Battery thermal model construction method and system and related equipment

Abstract

The invention discloses a battery thermal model construction method and system and related equipment, and relates to the technical field of battery thermal management. The battery thermal model construction method comprises the following steps that battery temperature prediction under multiple working conditions is achieved based on an electrochemical-thermodynamic coupling equation, and a physical model constraint result is output; simulating a surface temperature change relation of the battery under multiple working conditions based on a neural network temperature rise model, and outputting a prediction result; obtaining a relative error between the physical model constraint result and the neural network prediction result; based on the relative error, judging the physical model constraint result or the neural network prediction result as a temperature prediction value and outputting the temperature prediction value; and the neural network model is constrained through an electrochemical-thermodynamic coupling equation, so that the prediction stability and timeliness are enhanced.

Description

Technical Field

[0001] This application relates to the technical field of battery thermal management, and particularly relates to a method and system for constructing a battery thermal model and related devices. Background Art

[0002] The existing lithium battery thermal models have the following deficiencies:

[0003] 1. Low accuracy: Traditional soft-pack lithium battery thermal models mostly predict based on a single parameter (such as surface temperature), ignoring the coupling effects of current, SOC (state of charge), and SOH (state of health), and at the same time simplifying the temperature differences between various parts of the lithium battery.

[0004] 2. Lack of microscopic dynamic modeling: Traditional models are difficult to accurately describe internal microscopic reactions (such as SEI film decomposition and electrolyte gasification) and cannot effectively predict the critical point of thermal runaway.

[0005] 3. Limitations of neural network models: Existing neural network models rely on a large amount of experimental data for training, have poor generalization ability, and may have large prediction deviations under certain working conditions, resulting in system failures. Summary of the Invention

[0006] To solve the above problems, this application discloses a method for constructing a battery thermal model, which enhances the stability and timeliness of prediction by using an electrochemical-thermodynamic coupling equation to constrain a neural network model; at the same time, a corresponding system for constructing a battery thermal model is proposed to implement the method for constructing a battery thermal model under different conditions.

[0007] The first technical solution adopted by this application is: providing a method for constructing a battery thermal model, including the following steps:

[0008] Based on the electrochemical-thermodynamic coupling equation, perform battery temperature prediction under multiple working conditions and output the physical model constraint results;

[0009] Based on the neural network temperature rise model, simulate the surface temperature change relationship of the battery under multiple working conditions and output the prediction results;

[0010] Obtain the relative error between the physical model constraint results and the neural network prediction results; based on the relative error, determine whether the physical model constraint results or the neural network prediction results are output as the temperature prediction value.

[0011] Among them, the electrochemical-thermodynamic coupling equation includes the temperature change rate with time, the heat diffusion term, the heat generated by the current, and the heat source term. The specific formula is as follows:

[0012]

[0013] Among them, is the rate of change of temperature with time, is the heat diffusion term, and α is the heat diffusion coefficient, is the heat generated by the current, R is the resistance, I is the current, C p is the specific heat capacity, ρ is the density, SOC is the state of charge of the battery, and SOH is the state of health of the battery.

[0014] Among them, it also includes spatially and temporally discretizing the electrochemical-thermodynamic coupling equation to obtain a prediction model for the temperature distribution in each region of the battery.

[0015] Among them, the neural network temperature rise model uses a radial basis function neural network, and the input parameters include the discharge rate, SOC, SOH, and ambient temperature.

[0016] Among them, if the relative error between the constraint result of the physical model and the prediction result of the neural network is less than the error threshold, the prediction result of the neural network is output as the temperature prediction value; if the relative error is greater than or equal to the error threshold, the constraint result of the physical model is output as the temperature prediction value.

[0017] Among them, it also includes judging whether to issue a thermal runaway warning based on the SEI film decomposition rate and the rate of change of temperature; the SEI film decomposition rate is calculated by the SEI film decomposition rate equation; if the SEI film decomposition rate is greater than the rate threshold and the rate of change of temperature is greater than the temperature rate of change threshold, a thermal runaway warning is triggered.

[0018] Among them, it also includes modeling the battery aging characteristics, obtaining temperature rise data under different SOC and SOH conditions based on cyclic charge and discharge tests, and calibrating the heat source term in the thermal model based on the temperature rise data.

[0019] The second technical solution adopted in this application is: to provide a battery thermal model construction system applying the battery thermal model construction method described in any one of the above, including:

[0020] Data acquisition module: used to acquire the current, voltage, SOC, and SOH data of the lithium battery;

[0021] Neural network prediction module: used to predict the surface temperature distribution of the lithium battery;

[0022] Physical model constraint module: used to correct the prediction result of the neural network;

[0023] Warning module: based on the SEI film decomposition rate and the rate of change of temperature, judge whether the lithium battery is in a thermal runaway state.

