Method and device for modeling wind driven generator system by using artificial neural network

Abstract

The invention discloses a method and device for modeling a wind driven generator system by using an artificial neural network, and relates to the technical field of wind power generation. The method solves the problems that in the prior art, modeling of a wind driven generator system cannot be deployed on an operation site of a wind driven generator, and the future operation state of the wind driven generator cannot be accurately predicted, and comprises the steps that operation data of the wind driven generator are collected in a simulation environment, and data used for model training are constructed; according to the method, the environment data, the control quantity and the output quantity of the operation of the wind driven generator are comprehensively considered, the future state of the operation of the wind driven generator is predicted, the wind driven generator system prediction model is obtained, and the wind driven generator system prediction model is verified in a real environment. Comprise the blade rotating speed, the generated power and the blade load, and the relation between the operation data of the wind driven generator and the blade rotating speed, the generated power and the blade load can be described more accurately.

Description

Technical Field

[0001] The present application relates to the field of wind power generation technology, and in particular to a method and device for modeling a wind turbine system using an artificial neural network. Background Art

[0002] The operation of a wind turbine is a complex system that converts wind energy into electrical energy. It involves multiple links and control mechanisms, including:

[0003] Wind energy capture: The wind blows the blades, generating lift and drag, driving the blades to rotate.

[0004] Rotation transmission: The rotation of the blades is transmitted to the generator through the main shaft.

[0005] Electricity generation: A generator converts mechanical energy into electrical energy, typically using an AC generator (such as an asynchronous generator or a synchronous generator).

[0006] Power output: The electricity generated by the generator is transmitted to the grid or energy storage system via cables.

[0007] Several sensors are mounted on the wind turbine tower, serving as input parameters for the wind turbine control system. These primarily include wind force, wind direction, hub drive shaft speed, generated power, blade tip acceleration, and blade tip displacement. Tip acceleration and blade tip displacement reflect the load on the blades. Excessive tip acceleration indicates increased load, shortening blade life. Furthermore, excessive tip displacement can cause blades to strike the tower, potentially resulting in a safety incident. Therefore, the smaller these values, the better.

[0008] The operation of wind turbines mainly depends on the change of wind power. According to the different wind conditions, it can be divided into four control areas:

[0009] Start-up phase: The wind force is the smallest at this time, and the goal is to maximize the use of wind energy so that the blades can rotate smoothly.

[0010] Underpower stage: In this stage, the wind force is small and the goal is to control the rotation speed of the blades to keep it as close to the rated speed as possible.

[0011] Rated power stage: This is the ideal state and the wind turbine can operate at full power.

[0012] Protection operation stage: When the wind is strong, measures need to be taken to reduce the force on the blades to avoid safety accidents.

[0013] Currently, the common method for modeling wind turbine systems is to study the mechanical properties of the wind turbine system, the aerodynamic characteristics of the wind turbine blades, the material properties, the electromagnetic-mechanical characteristics of the generator, etc., to establish a mathematical model of the wind turbine and calculate the various parameters of the model. This process can be done using MATLAB software extensions or specialized software for the wind turbine industry.

[0014] The current shortcomings of wind turbine system modeling are: the software used is often large-scale commercial software that requires a large CPU, memory, and hard disk to run. It usually only supports the Windows operating system and cannot be deployed at the wind turbine operation site; it runs under human-computer interaction conditions; and it cannot accurately predict the future operating status of the wind turbine. Summary of the Invention

[0015] The purpose of this application is to overcome the problems in the prior art that the modeling of wind turbine systems cannot be deployed at the wind turbine operation site and the future operating status of the wind turbine cannot be accurately predicted, and to provide a method and device for wind turbine system modeling using artificial neural networks.

[0016] In a first aspect, a method for modeling a wind turbine system using an artificial neural network is provided, comprising:

[0017] Collect wind turbine operating data in a simulation environment;

[0018] The operating data at X consecutive time points are used as input data, and the blade speed, power generation and blade load at the next time point after X consecutive time points are used as the first output data, where X is a positive integer greater than 3, to construct a data set;

[0019] Using the data set to train a Transformer model to obtain a wind turbine system prediction model;

[0020] The wind turbine system prediction model is verified in a real environment.

