36 results about "Mean absolute percentage error" patented technology

A short-term combination forecasting method for wind power comprises the steps that (1) normalization is performed on wind speed and wind power data, and support vector machine regression, an Elman neural network and a BP neural network are respectively utilized to establish corresponding single forecasting models; (2) staging is performed on forecasting results obtained by training all the single forecasting models according to the magnitude of the wind speed; (3) parameters to be optimized are selected, and a combination forecasting model is established; (4) an objective function is determined according to the combination forecasting model, a constraint condition that the mean absolute percentage error minimum serves as the objective function is adopted, and optimized parameters are obtained; (5) all stages of weight coefficient values after staging are obtained according to the optimized parameters, and the combination forecasting model is updated; (6) the corresponding weight coefficient values are dynamically selected according to the magnitude of the wind speed, and the wind power test data are utilized to train and forecast the updated combination forecasting model to obtain a combination forecasting value. According to the short-term combination forecasting method for the wind power, the advantages of all the single forecasting models are effectively synthesized, forecasting risks are lowered, and forecasting accuracy is high.

The invention discloses a method for computing steady-state output power of a wind power station based on actual measured data, which is characterized by comprising the following steps: data acquisition, namely acquiring wind speed Vout at the outer end of the windward direction of the wind power station, output power Pi of each wind machine and actual measured wind direction angle alpha of the wind power station; data processing, namely dividing the data of different wind directions of the actual measured wind direction angle alpha of the wind power station respectively to acquire 36 databases according to alpha=10-360 degrees, and then establishing a data table for different wind directions respectively to acquire the wind power utilization factors of the wind power station; simulation computation, namely inputting simulation input quantity, selecting the database according to the actual measured wind direction angle alpha of the wind power station, and solving CP' and CPi corresponding to the Vout according to a CP'-Vwout curve and a CPi-Vwout curve to acquire the total output power of the wind power station; and error analysis, namely adopting a mean absolute percentage error evaluation criterion to carry out error computation for the steady-state output power of the wind power station computed by the method and the actual measured power through error evaluation criterion to provide the precision of the computation method. The method has the advantages of simple computation, high computation speed, higher precision and the like, and can meet on-line use requirement.

The invention discloses a system and a method for implementing sales forecasting in the catering industry. Acquisition and information mining are performed on external data such as online review platform data, geographic position information data, weather information, market information and the like and internal data such as pos data, store information, dish information, company market activity information and the like by adopting a crawler technology, an image recognition technology, a text analysis technology and a deep learning algorithm, a fused forecasting model is established, week-by-week dish sales data within future three months is given, and a future order plan is given in combination with dish BOM (Bill of Material), store inventory, total warehouse inventory, safety inventory MRP (Material Requirements Planning) and the like. Compared with other exiting forecasting method, the MAPE (Mean Absolute Percentage Error) can be improved from 30-40% to 10-15%.

The invention discloses a wind power prediction correction method. The method includes the steps that 1, the total capacity of a selected wind power plant is obtained, and wind power prediction data and wind power actual measurement data of the whole field in a recent civil year of the wind power plant are obtained; 2, normalization processing is carried out on the wind power data, obtained from the step1, of the wind power plant by means of the total capacity of the wind power plant; 3, an input and output data set is formed according to the wind power prediction data and the wind power actual measurement data obtained after preprocessing in the step 2; 4, 2 / 3 of the input and output data set obtained in the step 3 is selected randomly to serve as a training set, and the remaining 1 / 3 serves as a testing set; 5, a kernel function and training parameters of the support vector machine are selected, training is carried out by means of the training set obtained from the step 4, and the testing set is used for testing; 6, a grid searching method is utilized to correct the parameters of the support vector machine, and an average absolute percentage error and a root-mean-square relative error of a correction result are utilized to serve as evaluation criteria to obtain a local optimum support vector machine training model, namely a local optimum wind power prediction correction model.