[0024] The third technical solution adopted in this application is as follows: providing an electronic device, which includes a memory and a processor coupled to each other, and the processor is configured to execute program instructions stored in the memory to implement the battery thermal model construction method described in any one of the above.

[0025] The fourth technical solution adopted in this application is as follows: providing a computer-readable storage medium, which stores program data that can be executed by a processor to implement the battery thermal model construction method described in any one of the above.

[0026] Due to the adoption of the above technical solutions in this application, compared with the prior art, it has at least one of the following beneficial effects:

[0027] 1. By using the electrochemical-thermodynamic coupling equation to constrain the neural network model, the stability and timeliness of prediction are enhanced.

[0028] 2. The model comprehensively considers the effects of SOC (state of charge) and SOH (state of health), and can better reflect the temperature rise characteristics during the battery aging process, providing strong support for the full life cycle management of the battery.

[0029] 3. Based on the dynamic monitoring of the SEI film decomposition rate and the temperature change rate, the risk of thermal runaway of lithium batteries is pre-warned in advance, significantly improving the safety of the battery system.

[0030] 4. By spatially discretizing the internal temperature field of the battery, the temperature distribution in different regions inside the soft-pack lithium battery can be accurately predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of this application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0032] Among them:

[0033] Figure 1 is a schematic flowchart of an embodiment of the battery thermal model construction method provided by this application;

[0034] Figure 2 is a schematic framework diagram of an embodiment of the battery thermal model construction system provided by this application;

[0035] Figure 3 is a schematic structural diagram of an embodiment of the computer device of this application;

[0036] Figure 4Schematic structural diagram of an embodiment of the computer-readable storage medium of the present application. Detailed implementation manners

[0037] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. It can be understood that the specific embodiments described herein are only for explaining the present application, rather than limiting the present application. Additionally, it should be noted that, for the sake of description, only the parts related to the present application are shown in the drawings rather than all the structures. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0038] The terms "first", "second", etc. in the present application are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes unlisted steps or units, or optionally further includes other steps or units inherent to these processes, methods, products, or devices.

[0039] Referring to "embodiment" herein means that a specific feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The phrase appears in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0040] Existing methods for constructing thermal models have various drawbacks. For example, they only predict based on surface temperature, ignoring the thermal effects of current, factors such as the battery's SOC (state of charge) and SOH (state of health), resulting in low accuracy; existing neural networks rely on a large amount of model training and have poor generalization ability, etc. To solve the above problems, the present application provides a method for constructing a battery thermal model with neural network combined with physical model constraints. It should be clear that the battery thermal model construction method of the present application is applicable to various batteries, such as lithium batteries; as Figure 1 shown, Figure 1 is a schematic flowchart of an embodiment of the battery thermal model construction method provided by the present application, including the following steps:

[0041] Step S11: Construct an electrochemical-thermodynamic coupling equation. Based on physical principles, the electrochemical-thermodynamic coupling equation can accurately describe the complex heat transfer and electrochemical reaction processes inside the lithium battery, providing high-precision temperature prediction results. Based on the electrochemical-thermodynamic coupling equation, battery temperature prediction under multiple working conditions is realized and the constraint results of the physical model are output. The multiple working conditions include different currents, different SOCs, different SOHs, different ambient temperatures, etc. In one embodiment, the battery SOC and battery SOH can be kept unchanged, and by gradually changing the current value, the influence of different currents on the battery temperature is obtained, and then the relationship curve between the current and the battery temperature is generated. In other embodiments, the relationship curve between the battery SOC and the battery temperature and the relationship curve between the battery SOH and the battery temperature can be obtained, and no specific limitation is made here.

[0042] The battery thermal model construction method of this application considers the influence of multiple factors such as current, SOC, and SOH on the battery temperature, avoids the limitations of single-parameter prediction, and improves the applicability and reliability of the model.

[0043] Step S12: Based on the neural network temperature rise model, simulate the surface temperature change relationship of the battery under multiple working conditions and output the prediction results. During the actual operation process, data such as the real-time collected current, battery SOC, battery SOH, and ambient temperature are input into the neural network model. The neural network model outputs the current temperature value of the lithium battery as the prediction result.

[0044] The method based on the neural network temperature rise model can flexibly and efficiently simulate the surface temperature change relationship of the lithium battery under multiple working conditions and output accurate prediction results. The combination of the physical model constraints and the advantages of the neural network makes up for the deficiencies of a single model. The physical model can provide a reliable theoretical basis, while the neural network can capture the non-linear relationships under complex working conditions, thus significantly improving the prediction accuracy.

