopy quantitative analysis of samples with high fluorescence backgrounds, without requiring complex sample processing. This improves the portability and accuracy of blood glucose testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is an overall flow chart of the fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm of the present invention;

[0028] Figure 2 The middle is a data analysis diagram of the full-dynamic non-invasive blood glucose detection method based on the full-spectrum peak segment optimization algorithm of the present invention;

[0029] Figure 3 This is an overall structural diagram of the fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm of the present invention;

[0030] Figure 4 Schematic diagram of the principle of the full-dynamic non-invasive blood glucose detection method based on the full-spectrum peak segment optimization algorithm of the present invention;

[0031] Figure 5 This is the Clark error network diagram of the fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm of the present invention. DETAILED DESCRIPTION

[0032] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0033] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0034] Example 1

[0035] like Figure 1-Figure 5 As shown, the present invention provides a full-dynamic non-invasive blood glucose detection method based on a full-spectrum peak segment optimization algorithm, comprising the following steps:

[0036] Step S1, performing a blood glucose test on the nail bed of a human little finger using an infrared dual-wavelength semiconductor laser in conjunction with a spectrometer and recording blood glucose Raman spectrum data obtained from each blood glucose test;

[0037] In step S1, the infrared dual-wavelength semiconductor laser is selected to have dual wavelengths of 784nm and 785nm, the power of the infrared dual-wavelength semiconductor laser is selected to be 550mW, and the fixed focusing distance of the infrared dual-wavelength semiconductor laser is selected to be 1.5mm, and the Raman spectra of blood glucose at different wavelengths are obtained; the magnification of the objective lens is 100, the numerical aperture NA = 0.8, the wavelength range of the spectrometer is selected to be 780-1010nm, and the resolution is 0.2nm. Step S2, preprocessing the obtained blood glucose Raman spectrum data;

[0038] In step S2, the area integral of each blood glucose Raman spectrum obtained in step S1 is calculated. The product of the coefficient ratio and the subtraction spectrum is used as the difference spectrum. Constraint factors α, β, and γ are added to perform a multiple iterative deconvolution algorithm to obtain the blood glucose Raman spectrum after removing the fluorescence background. The constraint factors α, β, and γ are selected as 100, 1000, and 1, respectively.

[0039] In step S2, the blood glucose Raman spectrum is subjected to noise removal using moving average filtering, Savitzky-Golay filtering, wavelet transform denoising, fast Fourier transform, and multiplicative least squares method; and the blood glucose Raman spectrum is further preprocessed using an auxiliary peak shape search method;

[0040] To make the data more representative, we employed a spike denoising method. Specifically, we first used a dynamic thresholding method, using a sliding window to calculate the local mean and standard deviation, and then identified spikes through threshold detection. Linear interpolation was then performed: for each identified spike, the value at the peak was restored by linear interpolation of the preceding and following points, thereby smoothing the data and removing noise. After this removal, the SG filtering method, which applies a local polynomial fit to each data point using a small window, effectively denoised and smoothed the signal. An auxiliary peak shape detection method was then used as the input variable for the Raman spectral signal.

[0041] In step S2, the peak shape search method is used to accurately identify the peak position from the blood glucose Raman spectrum data, and the intensity of the peak shape correlated with the characteristic peak is extracted; a threshold is set, and when the intensity of a data point in the blood glucose Raman spectrum data is greater than the threshold, and the intensity of the adjacent left data point is increasing and the intensity of the right data point is decreasing, the point is determined to be the peak top, and the peak position is searched to the left and right. When the intensity of the position to the left of the peak position meets the threshold, the peak top is selected. K-L-1 >I K-L or I K+q+1 >I K+q When the peak intensity meets the threshold, the iteration is stopped and the noise signal is removed. In order to avoid the problem of insufficient accuracy of the single peak intensity, the full spectrum peak segment algorithm is adopted, that is, the peak intensity of the molecular bond and the extended intensity on both sides of each peak are used as the input variables of the PCA-PLS algorithm. The dimension of the blood glucose Raman spectrum is reduced by PCA, which further improves the robustness of the model.