[0021] In some possible implementations, collecting wind turbine operating data in a simulation environment includes:

[0022] S101, operating a wind turbine in a simulation environment and controlling the yaw, pitch, and torque of the wind turbine using a PI controller;

[0023] S102, simulating different wind conditions in a simulation environment and maintaining them for a specified period of time, and performing wind turbine operation simulation and operation data collection;

[0024] S103, simulating random switching between different wind conditions in a simulation environment, and performing wind turbine operation simulation and operation data collection;

[0025] S104: Repeat steps S102 and S103, and add random disturbances during the collection of running data.

[0026] In some possible implementations, the operating data includes environmental data, control data, and second output data, wherein the environmental data includes wind force, wind direction, and temperature; the control data includes the yaw angle, pitch angle, and torque of the wind turbine; and the second output data includes blade speed, generated power, and blade load.

[0027] In some possible implementations, before training the Transformer model, the method further includes: normalizing the dataset, and dividing the normalized dataset into a training set and a test set according to a preset ratio.

[0028] In some possible implementations, the wind turbine system prediction model uses a fully connected network as an input layer, a Sigmoid function as an output layer, a mean square error as a loss function, and uses the training set and a stochastic gradient descent algorithm to perform Transformer model training.

[0029] Some possible implementations further include: using a test set to test the trained wind turbine system prediction model; if the mean square error is greater than a preset threshold, adjusting the model parameters and retraining the wind turbine system prediction model.

[0030] In some possible implementations, validating the wind turbine system prediction model in a real environment includes:

[0031] Collect wind turbine operating data in a real environment;

[0032] Extracting operation data of N consecutive time points from operation data of a wind turbine collected in a real environment, where N is a positive integer greater than 3;

[0033] Inputting the extracted operating data of N consecutive time points as input data into the wind turbine system prediction model to predict the predicted value of the next time point of the extracted N consecutive time points;

[0034] Calculate the mean square error between the predicted value and the corresponding actual collected data;

[0035] If the mean square error is greater than a preset threshold, the model parameters are adjusted and the wind turbine system prediction model is retrained and verified.

[0036] In a second aspect, a device for modeling a wind turbine system using an artificial neural network is provided, comprising:

[0037] A data acquisition module is used to collect the operating data of the wind turbine in a simulation environment;

[0038] a data set construction module, configured to construct a data set using the operating data of X consecutive time points as input data and the blade speed, power generation, and blade load at the next time point after the X consecutive time points as first output data, where X is a positive integer greater than 3;

[0039] A training module, configured to train a Transformer model using the data set to obtain a wind turbine system prediction model;

[0040] The verification module is used to verify the wind turbine system prediction model in a real environment.

[0041] In a third aspect, a computer-readable storage medium is provided, wherein the computer-readable medium stores program code for execution by a device, the program code including steps for executing the method in any one of the implementations of the first aspect.

[0042] In a fourth aspect, an electronic device is provided, comprising a processor, a memory, and a program or instruction stored in the memory and executable on the processor, wherein the program or instruction, when executed by the processor, implements a method as in any one of the implementations of the first aspect described above.

[0043] The present application has the following beneficial effects: the wind turbine system prediction model provided by the present application comprehensively considers the environmental data of the wind turbine operation (wind direction, wind force, temperature, etc.); control quantities (yaw angle, pitch angle, torque, etc.) and output quantities (blade speed, power generation and blade load, etc.), and predicts the future state of the wind turbine operation, including blade speed, power generation and blade load, and uses the Transformer model as the basic model, which can more accurately describe the relationship between the operating data of the wind turbine and the blade speed, power generation and blade load, and can improve the accuracy of the blade speed, power generation and blade load prediction, so that the control strategy and control quantity of the wind turbine can be adjusted in real time according to the prediction results, so that the wind turbine can always operate in an ideal state, thereby improving the power generation efficiency while minimizing the load on the blades, extending the service life of the wind turbine, and reducing the failure rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings that constitute a part of this application are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation on this application.