[0045] Step S13: Obtain the relative error between the physical model constraint result and the neural network prediction result. The relative error calculation formula is as follows:

[0046]

[0047] where T1 is the physical model constraint result and T2 is the neural network prediction result.

[0048] Based on the relative error, determine whether the physical model constraint result or the neural network prediction result is output as the temperature prediction value. Based on the relative error judgment mechanism, a more credible result is dynamically selected to avoid the possible failure problem of a single model under specific working conditions and improve the stability of the entire system.

[0049] Through the organic combination of the physical model and the neural network, high-precision, high-stability, and strong adaptability of lithium battery temperature prediction are achieved; moreover, the physical model corrects the prediction results of the neural network to improve the accuracy of the neural network prediction results; in addition, the physical model calibrates the neural network model, enabling the neural network model to improve the prediction accuracy and generalization ability without excessive training samples for training.

[0050] In summary, the battery thermal model construction method of this embodiment includes the following steps: realizing the battery temperature prediction under multiple working conditions based on the electrochemical-thermodynamic coupling equation and outputting the physical model constraint results; simulating the surface temperature change relationship of the battery under multiple working conditions based on the neural network temperature rise model and outputting the prediction results; obtaining the relative error between the physical model constraint results and the neural network prediction results; determining whether the physical model constraint results or the neural network prediction results are output as the temperature prediction value based on the relative error; constraining the neural network model through the electrochemical-thermodynamic coupling equation to enhance the stability and timeliness of the prediction.

[0051] In one embodiment, the electrochemical-thermodynamic coupling equation includes the temperature change rate with time, the heat diffusion term, the heat generated by the current, and the heat source term. The specific formula is as follows:

[0052]

[0053] Among them, is the temperature change rate with time, is the heat diffusion term, α is the heat diffusion coefficient, is the heat generated by the current, R is the resistance, I is the current, C p is the specific heat capacity, ρ is the density, SOC is the state of charge of the battery, and SOH is the state of health of the battery.

[0054] The coupling equation comprehensively considers the effects of heat diffusion, heat generated by the current, and electrochemical reactions, and can more accurately describe the complex heat transfer process inside the lithium battery.

[0055] It also includes the spatial and temporal discretization processing of the electrochemical-thermodynamic coupling equation. The lithium battery is divided into i×j regions to obtain the temperature distribution prediction model of each region of the battery. The discretized electrochemical-thermodynamic coupling equation is as follows:

[0056]

[0057] Among them, is the temperature value of a certain region at the current moment, is the temperature value of a certain region at the next moment, Δt is the time step, and Δx and Δy are the spatial steps.

[0058] The discretization process and the calculation steps of the discretized electrochemical-thermodynamic coupling equations are described in detail below:

[0059] The lithium battery is divided into multiple grid regions (such as a two-dimensional grid of i×j), and each grid represents a local region of the battery.

[0060] Set the initial temperature distribution (such as the ambient temperature or the initial temperature measured in the experiment); set the initial values of the current I, SOC, SOH, and other parameters according to the actual working conditions.

[0061] Perform point-by-point iterative calculations according to the time step Δt to update the temperature values of each grid region:

[0062]

[0063] After the calculation is completed, output the temperature distribution values of each grid region at the next moment Form a temperature distribution prediction model for the entire battery.

[0064] The discretization process divides the battery into multiple regions, which can accurately describe the temperature changes at different positions inside the battery and avoid the deficiency of the traditional one-dimensional model ignoring spatial differences; through the iterative calculation with the time step Δt, the change process of the battery temperature over time can be simulated in real time, which is applicable to the temperature prediction under dynamic working conditions.

[0065] The following provides an embodiment to facilitate the understanding of the calculation process:

[0066] The target battery is a ternary lithium battery with a capacity of 60 Ah.

[0067] The specific working conditions are a discharge rate of 2C, an ambient temperature of 25°C, an initial SOC of 80%, and an SOH of 90%.

[0068] Grid division divides the battery into a 10×10 grid, and each grid represents a small area on the battery surface. The spatial step Δx = Δy = 0.01 m, and the time step Δt = 1 s.

[0069] Parameter setting: The thermal diffusivity α = 0.01 m 2 / s; specific heat capacity C p = 900 J / (kg·C°); density ρ = 2500 kg / m 3 ; internal resistance R(SOH) = 0.02 Ω.

[0070] Using the above discretization formula, calculate the temperature change of each grid region point by point, and simulate the temperature distribution of the battery during a 10-minute discharge process; the prediction results show that the temperature in the central region of the battery is the highest, reaching 42°C, and the temperature in the edge region is lower, about 35°C.