The invention belongs to the field of wind energy prediction, and particularly relates to a wind power plant wind speed prediction method based on a support vector machine. A continuous prediction method and a neural network algorithm are adopted, a wind speed prediction value of a mixed algorithm based on a time sequence and Kalman filtering is taken as input, a practical wind speed value is taken as output, a linear combination prediction model is established, and the linear combined prediction model is taken as a reference to analyze the prediction performance of the combined prediction model based on a least squares support vector machine. The prediction performance of each model adopts three error indexes including a prediction average absolute error, an average square error and an average absolute percentage error to carry out comparison analysis. Wind speed data is simulated to carry out simulation, each model is used for carrying out short-term prediction on the wind speed, and the effectiveness of the method is proved. A simulation experiment indicates that the wind speed prediction accuracy can be further improved by the combined prediction model. Compared with a traditional linear combined prediction model, the combined prediction model based on the least squares support vector machine has a large accuracy advantage.

The embodiment of the invention discloses a short-term traffic flow prediction method and system based on Bayesian optimization. The method comprises the steps of: collecting original traffic flow data passing through a fixed road position in a fixed time interval, carrying out preprocessing on the original traffic flow data according to a seasonal model algorithm to generate time sequence trafficflow data; constructing a short-term traffic flow prediction model based on a support vector regression machine, and training the short-term traffic flow prediction model; calculating a mean absolutepercentage error of the short-term traffic flow prediction model, and acquiring the prediction precision of the short-term traffic flow prediction model according to the mean absolute percentage error; optimizing the model parameters corresponding to the prediction precision according to a Bayesian optimization algorithm until a target short-term traffic flow prediction model is generated; and predicting the short-term traffic flow according to the target short-time traffic flow prediction model. According to the embodiment of the invention, the generalization ability of the short-term traffic flow prediction model is improved, the prediction precision is improved, and convenience is provided for intelligent traffic.

The invention belongs to the technical field of network communication, and discloses a communication network flow prediction method and system, a storage medium and computer equipment, and the communication network flow prediction method comprises the steps: constructing a network flow data set, and constructing a communication network structure topological graph; a network traffic prediction model based on the graph convolutional neural network and the Transform is constructed, and the graph convolutional neural network and the Transform structure are combined; constructing a network traffic prediction model, coding a communication network topology structure and network traffic time sequence information, and learning space and time characteristics of data; and training the constructed network flow prediction model, and testing the model error by adopting three evaluation methods of a root mean square error, a mean absolute error and a mean absolute percentage error. The graph convolutional neural network is adopted, the spatial features of the topological structure of the communication network switching node are extracted, the model is assisted in predicting the future network flow, and the precision and effectiveness of the model are improved.

The invention discloses an equivalent wind speed method for processing the static power equivalent dispersion problem of a wind power station and the method is characterized by comprising the following steps: analyzing the output dispersion of each wind turbine of the wind power station, carrying out the statistic processing on the actual running data of each wind turbine, analyzing the position differences of each wind turbine and the dispersion of the inside wind energy of the wind power stations which are mutually affected, searching the wind turbine which selects the integral running action and the inside dispersion of the wind power station by the smallest error in a circulating way; confirming the equivalent wind speed, when each wind turbine is arranged in a regular manner, carrying out statistic processing on the wind speed at the locations of the four vertex angles of the wind power station to work out the equivalent wind speed and taking the N times of the output power of the wind turbine under the drive of the equivalent wind speed as the arithmetic of the total output power of the wind power station; adopting an average absolute percentage error to carry out relative analysis on the output of the equivalent model of the wind power station and the actual output of the wind power station based on the error analyzing by using the equivalent wind speed to describe the static behavior equivalence of the wind power station, thus evaluating the precision of the method and the advantages relative to the traditional method.

The invention provides a joint prediction method of base station traffic. The problem that the traditional linear algorithm is bad in prediction performance when the traffic data is nonlinear and hasa sudden change value is solved. The method comprises the following steps: firstly collecting traffic data from a base station as a data set, performing data preprocessing on an abnormal value and a missing value; decomposing processed data by adopting wavelet transform, enabling the traffic data to be smooth and easy to predict; performing single reconstruction on a sequence obtained through decomposition, wherein a low-frequency signal is predicted by adopting an echo state network model, and a high-frequency signal performs prediction by adopting an autoregression integral sliding average model; and finally performing linear accumulation on the prediction numerical value of the single sequence to obtain a final result. Compared with the single model prediction, the joint model method disclosed by the invention can reach better prediction, the reduced average absolute percentage error can achieve 6%, and the normalization root mean square error is reduced to a certain degree; the traffic data prediction accuracy of the base station is improved, and the network resource reasonable allocation can be improved.