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0046] Figure 1 is a flow chart of a method for modeling a wind turbine system using an artificial neural network according to Example 1 of the present application;

[0047] Figure 2 This is a structural block diagram of an apparatus for modeling a wind turbine system using an artificial neural network according to Example 2 of the present application;

[0048] Figure 3 This is a schematic diagram of the internal structure of the electronic device of Example 4 of the present application.

[0049] Reference numerals:

[0050] 100, data acquisition module; 200, data set construction module; 300, training module; 400, verification module. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] Example 1

[0053] like Figure 1 As shown, a method for modeling a wind turbine system using an artificial neural network according to Example 1 of the present application includes:

[0054] S100, collecting operating data of a wind turbine in a simulation environment, specifically comprising the following steps:

[0055] S101. First, collect the operating data of the wind turbine in a simulation environment. In this embodiment, Blade software is used for simulation. The wind turbine is operated in the simulation environment and a PI controller is used to control the yaw, pitch, and torque of the wind turbine.

[0056] S102. Simulate different wind conditions in a simulation environment and maintain them for a specified duration. Specifically, adjust the wind intensity (i.e., wind speed) to place the wind turbine in a startup state, an underpower operation state, a rated power operation state, and a protection operation state. The wind direction remains constant after the wind turbine enters the specified state. Simulate the wind turbine operation for 24 hours to collect operational data.

[0057] S103. After completing the simulation of the above four operating states, simulate random switching between different wind conditions in the simulation environment, that is, change the wind conditions, simulate the wind intensity and wind direction to continuously change, so that the wind turbine continuously switches between the four operating states, and collects operating data;

[0058] S104. In order to make the simulation of the wind turbine closer to the actual operation, repeat steps S102 and S103, and manually add random disturbances during the collection of operation data, that is, randomly change the yaw angle, pitch angle, and torque values ​​of the wind turbine. The number of repetitions is set according to user needs, so that the wind force and wind direction can cover various situations that may be encountered in the operation of the wind turbine as much as possible, so as to obtain a large amount of operation data under different wind conditions.

[0059] S200, constructing a data set using operating data from X consecutive time points as input data and blade speed, power generation, and blade load at the next time point after the X consecutive time points as first output data, where X is a positive integer greater than 3;

[0060] Specifically, at each time point, data is selected: wind force, wind direction, temperature, wind turbine yaw angle, pitch angle, torque, blade speed, generated power, and blade load. Blade load is reflected by tip acceleration and tip displacement. Excessive tip acceleration indicates a greater load on the blade, impacting blade life. Furthermore, excessive tip displacement can cause the blade to strike the tower, resulting in a safety hazard. Therefore, the smaller these values, the better. The above data constitutes the data vector for that time point. The operating data for X consecutive time points is used as input data, and the blade speed, generated power, and blade load at the time point following the last of these X consecutive time points is used as the first output data. X is a positive integer greater than 3. The interval between time points can be set according to user requirements, for example, 0.5 seconds, 1 second, 3 seconds, and so on. A data set is constructed. In this embodiment, data vectors from 10 consecutive time points, separated by 1 second, form a data sequence, serving as input data. The blade speed, power generation, and blade load data at the next time point (for example, if the 10 consecutive time points are from 1 second to 10 seconds, with each second representing a time point, and there are exactly 10 time points, then the next time point is the 11th second) are used as output data. Each input data point and the corresponding output data point constitute a training data set. Following the above method, wind turbine simulation data records are used to construct a dataset for model training.

[0061] S300, using the data set to train a Transformer model to obtain a wind turbine system prediction model;

[0062] In order to improve the performance and stability of the model, the above dataset is preprocessed before model training, and the data is normalized to [0,1]. The preprocessing adopts the min-max method, that is, linear transformation of the data. The method is:

[0063]

[0064] Among them, X normalized is the data normalization value, X is the original data, X min is the minimum value in the data set, X max is the maximum value in the data set.