[0071] In one embodiment, the neural network temperature rise model adopts a radial basis function (RBF) neural network, and the input parameters include discharge rate, SOC, SOH, and ambient temperature; the RBF neural network can simulate complex nonlinear relationships, adapt to various working conditions, and does not rely on specific physical assumptions or simplified processing; the RBF neural network model trained based on a large amount of experimental data has strong generalization ability, can handle unseen working conditions, and avoid the limitations that may exist in traditional physical models.

[0072] In one embodiment, if the relative error between the physical model constraint result and the neural network prediction result is less than the error threshold, the neural network prediction result is output as the temperature prediction value; if the relative error is greater than or equal to the error threshold, the physical model constraint result is output as the temperature prediction value; in this embodiment, the error threshold is 2%, and in other embodiments, the error threshold can be set to other values, which is not limited here. The relative error calculation formula is as follows:

[0073]

[0074] where T1 is the physical model constraint result and T2 is the neural network prediction result; if the relative error is less than 2%, then T2 is output as the temperature prediction value; if the relative error is greater than or equal to 2%, then T1 is output as the temperature prediction value.

[0075] Through the relative error judgment mechanism, a more reliable prediction result is dynamically selected to avoid the deviation or failure problems that may exist in a single model, and significantly improve the prediction accuracy of the overall system; the neural network model performs excellently under normal working conditions, while the physical model is more reliable under extreme working conditions. The combination of the two can ensure the stable operation of the system under various conditions.

[0076] In one embodiment, the battery thermal model construction method further includes judging whether to issue a thermal runaway warning based on the SEI film decomposition rate and the temperature change rate; the SEI film decomposition rate is calculated by the SEI film decomposition rate equation; the SEI film decomposition rate equation is as follows:

[0077]

[0078] where, K SEI is the SEI film decomposition rate, A is the frequency factor, E a is the activation energy, R is the gas constant, and T is the battery temperature; according to the currently predicted battery temperature T, substitute it into the above equation to calculate the SEI film decomposition rate K SEIIf the decomposition rate of the SEI film is greater than the rate threshold and the temperature change rate is greater than the temperature change rate threshold, a thermal runaway warning is triggered; in this embodiment, the temperature change rate threshold is 3°C / s. In other embodiments, the temperature change rate threshold can be set to other values, which are not limited herein. It should be clear that this application also does not limit the rate threshold in any way.

[0079] Combining the temperature value predicted by the physical model and the SEI film decomposition rate equation can more accurately determine the thermal runaway critical point and avoid false alarms or missed alarms; through the thermal runaway warning method based on the SEI film decomposition rate and the temperature change rate, not only can early warning be achieved, but also the reliability and safety of the lithium battery thermal management system can be significantly improved.

[0080] In one embodiment, the battery thermal model construction method further includes modeling the battery aging characteristics, obtaining the temperature rise data under different SOC and SOH conditions based on cyclic charge and discharge tests; analyzing the performance changes of the battery under different cycle numbers (such as capacity attenuation, internal resistance increase, etc.) based on the cyclic charge and discharge test data of the battery, and establishing a battery aging characteristic model; the aging characteristics are mainly quantified by the SOH (state of health) parameter, which reflects the current health level of the battery; calibrating the heat source term in the thermal model based on the temperature rise data, and substituting the experimentally obtained temperature rise data into the heat source term f(SOC, SOH) in the electrochemical-thermodynamic coupling equation.

[0081]

[0082] where ΔQ is the heat increase generated per unit time, Δt is the time interval, and V is the battery volume; adjusting the expression or parameter value of the heat source term according to the experimental data to ensure that the model can accurately reflect the heat generation process inside the battery.

[0083] By modeling the battery aging characteristics and calibrating the temperature rise data, the heat generation process inside the battery can be more accurately described, and the prediction accuracy of the thermal model can be significantly improved; the calibration of the heat source term takes into account the change of the battery SOH and can dynamically reflect the influence of battery aging on the thermal behavior, avoiding prediction deviation caused by ignoring the aging effect.

[0084] This application also provides a battery thermal model construction system applying the battery thermal model construction method described in any of the above embodiments, as Figure 2 shown. Figure 2 is a schematic framework diagram of an embodiment of the battery thermal model construction system provided by this application, including the following modules:

[0085] Data acquisition module: used to acquire the current, voltage, SOC, and SOH data of the lithium battery;

[0086] Neural network prediction module: used to predict the surface temperature distribution of the lithium battery;

[0087] Physical model constraint module: used to correct the prediction results of the neural network;

[0088] Early warning module: determines whether the lithium battery is in a thermal runaway state based on the SEI film decomposition rate and the temperature change rate.