The invention provides a tensor-based vehicle network data loss multiple estimation method for the problem of data loss of the Internet of Vehicles, which is integrated Bayesian tensor decomposition (IBTD), and belongs to the field of Internet of Vehicles. According to the algorithm, in a data model construction stage, a random sampling principle is utilized, missing data is randomly extracted togenerate a data subset, and an optimized Bayesian tensor decomposition algorithm is used for interpolation. An integration idea is introduced, multiple interpolated error results are analyzed and sorted, space-time complexity is considered, and an optimal result is obtained through preferred average. the performance of the proposed model is carried out by an average absolute percentage error (MAPE) and a root-mean-square error (RMSE). Experimental results show that the new method provided by the invention can effectively carry out interpolation on traffic data sets with different missing amounts, and can obtain a very good interpolation result.

The invention provides a dairy cow daily ration digestion energy prediction method based on a nuclear extreme learning machine, and belongs to the field of livestock and poultry daily ration nutritional value evaluation, the method comprises the following steps: (1) actually measuring dairy cow daily ration nutrient intake and digestion energy data, generating dairy cow daily ration digestion energy prediction samples, and dividing the dairy cow daily ration digestion energy prediction samples into a training sample set and a test sample set; (2) constructing extreme learning machine network output for the established training sample set, and representing the extreme learning machine network output in a matrix form; (3) selecting a Gaussian kernel function to solve, determining a parameterset of the kernel function, and obtaining an output function based on the KELM prediction model; and (4) comparing the test sample with the prediction result of the KELM model, calculating the average absolute error, the average absolute percentage error and the root-mean-square error of the predicted digestion energy and the real value, and evaluating the effectiveness of the prediction method.The prediction method provided by the invention belongs to a non-parameter machine learning model, effective prediction can be carried out only by learning the training samples, and relatively high prediction precision can be obtained.

The invention discloses a commodity sales prediction method and system and belongs to the technical field of deep learning. The method comprises the steps of: obtaining the historical sales data of acommodity; preprocessing the historical sales data to obtain preprocessed sales data; performing first feature extraction on the preprocessed sales data to obtain first feature sales data; performingtraining according to the first feature sales data and the preprocessed sales data to obtain a sales initial prediction model; performing second feature extraction on the first feature sales data andthe preprocessed sales data to obtain second feature sales data; and training the sales initial prediction model according to the first feature sales data, the preprocessed sales data and the second feature sales data to obtain a commodity sales prediction model so as to predict the sales of the commodity. According to the commodity sales prediction model, a wavenet network and an LSTM network arefused; and the average absolute percentage error of the commodity sales model can reach five percent under the condition of sufficient historical sales data.

The invention discloses a method for estimating river humification index (HIX) and belongs to the field of river water environment assessment with an aim to solve the technical problem that HIX is affected by actual measurement and tedious calculation by instruments and measuring personnel with a three-dimensional fluorescence technique and an FRI (fluorescence regional integration) technology inan existing method. The method includes 1), performing sampling; 2), measuring CDOM (chromophoric dissolved organic matter) absorbancy of a water sample; 3), performing quantitative analysis of three-dimensional fluorescence spectrum with the FRI method, and calculating the HIX; 4), constructing the correlation between CDOM254 and HIX, performing description with following models: HIX=0.1093XCDOM254+1.4839, wherein R<2>=0.864, p is smaller than 0.01, and estimating the HIX by measuring CDOM254 of the water sample. The mean absolute percentage error (MAPE) of the measured HIX and the HIX calculated according to the method is only 18.27%, the specific value of the measured HIX to the HIX calculated with the method is 0.93, and the CDOM254 and HIX models are good in precision.

The invention discloses a container ship voyage encasement quantity prediction method, which comprises the following steps of firstly, determining the voyage encasement quantity influence factors, inputting variables, and obtaining the difference information between arrays; establishing a difference information space, and establishing and calculating a difference information grey correlation degree; establishing an order relation among the factors, and determining the weights among the influence factors; secondly, randomly generating a training set and a test set, performing normalization processing on the data, and introducing an insensitive loss function on the basis of classification of the support vector machine to obtain a regression type support vector machine; and finally, evaluating the performance and the prediction effect of the model by adopting a mean square error, an average absolute percentage error and a correlation coefficient. According to the method, the subsequent harbor box quantity information is predicted, and the influence of the subsequent harbor box quantity information on the subsequent harbor loading and unloading is taken into consideration during current harbor loading, so that the basis is provided for full-course loading optimization, and the method has the important practical significance.