[0065] In this embodiment, the normalized data set is divided into a training set and a test set in a ratio of 7:3. The ratio of the training set to the test set can also be other ratios, which can be set by the user according to needs, such as 8:1, 9:1, etc.

[0066] In this example, the Transformer model is used as the foundational model to construct a wind turbine system prediction model. The Transformer model is a deep learning architecture based on a self-attention mechanism. Unlike traditional recurrent neural networks (RNNs) and convolutional neural networks (CNNs), the Transformer significantly improves training efficiency and effectiveness by processing sequential data in parallel. The Transformer architecture has unique advantages when processing sequential data, enabling flexible capture of non-fixed-length contextual relationships. This makes it ideal for fitting thermodynamic systems with large delay effects within reduction furnaces. The Transformer model primarily consists of the following components:

[0067] Embedding layer: maps input features to a high-dimensional space for subsequent processing;

[0068] Self-attention mechanism: Capture the relationship between each position in the input sequence through a multi-head self-attention mechanism;

[0069] Feedforward neural network: performs nonlinear transformation on the output of self-attention to enhance the expressiveness of the model;

[0070] Output layer: maps the output of the model to a prediction result, usually using an activation function (such as Sigmoid or Softmax) to output a probability.

[0071] The wind turbine system prediction model uses a fully connected network as its input layer. Every neuron in the fully connected layer is connected to every neuron in the previous layer. This means that all input values ​​are fed into the Transformer network. The wind turbine system prediction model uses a Sigmoid function as its output layer. The Sigmoid function is an S-shaped curve function, also known as an S-type function. The mathematical expression is:

[0072] S(x)=1 / (1+e -x )

[0073] Where x is the input value and e is the base of the natural logarithm. The Sigmoid function converts the input value to the range [0, 1].

[0074] In this embodiment, the wind turbine system prediction model selects the mean square error (MSE) as the loss function, which evaluates the accuracy of the model by calculating the average of the squares of the differences between the predicted value and the actual value. The calculation formula of MSE is:

[0075]

[0076] Among them, MSE is the mean square error, is the actual value, is the predicted value, and n is the number of samples.

[0077] In this embodiment, the stochastic gradient descent (SGD) algorithm is used for model training. The core idea of ​​stochastic gradient descent is to gradually reduce the value of the loss function by continuously adjusting the model parameters. It improves computational efficiency by randomly selecting a sample in each iteration to calculate the gradient and update the model parameters. After the model training is completed, the model is evaluated using the data in the test set. In this embodiment, the preset threshold of the mean square error is set to 0.01, that is, the mean square error is ensured to be no greater than 0.01, so that the relationship between the operating data of the wind turbine and the blade speed, power generation and blade load can be more accurately described, so that the wind turbine system prediction model can accurately predict the operating status of the wind turbine. If the mean square error is greater than 0.01, the model parameters are adjusted and the wind turbine system prediction model is retrained.

[0078] S400: Verify the wind turbine system prediction model in a real environment.

[0079] Specifically, a data acquisition computer is deployed under the wind turbine tower of the actually operating wind turbine and is connected to the wind turbine control cabinet via a network or a data cable.

[0080] In the wind turbine control cabinet, run the data acquisition program to collect the actual operation data of the wind turbine in real time and transmit it to the data acquisition computer for storage.

[0081] The collected data includes environmental data: wind force, wind direction, and temperature; control data: wind turbine yaw angle, pitch angle, and torque; and output data: blade speed, generated power, and blade load.

[0082] The wind turbine system prediction model that has been trained and tested is run in the data acquisition computer.

[0083] At each sampling moment, the model's input data is constructed using wind turbine sampling data from the previous 10 time points at 1-second intervals. This input data is then fed into the wind turbine system prediction model to predict the wind turbine's blade speed, power generation, and blade load at the next time point.

[0084] At the next sampling moment, the actual output value of the wind turbine is compared with the predicted value of the model, and the mean square error (MSE) of the model prediction is calculated.