[0042] Step S3, dividing the pre-processed blood glucose Raman spectrum data into a training set and a prediction set, and analyzing them by principal component analysis and partial least squares regression analysis;

[0043] In step S3, the principal component number of the model is found through the principal component analysis method, so that the cumulative contribution rate of the independent variables and dependent variables to the model reaches more than 95%, and then the partial least squares regression analysis is performed to avoid the problem of too many or too few principal components that may exist in the traditional method, resulting in overfitting or underfitting of the model. Through multiple iterations, three-fold cross-validation is used to improve the stability of the model. The specific operation is to first divide the data set into three parts, one of which is taken out of the model as a validation set, and the remaining two parts are divided into training sets and prediction sets according to the ratio of 1:4. Then, the remaining two training sets are used to predict the prediction set. After a feasible model is obtained based on the principal components, the model is input into the validation set to find R 2 , RMSEP and MAPE optimal model, if R 2 <0.9, then return to step S1 and step S2 to re-collect blood glucose Raman spectrum data and blood glucose true value for pre-processing and model establishment until R 2 When the value is ≥0.9, the model is considered to have high accuracy. The closed loop of data collection and model optimization is combined. By continuously collecting new data and optimizing the selection of principal components in each round of iteration, the accuracy requirements of the model are guaranteed at each stage, avoiding the instability of the model in practical applications.

[0044] Using the coefficient of determination R 2 , root mean square prediction error RMSEP and mean absolute percentage error MAPE to evaluate the goodness of fit of the model;

[0045]

[0046] Where n is the number of samples, y i is the true value of the ith observation, is the model prediction for the ith observation, It is the average of the true values. When the value of the coefficient of determination R2 is closer to 1, it means that the model can fit the data more perfectly.

[0047]

[0048] The root mean square prediction error (RMSEP) reflects the average degree of error between the model's predicted value and the true value. It takes into account the squares of all prediction errors and takes the square root of their average value. The smaller the value of the root mean square prediction error (RMSEP), the higher the prediction accuracy of the model, that is, the smaller the deviation between the model's predicted value and the true value. It is more sensitive to situations with large prediction errors because the errors are first squared and then summed and averaged.

[0049]

[0050] The mean absolute percentage error (MAPE) expresses the prediction error in the form of a percentage. It measures the average deviation of the predicted value from the true value. The smaller the value of the mean absolute percentage error (MAPE), the better the prediction effect of the model.

[0051] Step S4: input the pre-processed blood glucose Raman spectrum data as an independent variable into the model of step S3, analyze the blood glucose concentration of the human body and provide a reference value.

[0052] The equipment for this fully dynamic, noninvasive blood glucose monitoring method, based on a full-spectrum peak optimization algorithm, includes a power supply, circuit control system, infrared dual-wavelength excitation module, Raman low-light detection module, micro-Raman spectroscopy information acquisition module, Raman spectroscopy information processing module, Raman spectroscopy peak position matching module, adaptive airbag finger fixation chamber, and data processing and display module. The entire device integrates all components and, through preprocessing and an intelligent algorithm based on partial least squares regression, establishes a relationship between the intensity of differential Raman spectroscopy of blood glucose and the blood glucose concentration, enabling rapid prediction of blood glucose concentration.

[0053] The power supply provides stable power support for the entire device. At the same time, the power module also has overcurrent, overvoltage, and short-circuit protection functions to prevent damage to the device due to abnormal conditions.

[0054] The circuit control system coordinates the work between various modules and processes and transmits data in real time. By selecting an FPGA board, the circuit control system provides precise timing control, ensuring that the infrared dual-wavelength excitation module emits lasers at preset intervals and sequences. It also controls the Raman low-light detection module and the micro-Raman spectroscopy information acquisition module to collect data at the appropriate time.

[0055] The infrared dual-wavelength excitation module emits two infrared laser beams with a slight wavelength offset, serving as the excitation light source for Raman spectroscopy. Utilizing a high-precision semiconductor laser, it delivers stable laser output at a specific wavelength, with a linewidth of less than 0.1nm. The module is also equipped with a laser power regulator to adjust the laser power according to specific detection requirements to achieve optimal Raman signal intensity.