The invention discloses a method for predicting the maximum resource utilization rate of a task in a cloud platform in a future period of time. The method includes the steps: based on historical resource usage information of multiple tasks of a cloud platform, extracting preliminary task resource usage characteristics by analyzing resource usage conditions of cloud platform tasks; further extracting features by using a sparse self-coding model; then, clustering the tasks by using a K-medoids clustering method, and training each task category by using an improved random forest regression model;and finally, predicting the maximum resource utilization rate of a given task in a future period of time by using the trained model based on the historical information of the resource utilization rate of the task in the latest period of time. Meanwhile, according to the resource use features of the cloud platform task, the invention also designs a resource use prediction performance evaluation function, namely an improved average absolute percentage error, suitable for the task, and the evaluation function can more visually reflect the performance difference of different task resource use prediction methods.

The invention provides a rail transit short-time passenger flow volume prediction method based on W-BiLSTM. The method comprises the following steps: acquiring time sequence historical data of urban rail transit passenger flow volume as sample data; preprocessing and normalizing the sample data; performing wavelet decomposition and single-branch reconstruction on the sample data through a wavelet neural network to obtain training data and test data; initializing the BiLSTM neural network model, setting a mechanism and hyper-parameters of the BiLSTM neural network model, and inputting training data to construct and train a prediction model; when an expected error or a preset number of iterations is reached, selecting an optimal BiLSTM neural network model to predict the test data to obtain a predicted value; analyzing a predicted value error by taking a root-mean-square error and an average absolute percentage error as evaluation indexes; capturing the short-time passenger flow change rule of the rail transit to accurately predicting the speed of the urban road in the future. The invention can be applied to intelligent traffic and smart city construction. And data support is provided for avoiding travel congestion and guaranteeing the travel safety and efficiency of residents.

The invention discloses a road monthly traffic volume prediction method based on an SARIMA-NAR combination model, and the method comprises the steps: collecting monthly traffic volume data over the years, and building a road monthly traffic volume time sequence; performing linear prediction on the monthly traffic volume time sequence by using an SARIMA model to obtain a linear result; calculating a residual error according to a linear result obtained by the SARIMA model and an original sequence, and extracting a residual error sequence; constructing an NAR model by using the residual sequence, and performing nonlinear prediction to obtain a nonlinear result; superposing the linear result and the nonlinear result to obtain a final monthly traffic volume prediction result; and finally, evaluating the prediction result of the combined model through a plurality of indexes including a mean absolute percentage error (MAPE), a mean absolute error (MAE) and a root-mean-square error (RMSE), wherein the prediction result has high effectiveness and reliability, and the prediction process is more convenient and efficient.

In a metrology sampling method with a sampling rate decision scheme, a mean absolute percentage error (MAPE) and a maximum absolute percentage error (MaxErr) of visual metrology values of all workpieces in a set of determinative samples (DS), and various index values that can detect various status changes of a process tool (such as maintenance operation, parts changing, parameter adjustment, etc.), and / or information abnormalities of the process tool (such as abnormal process data, parameter drift / shift, abnormal metrology data, etc.) appearing in a manufacturing process are applied to develop an automated sampling decision (ASD) scheme for reducing a workpiece sampling rate while VM accuracy is still sustained.

The invention provides a shield cutterhead torque multi-step prediction method and system. The shield cutterhead torque multi-step prediction method comprises the steps: collecting and preprocessing cutterhead torque signals into a cutterhead torque sequence; decomposing the cutterhead torque sequence into a plurality of subsequences and a residual sequence by using a VMD decomposition method, and further decomposing the residual sequence by using an EWT decomposition method; normalizing the torque subsequences and transmitting the normalized torque subsequences to an LSTM neural network; constructing and training a shield cutter torque neural network multi-step prediction model; predicting a cutterhead torque value at a preset future moment; and respectively calculating a root-mean-square error, a mean absolute error and a mean absolute percentage error according to the cutterhead torque value at the preset future moment, and testing the prediction precision of the cutterhead torque. High-precision real-time multi-step prediction of the cutterhead torque is achieved, a driver can be guided to adjust operation parameters of the shield tunneling machine in advance, efficient and safe propulsion of the shield tunneling machine is achieved, and therefore the automation level and the intelligent level of the shield tunneling machine are improved.