[0089] For the above embodiments, the present application provides a computer device. Please refer to Figure 3 , Figure 3 which is a schematic structural diagram of an embodiment of the computer device of the present application. The computer device includes a memory and a processor. Among them, the memory and the processor are coupled to each other. The memory stores program data, and the processor is used to execute the program data to implement the steps of any embodiment of the above battery thermal model construction method.

[0090] In this embodiment, the processor may also be referred to as a CPU (Central Processing Unit, central processing unit). The processor may be an integrated circuit chip with signal processing capabilities. The processor may also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0091] For the method of the above embodiments, it may be implemented in the form of a computer program. Therefore, the present application proposes a computer-readable storage medium. Please refer to Figure 4 , Figure 4 which is a schematic structural diagram of an embodiment of the computer-readable storage medium of the present application. The computer-readable storage medium stores program data that can be run by the processor. The program data can be executed by the processor to implement the steps of any embodiment of the above battery thermal model construction method.

[0092] The computer-readable storage medium of this embodiment may be a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc, etc., which can store program data. Or it may also be a server storing the program data. The server can send the stored program data to other devices for running, or it can also run the stored program data by itself.

[0093] In several embodiments provided by the present application, it should be understood that the disclosed methods and devices can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the modules or units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0094] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they can be located in one place, or they can be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0095] In addition, in each embodiment of the present application, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0096] The above is only the embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present application.

Claims

1. A method for constructing a battery thermal model, characterized in that, It includes the following steps: Based on the electrochemical-thermodynamic coupling equation, realize the battery temperature prediction under multiple working conditions and output the physical model constraint results; Based on the neural network temperature rise model, simulate the surface temperature change relationship of the battery under multiple working conditions and output the prediction results; Obtain the relative error between the physical model constraint results and the neural network prediction results; based on the relative error, determine whether the physical model constraint results or the neural network prediction results are output as the temperature prediction value.

2. The method for constructing a battery thermal model according to claim 1, wherein The electrochemical-thermodynamic coupling equation includes the temperature change rate over time, the heat diffusion term, the heat generated by the current, and the heat source term. The specific formula is as follows: Among them, is the rate of change of temperature with time, is the heat diffusion term, α is the thermal diffusivity, is the heat generated by the current, R is the resistance, I is the current, C p is the specific heat capacity, ρ is the density, SOC is the state of charge of the battery, and SOH is the state of health of the battery.

3. The method for constructing a battery thermal model according to claim 2, wherein It also includes performing spatial and temporal discretization processing on the electrochemical-thermodynamic coupling equation to obtain a temperature distribution prediction model for each region of the battery.

4. The method for constructing a battery thermal model according to claim 1, wherein The neural network temperature rise model uses a radial basis function neural network, and the input parameters include the discharge rate, SOC, SOH, and ambient temperature.

5. The method for constructing a battery thermal model according to claim 1, wherein If the relative error between the physical model constraint results and the neural network prediction results is less than the error threshold, the neural network prediction results are output as the temperature prediction value; if the relative error is greater than or equal to the error threshold, the physical model constraint results are output as the temperature prediction value.

6. The method for constructing a battery thermal model according to claim 1, wherein It also includes judging whether to trigger a thermal runaway warning based on the SEI film decomposition rate and the temperature change rate; the SEI film decomposition rate is calculated by the SEI film decomposition rate equation; if the SEI film decomposition rate is greater than the rate threshold and the temperature change rate is greater than the temperature change rate threshold, a thermal runaway warning is triggered.

7. The method for constructing a battery thermal model according to claim 1, wherein, It also includes modeling the battery aging characteristics, obtaining the temperature rise data under different SOC and SOH conditions based on cyclic charge and discharge tests, and calibrating the heat source term in the thermal model based on the temperature rise data.

8. A battery thermal model construction system applying the battery thermal model construction method according to any one of claims 1-7, characterized in that, It includes the following modules: Data acquisition module: used to acquire the current, voltage, SOC, and SOH data of the lithium battery; Neural network prediction module: used to predict the surface temperature distribution of the lithium battery; Physical model constraint module: used to correct the neural network prediction results; Warning module: judge whether the lithium battery is in a thermal runaway state based on the SEI film decomposition rate and the temperature change rate.

9. An electronic device, characterized in that, The electronic device includes: a memory and a processor coupled to each other, and the processor is used to execute the program instructions stored in the memory to implement the battery thermal model construction method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program data, and the program data can be executed by the processor to implement the battery thermal model construction method according to any one of claims 1-7.

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