[0056] The Raman low-light detection module is responsible for detecting weak Raman light signals scattered by human tissue. It uses a highly sensitive photodetector to accurately capture Raman light signals in low-light environments. To improve detection accuracy, the module is equipped with a narrowband filter that effectively filters out interference from background and stray light, allowing only Raman light signals within a specific wavelength range to pass through.

[0057] The micro-Raman spectroscopy information acquisition module combines microscopy and Raman spectroscopy technology to capture high-resolution Raman spectra of human fingers. Using a high-precision microscope objective, the module focuses the laser light onto a tiny area of ​​blood in the nail bed beneath the finger, improving the efficiency of Raman signal acquisition. Furthermore, the module is equipped with a high-grid count and high-resolution spectrometer, which performs spectroscopic processing on the Raman light signal and converts it into digital spectral data.

[0058] The adaptive airbag finger-holding chamber provides a stable finger placement environment for testing. This helps ensure the stability and consistency of the optical focus during testing, ensuring accurate and repeatable testing. The chamber incorporates an adaptive airbag design that automatically adjusts its inflation level based on the thickness and shape of the finger, tightly wrapping and securing the finger. Made of a soft, comfortable material, the airbag eliminates pressure on the finger, enhancing the user experience.

[0059] The finger airbag system precisely controls the inflation and deflation process to ensure the finger is accurately and stably positioned in the desired location. Communication between the airbag system and the computer uses a serial port protocol. Its workflow consists of three steps: power-on initialization, phone location detection and fixation, and reset after acquisition is complete. Details are as follows:

[0060] Power-on Initialization: After powering on, the device's vacuum pump automatically activates, and the airbag begins to deflate until the air pressure inside the bag drops to the set negative pressure. At this point, the vacuum pump stops and the valve closes, preparing for the insertion of a finger. During this process, minor leaks in the air passage may cause the air pressure to fail to reach the set value. If this is not the case, the vacuum pump will continue to operate until the required pressure is reached.

[0061] Finger Position Detection and Fixation: When a finger is inserted into the airbag device and touches the internal physical switch, the air pump begins to inflate the airbag until the following two conditions are met: the finger touches the upper touch button, indicating that the finger has reached the set fixed position; and the air pressure in the airbag reaches the set value, at which point the air pump stops inflating, completing the finger fixation process. At this point, the device sends a "Complete" signal to the computer, closes the valve, and waits for the computer to send a "Collection Complete" signal.

[0062] Reset after acquisition is completed: When the "acquisition completed" command sent by the computer is received, the whole process starts again.

[0063] Airbag inflation error: If your finger fails to touch the upper touch button during inflation, the air pump will continue to inflate until the airbag pressure reaches the maximum allowable value. If the pressure exceeds the maximum value, the airbag will automatically deflate and an alarm signal will be sent to the computer.

[0064] The data processing and display module's main function is to establish a relationship model between the differential Raman spectral intensity of human blood glucose and blood glucose concentration, analyze and calculate the currently collected spectral data, and thus quickly predict the human blood glucose concentration. Equipped with a high-resolution display and a high-speed CPU, the data processing and display module can clearly and quickly display information such as the predicted blood glucose concentration, test time, progress bar, previous results, and error. Furthermore, the module supports data storage and transmission, allowing test data to be stored in the device's internal memory. It can also be connected to a mobile app through other means, allowing users to manage and analyze all data at any time.

[0065] The device is portable and compact, weighing approximately 2.5kg. It integrates various modules into a single shell. When in use, just connect the external power cord, press the power button, place your finger, and the test will begin normally.

[0066] Example 2

[0067] In the mouse test, the mice were depilated and injected with sodium pentobarbital, and the Raman spectrum and blood glucose reference value of the mice were measured before the injection of glucose; then the glucose solution was injected, and the blood glucose Raman spectrum and blood glucose reference value of the mice were measured every half an hour.

[0068] The predicted and true values ​​of blood glucose concentrations in hyperglycemic mice corresponded well, with a relative error of 4.341%, and the Clark error grid fell entirely within areas A and B, demonstrating the effectiveness of the clinical utility.