[0085] The wind turbine system prediction model is validated over a long period of time using wind turbines in a real-world environment under varying wind directions and speeds. If the mean square error (MSE) between the actual wind turbine output and the model's predicted value, after normalization, is no greater than 0.01, the wind turbine system prediction model meets the required accuracy.

[0086] If the prediction mean square error of the wind turbine system prediction model does not meet the requirements, it is necessary to construct a training data set according to the method of step S200 using the actual operation data of the wind turbine when a large error occurs, retrain the wind turbine system prediction model, and then test and verify the modified model again.

[0087] Repeat the above steps until the prediction accuracy of the prediction model meets the requirements. Through the above process, a wind turbine system prediction model using artificial neural network is finally obtained.

[0088] In the prior art, neural network models are generally used to predict wind turbine power generation, without considering wind turbine operating data such as speed, torque, and pitch angle. In this application, a comprehensive consideration of wind turbine operating environmental data (wind direction, wind force, temperature, etc.); control variables (yaw angle, pitch angle, torque, etc.); and output variables (generated power, blade speed, blade load, blade displacement, etc.) is used to predict the wind turbine's operating state. Using the Transformer model as the foundational model, this model can more accurately describe the relationship between wind turbine operating data and blade speed, generated power, and blade load, improving the accuracy of blade speed, generated power, and blade load predictions. This allows for real-time adjustment of the wind turbine's control strategy and control variables based on the prediction results, ensuring that the wind turbine always operates in an ideal state. This improves power generation efficiency while minimizing blade load, extending the wind turbine's service life, and reducing failure rates. Furthermore, this wind turbine system prediction model can be deployed at the wind turbine's operating site.

[0089] Example 2

[0090] like Figure 2 As shown, a device for modeling a wind turbine system using an artificial neural network according to embodiment 2 of the present application includes:

[0091] The data acquisition module 100 is used to collect the operating data of the wind turbine in the simulation environment;

[0092] A data set construction module 200 is configured to construct a data set using the operating data of X consecutive time points as input data and the blade speed, power generation, and blade load at the next time point after the X consecutive time points as first output data, where X is a positive integer greater than 3;

[0093] A training module 300 is used to train a Transformer model using the data set to obtain a wind turbine system prediction model;

[0094] The verification module 400 is used to verify the wind turbine system prediction model in a real environment.

[0095] It should be noted that other specific implementations of the device for using artificial neural networks to model a wind turbine system in this embodiment can refer to the specific implementations of the method for using artificial neural networks to model a wind turbine system described above. To avoid redundancy, they will not be repeated here.

[0096] Example 3

[0097] A computer-readable storage medium according to embodiment 3 of the present application, wherein the computer-readable storage medium stores program code for execution by a device, the program code including steps for executing the method in any one of the implementations in embodiment 1 of the present application;

[0098] Among them, the computer-readable storage medium can be a read-only memory (ROM), a static storage device, a dynamic storage device or a random access memory (RAM); the computer-readable storage medium can store program code, and when the program stored in the computer-readable storage medium is executed by the processor, the processor is used to execute the steps of the method in any one of the implementation methods in Example 1 of the present application.

[0099] Example 4

[0100] like Figure 3 As shown, an electronic device involved in Example 4 of the present application includes a processor, a memory, and a program or instruction stored in the memory and executable on the processor, wherein the program or instruction, when executed by the processor, implements the method in any one of the implementations in Example 1 of the present application;

[0101] Among them, the processor can adopt a general central processing unit (CPU), a microprocessor, an application specific integrated circuit (ASIC), a graphics processing unit (GPU) or one or more integrated circuits to execute relevant programs to implement the method in any one of the implementation methods in Example 1 of the present application.

[0102] The processor may also be an integrated circuit electronic device with signal processing capabilities. In the implementation process, each step of the method in any one of the implementations in Example 1 of the present application may be completed by hardware integrated logic circuits in the processor or software instructions.