The invention discloses an energy demand prediction method based on a PSO-GA-SA algorithm. The method includes the following steps: selecting six energy demand impact factors including GDP, population, fixed-asset investment, energy efficiency, energy consumption structure and per capita energy consumption and taking the six factors as the input quantity of an energy demand assessment equation; adopting a secondary non-linear energy demand assessment equation; employing a PSO-GA-SA algorithm to obtain the optimal weight coefficient of the secondary non-linear energy demand assessment equation; and obtaining an energy demand prediction result in China by means of the secondary non-linear energy demand assessment equation and the six energy demand impact factors including GDP, population, fixed-asset investment, energy efficiency, energy consumption structure and per capita energy consumption. According to the method, the maximum relative error between an energy predicted value and an observed value can be controlled to be not more than 0.009%, the mean absolute percentage error (MAPE) is only 0.004%, and the prediction accuracy is high.

The invention discloses an aqueduct stress-strain prediction method under multi-factor association, and the method comprises the following steps: (1) firstly obtaining monitoring data information suchas a steel bar meter, a strain gauge and an environment temperature in an aqueduct body, and determining aqueduct stress-strain impact factors according to a hydraulic structure stress-strain statistical model; and (2) removing environmental noise by adopting an improved wavelet threshold noise reduction algorithm, and removing abnormal data noise according to historical statistical data of natural disasters; (3) carrying out dynamic correlation correction on the influence factors according to a data dynamic nonlinear relation measurement method (DNRM); (4) taking the corrected influence factor as input, taking the stress-strain data after noise reduction as output, and establishing an aqueduct stress-strain prediction model by adopting an SVM algorithm; (5) performing optimization parameter adjustment on the prediction model according to the root mean square error (RMSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE) evaluation indexes, and finally establishing an optimized aqueduct stress-strain prediction model.

The invention discloses a method for detecting content of oxygen in seawater for aquaculture, belonging to the technical field of detection of aquaculture water quality. The method is characterized in that the method for detecting the content of oxygen is an indirect measurement method which comprises the following steps: selecting characteristic variables which have the greatest influence on the content of oxygen in the seawater for aquaculture and are nearly not correlated; carrying out offline optimization on the weight of each characteristic variable by virtue of a genetic algorithm according to sample data (containing the characteristic variables and oxygen content) in a sample database by taking a mean absolute percentage error as an objective function, and storing the optimized weights into a weight database; and when water quality parameters need to be detected and controlled by virtue of the oxygen content data, multiplying the characteristic variables detected in real time by the respective weights and then summing so as to obtain the oxygen content. According to the method disclosed by the invention, the problems that an existing instrument for detecting the content of oxygen in the seawater for aquaculture is basically imported, is high in price, and is short in service life because of serious corrosivity of seawater to the probe of a sensor are scientifically and effectively solved; and the method disclosed by the invention is high in operability and practicability.

The invention specifically discloses a short-term power load prediction method and device based on hyper-parameter optimization, and the method comprises the steps: carrying out the normalization processing of original power load data, taking the data as the input of an LSTM (Long Short-Term Memory) network, taking the three hyper-parameters of the LSTM as to-be-optimized parameters of an IPSO (Improved Particle Swarm Optimization), setting an average absolute percentage error (MAPE) as a fitness function of the IPSO, and carrying out the optimization of the IPSO, changing the inertia weight from a fixed value to nonlinear change, and setting the inertia weight as an independent variable of a learning factor, so that the beneficial effect of improving the short-term power load prediction precision can be achieved.

The invention provides a MODWT-EMD-based time sequence hybrid prediction method to solve the problem for predication of a time sequence. The method comprises the following steps: firstly, performing maximum overlapping discrete wavelet decomposition on an original time sequence to obtain N frequency components; secondly, performing empirical mode decomposition on the obtained N frequency components to obtain a plurality of IMF components and residual errors; inputting a plurality of IMF components and residual errors obtained by decomposition into a random forest classifier, scoring and sorting the importance of each IMF component and residual error, and selecting feature information with relatively large influence; and finally, inputting the selected feature information into Bi-GRU for training, predicting an original time sequence by using a trained model, and evaluating the prediction capability of the method through a mean absolute error, a root-mean-square error, a mean absolute percentage error and goodness of fit. The prediction result can be obtained with less training time on the premise of ensuring the prediction accuracy.