[0069] Example 3

[0070] In human blood glucose, 15 volunteers with blood glucose concentrations ranging from 4.31-15.27 mmol / L were pre-tested, and blood glucose values ​​were tested with a blood glucose meter, and Raman spectra were tested with a portable non-invasive blood glucose detection system for prediction. The MAPE of the prediction set and the training set were 15.27% and 4.04%, respectively, both less than 16%. The Clark error grid fell in areas A and B, mainly in area A, proving that Raman predictions are valuable for correct clinical decision-making and are acceptable in either direction.

[0071] Therefore, the present invention adopts the above-mentioned fully dynamic non-invasive blood glucose detection method based on the full-spectrum peak segment optimization algorithm to achieve the accuracy of Raman spectroscopy quantitative analysis of high fluorescence background samples, without the need for complex sample processing, thereby improving the portability and accuracy of blood glucose detection.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A fully dynamic non-invasive blood glucose detection method based on a full spectrum peak segment optimization algorithm, characterized in that: The following steps are involved: Step S1, performing a blood glucose test on the nail bed of a human little finger using an infrared dual-wavelength semiconductor laser in conjunction with a spectrometer and recording blood glucose Raman spectrum data obtained from each blood glucose test; Step S2, preprocessing the obtained blood glucose Raman spectrum data; Step S3, dividing the pre-processed blood glucose Raman spectroscopy data into a training set and a prediction set model, analyzing them by principal component analysis and partial least squares regression analysis to establish a model; Step S4: input the pre-processed blood glucose Raman spectrum data as an independent variable into the model of step S3, analyze the blood glucose concentration of the human body and provide a reference value.

2. The fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm according to claim 1, characterized in that: In step S1, the laser dual wavelengths of the selected infrared dual-wavelength semiconductor laser are 784nm and 785nm, the power of the selected infrared dual-wavelength semiconductor laser is 550mW, and the fixed focusing distance of the selected infrared dual-wavelength semiconductor laser is 1.5mm, and the Raman spectra of blood glucose at different wavelengths are obtained; the magnification of the objective lens is 100, the numerical aperture NA=0.8, the selected spectrometer wavelength range is 780-1010nm, and the resolution is 0.2nm.

3. The fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm according to claim 1, characterized in that: In step S2, the area integral of each blood glucose Raman spectrum obtained in step S1 is calculated. The product of the coefficient ratio and the subtraction spectrum is used as the difference spectrum. Constraint factors α, β, and γ are added to perform a multiple iterative deconvolution algorithm to obtain the blood glucose Raman spectrum after removing the fluorescence background. The constraint factors α, β, and γ are selected as 100, 1000, and 1, respectively.

4. The fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm according to claim 1, characterized in that: In step S2, moving average filtering, Savitzky-Golay filtering, and wavelet transform are used to remove noise from the blood glucose Raman spectrum; and an auxiliary peak shape search method is used to further pre-process the blood glucose Raman spectrum.

5. The fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm according to claim 1, characterized in that: In step S2, the peak shape search method is used to accurately identify the peak position from the blood glucose Raman spectrum data, and the intensity of the peak shape correlated with the characteristic peak is extracted; a threshold is set, and when the intensity of a data point in the blood glucose Raman spectrum data is greater than the threshold, the blood glucose Raman spectrum is reduced in dimension by PCA.

6. The fully dynamic non-invasive blood glucose detection method based on the full spectrum peak segment optimization algorithm according to claim 1, characterized in that: In step S3, the principal component number of the model is found by principal component analysis method, so that the cumulative contribution rate of the independent variable and the dependent variable to the model reaches more than 95%, and partial least squares regression analysis is performed, and multiple iterations are performed to find R 2 , RMSEP and MAPE optimal model; Using the coefficient of determination R 2 , root mean square prediction error RMSEP and mean absolute percentage error MAPE to evaluate the goodness of fit of the model; Where n is the number of samples, y i is the true value of the i-th observation, is the model prediction value for the i-th observation; is the mean of the true values; The root mean square prediction error RMSEP reflects the average error between the model prediction value and the true value, and takes the square root of its average value; The mean absolute percentage error (MAPE) expresses the forecast error as a percentage.

Images