[0103] The above-mentioned processor can also be a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component. The various methods, steps, and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or being executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium mature in the art, such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and, in combination with its hardware, completes the functions required to be executed by the units included in the data processing device of the embodiment of the present application, or executes the method in any one of the implementation modes in Example 1 of the present application.

[0104] The above are only preferred specific implementations of this application; however, the scope of protection of this application is not limited thereto. Any person skilled in the art who, within the technical scope disclosed in this application, makes equivalent substitutions or modifications based on the technical solutions and improved concepts of this application shall be covered by the scope of protection of this application.

Claims

1. A method for modeling a wind turbine system using an artificial neural network, characterized in that: include: Collect wind turbine operation data in a simulation environment; The operating data of X consecutive time points are used as input data, and the blade speed, power generation and blade load at the next time point of the X consecutive time points are used as the first output data to construct a data set; Using the data set to train the Transformer model to obtain a wind turbine system prediction model; The wind turbine system prediction model is verified in a real environment.

2. The method for modeling a wind turbine system using an artificial neural network according to claim 1, characterized in that: Collect wind turbine operation data in a simulation environment, including: S101, operating a wind turbine in a simulation environment and using a PI controller to control the yaw, pitch and torque of the wind turbine; S102, simulating different wind conditions in a simulation environment and maintaining them for a specified period of time, and performing wind turbine operation simulation and operation data collection; S103, simulating random switching between different wind conditions in a simulation environment, and performing wind turbine operation simulation and operation data collection; S104, repeating steps S102 and S103, and adding random disturbances during the collection of running data.

3. The method for modeling a wind turbine system using an artificial neural network according to claim 1 or 2, characterized in that: The operating data includes environmental data, control data and second output data, wherein the environmental data includes wind force, wind direction and temperature, the control data includes the yaw angle, pitch angle and torque of the wind turbine, and the second output data includes blade speed, power generation and blade load.

4. The method for modeling a wind turbine system using an artificial neural network according to claim 1, characterized in that: Before training the Transformer model, the method further includes: normalizing the data set, and dividing the normalized data set into a training set and a test set according to a preset ratio.

5. The method for modeling a wind turbine system using an artificial neural network according to claim 4, characterized in that: The wind turbine system prediction model uses a fully connected network as an input layer, a Sigmoid function as an output layer, and a mean square error as a loss function, and uses the training set and a stochastic gradient descent algorithm to perform Transformer model training.

6. The method for modeling a wind turbine system using an artificial neural network according to claim 5, characterized in that: Also includes: The trained wind turbine system prediction model is tested using the test set. If the mean square error is greater than a preset threshold, the model parameters are adjusted and the wind turbine system prediction model is retrained.

7. The method for modeling a wind turbine system using an artificial neural network according to claim 3, characterized in that: The wind turbine system prediction model is validated in a real environment, including: Collect wind turbine operation data in real environment; Extracting operation data of N consecutive time points from the operation data of the wind turbine generator collected in a real environment; The operating data of the extracted N consecutive time points are input as input data into the prediction model of the wind turbine system to predict the predicted value of the next time point of the extracted N consecutive time points; Calculate the mean square error between the predicted value and the corresponding actual collected data; If the mean square error is greater than a preset threshold, the model parameters are adjusted to retrain and verify the wind turbine system prediction model.

8. A device for modeling a wind turbine system using an artificial neural network, characterized in that: include: A data acquisition module is used to collect the operation data of the wind turbine in the simulation environment; A data set construction module, used to construct a data set by taking the operation data of X consecutive time points as input data and the blade speed, power generation power and blade load at the next time point of the X consecutive time points as first output data; A training module, used to train the Transformer model using the data set to obtain a wind turbine system prediction model; The verification module is used to verify the wind turbine system prediction model in a real environment.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a program code for execution by a device, wherein the program code includes steps for executing the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that: The electronic device comprises a processor, a memory, and a program or instruction stored in the memory and executable on the processor, wherein the program or instruction, when executed by the processor, implements the method as claimed in any one of claims 1 to 7.

Images