The invention discloses a method for computing steady-state output power of a wind power station based on actual measured data, which is characterized by comprising the following steps: data acquisition, namely acquiring wind speed Vout at the outer end of the windward direction of the wind power station, output power Pi of each wind machine and actual measured wind direction angle alpha of the wind power station; data processing, namely dividing the data of different wind directions of the actual measured wind direction angle alpha of the wind power station respectively to acquire 36 databases according to alpha=10-360 degrees, and then establishing a data table for different wind directions respectively to acquire the wind power utilization factors of the wind power station; simulation computation, namely inputting simulation input quantity, selecting the database according to the actual measured wind direction angle alpha of the wind power station, and solving CP' and CPi corresponding to the Vout according to a CP'-Vwout curve and a CPi-Vwout curve to acquire the total output power of the wind power station; and error analysis, namely adopting a mean absolute percentage error evaluation criterion to carry out error computation for the steady-state output power of the wind power station computed by the method and the actual measured power through error evaluation criterion to provide the precision of the computation method. The method has the advantages of simple computation, high computation speed, higher precision and the like, and can meet on-line use requirement.

The invention belongs to the technical field of information and data processing, and discloses a method for quantitatively predicting microblog forwarding breadth and depth, which comprises the following steps: dividing extracted features into user features, microblog features and social features, and storing the user features, the microblog features and the social features into a file; reading all processed data, taking 70% of the data as a training data set, and taking 30% of the data as a test data set; extracting features useful for the training model in the training data set; establishing a model by using an improved random forest algorithm, and predicting the forwarding breadth and depth of each microblog; and testing the accuracy of the algorithm by using test set data, and calculating an average absolute percentage error and prediction precision. According to the invention, the propagation breadth and depth of user forwarding behaviors are predicted by using a machine learning algorithm; and the improved random forest algorithm is high in prediction precision, small in fluctuation, and insensitive to various characteristic changes, which indicates that the prediction result has a high reference value.

The invention provides a highway travel time prediction system. The system comprises a database, a K-value determination unit, and a travel time predicted value determination unit; the database is used for saving travel times of vehicles completely passing through a target highway and a traffic condition data association list; the K-value determination unit searches K travel times which are closest to the current traffic condition from training data, regards an average value of the K travel times as a training predicted value Ft (K) of the travel times of the target highway, calculates a MAPE (mean absolute percentage error) value of the travel time corresponding to each K value in sequence according to the formula (1), and regards the K value with the minimum MAPE value as a K determination value for predicting the travel time, wherein K value is increased from 3; and the travel time predicted value determination unit determines an average value of K-determination-value travel times which are closest to the current traffic condition in the training data as a travel time predicted value. Compared with the prior art, according to the scheme of the system and method, visualization and simplicity are realized, and the prediction precision is high.

The invention discloses an urban gas daily load prediction method based on a GRA-ABC-BP neural network. The method comprises the following steps: carrying out induction and quantitative analysis on factors influencing the urban gas daily load; a GRA (grey correlation analysis) method is adopted to eliminate influence factors with relatively small correlation, and variables input by the BP neural network are determined, so that a topological structure of the BP neural network is determined; when an ABC (artificial bee colony algorithm) is used for optimizing an initial weight and a threshold value of a BP neural network, the size of a population, the proportion of all bee species, the maximum number of iterations and restriction abandoning parameters are determined firstly; obtaining an optimal initial weight and an optimal threshold value through an ABC algorithm; gas daily load prediction is carried out by taking actual data of a certain city as a research example, a prediction result is obtained, and the accuracy and feasibility of the method are researched. According to the method disclosed by the invention, the gas load prediction problem is deeply researched from two aspects, namely screening research on a plurality of influence factors and optimization research on a BP neural network prediction model. And while the quality of the input neural network data is improved, the inherent defects of the BP neural network are optimized. Example research results show that the method is very high in prediction precision, the average absolute percentage error is as low as 0.5528%, and industrial requirements can be completely met.